# Magnetocaloric performance of RE5Pd2In4 (RE = Tb-Tm) compounds

Altifani Rizky Hayyu<EMAIL_ADDRESS>Jagiellonian
University, Doctoral School of Exact and Natural Sciences, Faculty of Physics,
Astronomy and Applied Computer Science, prof. Stanisława Łojasiewicza 11,
PL-30-348 Kraków, Poland  Jagiellonian University, Faculty of Physics,
Astronomy and Applied Computer Science, M. Smoluchowski Institute of Physics,
prof. Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland  Stanisław Baran
<EMAIL_ADDRESS>Jagiellonian University, Faculty of Physics,
Astronomy and Applied Computer Science, M. Smoluchowski Institute of Physics,
prof. Stanisława Łojasiewicza 11, PL-30-348 Kraków, Poland  Andrzej Szytuła
Jagiellonian University, Faculty of Physics, Astronomy and Applied Computer
Science, M. Smoluchowski Institute of Physics, prof. Stanisława Łojasiewicza
11, PL-30-348 Kraków, Poland

###### Abstract

Magnetocaloric performance of the RE5Pd2In4 (RE = Tb-Tm) rare earth compounds
has been investigated using measurements of magnetization in the function of
temperature and applied magnetic field. The maximum magnetic entropy change
($-\Delta S_{M}^{max}$) at magnetic flux density change ($\Delta\mu_{0}H$) of
0-9 T has been determined to be 3.3 J$\cdot$kg${}^{-1}\cdot$K-1 at 62 K for
Tb5Pd2In4, 7.0 J$\cdot$kg${}^{-1}\cdot$K-1 at 22 K for Dy5Pd2In4, 12.6
J$\cdot$kg${}^{-1}\cdot$K-1 at 22 K for Ho5Pd2In4, 12.1
J$\cdot$kg${}^{-1}\cdot$K-1 at 17 K for Er5Pd2In4 and 11.9
J$\cdot$kg${}^{-1}\cdot$K-1 at 9.0 K for Tm5Pd2In4. The temperature averaged
entropy change (TEC) with 3 K span equals 3.2, 7.0, 12.6, 12.2 and 11.8
J$\cdot$kg${}^{-1}\cdot$K-1 for RE = Tb-Tm, respectively. The relative cooling
power (RCP) and refrigerant capacity (RC) are equal to respectively 258 and
215 J$\cdot$kg-1 in Tb5Pd2In4, 498 and 325 J$\cdot$kg-1 in Dy5Pd2In4, 489 and
403 J$\cdot$kg-1 in Ho5Pd2In4, 403 and 314 J$\cdot$kg-1 in Er5Pd2In4 and 234
and 184 J$\cdot$kg-1 in Tm5Pd2In4. The magnetocaloric properties of RE5Pd2In4
are comparable to those of other known magnetocaloric materials, which show
good magnetocaloric performance at low temperatures. Among RE5Pd2In4, the
highest values of parameters characterizing the magnetocaloric effect are
found for RE = Ho and Er. Furthermore, for fixed RE element, the RE5Pd2In4
compound displays the highest RCP and RC values when compared to those of its
isostructural RE5T2In4 (T = Ni, Pt) analogues.

keywords: magnetocaloric effect, rare earth intermetallics, magnetic entropy
change, relative cooling power, refrigerant capacity, temperature averaged
magnetic entropy change

##  I Introduction

Magnetic materials with sizeable magnetocaloric effect (MCE) have attracted
global interest due to their potential application as solid magnetic
refrigerants. The MCE is a phenomenon where certain materials undergo
temperature changes in response to an externally applied magnetic field. Among
these materials, the ones containing rare earth elements with unfilled 4f
subshell stand out as prime candidates for magnetic refrigeration due to their
exceptional paramagnetic susceptibility, saturation magnetization, magnetic
anisotropy, and magnetocaloric performance. The results of recent
investigations can be found in both the review papers as well as in those
reporting the properties of individual compounds [1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39].

The RE5Pd2In4 (RE = Tb-Tm) intermetallics crystallize in an orthorhombic
crystal structure of the Lu5Ni2In4-type ($Pbam$ space group, No. 55) [40].
RE5Pd2In4, together with for example RE2Ni2In [41, 42], RE5Ni2In4 [43] and
RE11Ni4In9 [44] (RE = rare earth element), belongs to a family of compounds
with general composition REm+nT2nXm (T = transition metal element), where the
$m$ and $n$ refer respectively to the numbers of the CsCl- (REIn) and
AlB2-related (RET2) slabs the structure is composed of [45]. The crystal
structure of RE5Pd2In4 (RE = Tb-Tm) is a special case, where within the ab-
plane, the structure consists of the CsCl- and AlB2-related slabs taken in the
$m:n=8:2$ ratio, including InRE8 (distorted cubes) and PdRE6 (distorted
trigonal prisms), forming a Z = 2, a 2:1 intergrowth variant [46]. The rare
earth atoms occupy three nonequivalent Wyckoff sites: the 2(a) site and two
4(g) sites with different atomic positional parameters. The 4(g) sites are
referred as 4(g)1 and 4(g)2, following the convention introduced in [47].
Along the c-axis, the layers composed of the rare earth atoms (z = 0) are
separated by layers containing the Pd and In atoms (z = $\frac{1}{2}$).

The magnetocaloric properties of RE5Pd2In4 (RE = Tb-Tm) have not yet been
reported, although their basic magnetic properties are already known [47]. A
ferromagnetic order sets in Tb5Pd2In4 below T${}_{C}=97$ K followed by
appearance of antiferromagnetic component of magnetic structure with
decreasing temperature. Dy5Pd2In4 orders ferromagnetically at T${}_{C}=88$ K
with further transformation into ferrimagnetic structure at lower
temperatures. Ho5Pd2In4 is an antiferromagnet with the Néel temperature
T${}_{N}=28.5$ K. With decreasing temperature, a second low-temperature
antiferromagnetic phase develops in Ho5Pd2In4 and coexists with the high-
temperature one. Er5Pd2In4 is a canted antiferromagnet (T${}_{N}=16.5$ K) with
additional ferromagnetic components emerging at lower temperatures. An
antiferromagnetic incommensurate magnetic structure that involves two
propagation vectors ($[0.073(3),0.451(1),\frac{1}{2}]$ and
$[0,0.335(2),\frac{1}{2}]$) forms in Tm5Pd2In4 below T${}_{N}=4.3$ K.

Both magnetic as well as neutron diffraction measurements reveal the existence
of complex magnetic structures in RE5Pd2In4 (RE = Tb-Tm) at low-temperatures
accompanied by a cascade of temperature-induced magnetic transitions. Neutron
diffraction data show that in the majority of the compounds (RE = Tb-Er) the
rare earth moments located at the 2(a) and 4(g)2 sites order at higher
temperatures than the moments at the 4(g)1 site. The effective magnetic
moments are close to the values expected for the free RE3+ ions, whereas the
moments in the ordered state, as derived from magnetization measurements taken
at T = 2.0 K and H = 90 kOe, are significantly smaller than those of free RE3+
ions. The primary magnetization curves collected at 2.0 K show metamagnetic
transitions, characteristic of the antiferromagnetic component of the magnetic
structure, for RE = Tb, Dy and Tm. Coercivity fields, derived from the
magnetization curves at 2.0 K, decrease with increasing number of the 4f
electrons from 12.4 kOe for RE = Tb down to 0.10 kOe for RE = Tm [47].

In this work we report for the first time the magnetocaloric performance of
RE5Pd2In4 (RE = Tb-Tm), which is necessary for full characterization of
magnetic properties of these compounds as well as it is important from the
point of view of possible applications in low-temperature magnetic
refrigeration. The results are compared with those reported previously for the
isostructural RE5Ni2In4 and RE5Pt2In4 as well as for other rare earth
intermetallics with good MCE performance.

##  II Materials and methods

The samples are the same as used in our previous study [47]. They have been
prepared by arc melting. Their quality has been examined by X-ray powder
diffraction at room temperature using a PANalytical X’Pert PRO diffractometer.
Detailed information on sample preparation as well as refined parameters of
the crystal structure are reported in [47].

The magnetocaloric effect in RE5Pd2In4 (RE = Tb-Tm) has been investigated with
the use of a Vibrating Sample Magnetometer (VSM) option of the Physical
Properties Measurement System (PPMS) by Quantum Design, equipped with a
superconducting magnet running up to 9 T (90 kOe). Before each measurement,
the sample was heated to reach a paramagnetic state and then it has been
demagnetized by an oscillating magnetic field with an amplitude going to zero.
Afterward, the sample was cooled down to 2.0 K in the absence of a magnetic
field (zero field cooling (ZFC) regime). Next, the final value of the magnetic
field has been set. The magnetization has been measured over a temperature
interval from 2.0 K up to the one well above transition to the paramagnetic
state. This procedure has been repeated for individual sample several times
for selected values of external magnetic flux density (magnetic field) ranging
from 1 T (10 kOe) up to 9 T (90 kOe).

##  III Results and Discussion

Fig. 1 shows the magnetization vs. temperature M(T) curves of RE5Pd2In4 (RE =
Tb-Tm) collected at several fixed magnetic flux density values up to 9 T (90
kOe). All curves have an inflection point characteristic of the transition
from ferro-/ferri- to paramagnetic state. In the case of RE = Tb and Dy,
additional anomalies are visible.

To calculate the corresponding magnetic entropy changes under isothermal
conditions, the following equation has been used:

$\Delta S_{M}(T,\Delta\mu_{0}H)=\int_{0}^{\mu_{0}H_{max}}\left(\frac{\partial
M(\mu_{0}H,T)}{\partial T}\right)_{(\mu_{0}H)}\,\mathrm{d}\mu_{0}H$ (1)

where $\Delta\mu_{0}H$ represents the difference between the final
($\mu_{0}H_{f}$) and initial ($\mu_{0}H_{i}$) flux densities, while
$\left(\frac{\partial M(\mu_{0}H,T)}{\partial T}\right)_{(\mu_{0}H)}$ denotes
the derivative of magnetization over temperature at a fixed magnetic flux
density $\mu_{0}H$ [48].

Fig. 2 presents temperature dependences of the magnetic entropy change for
RE5Pd2In4 (RE = Tb-Tm) as derived from the ZFC magnetization curves shown in
Fig. 1. Maximum entropy changes $-\Delta S_{M}^{max}$ reach 3.3, 7.0, 12.6,
12.1 and 11.9 J$\cdot$kg-1 under magnetic flux density change of 0-9 T for RE
= Tb, Dy, Ho, Er, and Tm, respectively. The values of $-\Delta S_{M}^{max}$
for other magnetic flux density changes can be found in Table 1. For
comparison, the table also contains $-\Delta S_{M}^{max}$ reported for the
isostructural RE5T2In4 (T = Ni, Pt) as well as for selected rare earth
intermetallics.

Two distinct maxima are found in the magnetic entropy change vs. temperature
plots for Tb5Pd2In4 and Dy5Pd2In4 (see Figs. 2a and 2b). The high-temperature
maximum ($\sim$102 K for RE = Tb and $\sim$94 K for RE = Dy), which dominates
for low magnetic flux density changes, corresponds to the transition from
para- to a ferromagnetic state. The low-temperature maximum ($\sim$62 K for RE
= Tb and $\sim$22 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 of RE5Pd2In4 (RE = Tb, Dy) are shown separately in Figs. 2a and 2b. It
is worth noting that a similar effect, involving two separate maxima in
magnetic entropy change vs. temperature dependence, has also been reported for
the isostructural Tb5Pt2In4 and Dy5Pt2In4 [49].

Figure 1: ZFC magnetization vs. temperature curves under various magnetic flux
density values up to 9 T for RE5Pd2In4: (a) RE = Tb, (b) RE = Dy, (c) RE = Ho
(d) RE = Er, and (e) RE = Tm.

Figure 2: Temperature dependence of the magnetic entropy change $-\Delta
S_{M}^{max}$, as derived from the $M(H,T)$ data shown in Fig. 1, under various
magnetic flux density changes $\Delta\mu_{0}H$ up to 0–9 T, for RE5Pd2In4: (a)
RE = Tb, (b) RE = Dy, (c) RE = Ho (d) RE = Er, and (e) RE = Tm.

Figure 3: The values of $-\Delta S_{M}^{max}$, TEC(3 K), TEC(5 K), and TEC(10
K) plotted against magnetic flux density change $\Delta\mu_{0}H$ for
RE5Pd2In4: (a) RE = Tb, (b) RE = Dy, (c) RE = Ho, (d) RE = Er, and (e) RE =
Tm, respectively.

The temperature-averaged magnetic entropy change (TEC) is another parameter
used for characterizing a magnetocaloric material. TEC is defined by the
following formula [50]:

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

where $T_{\mathrm{mid}}$ is the center temperature of the temperature span
$\Delta T_{\mathrm{lift}}$. The value of $T_{\mathrm{mid}}$ is determined by
finding the one that maximizes the integral appearing in Eq. 2.

The TEC values of RE5Pd2In4 (RE = Tb–Tm), calculated for the temperature spans
of 3, 5 and 10 K, are presented in Fig. 3. Within the 3 K span and magnetic
flux density change of 0-9 T, TEC reaches 3.2 J$\cdot$kg${}^{-1}\cdot$K-1 (RE
= Tb), 7.0 J$\cdot$kg${}^{-1}\cdot$K-1 (RE = Dy), 12.6
J$\cdot$kg${}^{-1}\cdot$K-1 (RE = Ho), 12.2 J$\cdot$kg${}^{-1}\cdot$K-1 (RE =
Er) and 11.8 J$\cdot$kg${}^{-1}\cdot$K-1 (RE = Tm), respectively. TEC is
slightly decreased with increasing temperature span Tlift. The values of TEC
are close to the ones of corresponding $-\Delta S_{M}^{max}$, indicating that
magnetocaloric performance is maintained over temperature integral of at least
10 K. It is noticeable that for RE = Tb and Dy the TEC values are always
related 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. 3a and 3b).

Besides $\Delta S_{M}^{max}$ and TEC, the relative cooling power (RCP) [51]
and refrigerant capacity (RC) [52] are also used to characterize
magnetocaloric performance. The latter parameters correspond to the amount of
heat transfer between the cold and hot reservoirs in an ideal refrigeration
cycle [53]. RCP is defined as the product of the maximum magnetic entropy
change $-\Delta S_{M}^{max}$ and the full width at half maximum $\delta
T_{FWHM}$ in the -$\Delta S_{M}(T)$ curve by the equation:

$RCP=-\Delta S_{M}^{max}\times\delta T_{FWHM}$ (3)

RC is calculated by numerically integrating the area under the -$\Delta
S_{M}(T)$ curve, while taking the half maximum of the peak as the integration
limits:

$RC=\int_{T_{1}}^{T_{2}}|\Delta S_{M}|\,\mathrm{d}T$ (4)

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

Table 1:  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
RE5Pd2In4 (RE = Tb-Tm), isostructural RE5T2In4 (T = Ni, Pt) and selected rare
earth intermetallics.

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 | 103 | 1.8 | 3.6 | 4.7 | - | 49 | 178 | 286 | - | 37 | 130 | 209 | - | [54]
Ho5Ni2In4 | 19 | 2.6 | 7.1 | 10.1 | - | 84 | 298 | 458 | - | 66 | 234 | 352 | - | [54]
Er5Ni2In4 | 20 | 3.3 | 7.7 | 10.2 | - | 71 | 248 | 377 | - | 52 | 180 | 273 | - | [54]
Gd5Pt2In4 | 78 | 1.0 | 2.2 | 3.0 | 3.7 | 58 | 172 | 261 | 359 | 48 | 139 | 209 | 290 | [49]
Tb5Pt2In4 | 45, 110 | 0.8 | 1.7 | 2.5 | 3.4 | 82 | 198 | 303 | 428 | 57 | 165 | 248 | 340 | [49]
Dy5Pt2In4 | 25, 95 | 1.1 | 2.9 | 4.7 | 6.3 | 45 | 290 | 250 | 363 | 33 | 201 | 180 | 263 | [49]
Ho5Pt2In4 | 23 | 2.5 | 6.9 | 9.5 | 11.8 | 94 | 302 | 451 | 607 | 82 | 254 | 373 | 495 | [49]
Er5Pt2In4 | 14 | 3.6 | 7.5 | 9.6 | 11.4 | 79 | 218 | 328 | 434 | 63 | 175 | 256 | 341 | [49]
Tm5Pt2In4 | 8 | 3.2 | 7.7 | 9.2 | 10.2 | 34 | 125 | 189 | 260 | 27 | 98 | 150 | 205 | [49]
Tb5Pd2In4 | 62, 102 | 0.8 | 1.8 | 2.5 | 3.3 | 53 | 161 | 258 | 377 | 44 | 133 | 215 | 312 | this work
Dy5Pd2In4 | 22, 94 | 1.1 | 3.2 | 5.2 | 7.0 | 100 | 314 | 498 | 672 | 65 | 216 | 325 | 406 | this work
Ho5Pd2In4 | 22 | 2.5 | 7.2 | 10.0 | 12.6 | 94 | 326 | 489 | 661 | 81 | 269 | 403 | 541 | this work
Er5Pd2In4 | 17 | 3.3 | 7.7 | 10.1 | 12.1 | 103 | 287 | 403 | 528 | 91 | 227 | 314 | 409 | this work
Tm5Pd2In4 | 9 | 4.4 | 9.2 | 10.8 | 11.9 | 85 | 156 | 234 | 320 | 50 | 123 | 184 | 249 | this work
Gd11Co4In9 | 85 | 5.0 | 9.0 | 11.0 | - | 106 | 358 | - | - | 82 | 270 | - | - | [55]
Tb11Co4In9 | 42 | 1.2 | 3.3 | 4.4 | 5.5 | 45 | 180 | - | 522 | 35 | 140 | - | 391 | [56]
Dy11Co4In9 | 35 | 1.1 | 3.5 | 4.7 | - | 27 | 128 | - | - | 20 | 98 | - | - | [55]
Ho11Co4In9 | 20 | 3.0 | 9.2 | 12.3 | - | 87 | 307 | - | - | 66 | 229 | - | - | [55]
Er11Co4In9 | 12 | 6.0 | 10.9 | 12.8 | 14.3 | 85 | 265 | - | 605 | 66 | 205 | - | 463 | [56]
Gd11Ni4In9 | 98 | 1.4 | 2.9 | 3.6 | - | 54 | 171 | 269 | - | 38 | 131 | 206 | - | [57]
Dy11Ni4In9 | 19, 92 | 0.8 | 3.8 | 6.0 | - | 21 | 109 | 195 | - | 16 | 81 | 145 | - | [57]
Ho11Ni4In9 | 16 | 1.8 | 8.8 | 12.4 | - | 32 | 198 | 353 | - | 24 | 152 | 269 | - | [57]
Gd6Co2.2In0.8 | 42, 78 | 2.6 | 8.4 | 11.8 | - | 148 | 532 | 814 | - | 97 | 381 | 634 | - | [58]
Tb6Co2.2In0.8 | 38 | 1.4 | 5.9 | 9.0 | - | 39 | 214 | 394 | - | 28 | 157 | 284 | - | [58]
Dy6Co2.2In0.8 | 53 | 1.5 | 6.1 | 9.6 | - | 36 | 288 | 517 | - | 25 | 211 | 390 | - | [58]
Ho6Co2.2In0.8 | 19 | 3.8 | 15.4 | 20.8 | - | 74 | 370 | 626 | - | 57 | 279 | 466 | - | [58]
Gd2In | 194 | 2.8 | - | - | - | - | - | - | - | - | - | - | - | [5]
Tb2In | 165 | 3.5 | 6.6 | - | - | 200 | 660 | - | - | - | - | - | - | [6]
Dy2In | 130 | 4.6 | 9.2 | - | - | 230 | 736 | - | - | - | 545 | - | - | [11]
Dy2In | 125 | - | - | 8.8 | - | - | - | - | - | - | - | - | - | [59]
Ho2In | 85 | 5.0 | 11.2 | - | - | 125 | 560 | - | - | - | 360 | - | - | [7, 6]
Er2In | 46 | 7.9 | 16.0 | - | - | - | - | - | - | - | 490 | - | - | [8]
GdPt2 | 28 |  3.2a | - | 11.3 | - | - | - | - | - | - | - | - | - | [9]
DyPt2 | 10 | 5.0 | 9.4 |  21.2b | - | - | - | - | - | 50 | 150 | - | - | [60]

a $\Delta\mu_{0}H$ = 0–1 T | b $\Delta\mu_{0}H$ = 0–8 T

Table 1 shows the magnetocaloric performance of RE5Pd2In4 (RE = Tb-Tm) in
comparison with isostructural RE5T2In4 (T = Ni, Pt) and other selected rare-
earth-based intermetallics in terms of temperature at which $-\Delta
S_{\mathrm{M}}^{\mathrm{max}}$ is reached as well as the values of $-\Delta
S_{\mathrm{M}}^{\mathrm{max}}$, RCP and RC.

For a selected rare earth element, the MCE performance of a member of the
RE5Pd2In4 (RE = Tb-Tm) family of compounds shows similar performance to that
of the isostructural RE5T2In4 (T = Ni, Pt) as well as to that of its RE11T4In9
(T = Co, Ni) analogues. Much more effected is the temperature at which
$-\Delta S_{\mathrm{M}}^{\mathrm{max}}$ occurs. For example, for Er5T2In4 such
temperature varies from 14 K for T = Pt up to 20 K for T = Ni. Therefore, the
selection of transition metal (T) and stoichiometry enables us to get a
compound that shows maximum magnetocaloric performance at a certain
temperature. Moreover, combining different compounds allows to obtain hybrid
materials that show good magnetocaloric performance over desired temperature
interval. This feature is important from the point of view of application in
low-temperature refrigeration.

It is worth noting that RE5Pd2In4 (RE = Tb-Tm) have higher values of RCP and
RC when compared to their RE5T2In4 analogues with T = Ni or Pt. Among
RE5Pd2In4, the best magnetocaloric performance is found for RE = Ho and Er,
making these two compounds competitive to known rare-earth-based
magnetocaloric materials, which show good magnetocaloric performance at low
temperatures.

##  IV Conclusions

The magnetocaloric effect in RE5Pd2In4 (RE = Tb-Tm) has been investigated
using magnetometric measurements in the function of temperature and applied
magnetic field. Based on these data, $-\Delta S_{M}^{max}$, TEC, RC and RCP
values have been determined and compared to those of selected ternary rare-
earth-based intermetallics. The maximum of $-\Delta S_{M}^{max}$ is reached at
62 K, 22 K, 22 K, 17 K, and 9 K for RE = Tb, Dy, Ho, Er, and Tm, respectively.
For selected rare earth elements, the RE5Pd2In4 compound shows the highest RCP
and RC values when compared to those of its RE5T2In4 (T = Ni, Pt)
isostructural analogues [54, 49].

The magnetocaloric performance of RE5Pd2In4 (RE = Tb-Tm) is comparable to that
found for other magnetocaloric materials showing remarkable magnetocaloric
properties well below room temperature. The RE5Pd2In4 compounds with RE = Ho
and Er are of special interest as their $-\Delta S_{M}^{max}$, TEC, RC and RCP
parameters reach the highest values when compared to those of remaining
RE5Pd2In4 (RE = Tb, Dy and Tm).

## Declaration of Competing Interest

The authors declare no conflict of interest.

## Acknowledgements

The study was funded by “Research support module” as part of the “Excellence
Initiative – Research University” program at the Jagiellonian University in
Kraków.

The research was 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).

## References

  * Chai et al. [2023] S.-S. Chai, W.-B. Zhang, J.-L. Yang, L. Zhang, M. M. Theint, X.-L. Zhang, S.-B. Guo, X. Zhou, X.-J. Ma,  Sustainability applications of rare earths from metallurgy, magnetism, catalysis, luminescence to future electrochemical pseudocapacitance energy storage,  RSC Sustain. 1 (2023) 38–71. doi:10.1039/D2SU00054G.
  * Patiño and de Oliveira [2023] J. C. Patiño, N. de Oliveira,  Magnetocaloric effect in R2Cu2Cd (R = Gd, Tb, Er, Tm),  Physica B: Condensed Matter 650 (2023) 414496. doi:10.1016/j.physb.2022.414496.
  * Li and Yan [2020] L. Li, M. Yan,  Recent progresses in exploring the rare earth based intermetallic compounds for cryogenic magnetic refrigeration,  Journal of Alloys and Compounds 823 (2020) 153810. doi:10.1016/j.jallcom.2020.153810.
  * Guo et al. [2021] D. Guo, L. M. Moreno-Ramírez, C. Romero-Muñiz, Y. Zhang, J.-Y. Law, V. Franco, J. Wang, Z. Ren,  Recent progresses in exploring the rare earth based intermetallic compounds for cryogenic magnetic refrigeration,  Science China Materials 64 (2021) 2846–2857. doi:10.1007/s40843-021-1711-5.
  * Bhattacharyya et al. [2012] A. Bhattacharyya, S. Giri, S. Majumdar,  Field induced sign reversal of magnetocaloric effect in Gd2In,  Journal of Magnetism and Magnetic Materials 324 (2012) 1239–1241. doi:10.1016/j.jmmm.2011.11.023.
  * Zhang et al. [2009a] Q. Zhang, J. Cho, J. Du, F. Yang, X. Liu, W. Feng, Y. Zhang, J. Li, Z. Zhang,  Large reversible magnetocaloric effect in Tb2In,  Solid State Communications 149 (2009a) 396–399. doi:10.1016/j.ssc.2008.12.009.
  * Zhang et al. [2009b] Q. Zhang, J. H. Cho, B. Li, W. J. Hu, Z. D. Zhang,  Magnetocaloric effect in Ho2In over a wide temperature range,  Applied Physics Letters 94 (2009b) 182501. doi:10.1063/1.3130090.
  * Zhang et al. [2011] H. Zhang, B. Shen, Z. Xu, J. Chen, J. Shen, F. Hu, J. Sun,  Large reversible magnetocaloric effect in Er2In compound,  Journal of Alloys and Compounds 509 (2011) 2602–2605. doi:10.1016/j.jallcom.2010.11.108.
  * Samanta and Das [2006] T. Samanta, I. Das,  Negligible influence of domain walls on the magnetocaloric effect in GdPt2,  Phys. Rev. B 74 (2006) 132405. doi:10.1103/PhysRevB.74.132405.
  * Taskaev et al. [2020] S. Taskaev, V. Khovaylo, K. Skokov, W. Liu, E. Bykov, M. Ulyanov, D. Bataev, A. Basharova, M. Kononova, D. Plakhotskiy, M. Bogush, T. Gottschall, O. Gutfleisch,  Magnetocaloric effect in GdNi2 for cryogenic gas liquefaction studied in magnetic fields up to 50 t,  Journal of Applied Physics 127 (2020) 233906. doi:10.1063/5.0006281.
  * Zhang et al. [2009] Q. Zhang, X. G. Liu, F. Yang, W. J. Feng, X. G. Zhao, D. J. Kang, Z. D. Zhang,  Large reversible magnetocaloric effect in Dy2In,  Journal of Physics D: Applied Physics 42 (2009) 055011. doi:10.1088/0022-3727/42/5/055011.
  * de Souza [2016] M. de Souza,  Investigation on the magnetocaloric effect in RNi2 (r: Dy, tb) melt-spun ribbon,  Journal of Magnetism and Magnetic Materials 412 (2016) 11–14. doi:10.1016/j.jmmm.2016.03.078.
  * Ćwik et al. [2018] J. Ćwik, Y. Koshkid’ko, K. Nenkov, E. Tereshina, K. Rogacki,  Structural, magnetic and magnetocaloric properties of HoNi2 and ErNi2 compounds ordered at low temperatures,  Journal of Alloys and Compounds 735 (2018) 1088–1095. doi:10.1016/j.jallcom.2017.11.194.
  * Baran et al. [2020] S. Baran, Y. Tyvanchuk, B. Penc, Y. Kalychak, A. Hoser, A. Szytuła,  Crystal structure and complex magnetic properties of R11Pd4In9 compounds (R = Y, Gd–Er),  Intermetallics 123 (2020) 106837. doi:10.1016/j.intermet.2020.106837.
  * Liu et al. [2022] W. Liu, E. Bykov, S. Taskaev, M. Bogush, V. Khovaylo, N. Fortunato, A. Aubert, H. Zhang, T. Gottschall, J. Wosnitza, F. Scheibel, K. Skokov, O. Gutfleisch,  A study on rare-earth laves phases for magnetocaloric liquefaction of hydrogen,  Applied Materials Today 29 (2022) 101624. doi:10.1016/j.apmt.2022.101624.
  * K. Matsumoto et al. [2006] K. Matsumoto, T. Kouen, R. Nishida, S. Abe, K. Kamiya, T. Numazawa,  Magnetocaloric effect of RCo2 (r: Er, ho, dy) compounds for regenerative magnetic refrigeration,  AIP Conference Proceedings 850 (2006) 1581–1582. doi:10.1063/1.2355310.
  * Ma et al. [2008] S. Ma, W. B. Cui, D. Li, N. K. Sun, D. Y. Geng, X. Jiang, Z. D. Zhang,  Large cryogenic magnetocaloric effect of DyCo2 nanoparticles without encapsulation,  Applied Physics Letters 92 (2008) 173113. doi:10.1063/1.2919079.
  * Rajivgandhi et al. [2018] R. Rajivgandhi, J. Rajesh Krishna, J. Arout Chelvane, S. Quezado, S. Malik, R. Nirmala,  Magnetocaloric effect in melt-spun laves phase intermetallic compound HoCo2,  Journal of Magnetism and Magnetic Materials 448 (2018) 351–354. doi:10.1016/j.jmmm.2017.08.004, international Conference on Magnetic Materials and Applications – ICMAGMA2017.
  * Nikitin and Tishin [1991] S. Nikitin, A. Tishin,  Magnetocaloric effect in HoCo2 compound,  Cryogenics 31 (1991) 166–167. doi:10.1016/0011-2275(91)90171-R.
  * Jun-Ding et al. [2007] Z. Jun-Ding, S. Bao-Gen, S. Ji-Rong,  Magnetocaloric effect in ErCo2 compound,  Chinese Physics 16 (2007) 1817. doi:10.1088/1009-1963/16/7/001.
  * Wada et al. [1999] H. Wada, S. Tomekawa, M. Shiga,  Magnetocaloric effect of ErCo2,  Journal of Magnetism and Magnetic Materials 196-197 (1999) 689–690. doi:10.1016/S0304-8853(98)00894-4.
  * Burzo et al. [2010] E. Burzo, I. Pop, D. Kozlenko,  Magnetic and magnetocaloric properties of some ferrimagnetic compounds,  Journal of Optoelectronics and Advanced Materials – Rapid Communications 12 (2010) 1105–1113.
  * Singh et al. [2007] N. K. Singh, K. Suresh, A. Nigam, S. Malik, A. Coelho, S. Gama,  Itinerant electron metamagnetism and magnetocaloric effect in RCo2-based laves phase compounds,  Journal of Magnetism and Magnetic Materials 317 (2007) 68–79. doi:10.1016/j.jmmm.2007.04.009.
  * Duc and Anh [2002] N. Duc, D. Anh,  Magnetocaloric effects in RCo2 compounds,  Journal of Magnetism and Magnetic Materials 242-245 (2002) 873–875. doi:10.1016/S0304-8853(01)01328-2, proceedings of the Joint European Magnetic Symposia (JEMS’01).
  * Samanta et al. [2006] T. Samanta, I. Das, S. Banerjee,  Magnetocaloric effect in Ho5Pd2 : Evidence of large cooling power,  Applied Physics Letters 91 (8) (2006) 1–3. doi:10.1063/1.2775050.
  * Paramanik et al. [2015] T. Paramanik, T. Samanta, R. Ranganathan, I. Das,  Magnetic and magnetocaloric properties of Dy5Pd2: role of magnetic irreversibility,  RSC Adv. 5 (2015) 47860–47865. doi:10.1039/C5RA06970J.
  * Maji et al. [2018] B. Maji, M. K. Ray, M. Modak, S. Mondal, K. Suresh, S. Banerjee,  Magnetic properties and large reversible magnetocaloric effect in Er3Pd2,  Journal of Magnetism and Magnetic Materials 456 (2018) 236–240. doi:10.1016/j.jmmm.2018.02.036.
  * Wu et al. [2019] X. Wu, C. Guo, J. Wang, J. Deng, Y. Du, G. Rao, Z. Du,  Magnetic properties and large magnetocaloric effect in Ho3Pd2 compound,  Journal of Magnetism and Magnetic Materials 482 (2019) 168–172. doi:10.1016/j.jmmm.2019.03.048.
  * Rawat and Das [2006] R. Rawat, I. Das,  Heat capacity and magnetocaloric studies of RPd2Si (r = gd, tb and dy),  Journal of Physics: Condensed Matter 18 (2006) 1051. doi:10.1088/0953-8984/18/3/020.
  * Rawat and Das [2001] R. Rawat, I. Das,  Magnetocaloric and magnetoresistance studies of GdPd2Si,  Journal of Physics: Condensed Matter 13 (2001) L57. doi:10.1088/0953-8984/13/3/102.
  * Sahu et al. [2022] B. Sahu, R. D. Fobasso, B. M. Sondezi, A. M. Strydom,  Large magnetocaloric effect in Ho2Pd2Pb,  Materials Today Communications 31 (2022) 103327. doi:10.1016/j.mtcomm.2022.103327.
  * Zhang and Shen [2015] H. Zhang, B.-G. Shen,  Magnetocaloric effects in rtx intermetallic compounds (r = gd-tm, t = fe-cu and pd, x = al and si)*,  Chinese Physics B 24 (2015) 127504. doi:10.1088/1674-1056/24/12/127504.
  * Mo et al. [2015] Z.-J. Mo, J. Shen, X.-Q. Gao, Y. Liu, J.-F. Wu, B.-G. Shen, J.-R. Sun,  Magnetic properties and magnetocaloric effects in hopd intermetallic*,  Chinese Physics B 24 (2015) 037503. doi:10.1088/1674-1056/24/3/037503.
  * Huo et al. [2018] J. Huo, Y. Du, G. Cheng, X. Wu, L. Ma, J. Wang, Z. Xia, G. Rao,  Magnetic properties and large magnetocaloric effects of gdpd intermetallic compound,  Journal of Rare Earths 36 (2018) 1044–1049. doi:10.1016/j.jre.2018.03.016.
  * Shen et al. [2011] J. Shen, Z.-Y. Xu, H. Zhang, X.-Q. Zheng, J.-F. Wu, F.-X. Hu, J.-R. Sun, B. gen Shen,  Metamagnetic transition and magnetocaloric effect in antiferromagnetic tbpdal compound,  Journal of Magnetism and Magnetic Materials 323 (2011) 2949–2952. doi:10.1016/j.jmmm.2011.05.042.
  * Xu and Shen [2012] Z. Xu, B. Shen,  Large magnetocaloric effect in metamagnetic hopdal,  Sci. China Technol. Sci. 55 (2012) 45–450. doi:10.1007/s11431-011-4681-9.
  * Sharma et al. [2018] M. K. Sharma, K. Yadav, K. Mukherjee,  Complex magnetic behaviour and evidence of a superspin glass state in the binary intermetallic compound Er5Pd2,  Journal of Physics: Condensed Matter 30 (2018) 215803. doi:10.1088/1361-648X/aabbfe.
  * Sharma and Mukherjee [2018] M. K. Sharma, K. Mukherjee,  Evidence of large magnetic cooling power and double glass transition in Tb5Pd2,  Journal of Magnetism and Magnetic Materials 466 (2018) 317–322. doi:10.1016/j.jmmm.2018.07.029.
  * Sharma and Mukherjee [2019] M. K. Sharma, K. Mukherjee,  Field induced nature and nonlinear dc susceptibility studies of ni substituted Dy5Pd2 cluster glass system,  Physica B: Condensed Matter 572 (2019) 56–59. doi:10.1016/j.physb.2019.07.053.
  * Sojka et al. [2008] L. Sojka, M. Dashkevych, B. Belan, M. Manyako, V. Davydov, L. Akselrud, Ya. M. Kalychak,  Crystal structure of alloys R5Pd2In4 (R = Y, Tb, Dy, Ho, Er, Tm, Lu),  Ukr. Chem. J. 74 (2008) 90–94.
  * Zaremba et al. [1988] V. I. Zaremba, V. A. Bruskov, P. Yu. Zavalii, Ya. M. Kalychak,  Crystal structure of R2Ni2In compounds (R = Y, Sm, Gd, Tb, Ho, Er, Tm, Lu),  Izv. Akad. Nauk SSSR, Neorg. Mater. 24 (1988) 409–411.
  * Ya. M. Kalychak et al. [1990] Ya. M. Kalychak, V. I. Zaremba, V. M. Baranyak, P. Yu. Zavalii, V. A. Bruskov, L. V. Sysa, O. V. Dmytrakh,  Crystal structure of the compounds R2Ni2In, R2Ni2-xIn and R2Cu2In (R = La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu, Y),  Izv. Akad. Nauk SSSR, Neorg. Mater. 26 (1990) 94–96.
  * V. I. Zaremba et al. [1991] V. I. Zaremba, Ya. M. Kalychak, P. Yu. Zavalii, V. A. Bruskov,  Crystal structures of the compounds R5Ni2In4 (R = Ho, Er, Tm, Lu),  Kristallografiya 36 (1991) 1415–1418.
  * Pustovoychenko et al. [2010] M. Pustovoychenko, Y. Tyvanchuk, I. Hayduk, Y. Kalychak,  Crystal structure of the RE11Ni4In9 compounds (RE = La, Ce, Pr, Nd, Sm, Gd, Tb and Y),  Intermetallics 18 (2010) 929–932. doi:10.1016/j.intermet.2010.01.003.
  * Sojka et al. [2008] L. Sojka, M. Manyako, R. Černý, M. Ivanyk, B. Belan, R. Gladyshevskii, Ya. Kalychak,  Nd11Pd4In9 compound – a new member of the homological series based on AlB2 and CsCl types,  Intermetallics 16 (2008) 625–628. doi:10.1016/j.intermet.2008.01.001.
  * Zaremba et al. [2008] R. Zaremba, W. Hermes, M. Eul, R. Pöttgen,  Rare Earth-Transition Metal Indides with Lu5Ni2In4-type Structure,  Z. Naturforsch. 63b (2008) 1447 – 1449.
  * Baran et al. [2021] S. Baran, A. Deptuch, M. Reehuis, Y. Tyvanchuk, F. Yokaichiya, A. Szytuła,  Complex magnetic ordering in RE5Pd2In4 (RE = Tb-Tm) compounds investigated by neutron diffraction and magnetometric measurements,  Journal of Alloys and Compounds 877 (2021) 160171. doi:10.1016/j.jallcom.2021.160171.
  * A. M. Tishin and Y. I. Spichkin [2003] A. M. Tishin, Y. I. Spichkin, The Magnetocaloric Effect and its Applications, Institute of Physics Publishing, Bristol and Philadelphia, 2003.
  * Hayyu et al. [2023] A. R. Hayyu, S. Baran, A. Szytuła,  Characterization of magnetic properties, including magnetocaloric effect, of RE5Pt2In4 (RE = Gd-Tm) compounds (2023). doi:10.48550/arXiv.2212.07171.
  * L. D. Griffith et al. [2018] L. D. Griffith, Y. Mudryk, J. Slaughter, V. K. Pecharsky,  Material-based figure of merit for caloric materials,  J. Appl. Phys. 123 (2018) 034902. doi:10.1063/1.5004173.
  * K. A. Gschneidner, Jr. and V. K. Pecharsky [2000] K. A. Gschneidner, Jr., V. K. Pecharsky,  Magnetocaloric materials,  Annu. Rev. Mater. Sci. 30 (2000) 387–429. doi:10.1146/annurev.matsci.30.1.387.
  * M. E. Wood and W. H. Potter [1985] M. E. Wood, W. H. Potter,  General analysis of magnetic refrigeration and its optimization using a new concept: maximization of refrigerant capacity,  Cryogenics 25 (1985) 667–683. doi:10.1016/0011-2275(85)90187-0.
  * Li [2016] L.-W. Li,  Review of magnetic properties and magnetocaloric effect in the intermetallic compounds of rare earth with low boiling point metals*,  Chinese Physics B 25 (2016) 037502. doi:10.1088/1674-1056/25/3/037502.
  * Zhang et al. [2018] Z. Zhang, X. Dong, Q. Wang, L. Li,  Investigation of the crystal structure, magnetic phase transition and magnetocaloric effect in RE5Ni2In4 (RE = Dy, Ho and Er) compounds,  Intermetallics 100 (2018) 136–141. doi:10.1016/j.intermet.2018.06.012.
  * Zhang et al. [2020] Z. Zhang, P. Wang, N. Wang, X. Wang, P. Xu, L. Li,  Structural and cryogenic magnetic properties of rare earth rich RE11Co4In9 (RE= Gd, Dy and Ho) intermetallic compounds,  Dalton Trans. 49 (2020) 8764–8773. doi:10.1039/D0DT01212B.
  * Baran et al. [2023] S. Baran, A. R. Hayyu, Yu. Tyvanchuk, A. Szytuła,  Magnetocaloric performance of RE11Co4In9 (RE = Tb, Er),  accepted in Phase Trans. (2023). doi:10.1080/01411594.2022.2149398.
  * Zhang et al. [2021a] Z. Zhang, P. Wang, Y. Jia, X. Wang, L. Li,  Crystal structure, magnetic phase transitions and magnetocaloric effect (MCE) in layer-like RE11Ni4In9 (RE = Gd, Dy and Ho) compounds,  Journal of Alloys and Compounds 851 (2021a) 155863. doi:10.1016/j.jallcom.2020.155863.
  * Zhang et al. [2021b] Z. Zhang, I. Muts, L. Li, R. Pöttgen,  Magnetic properties and magnetocaloric performances of the rare earth-rich indides RE6Co2.2In0.8 (RE = Gd, Tb, Dy and Ho) with Ho6Co2Ga-type structure,  Intermetallics 136 (2021b) 107254. doi:10.1016/j.intermet.2021.107254.
  * Yao et al. [2019] G. Yao, F. Wei, J. Zhang, X. Fan, X. Yin, W. Cui, Q. Wang,  The enhanced magnetocaloric effect in dy2in1-xalx by a non-hysteresis metamagnetic phase transition,  Scripta Materialia 167 (2019) 37–40. doi:10.1016/j.scriptamat.2019.03.029.
  * Arora et al. [2009] P. Arora, M. K. Chattopadhyay, S. B. Roy,  Magnetic properties and large magnetocaloric effect of DyPt2,  Journal of Applied Physics 106 (2009) 093912. doi:10.1063/1.3253729.