# Characterization of magnetic properties, including magnetocaloric effect, of
RE5Pt2In4 (RE = Gd-Tm) compounds

Altifani Rizky Hayyu<EMAIL_ADDRESS>M. Smoluchowski
Institute of Physics, Jagiellonian University, prof. Stanisława Łojasiewicza
11, PL-30-348 Kraków, Poland  Stanisław Baran<EMAIL_ADDRESS>M.
Smoluchowski Institute of Physics, Jagiellonian University, prof. Stanisława
Łojasiewicza 11, PL-30-348 Kraków, Poland  Andrzej Szytuła  M. Smoluchowski
Institute of Physics, Jagiellonian University, prof. Stanisława Łojasiewicza
11, PL-30-348 Kraków, Poland

###### Abstract

The RE5Pt2In4 (RE = Gd-Tm) rare earth compounds have been investigated by
means of X-ray diffraction (XRD) as well as by DC and AC magnetometric
measurements. The compounds crystallize in an orthorhombic crystal structure
of the Lu5Ni2In4-type (Pbam space group, No. 55). With decreasing temperature
the intermetallics undergo a transition from para- to ferro-/ferri- (RE = Gd,
Tb, Ho, Er) or antiferromagnetic state (RE = Tm). In case of Dy5Pt2In4, the
ferromagnetic state is reached through an intermediate antiferromagnetic order
present in a limited temperature range. The critical temperatures of magnetic
ordering range from 4.1 K (RE = Tm) up to 108 K (RE = Tb). For the majority of
investigated compounds, a cascade of additional magnetic transitions is found
below the respective critical temperatures of magnetic ordering. The magnetic
moments are found solely on the rare earth atoms, while the moments of the
remaining Pt and In atoms are absent or are too small to be detected while
accompanied by the strong rare earth’s moments. The magnetocaloric (MCE)
performance of RE5T2In4 (RE = Gd-Tm) is found quite good, especially while
taking into account the compounds with RE = Ho and Er. Maximum magnetic
entropy change ($-\Delta S_{M}^{max}$) reaches 11.8 (RE = Ho) or 11.4
J$\cdot$kg${}^{-1}\cdot$K-1 (RE = Er) under magnetic flux density change of
0-9 T. Under the same conditions, the relative cooling power (RCP) and
refrigerant capacity (RC) equal 607 and 495 J$\cdot$kg-1 (RE = Ho) or 434 and
341 J$\cdot$kg-1 (RE = Er).

keywords: rare earth intermetallics, magnetic properties, magnetization,
magnetocaloric effect, magnetic entropy change, relative cooling power

##  I Introduction

Rare earth intermetallic compounds have been attracting researchers’ interest
due to a number of intriguing physical phenomena including multiple magnetic
transitions, metamagnetism, large magnetocaloric effect (MCE), spin glass
state, heavy fermion behavior, superconductivity, and many more. A review
paper by Gupta and Suresh [1], reporting the current state of knowledge for
the RTX (R = rare earths, T = Sc, Ti, Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os,
Ir, Pt, Au, and X = Al, Ga, In, Si, Ge, Sn, As, Sb, Bi) series of
intermetallics, may provide an idea of the multitude of interesting phenomena
observed in rare earth intermetallic compounds.

Nowadays, the compounds with complex crystal structure and magnetic properties
resulting from multiple magnetic sublattices are of particular interest. The
RE5Pt2In4 (RE = Gd-Tm) indides are a good example of such a family of
compounds, as they crystallize in an orthorhombic structure of the
Lu5Ni2In4-type (Pbam space group, No. 55) [2]. In this structure, reported for
the first time by Zaremba et al. [3], the rare earth atoms occupy three
different Wyckoff sites, namely, the 2(a) site and two 4(g) sites with
different atomic positional parameters.

Up to now magnetic properties of RE5Pt2In4 (RE = Gd-Tm) remain unexplored.
However, such properties including magnetic structures, have been reported for
the isostructural RE5Ni2In4 [4, 5, 6, 7, 8, 9, 10] and RE5Pd2In4 [11] (RE =
Tb-Tm). Both the Ni- and Pd-based intermetallics are found to order
magnetically at low temperatures with the critical temperatures of magnetic
ordering ranging from about 4 K in the Tm-based compounds up to 125 K reported
for Tb5Ni2In4. The magnetic moments are carried solely by the rare earth atoms
(Ni, Pd and In remain non-magnetic or have magnetic too small to be detectable
in presence of the strong rare earth moments). Below the respective critical
temperature, a cascade of temperature-induced magnetic transitions is observed
for most of the compounds. Neutron diffraction data reveal that these complex
magnetic properties can be attributed to either different ordering
temperatures in different rare earth sublattices or order-order magnetic
transitions. The low-temperature magnetic structures show a variety of forms
including ferro- and antiferromagnetic spin arrangements, as well as the
coexistence of both types of ordering in selected compounds. The reported
magnetic structures include both commensurate and incommensurate ones.

Magnetocaloric effect (MCE) in the rare earth-based compounds is recently of
great interest due to possible applications in refrigeration [12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22]. It is until now that MCE in the RE5T2In4 (RE =
rare earth element; T = transition metal) intermetallics has only been
reported for RE5Ni2In4 (RE = Dy, Ho, and Er) [10]. It has been found that for
RE = Ho and Er, the maximum entropy changes exceed 10
J$\cdot$kg${}^{-1}\cdot$K-1 under magnetic flux change 0-7 T. The maximum
entropy changes are reached in the vicinity of the respective Curie
temperatures, which are close to 20 K.

Complex magnetic properties, reported for the isostructural RE5Ni2In4 and
RE5Pd2In4 (RE = Tb-Tm), has inspired us to undertake the current study
concentrated on RE5Pt2In4 (RE = Gd-Tm). We report here not only the basic
magnetic properties, like magnetic transition temperatures, effective magnetic
moments, the moments under applied magnetic field, critical and coercivity
fields, etc., but also we report the magnetocaloric effect studied under
magnetic flux change up to 0-9 T. As a result, we determine the number of
parameters important from the point of view of potential application in a low-
temperature refrigeration. The parameters include temperature averaged
magnetic entropy change (TEC), relative cooling power (RCP), and refrigerant
capacity (RC). The experimental results reported in this work are compared
with those reported previously for the isostructural RE5Ni2In4 and RE5Pd2In4
(RE = Tb-Tm).

##  II Materials and methods

The samples have been prepared by arc melting of high-purity elements (at
least 99.9 wt %) under titanium-gettered argon atmosphere. The elements have
been taken in a stoichiometric ratio. The obtained ingots have been remelted a
few times in order to improve their homogeneity. No annealing have been
applied as our previous tests have shown that annealing leads to the
appearance of impurity phases. The crystal structure of the obtained samples
has been examined by X-ray powder diffraction at room temperature using a
PANalytical X’Pert PRO diffractometer (Cu K$\alpha$ radiation, Bragg-Brentano
geometry, measured angle interval of $2\theta=10-100^{\circ}$, $2\theta$ step
= 0.033∘, 150 s/step). The X-ray diffraction data have been processed using
the FullProf program package [23, 24].

For the DC and AC magnetic measurements, the powder samples have been
encapsuled in plastic containers and glued by varnish in order to prevent
grain rotation or movement during the measurement. A Vibrating Sample
Magnetometer (VSM) option of the Physical Properties Measurement System (PPMS)
by Quantum Design has been utilized for DC magnetic measurements. Magnetic
susceptibility data have been collected over a wide temperature range of
1.85–390 K using both the Zero Field Cooling (ZFC) and Field Cooling (FC)
regimes. Every time before collecting a ZFC curve, the sample has been heated
to a temperature exceeding the respective critical temperature of magnetic
ordering, then demagnetized by the oscillating magnetic field, and finally
cooled down to 1.9 K. The ZFC and FC collected at a low magnetic field of 50
Oe have been used to determine magnetic transition temperatures, while from
the ZFC data taken at 1 kOe the effective magnetic moments ($\mu_{eff}$) and
paramagnetic Curie temperatures ($\theta_{p}$) have been derived. In order to
follow the thermal evolution of magnetic order, isothermal magnetization
curves have been collected in magnetic fields up to 90 kOe (9 T) at a number
of selected temperatures. Before collecting a magnetization curve, the sample
has been demagnetized using the described above procedure.

AC magnetic susceptibility measurements have been performed using an AC
Measurement System (ACMS) option of PPMS. The data have been collected under
an oscillating magnetic field of 2 Oe amplitude at a number of selected
frequencies between 100 and 5000 Hz. The temperature interval has covered
1.9–300 K.

The crystal structure has been visualized (see Fig. 1 with the use of the
VESTA program [25].

##  III Results

###  III.1 Crystal structure

Figure 1: Perspective view of the crystal structure of RE5Pt2In4 showing its
layered nature.

X-ray powder diffraction data collected for the RE5Pt2In4 (RE = Gd-Tm) samples
at room temperature confirm that the compounds crystallize in an orthorhombic
crystal structure of the Lu5Ni2In4-type (Pearson symbol oP22, space group
Pbam, No. 55, $Z=2$). This result is in agreement with the previous report
[2]. The Lu5Ni2In4-type structure consists of distorted trigonal and square
prismatic slabs of the REPt and REIn compositions [3]. The structure is a
layered-one with atoms situated on the mirror planes at $z=0$ and
$z=\frac{1}{2}$. The layers formed by the rare earth atoms are separated by
the layers containing Pt and In (see Fig. 1). The rare earth atoms occupy
three different Wyckoff sites, namely, one 2a site (0,0,0) and two 4g sites
$(x,y,0)$ with different atom positional parameters. The Pt atoms occupy one
4h site $(x,y,\frac{1}{2})$, while the In atoms are located at two other 4h
sites with different atom positional parameters.

Figure 2: X-ray diffraction patterns collected at room temperature for RE5Pt2In4: (a) RE = Gd, (b) RE = Tb, (c) RE = Dy (d) RE = Ho, (e) RE = Er and (f) RE = Tm. The solid circles denote the experimental data, while the black lines show the Rietveld refinement results. The vertical bars indicate Bragg reflection positions, whereas the difference between the experimental data and the refinement is presented as the blue line at the bottom of each subfigure. Table 1:  Crystallographic data obtained from Rietveld refinement of the X-ray powder diffraction patterns collected at room temperature for RE5Pt2In4 (RE = Gd-Tm; Lu5Ni2In4-type structure, space group $Pbam$, No. 55). The agreement factors Rprofile, RF, RBragg, and $\chi^{2}$ characterizing quality of refinements are listed at the bottom of the table. RE | Gd | Tb | Dy | Ho | Er | Tm
---|---|---|---|---|---|---
$a$ [Å] | 18.2045(20) | 18.1218(14) | 18.0551(13) | 17.9991(15) | 17.9447(11) | 17.8935(18)
$b$ [Å] | 8.0461(9) | 8.0140(6) | 7.9886(5) | 7.9731(6) | 7.9524(5) | 7.9212(8)
$c$ [Å] | 3.6771(5) | 3.6500(5) | 3.6270(3) | 3.6115(4) | 3.5942(2) | 3.5776(5)
$V$ [Å3] | 538.61(23) | 530.08(16) | 523.13(14) | 518.28(16) | 512.92(12) | 507.08(20)
RE1 at 2a (0, 0, 0) | 0 | 0 | 0 | 0 | 0 | 0
RE2 at 4g (x, y, 0) | $x=0.2181(10)$ | 0.2192(8) | 0.2200(7) | 0.2180(9) | 0.2190(7) | 0.2184(8)
| $y=0.2394(28)$ | 0.2459(21) | 0.2399(19) | 0.2389(24) | 0.2470(18) | 0.2471(23)
RE3 at 4g (x, y, 0) | $x=0.4204(12)$ | 0.4181(10) | 0.4168(8) | 0.4215(11) | 0.4168(7) | 0.4181(9)
| $y=0.1238(21)$ | 0.1215(17) | 0.1150(15) | 0.1196(19) | 0.1244(14) | 0.1218(18)
Pt at 4h (x, y, $\frac{1}{2}$) | $x=0.3056(8)$ | 0.3031(6) | 0.3028(5) | 0.3043(6) | 0.3044(5) | 0.3012(8)
| $y=0.0217(20)$ | 0.0236(13) | 0.0265(12) | 0.0259(14) | 0.0257(12) | 0.0295(17)
In1 at 4h (x, y, $\frac{1}{2}$) | $x=0.5695(14)$ | 0.5678(9) | 0.5645(8) | 0.5652(10) | 0.5691(9) | 0.5606(11)
| $y=0.2152(26)$ | 0.2102(17) | 0.2175(17) | 0.2111(17) | 0.2056(15) | 0.2094(19)
In2 at 4h (x, y, $\frac{1}{2}$) | $x=0.8459(14)$ | 0.8494(10) | 0.8492(9) | 0.8511(11) | 0.8484(8) | 0.8516(12)
| $y=0.0753(27)$ | 0.0759(18) | 0.0748(18) | 0.0714(20) | 0.0778(18) | 0.0759(24)
Rprofile [%] | 2.76 | 3.07 | 2.40 | 3.59 | 3.07 | 4.39
RF [%] | 8.19 | 9.55 | 6.08 | 6.71 | 4.88 | 5.95
RBragg [%] | 12.5 | 11.3 | 9.34 | 10.9 | 6.96 | 9.70
$\chi^{2}$ | 7.30 | 6.87 | 6.46 | 10.4 | 8.14 | 16.3

Fig. 2 shows X-ray powder diffraction patterns of RE5Pt2In4 (RE = Gd-Tm)
collected at room temperature, together with the results of Rietveld
refinement. The refined parameters of the crystal structure are listed in
Table 1.

Figure 3: Reciprocal magnetic susceptibility with the fitted line represents
the Curie-Weiss law for RE5Pt2In4: (a) RE = Gd, (b) RE = Tb, (c) RE = Dy (d)
RE = Ho, (e) RE = Er, and (f) RE = Tm. The low-temperature behavior measured
at 50 Oe (ZFC and FC regimes) is shown in the upper insets, while the
isothermal magnetization vs. external magnetic field at selected temperatures
is presented in the lower insets.

Figure 4: AC magnetic susceptibility of RE5Pt2In4: (a) RE = Gd, (b) RE = Tb,
(c) RE = Dy (d) RE = Ho, (e) RE = Er, and (f) RE = Tm taken at frequencies
between 100 Hz and 5000 Hz. $\chi^{\prime}$ and $\chi$ refer to the real and
imaginary components, respectively.

###  III.2 Magnetic properties

####  III.2.1 DC and AC magnetic susceptibility data

The results of DC magnetic measurements of RE5Pt2In4 (RE = Gd–Tm) are
presented in Fig. 3 and summarized in Table 2. At a low magnetic field of 50
Oe, all compounds show transitions from para- to magnetically ordered state
with decreasing temperature, namely, for RE = Gd, Tb, Ho and Er a rapid
increase of magnetic susceptibility, characteristic of para- to ferromagnetic
transition, is visible, while for RE = Tm a maximum typical of para- to
antiferromagnetic transition is found (see the upper insets in Figs. 3a-f).
The case of Dy5Pt2In4 is more complicated as the ferromagnetic transition at
$T_{C}=80$ K is preceded by an intermediate antiferromagnetic state
manifesting itself by a maximum at $T_{N}=93$ K. Below the critical
temperatures of magnetic ordering, a number of additional magnetic transitions
are detected from either additional maxima or inflection points. The magnetic
transition temperatures are listed in Table 2. Large discrepancies between the
ZFC and FC curves, visible especially for RE = Gd–Ho below the corresponding
Curie temperatures, are magnetic domains-related effects, indicating presence
of a ferromagnetic component of the magnetic order. The discrepancy found for
RE = Tm, both below and above the Néel temperature of 4.1 K, can be attributed
to a very small amount of ferromagnetic impurity phase, whose content is too
small to be detectable by other experimental techniques like X-ray powder
diffraction (XRD).

The maxima visible in the AC magnetic susceptibility vs. temperature curves
(see Fig. 4) coincide with the magnetic transition temperatures derived from
the DC magnetic data (see Table 2). Some discrepancies between the DC and AC
data can be attributed to different experimental conditions, namely, the AC
data have been collected under the oscillating field of 2 Oe and no applied DC
field, while the DC data have been recorded under a constant field of 50 Oe.
Although relatively low, the latter field may influence temperatures of
magnetic transition sensitive to the applied magnetic field. It is worth
noting that for Dy5Pt2In4, the Néel temperature derived from the DC data
coincides with a distinct maximum observed in $\chi^{\prime}_{ac}$ at 93 K
(there is no anomaly at this temperature in $\chi^{\prime\prime}_{ac}$), while
the Curie point of 80 K is accompanied by maxima in both $\chi^{\prime}_{ac}$
and $\chi^{\prime\prime}_{ac}$.

Table 2: Parameters characterizing magnetic order: $T_{C}$ (Curie
temperature), $T_{N}$ (Néel temperature), $T_{t}$ (temperatures of additional
anomalies), $\theta_{p}$ (paramagnetic Curie temperature), $\mu_{eff}$
(effective magnetic moment), $\mu[\mu_{B}]$ (magnetic moment in the ordered
state), $H_{cr}[kOe]$ (the critical field) and $H_{coer}[kOe]$ (the coercivity
field) for RE5Pt2In4 (RE = Gd–Tm), as derived from DC and/or AC magnetometric
measurements. The $i$ and $m$ indices indicate whether the transition
temperature corresponds to an inflection point or to a maximum in the
$\chi(T)$ curve, respectively. The transition temperatures are calculated from
the ZFC data, except few cases based on the FC data and marked explicitly by
an additional index $f$.

RE |  $T_{C}$[K] |  $T_{N}$[K] |  $T_{t}$[K] | $\theta_{p}[K]$ | $\mu_{eff}[\mu_{B}]$ | $\mu[\mu_{B}]$ | $H_{cr}[kOe]$ | $H_{coer}[kOe]$
---|---|---|---|---|---|---|---|---
| $\chi_{dc}$ | $\chi^{\prime}_{ac}$ | $\chi^{\prime\prime}_{ac}$ | $\chi_{dc}$ | $\chi^{\prime}_{ac}$ | $\chi^{\prime\prime}_{ac}$ | $\chi_{dc}$ | $\chi^{\prime}_{ac}$ | $\chi^{\prime\prime}_{ac}$ |  | Exp. | Theor. | Exp. | Theor. |  |
Gd |  76i |  74m |  73m |  |  |  |  22.5i |  |  | +72 | 7.87 | 7.94 | 3.86 | 7.00 | T = 1.9 K: 0.16 | 0.11
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 40.0 K: 0.05 | 0.02
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 68.0 K: 0.02 |
Tb |  108i |  106m |  104m |  |  |  |  83i |  |  | +48 | 9.55 | 9.72 | 4.34 | 9.00 | T = 1.9 K: 44 | 23.7
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 20.0 K: 1.7 | 1.9
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 100.0 K: 0.03 |
Dy |  80i |  84m |  80m |  93m |  93m |  |  19.6m,f, 71i |  14.1m |  | +24.6 | 10.61 | 10.65 | 5.74 | 10.00 | T = 1.9 K: 24.3, 45 | 22.1
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 12.0 K: 13.5 | 11.5
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 25.0 K: 2.2 | 2.4
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 75.0 K: 0.1 | 0.03
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 87.0 K: 0.5 |
Ho |  23.5i |  22.7m |  22.1m |  |  |  |  9.1m,f, 13.5i |  8.1m |  | +10.1 | 10.62 | 10.61 | 6.98 | 10.00 | T = 1.9 K: 2.9 | 1.4
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 9.0 K: 0.22 | 0.23
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 15.0 K: 0.08 | 0.03
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 20.0 K: 0.02 |
Er |  12.6i |  12.1m |  11.9m |  |  |  |  6.9i, 8.8i |  |  7.1m | +11.1 | 9.44 | 9.59 | 3.24 | 9.00 | T = 1.9 K: 0.96 | 0.3
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 7.0 K: 0.21 | 0.09
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 9.5 K: 0.08 | 0.02
Tm |  |  |  |  4.1m |  4.2m |  4.2m |  |  |  | +4.6 | 7.45 | 7.57 | 3.54 | 7.00 | T = 1.9 K: 9.2 | 0.03
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 3.0 K: 7.6 | 0.04
|  |  |  |  |  |  |  |  |  |  |  |  |  |  | T = 4.0 K: 0.07 | 0.02

$i$ – inflection point; $m$ – maximum; $f$ – determined from the FC curve

The reciprocal magnetic susceptibility curves, collected at H = 1 kOe, become
linear at high-enough temperatures as predicted by the Curie-Weiss law [26]:

$\chi=\frac{C}{T-\theta_{p}}$ (1)

where $C$ is the Curie constant related to the effective magnetic moment
($\mu_{eff}$), while $\theta_{p}$ is a paramagnetic Curie temperature. The
values of $\mu_{eff}$ and $\theta_{p}$, as derived from fitting the linear
dependence to $\chi_{dc}^{-1}(T)$ at high temperature regions, are listed in
Table 2. The values of $\mu_{eff}$ are very close to those predicted for the
free RE3+ ions. It is worth noting that for all investigated compounds, the
determined paramagnetic Curie temperatures are positive, indicating the
predominant role of the ferromagnetic interactions.

####  III.2.2 Magnetization

The lower insets in Figs. 3a-f show magnetization curves for RE5Pt2In4 (RE =
Gd-Tm) taken in applied magnetic fields up to 90 kOe at a number of selected
temperatures. The shape of the curves, especially those collected at lower
temperatures, testifies to the coexistence of ferro- and antiferromagnetic
components of the magnetic structures as both metamagnetic transitions as well
as magnetic hysteresis are observed. The critical fields, corresponding to the
metamagnetic transitions, have been determined from inflection points in the
primary magnetization curves, i.e. the curves recorded directly after the
zero-field cooling (ZFC) procedure. The values of critical fields derived from
experimental data are listed in Table 2. The appearance of metamagnetic
transition confirms the existence of an antiferromagnetic component, which is
suppressed by application of a high-enough external magnetic field. The
ferromagnetic component of the magnetic structure manifests itself in non-zero
coercivity field. The observed values of coercivity fields are also reported
in Table 2.

It is worth noting that both the Tb- and Dy-based compounds show very high
values of critical and coercivity fields at 1.9 K, testifying to stronger
magnetic interactions than in the other investigated compounds. Such a result
coincides with the highest ordering temperatures observed for RE = Tb and Dy.

The case of Dy5Pt2In4 is very special as the critical field initially
decreases with increasing temperature, reaching 0.1 kOe at 75 K, and afterward
increases again to 0.5 kOe at 87 K. Such a result is in agreement with the
susceptibility data (see subsection III.2.1), which suggest suppression of the
ferromagnetic component of the Dy5Pt2In4 magnetic structure at $T_{C}=80$ K
with further development of the antiferromagnetic one, which exists up to
$T_{N}=93$ K.

The determined values of the magnetic moments in the ordered state, as derived
from magnetization data taken at 1.9 K and 90 kOe, are significantly lower
than the values expected for free RE3+ ions (for example, for Tb5Pt2In4 it is
4.34 $\mu_{B}$, which is only 48 % of the theoretical value for Tb3+ which
equals 9.00 $\mu_{B}$ – for other compounds, see Table 2). Nevertheless, one
should take into account that the magnetization curves collected at 1.9 K are
far away from saturation even at a relatively high magnetic field of 90 kOe.

####  III.2.3 Magnetocaloric effect

##### Magnetic entropy change and temperature averaged magnetic entropy change
(TEC)

Figure 5: Magnetization vs temperature curves under various magnetic flux
density values up to 9 T for RE5Pt2In4: (a) RE = Gd, (b) RE = Tb, (c) RE = Dy
(d) RE = Ho, (e) RE = Er, and (f) RE = Tm.

Figure 6: Temperature dependence of the magnetic entropy change $-\Delta
S_{M}^{max}$, as derived from the $M(H,T)$ data, under various magnetic flux
density changes $\Delta\mu_{0}H$ up to 0–9 T, for RE5Pt2In4: (a) RE = Gd, (b)
RE = Tb, (c) RE = Dy (d) RE = Ho, (e) RE = Er, and (f) RE = Tm.

Figure 7: The values of $-\Delta S_{M}^{max}$, TEC(3 K), TEC(5 K), and TEC(10
K) under various magnetic flux density changes $\Delta\mu_{0}H$ up to 0–9 T
for RE5Pt2In4: (a) RE = Gd, (b) RE = Tb, (c) RE = Dy, (d) RE = Ho, (e) RE =
Er, and (f) RE = Tm, respectively. For RE = Tb and Dy, the magnetic entropy
changes corresponding to the low- and high-temperature maxima are indicated by
black and brown lines, respectively.

Considering the magnetic entropy ($S_{M}$) as a function of magnetic flux
density ($\mu_{0}H$) and temperature ($T$), its differential $\mathrm{d}S_{M}$
can be expressed as:

$\mathrm{d}S_{M}=\left(\frac{\partial
S_{M}}{\partial{(\mu_{0}H)}}\right)_{T}\mathrm{d}(\mu_{0}H)+\left(\frac{\partial
S_{M}}{\partial T}\right)_{(\mu_{0}H)}\mathrm{d}T$ (2)

Taking into account one of the Maxwell’s relations, namely that of
$\left(\frac{\partial
S_{M}}{\partial{(\mu_{0}H})}\right)_{T}=\left(\frac{\partial M}{\partial
T}\right)_{(\mu_{0}H)}$, and inserting it to Eq. 2, leads to:

$\mathrm{d}S_{M}=\left(\frac{\partial M}{\partial
T}\right)_{(\mu_{0}H)}\mathrm{d}(\mu_{0}H)+\left(\frac{\partial
S_{M}}{\partial T}\right)_{(\mu_{0}H)}\mathrm{d}T$ (3)

where $M$ denotes magnetization.

By applying the isothermal condition ($\mathrm{d}T=0$) and integrating Eq. 3
over magnetic flux density, one gets:

$\Delta S_{M}(T,\Delta\mu_{0}H)=\int_{0}^{\mu_{0}H_{max}}\left(\frac{\partial
M(\mu_{0}H,T)}{\partial T}\right)_{(\mu_{0}H)}\,\mathrm{d}\mu_{0}H$ (4)

where $\Delta\mu_{0}H$ is a change of the magnetic flux density (usually
calculated with respect to the initial flux equal to zero), while
$\left(\frac{\partial M(\mu_{0}H,T)}{\partial T}\right)_{(\mu_{0}H)}$ is a
derivative of magnetization over temperature at fixed magnetic flux density of
$\mu_{0}H$. Details of mathematical formalism related to the magnetocaloric
effect can be found for example in the book by Tishin and Spichkin [27].

Fig. 5 shows the magnetization vs. temperature $M(T)$ curves collected at a
number of fixed magnetic flux density values up to 9 T for the RE5Pt2In4 (RE =
Gd–Tm) compounds. Based on the above data, the corresponding magnetic entropy
changes have been calculated using Eq. 4. The results are presented in Fig. 6.
Maximum entropy changes around corresponding magnetic transition temperatures
reach 3.7, 3.4, 6.3, 11.8, 11.4, and 10.2 J$\cdot$kg${}^{-1}\cdot$K-1 under
magnetic flux density change of 0–9 T for RE = Gd, Tb, Dy, Ho, Er, and Tm,
respectively. The values for other magnetic flux density changes are listed in
Table 3. The cases of Tb5Pt2In4 and Dy5Pt2In4 need an extra comment, as two
distinct maxima are found in the magnetic entropy change vs. temperature plots
(see Figs. 6b and 6c). The high-temperature maximum ($\sim$110 K for RE = Tb
and $\sim$95 K for RE = Dy), which dominates for low magnetic flux density
changes, corresponds to the transition from para- to ferromagnetic state. The
low-temperature maximum ($\sim$45 K for RE = Tb and $\sim$25 K for RE = Dy),
which dominates for high magnetic flux density changes, indicates an extra
transformation of the magnetic structure. The magnetic entropy changes
corresponding to the low- and high-temperature maxima are shown separately in
Figs. 6b and 6c.

The temperature averaged magnetic entropy change (TEC) is another parameter
used for evaluating MCE. TEC is defined by the following formula [28]:

$\displaystyle TEC(\Delta T_{\mathrm{lift}},\Delta\mu_{0}H)=$
$\displaystyle\frac{1}{\Delta
T_{\mathrm{lift}}}\max_{T_{\mathrm{mid}}}\Bigg{\\{}\int_{T_{\mathrm{mid}}-\frac{\Delta
T_{\mathrm{lift}}}{2}}^{T_{\mathrm{mid}}+\frac{\Delta
T_{\mathrm{lift}}}{2}}\Delta
S_{\mathrm{M}}(T,\Delta\mu_{0}H)\,\mathrm{d}T\Bigg{\\}}$ (5)

where $T_{mid}$ is the center temperature of the temperature span ${\Delta
T_{lift}}$. The value of $T_{mid}$ is determined by finding the one that
maximizes the integral appearing in Eq. 5. The TEC values of RE5Pt2In4 (RE =
Gd–Tm), calculated for the temperature spans of 3, 5 and 10 K, are presented
in Fig. 7. It is worth noting that the TEC values for RE = Tb and Dy are
always related to the dominating maximum, i.e. to the high-temperature maximum
for the low magnetic flux density changes and the low-temperature one for the
high magnetic flux density changes (see Figs. 7b and 7c).

##### Relative Cooling Power (RCP) and Refrigerant Capacity (RC)

Besides $\Delta S_{M}^{max}$ and TEC, the relative cooling power (RCP) [29]
and refrigerant capacity (RC) [30] are another important parameters that can
be used to assess the MCE performance. RCP is defined by the equation:

$RCP=-\Delta S_{M}^{max}\times\delta T_{FWHM}$ (6)

where $\delta T_{FWHM}$ is the full width at half maximum of the entropy
change vs. temperature curve. RC is calculated from the following integral:

$RC=\int_{T_{1}}^{T_{2}}|\Delta S_{M}|\,\mathrm{d}T$ (7)

where $T_{1}$ and $T_{2}$ denote the lower and upper limits of the FWHM
temperature range, respectively.

Table 3:  The temperatures of maximum entropy change, maximum entropy changes
$-\Delta S_{M}^{max}$ together with RCP and RC values under magnetic flux
density changes $\Delta\mu_{0}H$ = 0–2 T, 0–5 T, 0–7 T and 0–9 T for the
RE5Pt2In4 (RE = Gd–Tm) and isostructural compounds.
Materials |  Temp. for $-\Delta S_{\mathrm{M}}^{\mathrm{max}}$ [K] |  $-\Delta S_{\mathrm{M}}^{\mathrm{max}}$[J$\cdot$kg${}^{-1}\cdot$K-1] |  RCP [J$\cdot$kg-1] |  RC [J$\cdot$kg-1] | Ref.
---|---|---|---|---|---
|  | 0–2 T | 0–5 T | 0–7 T | 0–9 T | 0–2 T | 0–5 T | 0–7 T | 0–9 T | 0–2 T | 0–5 T | 0–7 T | 0–9 T |
Dy5Ni2In4 | 19 | 1.8 | 3.6 | 4.7 | - | 49 | 178 | 286 | - | 37 | 130 | 209 | - | [10]
Ho5Ni2In4 | 103 | 2.6 | 7.1 | 10.1 | - | 84 | 298 | 458 | - | 66 | 234 | 352 | - | [10]
Er5Ni2In4 | 20 | 3.3 | 7.7 | 10.2 | - | 71 | 248 | 377 | - | 52 | 180 | 273 | - | [10]
Gd5Pt2In4 | 78 | 1.0 | 2.2 | 3.0 | 3.7 | 58 | 172 | 261 | 359 | 48 | 139 | 209 | 290 | this work
Tb5Pt2In4 | 45, 110 | 0.8 | 1.7 | 2.5 | 3.4 | 82 | 198 | 303 | 428 | 57 | 165 | 248 | 340 | this work
Dy5Pt2In4 | 25, 95 | 1.1 | 2.9 | 4.7 | 6.3 | 45 | 290 | 250 | 363 | 33 | 201 | 180 | 263 | this work
Ho5Pt2In4 | 23 | 2.5 | 6.9 | 9.5 | 11.8 | 94 | 302 | 451 | 607 | 82 | 254 | 373 | 495 | this work
Er5Pt2In4 | 14 | 3.6 | 7.5 | 9.6 | 11.4 | 79 | 218 | 328 | 434 | 63 | 175 | 256 | 341 | this work
Tm5Pt2In4 | 8 | 3.2 | 7.7 | 9.2 | 10.2 | 34 | 125 | 189 | 260 | 27 | 98 | 150 | 205 | this work

Table 3 lists the determined values of RCP and RC for RE5Pt2In4 (RE = Gd–Tm)
under selected changes of magnetic flux densities. It is worth noting that for
Dy5Pt2In4, the RCP and RC values under magnetic flux density changes of 0–5 T
are higher than those under 0–7 T. This unusual behavior is due to the fact
that under $\Delta\mu_{0}H$ = 0–5 T, the low- and high-temperature maxima in
$-\Delta S_{M}(T)$ are of similar heights and they overlap, leading to FWHM
temperature interval being significantly wider than the one at higher magnetic
flux density changes where low-temperature maximum dominates.

##  IV Discussion

This work reports the results of X-ray, DC, and AC magnetic measurements for
the RE5Pt2In4 (RE = Gd-Tm) compounds. The X-ray diffraction data confirm that
RE5Pt2In4 (RE = Gd-Tm) have an orthorhombic crystal structure of the
Lu5Ni2In4-type. The crystal structure is a typical two-layered one with layers
formed by the rare earth atoms $(z=0)$ separated by layers containing the
remaining Pd and In atoms $(z=\frac{1}{2})$. The refined lattice parameters
and atomic coordinates, presented in Table 1, are in good agreement with the
previously reported ones [2].

The results of magnetometric measurements reveal that all investigated
compounds order magnetically with decreasing temperature. The shapes of the
magnetic susceptibility vs. temperature curves (see Figs. 3, 4) suggest para-
to ferromagnetic transition for RE = Gd, Tb, Ho and Er, while for RE = Tm a
para- to antiferromagnetic transition is found. The case of RE = Dy is more
complicated as the ferromagnetic state is reached through an intermediate
antiferromagnetic state occuring in realtively narrow temperature range.
Anomalies in the $\chi(T)$ curves, observed below the respective critical
temperatures of magnetic ordering for all compounds except RE = Tm, suggest
presence of additional temperature-induced magnetic transitions. Such a
behavior has been observed in the isostructural RE5Ni2In4 [4, 5, 6, 7, 8, 9,
10]. It can be attributed to complexity of the crystal structure as the rare
earth atoms occupy three nonequivalent Wyckoff sites, which leads to
competition of different interactions. Complex magnetic properties manifest
themselves also in coexistance of the ferro- and antiferromagnetic
contributions to the magnetic structure, as confirmed by the shapes of the
magnetization vs. applied magnetic field curves, which show both presence of
coercivity fields characteristic of ferromagnetic order as well as
metamagnetic transitions characteristic of antiferromagnetic ordering (see the
lower insets in Figs. 3a-f). It has to be mentioned that the exact thermal
evolution of the magnetic structures cannot be determined solely from the
magnetic data, but further neutron diffraction studies are required.

Figure 8: Critical temperatures of magnetic ordering ($T_{C,N}$) along with
paramagnetic Curie temperatures $\theta_{p}$ vs. de Gennes factor for RE5T2In4
(RE = rare earth element, T = Ni, Pd, Pt). The data for T = Ni have been taken
after [4, 5, 6, 8, 9], while those for T = Pd after [11]. The dotted lines
indicate theoretical de Gennes scaling for RE5Pt2In4 while taking the
characteristic temperatures of Gd5Pt2In4 as reference.

Reciprocal magnetic susceptibilities of RE5Pt2In4 (RE = Tb-Tm) follow the
Curie-Weiss law at high temperatures (see Fig. 3). The deviations from
linearity, as observed at lower temperatures, indicate influence of the
crystalline electric field (CEF). The determined Curie temperatures are
positive revealing that the ferromagnetic interactions are dominant. The
obtained values of the effective magnetic moments are close to those redicted
for the free RE3+ ions. Small discrepancies between the experimental and
theoretical values do not exceed systematic errors of the experiment.
Therefore the magnetism of RE5Pt2In4 (RE = Tb-Tm) is strictly related to the
rare earth magnetic moments, while the magnetic moments of the remaining Pt
and In elements are either zero or they are too small to be detectable when
accompanied by high rare earth moments.

According to the crystallographic data reported in Tables 1 and 4 in [2], the
rare earth interatomic distances in RE5Pt2In4 (RE = Tb-Tm) exceed 3.3 Å.
Therefore, they are high enough to exclude any direct interactions and the
indirect interactions of the RKKY-type are expected in this family of
compounds. One of the predictions of the RKKY theory is so called de Gennes
scaling, which assumes direct proportionality between the critical temperature
of magnetic ordering and the de Gennes factor defined as
$(g_{J}-1)^{2}J(J+1)$, where $g$ is a Landé factor, while $J$ is a total
angular momentum of the RE3+ rare earth ion. Figure 8 presents the critical
temperatures of magnetic ordering for RE5T2In4 (T = Ni, Pd, Pt) plotted
against de Gennes factor. In addition, the paramagnetic Curie temperatures,
which are also a measure of the strength of magnetic interactions, are shown.
The lack of theoretically predicted proportionality is yet another evidence of
significant influence of CEF on magnetic properties of RE5T2In4 (RE = rare
earth element, T = Ni, Pd, Pt). It is worth noting that the critical
temperature of magnetic ordering of a particular Ni-based compound is in the
most cases higher than those of its Pd- and Pt-based analogues. This finding
coincides with increase of the interatomic distances due to increasing number
of the atomic number of the d-electron element (compare the lattice parameters
for T = Ni [3, 31, 5], Pd [32] and Pt [2]). Therefore, the increase of the
interatomic distances leads to weaken the magnetic interactions.

Figure 9: The plots of $M^{2}$ versus $\mu_{0}H/M$ at selected temperatures
for RE5Pt2In4: (a) RE = Gd, (b) RE = Tb, (c) RE = Dy (d) RE = Ho, (e) RE = Er
and (f) RE = Tm.

The type of magnetic transition (the first or second order) can be derived
from shapes of the Arrott plots ($M^{2}$ vs. $\mu_{0}H/M$) collected at
selected temperatures [33]. Positive slope of the Arrott curve corresponds to
the second order phase transitions (SOPT), while the negative slope to the
first order phase transitions (FOPT). Fig 9 shows the Arrott plots for
RE5Pt2In4 (RE = Gd-Tm). For RE = Gd, Ho, Er and Tm only positive slopes are
found, indicating magnetic transition of the second order type. The situation
is more complicated for RE = Tb and Dy, as positive slopes characteristic of
SOPT are found below the critical temperature of magnetic ordering, except the
lowest temperature of 2 K, where positive slope characteristic of FOPT is
observed within limited range. This behavior is consistent with the shapes of
the magnetization vs. temperature curves (see Fig. 5). For the low values of
the applied magnetic field, magnetization initially increases with decreasing
temperature, but finally undergoes a sudden drop below 20 K. Such a behavior
indicates that the high-temperature ferro-/ferrimagnetic structure transforms
into an antiferromagnetic one with decreasing temperature. According to the
shape of Arrott plots this phase transition is of the first order type (FOPT).

Table 4: Comparison of the magnetocaloric performance under magnetic flux
density change of 0-7 T for RE5Pt2In4 (RE = Gd-Tm), isostructural RE5Ni2In4
(RE = Dy, Ho, Er) and other selected ternary rare earth-based indides.
$T_{cr}$ denotes critical temperature of the magnetic ordering (Curie or Néel
temperature).
Material |  $T_{cr}$ [K] |  $-\Delta S_{\mathrm{M}}^{\mathrm{max}}$ [J$\cdot$kg${}^{-1}\cdot$K-1] | RCP $[\mathrm{J}$$\cdot$$\mathrm{kg}^{-1}$] | RC $[\mathrm{J}$$\cdot$$\mathrm{kg}^{-1}$] | Ref.
---|---|---|---|---|---
Gd5Pt2In4 | 76 | 3.0 | 261 | 209 | this work
Tb5Pt2In4 | 108 | 2.5 | 303 | 248 | this work
Dy5Pt2In4 | 93 | 4.7 | 250 | 180 | this work
Ho5Pt2In4 | 23.5 | 9.5 | 451 | 373 | this work
Er5Pt2In4 | 12.6 | 9.6 | 328 | 256 | this work
Tm5Pt2In4 | 4.1 | 9.2 | 189 | 150 | this work
Dy5Ni2In4 | 105 | 4.7 | 286 | 209 | [10]
Ho5Ni2In4 | 31 | 10.1 | 458 | 352 | [10]
Er5Ni2In4 | 21 | 10.2 | 377 | 273 | [10]
Gd11Co4In9 | 86 | 10.95 | 538.1 | 405.9 | [34]
Tb11Co4In9 | 95∗ | 4.43 | 376.8 | 274.4 | [35]
Dy11Co4In9 | 37 | 4.66 | 213.9 | 165.9 | [34]
Ho11Co4In9 | 20 | 12.29 | 475.2 | 357.4 | [34]
Er11Co4In9 | 5.4∗ | 12.80 | 416.1 | 320.0 | [35]
Gd11Ni4In9 | 91 | 3.58 | 269.0 | 206.4 | [36]
Dy11Ni4In9 | 18 | 6.02 | 194.9 | 144.7 | [36]
Ho11Ni4In9 | 13.5 | 12.44 | 353.0 | 269.2 | [36]
Gd6Co2.2In0.8 | 76 | 11.84 | 814.23 | 633.55 | [37]
Tb6Co2.2In0.8 | 32 | 8.96 | 394.15 | 284.32 | [37]
Dy6Co2.2In0.8 | 50 | 9.59 | 517.01 | 389.77 | [37]
Ho6Co2.2In0.8 | 18 | 20.83 | 626.36 | 466.07 | [37]

Table 4 contains comparison of the MCE performance under magnetic flux density
change of 0-7 T for RE5Pt2In4 (RE = Gd-Tm), isostructural RE5Ni2In4 (RE = Dy,
Ho, Er) and other selected ternary rare earth-based indides. For a selected
rare earth element, the MCE performance of a member of the RE5Pt2In4 (RE = Gd-
Tm) family of compounds shows similar performance to that of its RE5Ni2In4 and
RE11T4In9 (T = Co, Ni) analogues. It is worth mentioning that the MCE
performance of RE5Pt2In4 (RE = Ho and Er), which is reported in this work, is
quite high and comparable to that of the best known low-temperature
magnetocaloric materials [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 34, 39,
40, 36, 10, 37].

##  V Conclusions

The RE5Pt2In4 (RE = Gd-Tm) compounds crystallize in an orthorhombic crystal
structure of the the Lu5Ni2In4-type (Pbam space group) in which the rare earth
atoms occupy three nonequivalent sites. The compounds show complex magnetic
properties and quite good MCE performance at low temperatures. With decreasing
temperature all investigated compounds undergo a transition to magnetically
ordered state, in the most cases followed by a cascade of extra magnetic
transitions appearing below the respective critical temperature of magnetic
ordering. The rare earth atoms are found to possess magnetic moments, while
the moments of the remaining Pt and In atoms are absent or are too small to be
detected while accompanied by the strong rare earth’s moments. The MCE
performance of RE5Pt2In4 (RE = Gd-Tm) is comparable to that of the best known
low-temperature magnetocaloric materials, especially while taking into account
the compounds with RE = Ho and Er.

## Declaration of Competing Interest

The authors declare no conflict of interest.

## Acknowledgements

This research was supported in part by the Excellence Initiative – Research
University Program at the Jagiellonian University in Kraków. The research was
partially carried out with the equipment purchased thanks to the financial
support of the European Regional Development Fund in the framework of the
Polish Innovation Economy Operational Program (contract
no.POIG.02.01.00-12-023/08).

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11institutetext: Zentrum für Astronomie der Universität Heidelberg,
Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany
11email<EMAIL_ADDRESS>22institutetext: Department of
Astronomy, Stockholm University, AlbaNova University Center, SE-106 91
Stockholm, Sweden
33institutetext: Research School of Astronomy and Astrophysics, Australian
National University, Canberra, ACT 2611, Australia
44institutetext: ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), Australia
55institutetext: George P. and Cynthia Woods Mitchell Institute for
Fundamental Physics and Astronomy, Texas A&M University, College Station, TX
77843, USA
66institutetext: Department of Physics & Astronomy, Texas A&M University, 4242
TAMU, College Station, TX 77843, USA

# Metallicities for more than 10 million stars derived from $Gaia$ BP/RP
spectra ††thanks: Table 3 is only available in electronic form at the CDS via
anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/.

T. Xylakis-Dornbusch  0000-0002-1296-2907 11 N. Christlieb
0000-0002-4043-2727 11 T.T. Hansen  0000-0001-6154-8983 22 T.Nordlander
0000-0001-5344-8069 3344 K. B. Webber  0000-0002-9762-4308 5566 J. Marshall
0000-0003-0710-9474 5566

###### Abstract

Context. The third $Gaia$ Data Release, which includes BP/RP spectra for 219
million sources, has opened a new window in the exploration of the chemical
history and evolution of the Milky Way. The wealth of information encapsulated
in these data is far greater than their low resolving power ($R\sim 50$) at
first glance would suggest, as shown in many studies. We zero in on the use of
this data for the purpose of the detection of ‘new’ metal-poor stars, which
are hard to find yet essential for understanding - among other - several
aspects of the origin of the Galaxy, star formation and the creation of the
elements.

Aims. We strive to refine a metal-poor candidate selection method which was
developed with simulated $Gaia$ BP/RP spectra, with an ultimate objective of
providing the community with both a recipe to select stars for medium/high
resolution observations and a catalogue of stellar metallicities.

Methods. We used a datased comprised of GALAH DR3 and SAGA database stars in
order to verify and adjust to real world data our selection method. For that
purpose, we used dereddening as a mean to tackle the issue of extinction, and
then we applied our fine-tuned method to select metal-poor candidates, which
we thereafter observed and analysed.

Results. We were able to infer metallicities for GALAH DR3 and SAGA stars -
with color excesses up to $E(B-V)<1.5$ \- with an uncertainty of
$\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.36$, which is good enough for the
purpose of identifying new metal-poor stars. Further, we selected 26 metal-
poor candidates - via our method - for observations. As spectral analysis
showed, 100% of them had $\mathrm{[Fe/H]}<-2.0$, 57% had
$\mathrm{[Fe/H]}<-2.5$ and 8% had $\mathrm{[Fe/H]}<-3.0$. We inferred
metallicities for these stars with an uncertainty
$\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.31$, as was proven when comparing to the
spectroscopic $\mathrm{[Fe/H]}$. Finally, we assembled a catalogue of
metallicities for 10 861 062 stars.

###### Key Words.:

stars: Population II - Catalogs - Surveys

##  1 Introduction

The oldest stars that are still alive today and are located nearby, have
metallicities $<-3$ (extremely metal-poor (EMP) stars (Beers & Christlieb,
2005)). EMP stars are rare and difficult to find. They are the descendants of
the first generation of stars. Hence, EMP stars carry information that can
shed light on the properties of their predecessors, as well as on how the
latter exploded and ended their lives. Consequently, finding a large number of
new EMP stars for which detailed studies of their chemical composition could
be conducted is of the essence, since that would provide constraints on the
assembly of the Galaxy, on the initial mass function of the first stars and on
the nucleosynthesis processes that formed the heavy elements. The $Gaia$
Survey (Gaia Collaboration et al., 2016) released in 2022 the low-resolution
(R$\sim 50$) $Gaia$ BP/RP spectra for 219 million sources (De Angeli et al.,
2023), and there have already been many studies that provide metallicity
estimates for several thousands to millions of objects by extracting
information from BP/RP spectra, often complementary to the use of additional
data from $Gaia$ itself (for example Radial Velocity Spectrometer (RVS)
spectra; Katz et al. 2023) or other surveys. Bellazzini et al. (2023) derived
metallicities for $\sim 700\,000$ stars, and Andrae et al. (2023a) delivered a
catalog of stellar parameters - including the metallicity - using a Bayesian
forward-modelling approach (Bailer-Jones et al., 2013). Yao et al. (2024) used
a classification algorithm (XGBoost; Chen & Guestrin 2016) to identify 188 000
very metal-poor star candidates. Rix et al. (2022) used the machine learning
algorithm XGBoost to estimate $\mathrm{[M/H]}$ for 2 million stars, with 18
000 of them in the very- and metal-poor regime. Andrae et al. (2023b) produced
a new catalogue, improving the Rix et al. (2022) one. The new catalogue was
assembled by training the XGBoost algorithm on stellar parameters taken from
the Data Release 17 (DR17) of the Sloan Digital Sky Survey’s (SDSS) APOGEE
survey (Abdurro’uf et al., 2022), and from Li et al. (2022) who derived
stellar parameters for 400 extremely and ultra metal-poor stars . Andrae et
al. (2023b) delivered a catalogue for $\sim$ 175 million stars, with a mean
precision of 0.1 dex for $\mathrm{[M/H]}$. Zhang et al. (2023) used a forward
model to estimate effective temperature, surface gravity, metallicity,
distance, and extinction for 220 million stars. In order to do so, they used
Gaia XP based data-driven models along with 2MASS (Skrutskie et al., 2006),
and WISE (Schlafly et al., 2019) photometry. The forward model was then
trained and validated on stellar parameters from the LAMOST survey (Wang et
al., 2022), yielding $\mathrm{[Fe/H]}$ with a typical uncertainty of 0.15 dex.
Martin et al. (2023) used the BP/RP spectra to derive synthetic photometry of
the Ca H & K region, based on the narrow-band photometry of the Pristine
Survey (Starkenburg et al., 2017). They updated the Pristine metallicity
inference model, so that it is exclusively based on Gaia magnitudes ($G$,
$G_{BP}$, and $G_{RP}$), and produced a catalogue of metallicities for more
than 52 million stars. Martin et al. (2023) show that their photometric
metallicities are accurate down to $\mathrm{[Fe/H]}\sim\,-3.5$, and thus very
much suited for the study of the metal-poor Galaxy. Another study that take
advantage of the BP/RP spectra in order to derive stellar parameters and/or
metallicities is Cunningham et al. (2023).
Xylakis-Dornbusch et al. (2022) (Paper I) developed an empirical method based
on flux-ratios of synthetic $Gaia$ BP/RP spectra for the purpose of
identifying new metal-poor stars. Specifically, the flux-ratios were those of
the Ca H & K lines to the H$\beta$ region ($fr\mathrm{{}_{CaHK/H\beta}}$ with
$388\mathrm{nm}<\lambda<401\mathrm{nm}$ and
$479\mathrm{nm}<\lambda<501\mathrm{nm}$), and the G-band region to the Ca near
infrared triplet (Ca NIR) ($fr\mathrm{{}_{G/CaNIR}}$ with
$420\mathrm{nm}<\lambda<444\mathrm{nm}$ and
$846\mathrm{nm}<\lambda<870\mathrm{nm}$). It was shown that for roughly
constant $fr\mathrm{{}_{G/CaNIR}}$, the $fr\mathrm{{}_{CaHK/H\beta}}$ is
exponentially declining as metallicity increases. This work is a follow-up to
Paper I, aiming at verifying the metal-poor star selection recipe presented
therein by applying it to $Gaia$ DR3 BP/RP spectra. The paper is laid out in
the following manner: in Section 2 we describe the dataset we used for the
purpose of the validation of the method in Paper I, as well as how we
addressed the issue of extinction which was not dealt with in our previous
work. We close the Section with the description of the modifications we
performed on the selection procedure and metallicity estimation of the metal-
poor candidate stars compared to that introduced in Paper I. Next, we present
in Section 3 the results of the method verification, including the expected
success rate in selecting stars that are very metal-poor
($\mathrm{[Fe/H]}<-2$) and below that threshold, and the purity of that
ensemble. Then we investigate the plausibility of OBA stars being selected as
metal-poor stars via our method. Furthermore, in Section 5 we describe the
application of our fine-tuned recipe by selecting candidate metal-poor stars
and subsequently observing them. We then present the results of our
observations. Finally, in Section 6 we present a catalogue of metallicities
including stars in both the metal-poor and -rich regimes.

##  2 Methods

For the verification of the selection process we used stellar parameters from
high and medium resolution surveys/studies, and the respective flux dereddened
Gaia BP/RP spectra. The software GaiaXPy 111Software available at
https://gaia-dpci.github.io/GaiaXPy-website/, version: DOI v2.0.1:
10.5281/zenodo.7566303 was used to generate the $Gaia$ BP/RP spectra,
dust_extinction 222https://github.com/karllark/dust_extinction and dustmaps
333https://github.com/gregreen/dustmaps (Green, 2018) were used to deredden
the spectral flux.

###  2.1 Dataset

The dataset we used for this work is comprised of two different cross-matches
with $Gaia$ BP/RP externally calibrated spectra (Montegriffo et al., 2023;
Gaia Collaboration et al., 2023, 2016): the first one with the Stellar
Abundances for Galactic Archaeology (SAGA) database (Suda et al., 2008, 2011;
Yamada et al., 2013; Suda et al., 2017), and the second with the Galactic
Archaeology with HERMES data release 3 (GALAH DR3) (Buder et al., 2021). Both
datasets together consist of 21 812 stars. We applied quality cuts on the
aforementioned dataset by finding correlations between falsely identified
metal-poor stars and quality parameters and ended up with 20 850 stars. Since
this procedure could only be done after the application of our method to the
dataset, we will be elaborating on it both in this section, as well as in the
results section. The quality cuts we applied were twofold: one with respect to
the quality of the stellar parameters of the dataset and another stemming from
the quality of the $Gaia$ BP/RP spectra themselves, as well as of the effect
of reddening. Concerning the first, stars for which there was no reliable
metallicity estimate from GALAH were dropped (flag_fe_h=0). The mean
uncertainty in the iron abundance for the remaining GALAH stars is 0.12 dex.
We did not use any quality flag for the SAGA stars, but we resorted to the
provided iron abundance uncertainties ($\overline{\sigma}_{SAGA}\sim 0.17$
dex). The GALAH $\mathrm{[Fe/H]}$ were computed using
$\mathrm{A(Fe)_{\odot}=7.38}$ (for details see Buder et al. 2021), while the
SAGA database utilizes the Asplund et al. (2009) solar chemical composition,
that is, $\mathrm{A(Fe)_{\odot}=7.50}$. We consider this difference in the
normalization of the metallicities of the two components comprising our
dataset to be negligible, since we are not aiming at delivering high precision
iron abundances, but rather intent to identify metal-poor stars. Further, as
appears in the Kiel Diagram (Figure 2), the final dataset we used spans from
dwarf to giant stars, with most of the GALAH stars having disk-like kinematics
(Buder et al., 2021) and a mean distance of $\overline{D}\sim 1.9$ kpc
(distances taken from Bailer-Jones et al. 2018), and the SAGA stars having
$\overline{D}\sim 1.8$ kpc (distances taken from Fouesneau et al. 2023) and
belonging to the Galactic halo. Regarding the spectra quality, we set a limit
to the blending fraction $\beta$ of the BP/RP spectra and the color excess
($E(B-V)$). The former was defined by Riello et al. (2021) as “…the sum of the
number of blended transits in BP and RP divided by the sum of the number of
observations in BP and RP”. We slightly modified it, specifically as

$\displaystyle\beta=\mathrm{(bp\\_n\\_blended\\_transits+rp\\_n\\_blended\\_transits}+$
$\displaystyle\mathrm{bp\\_n\\_contaminated\\_transits}+\mathrm{rp\\_n\\_contaminated\\_transits)}/$
$\displaystyle\mathrm{(bp\\_n\\_transits+rp\\_n\\_transits)}$

We set $\beta\leq 0.5$.

Finally, complementary to our work in Paper I, we include objects in our
dataset whose reddening is well above $E(B-V)=0.06$ (see Figure 2), which
mandates that we tackle the issue of extinction.

Figure 1: Kiel Diagram of the dataset.

Figure 2: Histogram of the reddening distribution of our dataset.

###  2.2 Reddening

As a first approach we aimed at finding a reddening independent index, similar
to Bonifacio et al. (2000a). Since the region of the H$\beta$ line is part of
the $fr_{\mathrm{CaHK/H\beta}}$ ratio (see Paper1 for details), we decided to
test if the Strömgren $\beta$ index withstands extinction and replace the
H$\beta$ region in $fr_{\mathrm{CaHK/H\beta}}$ with the former. The results
were not those we anticipated: the $\beta$ index changed with extinction, even
though it showed a sensitivity to effective temperature. As we were not able
to define a reddening-independent metallicity calibration, we instead sought
to implement reddening corrections for the metallicity calibration by means of
dereddening the spectra. Therefore, we used the dust maps of Schlegel et al.
(1998) (SFD) re-calibrated by Schlafly & Finkbeiner (2011), the extinction
model of Fitzpatrick (1999) and $R_{v}=3.1$ to deredden the externally
calibrated BP/RP spectra. We repeated the above procedure using the extinction
model of Cardelli et al. (1989) and found that the resulting flux-ratios have
minimal differences with those calculated with the Fitzpatrick (1999) model.
We chose the SFD maps because they cover the entire sky. Considering the fact
that the SFD maps account for the foreground dust, our stars need to be
distant enough or at a galactic latitude great enough for the distance
dependence to be neglected. The SAGA stars are halo stars, and thus distant
enough (D $\geq 1$ kpc ; Schlafly & Finkbeiner 2011). In total, 81% of the
stars in our dataset are either at a distance D $\geq 1$ kpc or at a latitude
$\mid b\mid>30\degree$. For the remaining 19%, we calculated the reddening
correction from Bonifacio et al. (2000b). For most of the stars we found no or
very small (¡0.001 mag) correction. Only for 4% of the total sample we found
$E(B-V)$ corrections $\geq 0.02$ mag, so applying such a correction would have
a negligible effect on the distribution in the dereddened flux-ratio plane
(Figure 3).

###  2.3 Application of the method

In Paper I we provided coefficients for different pairs of $\mathrm{T_{eff}}$
and $\log g$ for the estimation of $\mathrm{[Fe/H]}$. We calibrated the
coefficients for application to the real data, but the results were not
corresponding to the theoretical expectations. Further, the problem of
acquiring well-defined effective temperatures and surface gravities for
millions of stars -so that the metal-poor ones among them could be identified-
became apparent. We decided to use only quantities that can be directly
derived from the spectra, i.e. the flux-ratios. The plane of the
$fr_{\mathrm{CaHK/H\beta}}$ and $fr_{\mathrm{G/CaNIR}}$ flux-ratios (see
Figure 3), enables us to find the loci of metal-poor ($\mathrm{[Fe/H]}<-1.0$)
and further metal-deficient stars. The grey lines in Figure 3 represent
different metallicity regimes, with the stars below the dashed-dotted and
dotted ones being metal-poor ($\mathrm{[Fe/H]}<-1$) and very metal-poor
($\mathrm{[Fe/H]}<-2$) respectively.

##  3 Results

The results in the right panel of Figure 3, depict a clear correlation between
metallicity, $fr_{\mathrm{CaHK/H\beta}}$ and $fr_{\mathrm{G/CaNIR}}$ flux-
ratios. The left panel shows the flux-ratios before dereddening and the right
panel shows the dereddened values. We overplot a dashed-dotted (Cutoff1) and a
dotted line (Cutoff2), to designate flux-ratio areas where objects with
$\mathrm{[Fe/H]}_{ref}\leq-1$ and $\mathrm{[Fe/H]}_{ref}\leq-2$ respectively,
are primarily found ($\mathrm{[Fe/H]}_{ref}$ is the reference
$\mathrm{[Fe/H]}$). By selecting metal-poor stars in that way, we found that
there was a correlation between a high blending fraction $\beta$ and
contaminants, i.e. stars with $\mathrm{[Fe/H]}_{ref}>-1$. We chose the $\beta$
such that there is a balance between acceptable contamination and
completeness, since a greater $\beta$ means a greater number of stars. We
define the completeness as the ratio of the number of selected stars below a
certain metallicity threshold to the total number of stars in the dataset that
have $\mathrm{[Fe/H]}_{ref}\leq\mathrm{threshold}$, the success rate as the
percent of the selected stars that have $\mathrm{[Fe/H]}_{ref}$ below a
certain specified value, and the contamination as the percent of selected
stars that have a metallicity above the specified threshold.
The results in Figure 3 were generated after the application of the quality
cuts described above. By choosing all the stars below Cutoff1 in Figure 3, we
are able to recover from the GALAH-SAGA sample more than 98% of the stars with
$\mathrm{[Fe/H]}\leq-2$, all the ultra metal-poor stars
($\mathrm{[Fe/H]}\leq-4$) and 70% of stars $\mathrm{[Fe/H]}<-1$. We record a
success rate of $\sim 80\%$, 44% and 20% for stars with
$\mathrm{[Fe/H]}\leq-1,-1.5$ and -2 respectively. When we select stars below
Cutoff2 we make a trade-off between the success rate and the completeness: we
still recover more than 90% and 94% of very and extremely metal-poor stars
respectively, but lose about 40% of those with $-2<\mathrm{[Fe/H]}\leq-1$
compared to the other cut off. The success rate increases significantly to
$\sim 99\%$, 95% and 60% for stars with $\mathrm{[Fe/H]}\leq-1,-1.5$ and -2
respectively (summarized in Figure 4). For comparison, we selected all stars
that fall below the same -as before- dotted and dashed-dotted line without
dereddening (left panel of Figure 3) and calculated the statistics as above.
Even though the completeness for different metallicity categories are fairly
similar and in some cases even slightly better, the success rate is much lower
and in consequence the contamination is much higher.

Figure 3: Flux-ratios of raw (left) and dereddened (right) fluxes from $Gaia$
BP/RP spectra are shown in the left and right panel respectively. The color-
coding reflects the metallicity of the stars of the dataset we used. Below the
dashed-dotted and dotted lines are the flux-ratio areas where stars with
$\mathrm{[Fe/H]}\leq-1$ and $\mathrm{[Fe/H]}\leq-2$ respectively, are
primarily found.

Figure 4: Completeness, success rate and contamination of the stars that were
selected from below the dashed-dotted (left panel) and dotted line (right
panel). The stars were selected from a dereddened flux-ratio plane.

Further, we find that by selecting the metal-poor candidates through the flux-
ratio plane, we can extrapolate the theoretical method described in Paper I,
to a broader parameter space. Specifically, in Paper I the recipe was
developed for FGK stars in the effective temperature range of 4800-6300 K, and
in this study we retrieve metal-poor stars that have
$4636\,K\leq\mathrm{T_{eff}}\leq 7150\,K$.
Finally, we estimated the iron abundances of our dataset as follows. First, we
randomly sampled our GALAH-SAGA dataset, and split it into two equal parts. We
divided the flux-ratios of the first sampled sub-dataset into
$fr\mathrm{{}_{G/CaNIR}}$ bins. Then, we split each of those bins into
metallicity bins, for which we calculated the mean
$fr_{\mathrm{CaHK/H\beta}}$. Next we found best fits to the sets of
$fr_{\mathrm{CaHK/H\beta}}$ \- $\mathrm{[Fe/H]}$ pairs (Figure 5), which we
subsequently used to estimate the iron abundance of the second sub-dataset. We
used the following function in order to perform the fittings:

$fr\mathrm{{}_{G/CaNIR}}=-a\cdot fr\mathrm{{}_{CaHK/H\beta}}^{b}+c$ (1)

where $a,b$ and $c$ are the coefficients of the best fit, which are shown in
Table 1. The respective results of the metallicity estimation are presented in
Figure 6. We were able to infer $\mathrm{[Fe/H]}$ with an uncertainty of
$\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.36$ dex. This precision is sufficient
for reliably identifying metal-poor stars.

Table 1: Coefficients of the best fit.

$a$ | $b$ | $c$ | $fr\mathrm{{}_{G/CaNIR}}$
---|---|---|---
17.497139 | 1.119316 | 2.506009 | [1.3-1.8)
22.219935 | 1.512732 | 2.800237 | [1.8-2.3)
29.101554 | 2.624439 | 1.18252 | [2.3-2.8)
32.268827 | 3.351201 | 0.815609 | [2.8-3.3]
444The $fr\mathrm{{}_{G/CaNIR}}$ values, are the ranges of applicability of
each set of coefficients.

Figure 5: Best fits to the $fr_{\mathrm{CaHK/H\beta}}$ \- $\mathrm{[Fe/H]}$
pairs. The different line colors convey the $fr\mathrm{{}_{G/CaNIR}}$ range of
applicability. Figure 6: Metallicity estimation of a subset of the GALAH-SAGA
dataset. The points that have a black circle around them, are located below
the black-dotted line in the flux-ratio plane (Figure 3). The color-coding
reflects the effective temperature of the stars. We plot the inferred and
reference $\mathrm{[Fe/H]}$ on the x- and y-axis respectively.

##  4 OBA stars

OBA stars are young hot stars that can present emission lines in their
spectra. When OB stars are highly reddened, they can appear as K-type stars,
hence good reddening values are essential in order to tell them apart from
metal-poor FGK stars. Also, young or accreting stars can show emission lines
at various spectral regions, including the Ca H&K absorption lines.
Consequently, the emission in the Ca II H&K lines results in a net weak
absorption line, masking those stars as being metal-poor. Therefore we wish to
test to which degree those stars are expected to contaminate a selected metal-
poor-candidate sample.

We select a random subset of 200 stars from the OBA stars golden sample
(European Space Agency & DPAC Consortium(2022), ESA). From those, 193 stars
have an externally calibrated BP/RP spectrum, and 173 have a blending fraction
$\beta\leq 0.5$. We deredden the externally calibrated spectra as described in
section 2.2 and subsequently compute the flux-ratios. In Figure 7 we plot the
flux-ratios of the OBA golden sample subset. In order to show the effect of
extinction, which depends on the color-excess rather than on the flux-ratios,
we use logarithmic axes. The effect of extinction is demonstrated with an
arrow (orange arrow), where its nock and point represent the flux-ratios
before and after dereddening, respectively, for $E(B-V)\approx 0.3$ mag. As
can be seen, none of the 173 stars appear in the region of the flux-ratio
plane where the metal-poor stars frequent (Figure 3). However, due to the fact
that the location of the stars on the flux-ratio plane depends on the
extinction, we caution the reader that highly reddened OBA stars with
underestimated color-excess values could appear in the region of metal-poor
stars (yellow area in Figure 7) and hence, contaminate the sample of metal-
poor stars selected via this method.

Figure 7: Flux-ratios of OBA stars. The solid and dotted lines represent the
Cutoff1 and Cutoff2 respectively, while the yellow shaded area designates the
region that is populated by very-metal poor (VMP) stars (see Figure 3). The
color-coding indicates the Galactic Latitude $b$ of each star. As can be seen,
most of the stars are located on the Galactic plane ($\mid b\mid\leq
10\degree$),. The orange arrow illustrates the effect of extinction for a
color excess $E(B-V)\approx 0.3$ mag. The nock and the point of the arrow
represent the flux-ratios before and after dereddening, respectively.

##  5 Observational metal-poor star candidate verification

In order to verify our metal-poor candidate selection method as well as the
metallicity estimation presented herein, we selected a sample of stars from
$Gaia$ DR3, which had not been observed before. We opted to select fairly
bright giant stars, in order to achieve a good enough signal-to-noise ratio
(SNR) for the purpose of deriving precise $\mathrm{[Fe/H]}$. Further, the
location of the telescope to be used was known beforehand, hence we used the
following selection criteria: G=12-13 mag, Ra=16-02h, Dec=
00$\degree$-+20$\degree$, $\mid b\mid>20\degree$ and $\beta\leq 0.5$, which
rendered 90 798 stars. Following, we computed the flux-ratios. From the 90 798
stars, we chose those with flux-ratios $1\leq fr\mathrm{{}_{G/CaNIR}}\leq 5$,
which left us with 70 509 stars. Then, we selected all the stars below a more
stringent cut than Cutoff2, which is a line that is shifted parallel to
Cutoff2 by 0.1+$fr\mathrm{{}_{CaHK/H\beta}}$. That cutoff left us with 77
stars, of which 10 stars had already been observed in high resolution and
their metallicities are -or will be- in the literature. It is worth noting,
that all the 10 stars that appear in literature, are metal-poor. The reason we
used a more stringent cut was, that there is a clear correlation between the
inferred metallicity and the position of the star on the flux-ratio plane. We
opted to observe candidates with the lowest predicted metallicities, so if we
would have used Cutoff2, most of the stars above the more stringent cut off
would have not made it into the final target list due to the higher estimated
$\mathrm{[Fe/H]}_{inf}$. We show the distribution of the inferred
$\mathrm{[Fe/H]}_{inf}$ for metal-poor candidates that were located between
Cuttoff2 and our chosen cut off in Figure 10. Finally, we estimated the
$\mathrm{[Fe/H]}$ for the remaining 67 stars, and our final target list was
comprised of 32 stars with $\mathrm{[Fe/H]}_{inf}\leq-2.35$, of which we
managed to observed 26. Of the 35 stars that were not included in the target
list, 8 of them were outside the metallicity inference range
($fr\mathrm{{}_{G/CaNIR}}>3.3$). The distribution of the inferred
metallicities for the remaining 27 metal-poor candidates that were not
included in the final target list is show in Figure 11.

###  5.1 Observations and metallicity determinations

The targets were observed at the McDonald Observatory with the Harlan J. Smith
2.7m telescope and the TS23 echelle spectrograph (Tull et al., 1995). The
spectra were obtained using a 1.2” slit and 1x1 binning, yielding a resolving
power of $R\sim 60,000$ and covering a wavelength range of 3600-10000 Å. The
26 stars were observed over four nights in August 2023. The data was reduced
using standard IRAF packages (Tody, 1986, 1993), including correction for
bias, flatfield, and scattered light. Table 2 lists the Gaia DR3 id, right
ascension, declination, Heliocentric Julian Date (HJD), exposure times, the
signal-to-noise ratio per pixel (SNR) at 5000$\AA$ and heliocentric radial
velocities. The heliocentric radial velocities were determined via cross-
correlation with a spectrum of the standard star HD 182488 ($V_{hel}=-21.2$
kms-1; Soubiran et al. (2018)) obtained on the same run.

We determined stellar parameters ($\mathrm{T_{eff}}$, $\log g$,
$\mathrm{[Fe/H]}$, and $v_{t}$) for the observed stars from a combination of
photometry and equivalent width (EW) measurements of Fe i and Fe ii lines, and
using the software smhr 555https://github.com/andycasey/smhr (Casey, 2014) to
run the radiative transfer code MOOG 666https://github.com/alexji/moog17scat
(Sneden, 1973; Sobeck et al., 2011) assuming local thermodynamical
equilibrium. We used one dimensional plane-parallel, $\alpha$-enhanced
($\mathrm{[\alpha/Fe]=+0.4}$) stellar model atmospheres computed from the
ATLAS9 grid (Castelli & Kurucz, 2003), line lists from linemake
777https://github.com/vmplacco/linemake (Placco et al., 2021), and Solar
abundances were taken from Asplund et al. (2009). $\mathrm{T_{eff}}$ for the
stars was determined from dereddened $Gaia$ $G$, $BP$, $RP$ (Anders et al.,
2022; Gaia Collaboration et al., 2018) and 2MASS $K$ magnitudes (Cutri et al.,
2003) using the color-$\mathrm{T_{eff}}$ relations from Mucciarelli et al.
(2021). For the $K$ magnitudes, we used the extinction coefficient from McCall
(2004). The $\log g$ were then determined by requiring ionisation equilibrium
between the Fe i and Fe ii lines and $v_{t}$ by requiring no correlation of Fe
i line abundances with reduced EW. Final $\mathrm{[Fe/H]_{spec}}$ of stars is
taken as the mean abundances of the Fe i lines and the uncertainties are the
standard deviation of these. Final stellar parameters are listed in Table 2.

###  5.2 Results

The stellar parameters of the observed stars are shown in Table 2. As the
parameters show, all observed stars are metal-poor FGK stars. The uncertainty
in our metallicity inference is $\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.31$,
which agrees with the uncertainty in deriving metallicities for the GALAH-SAGA
sample ($\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.36$), as described above. Figure
8 shows $\mathrm{[Fe/H]}_{inf}$ versus the spectroscopic determined
$\mathrm{[Fe/H]_{spec}}$. Further, 100% of the observed stars are very metal-
poor, 58% have $\mathrm{[Fe/H]}<-2.5$ and 8% are EMP. Lastly, we did not have
any contamination from OBA stars, which agrees with our finding in Section 4.

Figure 8: $\mathrm{[Fe/H]}_{inf}$ versus $\mathrm{[Fe/H]}_{spec}$. The solid
grey line is the 1 to 1 line, and the dashed grey line designates the
1$\sigma$ uncertainty ($\sigma_{\mathrm{[Fe/H]}_{spec}}=0.31$ dex) in
$\mathrm{[Fe/H]}_{spec}$. Table 2: Stellar Parameters and observation log of
observed metal-poor candidates.

Gaia DR3 ID | RA (J2000) | Dec (J2000) | HJD | exp time | SNR | $V_{hel}\pm\sigma$ | $\mathrm{[Fe/H]}_{inf}$ | $G$ | $\mathrm{T_{eff}}$ | $\log g$ | $\mathrm{[Fe/H]}_{spec}$ | $\sigma_{\mathrm{[Fe/H]}_{spec}}$ | $v_{t}$ | $E(B-V)$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (hrs) | ($\degree$) |  | (s) | 5000Å | (kms-1) | (dex) | (mag) | (K) | (dex) | (dex) | (dex) | (kms-1) | (mag)
4560234719702983552 | 17 00 58.86 | +18 12 48.76 | 2460177.61 | 3x1200 | 38 | $-200.2\pm 0.7$ | -3.49 | 12.95 | 5512 | 1.81 | -2.67 | 0.12 | 2.26 | 0.067
2770306858573498880 | 23 54 36.90 | +13 43 33.61 | 2460175.83 | 3x900 | 43 | $-91.8\pm 0.9$ | -3.19 | 12.75 | 5280 | 2.42 | -2.69 | 0.14 | 1.63 | 0.043
2740778202499153280 | 00 09 13.91 | +03 34 27.64 | 2460175.88 | 3x1200 | 29 | $-63.3\pm 0.7$ | -3.17 | 12.52 | 5172 | 2.18 | -2.89 | 0.12 | 1.58 | 0.024
2783063972298129280 | 00 42 31.57 | +18 34 52.58 | 2460175.93 | 3x1200 | 23 | $-349.7\pm 0.7$ | -3.13 | 12.53 | 5463 | 1.92 | -2.49 | 0.16 | 1.98 | 0.058
38721161695303808 | 03 55 46.04 | +13 28 40.99 | 2460178.96 | 3x1200 | 11 | $59.1\pm 1.1$ | -2.99 | 12.89 | 5666 | 3.09 | -2.18 | 0.21 | 1.95 | 0.298
1788649988097920768 | 21 20 25.52 | +19 16 40.19 | 2460175.75 | 3x1200 | 35 | $2.1\pm 1.4$ | -3.24 | 12.84 | 5868 | 1.95 | -3.01 | 0.13 | 2.65 | 0.078
2739719922558093440 | 23 50 58.88 | +02 36 12.99 | 2460176.84 | 3x600 | 38 | $15.4\pm 1.3$ | -2.89 | 12.10 | 6488 | 3.40 | -2.85 | 0.15 | 1.77 | 0.033
3268830653286376704 | 03 15 35.79 | +02 25 49.29 | 2460176.96 | 3x1200 | 27 | $203.3\pm 0.7$ | -2.72 | 12.81 | 5114 | 2.18 | -2.59 | 0.18 | 1.49 | 0.095
4446252678577892224 | 16 34 16.18 | +08 49 40.19 | 2460178.63 | 3x900 | 22 | $-12.1\pm 0.8$ | -2.71 | 12.27 | 4995 | 1.88 | -2.48 | 0.15 | 1.81 | 0.065
2719036833232602752 | 22 57 03.19 | +12 58 25.60 | 2460175.80 | 3x600 | 41 | $-242.8\pm 0.5$ | -2.68 | 12.15 | 5316 | 1.90 | -2.34 | 0.12 | 2.06 | 0.047
4229999872631438848 | 20 32 11.41 | +01 02 05.16 | 2460177.71 | 3x1200 | 37 | $-240.6\pm 0.5$ | -2.67 | 12.82 | 5221 | 2.71 | -2.49 | 0.17 | 1.36 | 0.097
1757147197551005952 | 21 09 25.50 | +11 48 44.80 | 2460175.70 | 3x1200 | 26 | $71.0\pm 1.3$ | -2.86 | 12.60 | 5440 | 1.23 | -2.80 | 0.11 | 2.29 | 0.108
1730672812979631104 | 20 56 02.56 | +02 07 13.56 | 2460178.69 | 3x1200 | 14 | $-160.8\pm 1.0$ | -2.58 | 12.84 | 5194 | 1.09 | -2.35 | 0.21 | 2.38 | 0.107
2814304091236720000 | 23 27 36.00 | +15 23 54.70 | 2460177.80 | 3x1200 | 31 | $-81.5\pm 0.9$ | -2.56 | 12.96 | 5096 | 1.95 | -2.76 | 0.12 | 2.05 | 0.054
4561199025759521920 | 17 02 37.48 | +19 17 21.35 | 2460177.66 | 3x1200 | 31 | $-174.7\pm 0.5$ | -2.54 | 12.79 | 5267 | 2.57 | -2.38 | 0.18 | 1.73 | 0.088
4503007613380083328 | 17 53 57.89 | +17 45 19.99 | 2460176.64 | 3x1200 | 50 | $-100.9\pm 1.0$ | -2.69 | 12.42 | 6030 | 4.22 | -2.78 | 0.15 | 1.72 | 0.081
4449403019908847488 | 16 48 40.46 | +13 32 43.83 | 2460176.61 | 3x600 | 36 | $195.9\pm 0.7$ | -2.45 | 12.15 | 5214 | 2.33 | -2.65 | 0.17 | 1.48 | 0.060
2574400790177777408 | 01 58 30.71 | +11 18 42.38 | 2460177.93 | 3x1200 | 38 | $-101.6\pm 1.0$ | -2.42 | 12.58 | 6547 | 4.04 | -2.23 | 0.13 | 1.62 | 0.116
2554217295745049856 | 00 39 13.34 | +04 23 33.16 | 2460176.87 | 3x1200 | 38 | $-145.0\pm 0.9$ | -2.39 | 12.81 | 6235 | 3.51 | -2.32 | 0.10 | 1.55 | 0.027
2580053787477560576 | 01 19 10.86 | +10 07 08.75 | 2460177.85 | 3x1200 | 40 | $-29.0\pm 0.6$ | -2.45 | 12.55 | 5139 | 2.33 | -2.47 | 0.14 | 1.68 | 0.070
2732958716319826048 | 22 33 41.08 | +14 49 05.58 | 2460178.73 | 3x900 | 20 | $26.8\pm 0.9$ | -2.35 | 12.23 | 5636 | 2.59 | -2.54 | 0.17 | 1.24 | 0.069
2756350516963035904 | 23 40 19.64 | +05 34 00.66 | 2460176.80 | 3x1200 | 33 | $111.7\pm 1.7$ | -2.35 | 12.91 | 6235 | 2.40 | -2.73 | 0.12 | 1.50 | 0.081
2698131578134995456 | 21 34 27.89 | +04 04 38.23 | 2460177.76 | 3x900 | 39 | $-299.1\pm 0.6$ | -2.35 | 12.27 | 5294 | 2.90 | -2.51 | 0.15 | 1.39 | 0.054
4432234794379005952 | 16 34 54.04 | +02 06 14.94 | 2460178.60 | 3x900 | 17 | $85.5\pm 0.8$ | -2.35 | 12.23 | 5257 | 1.60 | -2.30 | 0.16 | 1.99 | 0.062
2706127364131151744 | 22 41 26.08 | +05 07 30.91 | 2460178.77 | 3x1000 | 21 | $-139.7\pm 2.1$ | -2.83 | 12.65 | 5648 | 2.56 | -3.29 | 0.14 | 2.09 | 0.077
1733398605383859840 | 21 09 34.21 | +05 14 05.85 | 2460176.69 | 3x1200 | 30 | $-52.3\pm 0.7$ | -2.74 | 12.70 | 5200 | 1.26 | -2.62 | 0.11 | 1.97 | 0.112

##  6 Catalogue of stellar $\mathrm{[Fe/H]}$

For the purpose of providing the community with a catalogue of metallicities,
we used the following criteria from ”The Milky Way Halo High-Resolution
Survey´´ (Christlieb et al., 2019) of the 4-metre Multi-Object Spectroscopic
Telescope ($4MOST$) (De Jong et al., 2019), combined with those developed for
this work, to select stars from $Gaia$ DR3:

  * •

$\mid b\mid>10\degree$

  * •

$0.15\,\mathrm{mag}\leq\mathrm{(BP-RP)}_{0}<1.1\,$mag

  * •

blending index $\beta\leq 0.5$

  * •

$1.3\leq fr\mathrm{{}_{G/CaNIR}}\leq 3.3$

  * •

$E(B-V)\leq 1.5\,$mag

The above criteria turned over 10 861 062 stars, for which we estimated the
metallicity. 225 498 stars in this catalogue have
$\mathrm{[Fe/H]}_{inf}<-2.0$. Further, in our catalogue 2236 stars have
$\mathrm{[Fe/H]}_{inf}<-5.0$, which suggests that these stars have probably
emission lines rather than being metal-poor. We cross-matched the stars of our
catalogue that have $\mathrm{[Fe/H]}_{inf}<-2.0$ with the Gaia OBA golden
sample (European Space Agency & DPAC Consortium(2022), ESA), and found that
104 of those stars are indeed OBA stars. Out of those OBA contaminants, 8 have
an estimated metallicity $\mathrm{[Fe/H]}_{inf}<-5.0$ in the catalogue.
Finally, a sample of the catalogue is shown in Table 3.

Table 3: Sample of the metallicities catalogue.

$source\\_id$ | $RA(J2000)$ | $DEC(J2000)$ | $E(B-V)$ | $fr\mathrm{{}_{CaHK/H\beta}}$ | $fr\mathrm{{}_{G/CaNIR}}$ | $\mathrm{[Fe/H]}_{inf}$ | $G$ | $G_{BP}$ | $G_{RP}$
---|---|---|---|---|---|---|---|---|---
| (°) | (°) | (mag) |  |  | (dex) | (mag) | (mag) | (mag)
1736084918450522624 | 311.672374 | 6.454326 | 0.086352 | 0.395785 | 3.040589 | -0.65 | 14.839189 | 15.116240 | 14.387665
1736086121041383936 | 311.640473 | 6.501470 | 0.080705 | 0.386366 | 2.951276 | -0.53 | 12.410907 | 12.699553 | 11.959683
1736086464640617472 | 311.605184 | 6.517305 | 0.079810 | 0.384081 | 3.279787 | -0.51 | 12.523436 | 12.753575 | 12.055906
1736086769579627008 | 311.686028 | 6.547942 | 0.081594 | 0.440737 | 2.951817 | -1.27 | 14.591786 | 14.878093 | 14.132823
1736089213417835264 | 311.740409 | 6.639877 | 0.088562 | 0.383000 | 2.963972 | -0.50 | 14.826837 | 15.120335 | 14.363322
1736089934974194688 | 311.614227 | 6.572804 | 0.078512 | 0.320748 | 2.815581 | 0.09 | 12.647016 | 12.943399 | 12.197193
1736090381648971776 | 311.524228 | 6.550632 | 0.083777 | 0.382586 | 2.909278 | -0.49 | 13.581572 | 13.875311 | 13.124882
1736093847685000960 | 311.868064 | 6.611197 | 0.092579 | 0.410637 | 3.239939 | -0.84 | 14.073834 | 14.347256 | 13.636151
1736099693138064384 | 311.706790 | 6.756967 | 0.085753 | 0.351283 | 2.938921 | -0.17 | 13.712016 | 14.000586 | 13.259321
1736099693138065408 | 311.698148 | 6.754874 | 0.084601 | 0.376363 | 2.852484 | -0.42 | 15.257664 | 15.554148 | 14.791958

888The color excess values, $E(B-V)$, are taken from Schlegel et al. (1998)
(re-calibrated by Schlafly & Finkbeiner (2011)). The full catalogue is
available at the CDS.

##  7 Comparison to other catalogues

As already described in the introduction, many studies have taken advantage of
the wealth of information encapsulated in the Gaia BP/RP spectra, and have
provided to the community catalogues of stellar atmospheric parameters.
Specifically, the catalogues of Andrae et al. (2023b) and Martin et al. (2023)
have been shown to work very well in the metal-poor regime. We used the GALAH-
SAGA verification sub-dataset (Figure 6) to compare the metallicities we
estimated versus those of Andrae et al. (2023b) and Martin et al. (2023). The
$\mathrm{[Fe/H]}_{inf}$ we estimated for this sub-dataset are independent of
the fitting procedure. Figure 9 shows the performance of each catalogue. At
first glance it is visible that the catalogue of Martin et al. (2023) performs
better in the metal-poor regime than ours, and that of Andrae et al. (2023b).
However, the difference in accuracy of the inferred metallicities in all three
catalogues is comparable, specifically for $\mathrm{[Fe/H]}_{ref}<-2$ the iron
abundances of Martin et al. (2023) and Andrae et al. (2023b) have $\sigma\sim
0.39$ and are 0.1 dex better than ours. For $\mathrm{[Fe/H]}_{ref}<-3$ the
standard deviation of the estimated metallicities in all three catalogues is
the same, that is $\sim 0.36$ dex. In the metal-rich regime, our metallicities
have uncertainties that are $\sim 0.2$ dex higher than those of the other two
catalogues, whose performance is similar, $\sigma\sim 0.24$ dex.

Figure 9: Comparison of our derived metallicities with those from the Andrae
et al. (2023b) (XGBOOST), and Martin et al. (2023) ($\mathrm{CaHK}_{synth}$)
catalogues. Top: from left to right the metallicities of our, XGBOOST, and
$\mathrm{CaHK}_{synth}$ catalogues are plotted, respectively, for the GALAH-
SAGA validation dataset ($\mathrm{[Fe/H]}_{ref}$). The color-coding reflects
the effective temperature of the stars. Middle and bottom: as in the top
panels, but here the color-coding depicts the color excess and surface
gravity, respectively. The solid black line shows the 1-1 line, while the
dashed lines show a $\sigma=$0.36 dex uncertainty.

##  8 Summary

We applied the metal-poor star candidate selection recipe described in Paper I
(Xylakis-Dornbusch et al., 2022) on $Gaia$ DR3 BP/RP spectra. In order to do
so, we updated the selection method. Specifically, instead of using effective
temperature and surface gravity information, we only used the flux-ratios -
$fr\mathrm{{}_{G/CaNIR}}$ and $fr\mathrm{{}_{CaHK/H\beta}}$ \- determined in
Paper I to estimate the metallicity of stars. We addressed the extinction by
means of dereddening the spectra before computing the flux-ratios, and found
that the method can be applied to stars with color excesses $E(B-V)\leq 1.5$.
We then used BP/RP spectra through a cross-match between $Gaia$ DR3 and GALAH
DR3, as well as with the SAGA database, to validate the selection method. We
were able to estimate the $\mathrm{[Fe/H]}$, solely with the use of the flux-
ratios, with an uncertainty of $\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.36$ dex.
Next, we assessed to which degree OBA stars could contaminate a metal-poor
candidate sample selected via the method described herein. We found that it is
not very likely, as long as one has high level color excesses at their
disposal to perform the dereddening of the spectra. Following, we selected
stars from $Gaia$ DR3 via our updated selection procedure for spectroscopic
validation. We observed 26 stars of which 100% had $\mathrm{[Fe/H]}<-2.0$, 58%
had $\mathrm{[Fe/H]}<-2.5$ and 8% had $\mathrm{[Fe/H]}<-3.0$. We inferred
metallicites for this sample of stars prior to observations with an
uncertainty $\sigma_{\mathrm{[Fe/H]}_{inf}}\sim 0.31$. Finally, we assembled a
catalogue of metallicities for 10 861 062, of which 225 498 have
$\mathrm{[Fe/H]}_{inf}<-2.0$.

###### Acknowledgements.

We thank the anonymous referee for their comments, which helped improve this
manuscript. This work was funded by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) – Project-ID 138713538 – SFB 881 (“The Milky Way
System”, subproject A04). This research was supported by the Australian
Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO 3D), through project number CE170100013. This work was supported by
computational resources provided by the Australian Government through the
National Computational Infrastructure (NCI) under the National Computational
Merit Allocation Scheme and the ANU Merit Allocation Scheme (project y89). TXD
acknowledges support from the Heidelberg Graduate School for Physics (HGSFP).
TTH acknowledges support from the Swedish Research Council (VR 2021-05556).
This work made use of the Third Data Release of the GALAH Survey (Buder et al.
2021). The GALAH Survey is based on data acquired through the Australian
Astronomical Observatory, under programs: A/2013B/13 (The GALAH pilot survey);
A/2014A/25, A/2015A/19, A2017A/18 (The GALAH survey phase 1); A2018A/18 (Open
clusters with HERMES); A2019A/1 (Hierarchical star formation in Ori OB1);
A2019A/15 (The GALAH survey phase 2); A/2015B/19, A/2016A/22, A/2016B/10,
A/2017B/16, A/2018B/15 (The HERMES-TESS program); and A/2015A/3, A/2015B/1,
A/2015B/19, A/2016A/22, A/2016B/12, A/2017A/14 (The HERMES K2-follow-up
program). We acknowledge the traditional owners of the land on which the AAT
stands, the Gamilaraay people, and pay our respects to elders past and
present. This paper includes data that has been provided by AAO Data Central
(datacentral.org.au). This work has made use of data from the European Space
Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This work has made use of
the Python package $Gaia$XPy, developed and maintained by members of the
$Gaia$ Data Processing and Analysis Consortium (DPAC) and in particular,
Coordination Unit 5 (CU5), and the Data Processing Centre located at the
Institute of Astronomy, Cambridge, UK (DPCI).

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##  Appendix A Additional figures.

We present additional figures which are described in Section 5. We show the
inferred metallicity distribution of candidate metal-poor stars that are
located on the flux-ratio plane between Cutoff2 and the more stringent cut we
used to select stars for observations. Lastly, we show the metallicity
distribution of metal-poor candidates below the stringent cut off that were
not included in the target list.

Figure 10: Distribution of $\mathrm{[Fe/H]}_{inf}$ for metal-poor candidates
located between Cutoff2 and the cut off we used to select candidates for
observations. Figure 11: Distribution of $\mathrm{[Fe/H]}_{inf}$ of the 27
metal-poor candidates that were not included in the final target list.