Current address: ]Max Planck Institute for Chemical Physics of Solids, 01187
Dresden, Germany Current address: ]National High Magnetic Field Laboratory,
Florida State University, Tallahassee, Florida 32310, USA

# Magnetism and $T-x$ phase diagrams of Na and Ag substituted EuCd2As2

Brinda Kuthanazhi  Ames National Laboratory, Iowa State University, Ames,
Iowa-50011, USA  Department of Physics and Astronomy, Iowa State University,
Ames, Iowa-50011, USA  Kamal R. Joshi  Ames National Laboratory, Iowa State
University, Ames, Iowa-50011, USA  Department of Physics and Astronomy, Iowa
State University, Ames, Iowa-50011, USA  Sunil Ghimire  Ames National
Laboratory, Iowa State University, Ames, Iowa-50011, USA  Department of
Physics and Astronomy, Iowa State University, Ames, Iowa-50011, USA  Erik
Timmons  Ames National Laboratory, Iowa State University, Ames, Iowa-50011,
USA  Department of Physics and Astronomy, Iowa State University, Ames,
Iowa-50011, USA  Lin-Lin Wang  Ames National Laboratory, Iowa State
University, Ames, Iowa-50011, USA  Elena Gati  [  Ames National Laboratory,
Iowa State University, Ames, Iowa-50011, USA  Department of Physics and
Astronomy, Iowa State University, Ames, Iowa-50011, USA  Li Xiang  [  Ames
National Laboratory, Iowa State University, Ames, Iowa-50011, USA  Department
of Physics and Astronomy, Iowa State University, Ames, Iowa-50011, USA  Ruslan
Prozorov  Ames National Laboratory, Iowa State University, Ames, Iowa-50011,
USA  Department of Physics and Astronomy, Iowa State University, Ames,
Iowa-50011, USA  Sergey L. Bud’ko  Ames National Laboratory, Iowa State
University, Ames, Iowa-50011, USA  Department of Physics and Astronomy, Iowa
State University, Ames, Iowa-50011, USA  Paul C. Canfield
<EMAIL_ADDRESS>Ames National Laboratory, Iowa State University, Ames,
Iowa-50011, USA  Department of Physics and Astronomy, Iowa State University,
Ames, Iowa-50011, USA

###### Abstract

EuCd2As2 is an antiferromagnetic semimetal, that can host non-trivial
topological properties, depending upon its magnetic state and excitations.
Here, we report the synthesis and characterization of Eu(Cd1-xAgx)2As2 and
Eu1-yNayCd2As2, and study the evolution and nature of magnetic order with
doping. Temperature-substitution phase diagrams are constructed from the
electrical resistance and magnetic susceptibility data. We observe a splitting
of the magnetic transition into two different transitions, and the gradual
increase in one of the transition temperatures with Ag- and Na-substitution.
The other transition remains more or less independent of doping. We further
show that a magnetic state with a net ferromagnetic moment is stabilized by
both Ag and Na doping and this can be explained by considering the changes in
band filling due to substitution as suggested by density functional theory
(DFT) calculations. We thus show that chemical substitution and the subsequent
changes in band filling could be a pathway to tune the magnetic ground state
and to stabilize a ferromagnetic phase in EuCd2As2.

##  I Introduction

The search for new topological materials and the realization of novel surface
states and magneto-transport phenomena has driven condensed matter research in
the recent years. Hsieh et al. (2008); Hasan and Kane (2010); Burkov and
Balents (2011); Burkov (2016); Chiu et al. (2016); Yan and Felser (2017);
Armitage et al. (2018); Tokura et al. (2019) One such material class is Weyl
semimetals, which are expected to show a chiral anomaly, large anomalous Hall
effect, Fermi arc surface states, unconventional optical response etc. Wan et
al. (2011); Parameswaran et al. (2014); Chan et al. (2016); Jia et al. (2016);
Chan et al. (2017); Shekhar et al. (2018) Weyl semimetals can be realized from
a Dirac semi-metal, which hosts linear band dispersion at certain symmetry
protected Dirac points. Breaking either time reversal or inversion symmetry
lifts the degeneracy of Dirac points, giving rise to a Weyl semi-metal. A
minimum number of Weyl points can be attained by breaking the time reversal
symmetry, Armitage et al. (2018) which can be achieved through magnetic
ordering. Despite a large number of materials being identified as magnetic
Weyl semimetal candidates, unambiguous experimental signatures, especially in
magneto-transport, have remained difficult to attain and challenging to
untangle from other contributions. One among the major road blocks for this is
the presence of other topologically trivial bands close to the Fermi level,
Ramshaw et al. (2018) combined with a large number of Weyl points usually
observed. Weng et al. (2015); Huang et al. (2015); Arnold et al. (2016); Chang
et al. (2018) It is in this context that Weyl semimetal candidate EuCd2As2
garnered a lot of attention, as DFT calculations predicted it to host a single
pair of Weyl points, when stabilized in a ferromagnetic state with moments
along the crystallographic $c-$direction. Hua et al. (2018); Wang et al.
(2019)

Subsequent experimental work showed direct and indirect signatures of Weyl
physics, as well as the possibility of this system being tunable between
various magnetic ground states. Rahn et al. (2018); Ma et al. (2019); Niu et
al. (2019); Jo et al. (2020); Ma et al. (2020); Taddei et al. (2022); Sanjeewa
et al. (2020); Gati et al. (2021); Xu et al. (2021) Early experiments on
EuCd2As2 reported it to crystallize in the hexagonal space group $P\bar{3}m1$
with an antiferromagnetic (AFM) transition around $10~{}$K. Artmann et al.
(1996); Schellenberg et al. (2010) Later, the magnetic ground state was
reported to be AFM-A, where moments are aligned ferromagnetically (FM) in-
plane and antiferromagnetically inter-plane. Rahn et al. (2018) Whereas a
c-polarized ferromagnetic state was predicted to be favorable for a single
pair of Weyl points, other magnetic ground states were still expected to show
topologically non-trivial states. Wang et al. (2019); Jo et al. (2020)
Observation of anomalous Hall effect in transport measurements, Soh et al.
(2019) soon followed by the direct observation of Weyl points by angle
resolved photo emission spectroscopy (ARPES) in the paramagnetic state have
confirmed this prediction. Ma et al. (2019) This was followed by reports of a
modified synthesis procedure stabilizing a ferromagnetic ground state, Jo et
al. (2020) which was later reproduced and the FM ground state confirmed by
neutron diffraction. Taddei et al. (2022) Furthermore, Ba-substitution in
EuCd2As2, has also shown an FM state with spin canting. Sanjeewa et al. (2020)
Hydrostatic pressure has also been used to tune the magnetic ground state
revealing that pressures as low as $2~{}$GPa can change the ambient-pressure,
AFM ordering of pure EuCd2As2 into an ordered state with a net ferromagnetic
component with moments in-plane. Gati et al. (2021); Yu et al. (2022); Du et
al. (2022) It is also known to go through a metallic - insulating - metallic
transition below the magnetic transition with applied pressures. Du et al.
(2022) A recent study suggests that higher pressures ($\sim 19~{}$GPa) turn
the magnetic ordering in to ferromagnetic with moments out of plane. Yu et al.
(2022)

In this paper, we further probe the effect of chemical tunability on
magnetism, by careful chemical substitution of Ag and Na on Cd and Eu sites
respectively of EuCd2As2. Electrical resistivity and magnetic susceptibility
measurement results are presented, and the temperature-substitution phase
diagrams are constructed from them. Furthermore, we use magneto-optical Kerr
effect measurements to further support the conclusion that whereas pure
EuCd2As2 is in an AFM state, Na and Ag substituted EuCd2As2 has a measurable
FM component, even for the smallest doping we have. Finally, we also discuss a
possible mechanism that is leading to stabilization of different magnetic
states, supported by DFT calculations.

Sample | Nominal $x$, $y$ | Measured $x$, $y$
---|---|---
Eu(Cd1-xAgx)2As2 | $x=0$ | $x=0$
| $x=0.05$ | $x=0.0008(1)$
| $x=0.10$ | $x=0.0019(3)$
| $x=0.20$ | $x=0.0040(3)$
| $x=0.30$ | $x=0.0055(3)$
Eu1-yNayCd2As2 | $y=0$ | $y=0$
| $y=0.10$ | $y=0.005(1)$
| $y=0.20$ | $y=0.008(1)$
Table 1: The nominal and measured concentrations of Ag and Na in various
substituted EuCd2As2 crystals. Figure 1: (a) Powder x-ray diffraction patterns
of various Ag and Na substituted EuCd2As2 samples. The intensities have been
normalized such that the strongest peak (the (101) peak located at
$2\theta\sim$ $26~{}$degrees) has 1000 counts. The impurity peaks marked by
black and green stars are from Sn and NaSn2As2 respectively. Each data set is
offset by a constant to show the diffraction patterns clearly. (b) Lattice
parameter $a$ and (c) $c$ as a function of Ag-substitution $x$ and Na-
substitution $y$.

##  II Methods

The single crystals of pure and Na- and Ag-substituted EuCd2As2 were grown out
of Sn flux with following procedures. For pure EuCd2As2 an initial
stoichiometry of Eu:Cd:As:Sn = 1:2:2:10 (Eu - Ames Laboratory, 99.99+ %, Cd -
Alfa Aesar, 99.9997 %, As - Alfa Aesar, 99.9999 %, and Sn - Alfa Aesar, 99.99%
) was put into a fritted alumina crucible (CCS) Canfield et al. (2016) and
sealed in fused silica tube under a partial pressure of argon. The thus
prepared ampoule was heated up to $900\degree$ C over 24 hours, and held there
for 20 hours. This was followed by a slow cooling to $550\degree$ C over 200
hours, and decanting of the excess flux using a centrifuge. Canfield and Fisk
(1992); Canfield (2020) For the synthesis of Ag and Na substituted samples,
the initial composition was modified as; Eu1(Cd1-xAgx)2As2Sn10 for
$x=0.05,0.10,0.20,0.30$ and Eu1-yNayCd2As2Sn10 for $y=0.10,0.20$ respectively.
Further increasing the Ag and Na content in the initial melt resulted in
secondary phase inclusions appearing in the crystal.

Figure 2: Resistivity as a function of temperature, $\rho(T)$, plotted on a
semi-log scale for undoped EuCd2As2 and various (a) Ag doped samples and (b)
Na doped samples. The undoped sample has two orders of magnitude higher
resistivity than the doped samples. It also has a significant upturn above the
magnetic transition, whereas this feature is less pronounced in all
substituted samples. Inset shows the low temperature regime for the doped
samples. Two features are observed for samples with higher doping, illustrated
by two red arrows for $x=0.0055(3)$ and $y=0.008(1)$ samples. Figure 3:
Temperature dependent magnetization divided by applied field, $M(T)/H$, as a
function of temperature for various Ag substituted samples with an applied
field of $H=50~{}$Oe (a) parallel to crystallographic $c$ direction and (b) in
the $ab-$plane. The data shown is above $T=3.8~{}$K, as there were slight
features below that, due to presence of Sn (flux) in the sample which goes
superconducting below this temperature. Right $y-$ axis shows the scale in
units of $\mu_{B}/$f. u.-Oe. Figure 4: Temperature dependent magnetization
divided by applied field, $M(T)/H$, as a function of temperature for various
Na substituted samples with an applied field of $H=50~{}$Oe (a) parallel to
crystallographic $c$ direction and (b) in the $ab-$plane. The data shown is
above $T=3.8~{}$K, as there were slight features below that, due to presence
of Sn (flux) in the sample which goes superconducting below this temperature.
Right $y-$ axis shows the scale in units of $\mu_{B}/$f. u.-Oe.

Powder x-ray diffraction measurements were carried out to determine the phase
purity and track the changes in lattice parameters. Each powder x-ray
diffraction pattern was collected on ground crystals using a Rigaku Miniflex-
II diffractometer, with Cu$K_{\alpha}$ radiation. Lattice parameters were
obtained from a Rietveld refinement on it using GSAS-II software. Toby and Von
Dreele (2013)

The actual concentrations of Na and Ag in the grown crystals (as opposed to
the compositions of the initial, high temperature melt), were determined using
Energy dispersive X-ray Spectroscopy (EDS) and Wavelength dispersive X-ray
Spectroscopy (WDS). The SEM was an FEI Quanta-FEG 250 outfitted with Oxford
Instruments EDS and WDS. All was run under Aztec software, version 5.0.
Initial experiments with EDS showed no discernible peaks for Ag or Na due to
peak overlap with Cd and Eu, respectively. Hence, WDS analysis was used to
quantify Na and Ag content, whereas other elements were determined with EDS.
Na- and Ag-substituted EuCd2As2 samples were analyzed in the SEM at 20 kV,
8-16 nA, and 90-260 seconds of acquisition time. For Na-substituted samples,
measurements were done on 1-4 different points each for two different crystals
of each nominal substitution. The WDS analyses ran about 90 seconds each, to
achieve 0.01 weight% reproducibility. For crystals with various Ag
substitutions, the samples were embedded and polished along the cross section
for the best results. Samples were coated with 10 nm of carbon for
conductivity. Wavelength scans over the Ag$-L_{\alpha}$ peak showed a small,
but discernible peak. Samples were measured at a minimum of two points for
each of the embedded crystals. The WDS analyses ran about 260 seconds each to
attain 0.02% reproducibility.

The magnetic measurements were carried out in a Quantum Design, Magnetic
Property Measurement System with applied fields up to 50 kOe. The samples were
mounted on a Poly-Chloro-Tri-Fluoro-Ethylene disk, and the separately measured
background of the disk was subtracted. The AC resistivity measurements were
done in a Quantum Design, Physical Property Measurement System in the standard
four point configuration. The current was passed in the $ab-$ plane with
$I=3~{}$mA and $f=17~{}$Hz. Contacts were made using Epo-tek H20E silver
epoxy. Pure EuCd2As2 crystals were very difficult to make low resistance
contacts on, as the contact resistance remained several tens of Ohms despite
best efforts, which makes the measurements challenging. As will be discussed
below, pure EuCd2As2 has semiconducting- like resistivity values as well as
low temperature behavior. Any finite substitution/doping level we add results
in much lower contact resistances as well as lower resistivity values. A lot
of the resistance data shown later is represented as normalized resistances
for comparison between the samples and to get rid of the errors in geometrical
factors. As soon as we substitute Ag or Na, the contact resistances values
drops to 3-4 ohms. Along with this, the absolute value of measured resistance
also drops by two orders of magnitude as we go from pure EuCd2As2 to any of
the substituted sample.

Magneto optical Kerr effect measurements were carried out to confirm the
existence of ferromagnetic domains. The off-diagonal components of anisotropic
permittivity depend on magnetization vector amplitude and orientation. This
leads to the anisotropy of the speed of light in different directions, causing
linearly polarized light to rotate and become elliptically polarized.
Depending on the angle of incidence and the direction of polarization,
different components of the magnetization vector are engaged. We used the
magneto-optical polar Kerr effect for a real-space 2D imaging of the
magnetization component perpendicular to the reflection surface.

In the experiment, linearly polarized light is incident perpendicular to the
sample face, thus, it is only sensitive to the perpendicular component of the
surface magnetization vector. Unlike Kerr spectroscopies, we use a polarized-
light optical microscope where the transmitted through an analyzer light
intensity reveals a real-space 2D image of the Kerr rotation angle,
proportional to local magnetization amplitude. Up and down directions of
surface magnetization cause rotation clockwise and counter-clockwise. With a
slightly misaligned analyzer (1-3 degrees away from 90 degrees) this results
in the optical contrast where “up” domains are lighter and “down” domains are
darker. The imaging was performed with Olympus polarized microscope mounted
above a closed cycle 4He cryostat (Montana Instruments) with the ability to
apply a magnetic field along and perpendicular to the sample. The sample was
mounted on a gold-plated copper cold finger with a dash of Apiezon grease.

Total energy and density of states with spin-orbit coupling (SOC) in density
functional theory Hohenberg and Kohn (1964); Kohn and Sham (1965) (DFT) have
been calculated with PBE Perdew et al. (1996) exchange-correlation functional,
a plane-wave basis set and projected augmented wave method Blöchl (1994) as
implemented in VASP. Kresse and Furthmüller (1996, 1996) To account for the
half-filled strongly localized Eu 4f orbitals, a Hubbard-like Dudarev et al.
(1998) U is used. For A-type anti-ferromagnetic (AFMA) and ferromagnetic (FM)
EuCd2As2, the hexagonal unit cell is doubled along the c-axis and calculated
on a $\Gamma-$centered Monkhorst-Pack Monkhorst and Pack (1976) (11$\times$
11$\times$ 3) $k-$point mesh with a Gaussian smearing of 0.05 eV. A kinetic
energy cutoff of 254 eV and experimental lattice parameters Schellenberg et
al. (2011) have been used with atoms fixed in their bulk positions. To
calculate the energy difference between AFMA and FM with doping, the total
energy of a charged cell with a uniform neutralizing background Makov and
Payne (1995) has been used.

##  III Results and Discussion

Figure 5: The low temperature dependences of normalized resistance
$R/R_{300K}$, the temperature derivative of the normalized resistance
$d[R(T)/R_{300K}]/dT$, temperature dependent magnetization divided by field
$M(T)/H$, and the derivative $dM/dT$ plotted together for $T\leq 30~{}$K for
$x=0.0008(1)$ and $x=0.0040(3)$ Ag substituted samples. (a) $M(T)/H$ plotted
along with the temperature derivative $dM/dT$ for $H=50~{}$Oe field cooled in
$H\parallel c$ direction and (b) $H\perp c$ direction for $x=0.0008(1)$
substitution. (c) $R/R_{300K}$ and $d[R(T)/R_{300K}]/dT$ for $x=0.0008(1)$
substitution. The peak positions in $d[R(T)/R_{300K}]/dT$, more or less
coincides with the feature in $M(T)/H$. Panels (d), (e), and (f) show similar
data for $x=0.0040(3)$ sample. The low field $M(T)$ and zero field $R(T)$ have
small Sn features, therefore we truncate data below $T_{c}$ of Sn. Dotted
lines show the transition temperatures determined from $d[R(T)/R_{300K}]/dT$.

###  III.1 Structure and substitution

The concentration of Ag and Na determined from WDS for various initial
concentrations used for synthesis are given in Table 1. It is worth
highlighting the extremely small amounts of Ag and Na that can be incorporated
in to the EuCd2As2 system. Although we started the synthesis with nominal
concentration of $10\%$ \- $20\%$ for Na and $5-30\%$ for Ag, the actual
concentration of dopants in the crystals, as determined from WDS are orders of
magnitude smaller. With very small concentrations of Ag and Na going in, and
the changes in carrier density (indicated by resistivity behavior as will be
discussed later), we are using the words substitution and doping
interchangeably from here on. For Ag substituted samples, there is a very
small but discernible decrease in the amount of Cd obtained in EDS, which
suggests that Ag is going into the Cd sites. No such trends were seen in Na
doped samples, we are assuming it is going into the Eu sites. These data
indicate that there is a rather narrow width of formation for Na and Ag to go
into the EuCd2As2 structure. For many compounds such small doping levels would
be irrelevant, but given EuCd2As2’s extreme sensitivity to small deviations
from stoichiometry Jo et al. (2020); Sanjeewa et al. (2020); Taddei et al.
(2022) probing even this narrow width of formation is necessary and revealing.

Figure 1 (a) shows the powder x-ray diffraction data for various samples. This
confirms the $P\bar{3}m1$ structure for all the substituted crystals with
minimal change in peak position. The small impurity peaks, denoted by black
and red stars in Fig. 1, identified in some of the patterns are from Sn and
NaSn2As2 impurity phases respectively. The lattice parameters $a$ and $c$, as
determined by fitting the power x-ray diffraction data, are shown in Fig. 1
(b) and (c) respectively. This shows the changes in lattice parameters with
Ag- and Na-substitution are minimal and within error bars, which would be
consistent with very small amounts of Ag and Na content in the crystals.

###  III.2 Temperature dependent magnetization and resistivity data and
constructing the phase diagrams

Figure 6: The low temperature dependences of normalized resistance
$R/R_{300K}$, the temperature derivative of the normalized resistance
$d[R(T)/R_{300K}]/dT$, temperature dependent magnetization divided by field
$M(T)/H$, and the derivative $dM/dT$ plotted together for $T\leq 30~{}$K for
$y=0.005(1)$ and $x=0.008(1)$ Na substituted samples. (a) $M(T)/H$ plotted
along with the temperature derivative $dM/dT$ for $H=50~{}$Oe field cooled in
$H\parallel c$ direction and (b) $H\perp c$ direction for $y=0.005(1)$
substitution. (c) $R/R_{300K}$ and $d[R(T)/R_{300K}]/dT$ for $x=0.005(1)$
substitution. The peak positions in $d[R(T)/R_{300K}]/dT$, more or less
coincides with the feature in $M(T)/H$. Panels (d), (e), and (f) show similar
data for $x=0.008(1)$ sample. The peak positions in $d[R(T)/R_{300K}]/dT$,
more or less coincides with the feature in $M(T)/H$. The low field $M(T)$ and
zero field $R(T)$ have small Sn features, therefore we truncate data below
$T_{c}$ of Sn. Dotted lines show the transition temperatures determined from
$d[R(T)/R_{300K}]/dT$.

We will first present the temperature dependent electrical resistance and
magnetization data, examine the effects of Na- and Ag-substitutions on the
ground state as well as the higher temperature properties and construct a
temperature-substitution phase diagram. Figure 2 (a) and (b) shows the
resistivity $\rho$ as a function of temperature for Ag and Na-substituted
samples on a semi-log scale, with the inset showing low temperature behavior
for the substituted samples more clearly. Figure 12 in the appendix shows the
data for the undoped EuCd2As2 in an Arrhenius plot, showing that below roughly
$50~{}$K the temperature dependence of the resistivity data can be fit well
with an $\sim$ 5-6 meV gap. Although the absolute value of resistivity for the
undoped sample might be prone to error because of the relatively high contact
resistances, the orders of magnitude difference is probably inherent to the
sample itself. It is also worth noting that this value differs from that
reported in the literature, Ma et al. (2019); Du et al. (2022) but given that
EuCd2As2 appears to be close to the realm of semiconducting physics, where
small doping changes the resistivity immensely, widely varying resistivity
depending on the differing sample quality are not surprising. High purity Ames
Laboratory Eu, along with other elements used in the synthesis of samples for
this study may lead to lower accidental doping levels, thereby changing the
resistivity drastically. As soon as we start chemical substitution the
resistivity values drop two orders of magnitude at $300~{}$K, and the
significant upturn in resistance of undoped EuCd2As2 became less pronounced,
but remains clearly resolvable (Fig. 2 inset). The upturn in the undoped
sample has been attributed to strong magnetic fluctuations existing in this
low carrier density system, Rahn et al. (2018); Ma et al. (2019) or formation
of ferromagnetic clusters in similar systems. Sunko et al. (2022) Hence a
reduced up turn might be denoting reduced magnetic fluctuations, possibly
along with a higher carrier density leading to more metallic-like behavior.
Two clear features (denoted by red arrows for $x=0.0055(3)$ sample as an
example) are seen in the low temperature resistance data for both Ag and Na
doped samples, shown in the inset of Figs. 2 (a) and (b), corresponding to the
two transitions which will be discussed in detail later in the text.

Temperature dependent magnetization, $M(T)$, divided by applied field, $H$,
for $3.8~{}$K$\leq T\leq 35~{}$K, for various Ag-substituted samples are shown
in Fig. 3 (a) for applied magnetic field parallel to the crystallographic
$c$-axis and (b) for field in the $ab-$plane. The data were taken while
cooling down with the applied field of $50~{}$Oe (zero field cooled data shown
in Appendix Fig. 15). There is roughly an order of magnitude difference
between the $M(T)/H$ for the $H\parallel c$ and $H\perp c$ directions with the
$c-$axis being the harder direction and the basal plane being the easier
direction. Additionally, whereas the in-plane magnetization shows a rapid
increase and lower temperature plateau like a transition with a ferromagnetic
component, in the $T$ range 12-18 K for various samples, field parallel to
$c-$axis data shows more complicated behavior. There is a clear transition
around 10 K, below which $M/H$ is decreasing for samples with low
substitution, and increasing for samples with high Ag-substitution. At the
same time, there also exists a less noticeable feature at a higher temperature
(e. g. $T\sim 18~{}$K for $x=0.004$ sample), which shifts further upward with
increased doping.

Figure 4 shows the temperature dependent magnetization (field cooled) data for
the Na doped samples. The behavior of $M(T)/H$ for the Na-substituted samples
is very similar to that of Ag-substituted samples. Crystallographic $c-$ axis
remains the harder direction with $M(T)/H$ values with applied field along the
$c-$axis being almost 10 times smaller than the in-plane magnetization. The
in-plane $M(T)/H$ shows a sudden jump around $15-17~{}$K for both the Na doped
samples, whereas magnetization with applied field parallel to $c-$axis shows a
clear feature around $10~{}$K with a subtle higher temperature ($\sim 17~{}$K)
feature for the $y=0.008$ sample, similar to the Ag doped samples.

In order to follow the features in $R/R_{300K}(T)$ and $M(T)/H$ more clearly
and to understand their behavior, we have plotted the magnetization divided by
field $M(T)/H$ measured at $H=50~{}$Oe in both directions with it’s
temperature derivatives $dM/dT$ along with the normalized resistance
$R(T)/R_{300~{}K}$ measured at zero field, and derivative of resistance
$d[R(T)/R_{300~{}K}]/dT$, for two samples with Ag-substitution in Fig. 5 and
Na substituted samples in Fig. 6. Similar plots for the rest of the Ag doped
samples are shown in Appendix Fig. 16.

Figures 5 (a) and (b) show the anisotropic $M(T)/H$ and $dM/dT$ for the
$x=0.0008$ Ag substituted sample. Figure 5 (c) shows the normalized resistance
and temperature derivative of the normalized resistance for the same sample.
Similar plots for Ag doping $x=0.0040$ are shown in Figs. 5 (d), (e), and (f).
Whereas the $R(T)/R_{300~{}K}$ data, and its temperature derivative show two
clear features, the anisotropic $M(T)/H$ sets each show only one conspicuous
feature. For $H\perp c$, the rapid increase in magnetization that suggests a
ferromagnetic component to the ordering agrees well with the higher
temperature feature in the resistance data. For $H\parallel c$, the clearer
feature in the $M(T)/H$ data agrees with the lower temperature feature seen in
the $R(T)/R_{300~{}K}$ data, and its temperature derivative. For higher Ag-
substitution levels there may be a small higher temperature shoulder
associated with the higher transition temperature for $H\parallel c$, but this
is subtle. The two transitions from $d[R(T)/R_{300~{}K}]/dT$ and $dM/dT$ have
been identified as $T_{mag1}$ and $T_{mag2}$, and are plotted in the phase
diagram in Fig. 7 (a).

A similar analysis has been carried out on the data for the Na-substituted
compound. Fig. 6 (a) and (b) show the anisotropic $M(T)/H$ and $dM/dT$ for the
$y=0.005$ Na substituted sample. Figure 6 (c) shows the normalized resistance
and temperature derivative of the normalized resistance for the same sample.
Similar plots for Na doping $y=0.008$ are shown in Figs. 6 (d), (e), and (f).
The two features are clearly seen in the resistance data and its derivatives
shown in blue. Anisotropic $M(T)/H$ shows features similar to Ag-substituted
samples. Whereas for $H\perp c$, $M(T)/H$ shows a sudden increase, with the
transition temperature agreeing with the higher temperature feature in
$R(T)/R_{300~{}K}$, $H\parallel c$ data has a prominent feature corresponding
to the lower temperature transition and a subtle feature for the higher
temperature one. The transition temperatures $T_{mag1}$ and $T_{mag2}$
determined form $d[R(T)/R_{300~{}K}]/dT$ and $dM/dT$ are used to plot the
phase diagram in Fig. 7 (b).

Figure 7: (a) Temperature-doping ($T-x$) phase diagrams for Ag substituted
EuCd2As2. Open-crossed and closed symbols show the transition temperatures
from $dM/dT$ and $d[R(T)/R_{300K}]/dT$ respectively. (b) Temperature-doping
($T-y$) phase diagrams for Na substituted EuCd2As2

The transition temperatures obtained from $R(T)$ and $M(T)$ curves can now be
used to construct $T-x$ phase diagrams as shown in Fig. 7 for Ag- and Na-
substituted EuCd2As2. The transition temperatures were determined by taking
the extrema in $d[R/R_{300~{}K}]/dT$ Fisher and Langer (1968) and $dM/dT$. For
Ag- and Na-substitution (Fig. 7 (a) and (b) respectively), one can clearly see
$T_{mag1}$ remaining more or less constant with substitution, and with finite,
and increasing substitution a new transition, at $T_{mag2}$, appears and
increases with substitution level. We can try to understand this along with
the insights from the magnetization and resistance data as follows: With Ag-
and Na-substitution in EuCd2As2, we are splitting the magnetic transition that
was initially at $T_{N}=9.2~{}$K in to two, one that is denoted by $T_{mag1}$
that is remaining unchanged, and one denoted by $T_{mag2}$ that shows a
gradual increase with increased chemical substitution. One can further
speculate, the transition corresponding to $T_{mag2}$ is associated with a
ferromagnetic alignment of moments in the $ab-$plane, as would be supported by
the prominent feature in the in-plane $M/H$ measurement. In this case, the
chemical substitution seems to play a key role in splitting a transition into
two separate transitions, which is similar to what was observed in La doped
EuPd3S4. Ryan et al. (2022)

Figure 8: Magneto optical images of EuCd2As2, Ag doped sample $x=0.0055$, and
Na doped sample with $y=0.008$. (a) Undoped EuCd2As2 at $T=5.2~{}$K, which is
below $T_{N}$, not showing magnetic domains. (b) Eu0.992Na0.008Cd2As2 crystal
at $T=20~{}$K, above $T_{mag2}$, not showing any contrast due to domain
formation. (c) Same sample at $T=5.2~{}$K, below both magnetic transitions,
after cooling in zero field and $H=0$, showing ferromagnetic domain formation
seen as green and purple colored regions in the images. Similar images for
Eu(Cd0.9945Ag0.0055)2As2 shown in (d) at $T=50~{}$K above Tmag2 and (e) at
$T=4~{}$K, with no applied field. (f) Eu(Cd0.9945Ag0.0055)2As2 sample at
$T=4~{}$K with an in-plane magnetic field $H=250~{}$Oe applied. Both (e) and
(f) show formation of domains.

###  III.3 Magneto-optical Kerr effect

Before studying the field dependent magnetization and magnetoresistance of
these samples, it is useful to further confirm that the low temperature state
of these substituted samples indeed have a zero field, ferromagnetic
component. As was the case for the EuCd2As2 samples grown from NaCl/KCl salt
mixtures Jo et al. (2020) magneto optical measurements, shown in Fig. 8, show
the formation of clear magnetic domains below the transition temperatures for
$x=0.0055$ and $y=0.008$ Ag- and Na-substitution. Figure 8 (a) shows the pure
EuCd2As2 sample, where no domains are visible even below the magnetic
transition temperature. Furthermore, Figs. 8 (b) and (d) show the Na and Ag
doped samples $y=0.008$ and $x=0.0055$, at $20~{}$K and $50~{}$K respectively,
above both magnetic transitions. Once again, these show no domain formation.
At lower temperatures, both these samples show clear domain formation as shown
in Figs. 8 (c) and (e). Comparison of Figs. 8 (e) and (f) demonstrates that
the application of $250~{}$Oe along the $ab-$plane changes the size of the
observed domains, which indicates that the domains are indeed magnetic in
origin. Similar experiments were conducted with application of a magnetic
field along the $c-$axis. Even though this is the harder magnetic axis,
domains showed a change in size and shape (Appendix Fig. 26). These data
demonstrate that at low temperatures, the zero field magnetic state in the
doped samples has an unambiguous ferromagnetic component in the $ab-$plane.

Figure 9: (a) Magnetization $M$ as a function of $H$, with applied field
$H\parallel c$, for Eu(Cd1-xAgx)2As2 samples. (b) $M(H)$ with field $H\perp c$
for Ag doped EuCd2AS2 samples. Inset: $M(H)$ at the low field region
$H<1.2~{}$kOe for $H\perp c$ direction, showing the sharp rise. (c)
Magnetization $M$ as a function of $H$, with applied field $H\parallel c$, for
Eu1-yNayCd2As2 samples. (d) $M(H)$ with field $H\perp c$ for Na doped EuCd2AS2
samples. Inset: $M(H)$ at the low field region $H<1.2~{}$kOe. All $M(H)$ data
were normalized to give the saturated moment of $7~{}\mu_{B}$, which is the
value expected for Eu2+. Figure 10: Normalized resistance $R/R_{0}$ (where
$R_{0}$ is the resistance at zero field) as a function of $H$ for Ag-
substituted samples with (a) $H\parallel c$ and (b) $H\perp c$. Panels (c) and
(d) show the measurement results for Na-substituted samples

###  III.4 Magnetization and magnetoresistance

Figure 11: (a) Energy difference $\Delta E_{(AFM-FM)}$ in meV per formula unit
(meV/f. u.) as a function of doping $(\Delta Q)$ for various values of $U$.
Positive values in $\Delta E$ show the doping region for which FM state is
stable. (b) The density of states (DOS) projected on Eu 4f, showing the change
of the distance between Eu 4f band and $E_{F}$ upon doping.

In order to gain further insight into how Ag- and Na-substitutions affect the
magnetic ground state of EuCd2As2 we have performed anisotropic $M(H)$ and
$R(H)$ measurements on our samples. The base temperature anisotropic $M(H)$
for Ag-substituted EuCd2As2 data is shown in Fig. 9 (a) and (b) whereas the
anisotropic $M(H)$ for Na-substituted EuCd2As2 data is shown in Fig. 9 (c) and
(d). All $M(H)$ data were normalized to give the saturated moment of
$7~{}\mu_{B}$, which is the value expected for Eu2+. This is to avoid sample
dependence and errors due to different mounting. Figure 10 shows the base
temperature anisotropic $R(H)$ data for Ag- and Na-substituted EuCd2As2. In
the appendix (Figs. 20 \- 25) we plot the $M(H)$ (without normalization) and
$R(H)$ data for each sample and direction of field separately for more direct
comparison of field induced features.

From the $M(H)$ data we can see that as Ag and Na are substituted, a
ferromagnetic component develops in the basal plane, whereas the changes in
the $M(H)$ behavior for $H\parallel c$ are far more subtle. For $H\perp c$, as
$x$ or $y$ increases there is a dramatic increase in the low field slope and,
as shown in the previous section, the establishment of a ferromagnetic
component along with ferromagnetic domains. There is a step-like change in the
magnetization between pure EuCd2As2 and the lowest $x-$ or $y-$values with the
pure sample being in a clear antiferromagnetic state and the samples with
finite Ag- or Na-substitution exhibiting $M(H)$ data consistent with a degree
of ferromagnetic ordering. The rapid rise in $M(H)$ persists to roughly
$0.5~{}$kOe, after which the $M(H)$ enters an intermediate state, finally
saturating by $\sim 8~{}$kOe. As $x$ or $y$ increases the size of the moment
associated with the low field roll over increases, reaching roughly
$4~{}\mu_{B}$ per Eu2+ (out of the $7~{}\mu_{B}$ associated with fully
saturated Eu2+). The temperature evolution of the various features in $M(H)$
for the Ag doped sample with $x=0.0019$, with applied field $H\perp c$ was
studied systematically, and plotted in the $H-T$ phase diagram shown in Fig.
19 in Appendix.

For $H\parallel c$ the effect of substitution is relatively small. Whereas for
pure EuCd2As2 it takes $\sim 17~{}$kOe to complete a spin flip process, Ag-
and Na-substitution lower this field to $\sim 12$ or $\sim 15~{}$kOe
respectively. As will be discussed below, there are subtle changes in the
slope of $M(H)$ below this saturation field, but these changes are more
clearly inferred from the $R(H)$ data.

The anisotropic $R(H)$ data is shown in Fig. 10. Figure 10 (a) and (b) show
the anisotropic $R(H)$ data for the Ag substituted samples and Fig. 10 (c) and
(d) show the data for Na substituted samples. The primary point that can be
extracted from Fig. 10 is that, for each direction of applied field, the
$R(H)$ saturates once the $M(H)$ saturates. Given that magnetic anisotropy
seen in Fig. 9, the saturation in $R(H)$ occurs around $5-8~{}$kOe for $H\perp
c$ and around $15-18~{}$kOe for $H\parallel c$. It is worth emphasizing that
the $M(H)$ and $R(H)$ data demonstrate that for pure and doped EuCd2As2, the
base temperature $R(H)$ is dominated by scattering off of the Eu2+ moment and
its excitations.

More detailed insight can be drawn from individual comparison of the
anisotropic $M(H)$ and $R(H)$ data shown for each sample in Figs. 20-25 in the
appendix section. For $H\perp c$, the majority of the change in resistance
occurs between the $\sim 0.5~{}$kOe saturation of the FM component and the
$\sim 5-8~{}$kOe saturation. This suggests that whereas aligning the FM
domains does not significantly change scattering, aligning the Eu moments
through what is most likely some form of spin rotation leads to a significant
reduction of scattering. Once the Eu moments are fully aligned with the
applied field the $R(H)$ saturates and becomes essentially field independent.
For $H\parallel c$, $R(H)$ data show clear signs of an intermediate field
transition. This is particularly clear for the Na-doped samples (Figs. 24 and
25 ). For example, for $y=0.005$, although the $M(H)$ and $R(H)$ data saturate
around $17~{}$kOe, there is a broad feature in $R(H)$ around $6~{}$kOe. At the
same field the $M(H)$ has a subtle, but discernible, change to a slightly
shallower, higher field, slope. Similar features in both $H\parallel c$,
$R(H)$ and $M(H)$ can be seen for other Na-substituted sample as well as some
of the Ag-substituted ones. These features suggest that for $H\parallel c$
there may be an intermediate field change in ordered state. Ultimately this
will need to be examined by diffraction measurements.

Given the ability to compare $R(H)$ and $M(H)$ for the Ag- and Na-substituted
samples it is worthwhile to compare these data with $R(H)$ data taken under
pressure. Gati et al. (2021) In Ref. Gati et al., 2021 the saturation field
for the $H\perp c$, $R(H)$ data was tracked as a function of pressure and when
it was suppressed to zero a transition to a pressure induced FM state was
inferred. As we can now see for Ag- and Na-substituted samples, we can have a
FM component to our zero field ground state without having reached a
saturation point in the $R(H)$ data. Indeed, what we do see is that for the
Ag- and Na- substituted samples we have studied the $R(H)$ is decreasing with
field rather than increasing (as it does for pure EuCd2As2 at ambient pressure
as well as for $p\lesssim 1.67~{}$GPa) when the sample is in a state with an
FM component. Based on the Ag- and Na-substituted data we may now speculate
that for $1.67~{}$GPa $<p<2.05$ GPa, pure EuCd2As2 may be in a magnetic state
with a ferromagnetic component similar to what we find for Ag- and Na-
substituted compounds. This range of pressure is also where an insulator to
metal transition at low temperatures is reported for the undoped compound. Du
et al. (2022) For $p>2.05~{}$GPa pure EuCd2As2 would then be in a FM state
with full Eu moments all co-aligned (i.e. fully saturated). This possibility
was already allowed for in Ref. Gati et al., 2021, specifically in the
shading/color coding of the temperature - pressure phase diagram shown in its
figure 3 and associated text.

###  III.5 DFT Calculations

Since chemical substitution both at the magnetic Eu site (by Na), and at the
non magnetic Cd site (by Ag), lead to similar magnetic behavior and $T-x$
phase diagrams, one likely mechanism behind it can be a change in band
filling/density of states near the Fermi energy ($E_{F}$) and its effect on
magnetic coupling. This is further supported by the DFT calculation shown in
Fig. 11. In rare-earth containing compounds, the magnetic interaction between
the $f-$electrons is often mediated by the conduction electrons through the
$RKKY$ mechanism. In the case of EuCd2As2, Eu $4f$ magnetic exchange
interaction between layers is mediated by the free electron like hole pockets
from As $p$ derived bands around $E_{F}$. The preference of AFM or FM ground
state is affected by the energy separation ($\sim 1.0~{}$eV) between Eu $4f$
and As $p$ bands at $E_{F}$, which can be tuned by exchange splitting strength
$U$ and number of electrons removed $\Delta Q$. The calculated difference in
energy between the AFM-A state and FM state, $\Delta E(AFM-FM)(\Delta Q)$ for
various values of $U$ are shown in Fig. 11 (a), capturing the FM phase being
stabilized by very small changes in band filling at $E_{F}$, consistent with
the substitution levels actually used in this work. The calculations were made
with the moments along one of the equivalent $a-$ or $b-$axis. The $U$ values
chosen are close to those in recent studies,Gati et al. (2021); Yu et al.
(2022) which use lower values of $U$ than earlier studies, Wang et al. (2019);
Jo et al. (2020) in order to predict the transitions with pressure more
precisely. Fig. 11 (b) shows the density of state (DOS) projected on Eu 4f,
showing the change of the distance between Eu 4f band and $E_{F}$ upon doping.
When electrons being removed, i. e. hole doping, moves Eu-$4f-$ DOS closer to
$E_{F}$, the inter layer FM coupling becomes more favorable than AFM.

##  IV Conclusion

In summary, we have synthesized single crystals of Eu(Cd1-xAgx)2As2 and
Eu1-yNayCd2As2 and constructed temperature-substitution phase diagrams. We
have shown that Ag and Na substituted EuCd2As2 shows a splitting of a single
magnetic transition in pure EuCd2As2 into two transitions, with a
ferromagnetic component stabilized below both the transitions. We also propose
a change in band filling as the possible mechanism to stabilize
ferromagnetism, supported by theoretical calculations. These data underscore
just how delicately balanced the magnetic state in EuCd2As2 is and illustrates
how chemical substitution and changing the band filling can be the pathways to
stabilize a ferromagnetic ground state, and thereby possibly tune the various
topological features predicted in the electronic structure of this material.

###### Acknowledgements.

We thank Warren Straszheim for the EDS/WDS measurements. We also acknowledge
D. H. Ryan, T. J. Slade, and N. H. Jo for the useful discussions. Work at the
Ames National Laboratory was supported by the U.S. Department of Energy,
Office of Science, Basic Energy Sciences, Materials Sciences and Engineering
Division. The Ames National Laboratory is operated for the U.S. Department of
Energy by Iowa State University under Contract No. DEAC0207CH11358. B. K. was
supported by the Center for the Advancement of Topological Semimetals, an
Energy Frontier Research Center funded by the U.S. DOE, Office of Basic Energy
Sciences. L.X. was supported, in part, by the W. M. Keck Foundation and the
Gordon and Betty Moore Foundations EPiQS Initiative through Grant GBMF4411.

## Appendix

###  IV.1 X-ray diffraction

Lattice parameters obtained from the Rietveld refinement of powder X-ray
diffraction data are given in Table 2 and 3. For Ag-substituted data, the
values given are average of three runs on three different samples from each
batch of sample. The goodness of fit $wR$ value given in the table are the
worst among various fits for each Ag-substituted sample. The refinements (for
both Ag and Na) were carried out with fixing the fraction of all the elements
to full occupancy, as allowing them to vary ended up with nonphysical results.
The variation in lattice parameters is not resolvable and within the error
bars.

Eu(Cd1-xAgx)2As2 | $x=0.0008(1)$ | $x=0.0019(3)$ | $x=0.0040(3)$ | $x=0.0055(3)$
---|---|---|---|---
$a(\AA)$ | 4.4410(4) | 4.4407(5) | 4.440(1) | 4.4404(4)
$c(\AA)$ | 7.3292(3) | 7.3296(2) | 7.327(1) | 7.328(3)
$wR$(%) | 17.62 | 19.19 | 17.72 | 17.01
Table 2: The average lattice parameters obtained from Rietveld refinements of Ag substituted EuCd2As2. The goodness of fit $wR$ values given are the worst among the various fits on each sample. Eu1-yNayCd2As2 | $y=0$ | $y=0.005(1)$ | $y=0.008(1)$
---|---|---|---
$a(\AA)$ | 4.4408(5) | 4.4412(3) | 4.4415(3)
$c(\AA)$ | 7.3289(4) | 7.3291(3) | 7.3284(3)
$wR$(%) | 14.49 | 12.27 | 13.98
Table 3: The lattice parameters obtained from Rietveld refinement of pure and
Na substituted EuCd2As2.

###  IV.2 Temperature dependent conductivity of pure EuCd2As2

Figure 12 presents the temperature dependent conductivity of EuCd2As2 on an
Arrhenius plot. Below $\sim 50~{}$K there is an activated behavior the
persists down to the magnetic ordering temperature, at which point there is a
loss of spin-disorder scattering feature. The gap value that can be extracted
from this behavior is roughly $5-6~{}$meV, consistent with the temperature
range over which we see the Arrhenius behavior.

Figure 12: Arrhenius plot showing logarithm of electrical conductivity,
$\ln\sigma$ as a function of $1/T$ for the undoped EuCd2As2. Inset shows the
region where a linear fit has been done for temperatures between $14~{}$K and
$29~{}$K. An energy gap of $\Delta=5.5~{}$meV is obtained from the slope,
using $\sigma\propto\exp(-E_{g}/2k_{B}T)$.

###  IV.3 Magnetization

Figure 13: Polycrystalline average of magnetization divided by field $M/H$, as
a function of temperature for undoped EuCd2As2, and Ag doping $x=0.0019$, with
an applied field of $H=1~{}$kOe. Inverse susceptibility, $H/M$, plotted on the
right axis for the two samples, along with Curie-Weiss fit for each. The
effective moment and Weiss temperature obtained from the fitting parameters
are given in Table 4.

The Curie-Weiss fit of the inverse of magnetic susceptibility, $H/M$, in the
temperature range $50-250~{}$K, is shown in Fig. 13 for the undoped EuCd2As2
and Ag-doped sample with $x=0.0019$. The fitting parameters give an effective
moment, $\mu_{eff}=7.82\pm 0.02~{}\mu_{B}$, and Weiss temperature,
$\theta=10.30\pm 0.04$ K for the pure compound. Similar fits were done on the
inverse of polycrystalline averaged $M(T)/H$ for all the substituted samples.
The values obtained from those are tabulated in Table. 4. The $\mu_{eff}$
values are more or less consistent with the expected value of
$7.94~{}\mu_{B}$. The Weiss temperature $\theta$ varies with doping, showing a
slight increase with doping. A plot showing the variation of $\theta$ with the
substitution concentration $x$ and $y$ is shown in Fig. 14. The bottom
$x-$axis show the Ag concentration, and the top $x-$axis show Na
concentration, scaled by a factor of two. This is because Ag doping
corresponds to 2 electrons being removed per formula unit, as Ag atoms are
replacing two Cd atoms in each formula unit. There is an increase in $\theta$
with doping, roughly corresponding to the increase in transition temperatures
$T_{mag2}$.

Sample |  $\mu_{eff}$($\mu_{B}$) |  $\theta$ (K)
---|---|---
$x=0$, $y=0$ | 7.82$\pm$0.02 | 10.30$\pm$0.04
$x=0.0008(1)$ | 7.83$\pm$0.02 | 15.34$\pm$0.04
$x=0.0019(3)$ | 7.85$\pm$0.03 | 15.12$\pm$0.06
$x=0.0040(3)$ | 7.62$\pm$0.04 | 17.6$\pm$0.1
$x=0.0055(3)$ | 7.68$\pm$0.03 | 17.55$\pm$0.06
$y=0.005(1)$ | 7.7$\pm$0.2 | 14.2$\pm$0.4
$y=0.008(1)$ | 7.78$\pm$0.09 | 14.5$\pm$0.2
Table 4: The effective moment and Weiss temperature for various Ag and Na
substituted EuCd2As2 samples, obtained from Curie-Weiss fits to the inverse
magnetic susceptibility data above the transition temperature. The error bars
are calculated considering error in mass of the crystals and fitting errors.
Figure 14: Curie-Weiss fitting parameter $\theta$ as a function of Ag- and Na-
substitution, $x$ and $y$. Top axis has been scaled by two, as Na-substitution
nominally changes 1 electron per formula unit, where as Ag-substitution
changes two electrons per formula unit, as there are two Cd atoms. Figure 15:
$M/H$ as a function of temperature for selected samples with an applied field
of $H=50~{}$Oe. Measurements done with increasing temperature after zero field
cooling (ZFC), and with decreasing temperature with field cooling (FC),
denoted by open and closed symbols respectively. The data shown is above
$T=3.8~{}$K, as there were slight features below that, due to presence of Sn
(flux) in the sample which goes superconducting below this temperature. (a)
Applied field parallel to crystallographic $c$ direction and (b) Field in the
$ab-$plane.

Figure 15 shows $M(T)/H$ data for zero field cooled (ZFC) and field cooled
(FC) measurements for a selected set of Ag and Na substituted samples of
EuCd2As2 above $T=3.8~{}$K to avoid features due to superconductivity from Sn
flux present in some samples. The in-plane measurement shows almost
overlapping data for ZFC and FC measurements on Ag substituted samples,
whereas the ZFC and FC curves split with increased substitution with field
$H\parallel c$. This could be indicating a possible non-collinear or helical
order along the $c-$ direction with moments aligned ferromagnetically in-
plane. The splitting of ZFC FC in both directions for the Na doped sample
might be indicating a possible canting.

Figures 16 (a) and (b) show the anisotropic $M(T)/H$ and $dM/dT$ for the
$x=0.0019$ Ag substituted sample. Figure 5 (c) shows the normalized resistance
and temperature derivative of the normalized resistance for the same sample.
Similar plots for Ag doping $x=0.0055$ are shown in Figs. 16 (d), (e), and
(f). Whereas the $R(T)/R_{300~{}K}$ data, and its temperature derivative show
two clear features, the anisotropic $M(T)/H$ sets each show only one
conspicuous feature. For $H\perp c$, the rapid increase in magnetization that
suggests a ferromagnetic component to the ordering agrees well with the higher
temperature feature in the resistance data. For $H\parallel c$, the clearer
feature in the $M(T)/H$ data agrees with the lower temperature feature seen in
the $R(T)/R_{300~{}K}$ data, and its temperature derivative.

Figure 16: The low temperature dependences of normalized resistance
$R/R_{300K}$, the temperature derivative of the normalized resistance
$d[R(T)/R_{300K}]/dT$, temperature dependent magnetization divided by field
$M(T)/H$, and the derivative $dM/dT$ plotted together for $T\leq 30~{}$K for
$y=0.005(1)$ and $x=0.008(1)$ Na substituted samples. (a) $M(T)/H$ plotted
along with the temperature derivative $dM/dT$ for $H=50~{}$Oe field cooled in
$H\parallel c$ direction and (b) $H\perp c$ direction for $y=0.005(1)$
substitution. (c) $R/R_{300K}$ and $d[R(T)/R_{300K}]/dT$ for $x=0.005(1)$
substitution. The peak positions in $d[R(T)/R_{300K}]/dT$, more or less
coincides with the feature in $M(T)/H$. Panels (d), (e), and (f) show similar
data for $x=0.008(1)$ sample. The peak positions in $d[R(T)/R_{300K}]/dT$,
more or less coincides with the feature in $M(T)/H$. The low field $M(T)$ and
zero field $R(T)$ have small Sn features, therefore we truncate data below
$T_{c}$ of Sn. Dotted lines show the transition temperatures determined from
$d[R(T)/R_{300K}]/dT$.

###  IV.4 $H-T$ Phase diagram for Eu(Cd1-xAgx)2As2 with $x=0.0019$ and applied
field $H\perp c$

Figure 17: (a) Magnetization as a function of applied field, $M(H)$, up to
$10~{}$kOe for various temperatures between $1.8~{}$K and $20~{}$K. (b)
Derivative of magnetization with field, $dM/dH$ as a function of field up to
$10~{}$kOe for various temperatures between $1.8~{}$K and $20~{}$K. Inset
shows the criteria for determining the transition points (marked by arrows
pointing at them), where change of slope is determined by taking the
intersection of straight lines drawn. All measurements shown are for field
applied $H\perp c$, on the Ag doped sample with $x=0.0019$. Figure 18: (a)
Magnetization divided by field as a function of temperature, $M(T)/H$, for
various applied fields between $50~{}$Oe and $10~{}$kOe. Inset: Derivative of
magnetization with temperature, $dM/dT$, for various applied fields. The
minima in these curves were chosen as the transition temperature for the $H-T$
phase diagram. (b) Normalized resistivity $R/R_{100~{}K}$ as a function of
temperature for various applied fields between $50~{}$Oe and $10~{}$kOe.
Inset: Temperature derivative of normalized resistance, $d(R/R_{100~{}K})/dT$,
for various applied fields. The extrema in these curves were chosen as the
transition temperature for the $H-T$ phase diagram. All measurements shown are
for field applied $H\perp c$, on the Ag doped sample with $x=0.0019$. Figure
19: $H-T$ phase diagram obtained from various $M(T)$, $M(H)$, and $R(T)$
measurements on Eu(Cd1-xAgx)2As2 with $x=0.0019$, for applied magnetic field
$H\perp c$. Points obtained from $M(H)$ measurements at various temperatures
are denoted by solid squares. Data points from $M(T)$ measurements at various
applied fields are plotted in open-crossed symbols, and those from $R(T)$ at
various fields are plotted with star symbols. Magnetic transition temperatures
at zero field $T_{mag1}$ and $T_{mag2}$ are shown by arrows.

The $T-x$ phase diagrams show existence of two magnetic phases with
temperature in low fields. In addition to this, field dependent magnetization
data $M(H)$ for Ag-doped samples with low doping, as well as Na-doped samples
show, a clear intermediate field phase existing in these samples, with applied
field $H\perp c$. In order see the temperature and field evolution of all
these different magnetic phases, we did systematic measurements of $M(T)$ at
various applied fields, $M(H)$ at various temperatures, and $R(T)$ at various
applied fields, to construct an $H-T$ phase diagram for the $x=0.0019$ Ag
doped EuCd2As2 sample. All the $M(T)$ and $R(T)$ data were measured on cooling
the sample from above $T_{mag2}$, with various applied fields. $M(H)$ data
were taken with increasing and decreasing magnetic fields up to $10~{}$kOe for
each temperature. There was no discernible hysteresis, and the data shown in
Fig. 17 were measured with decreasing fields. The transition temperatures and
fields were determined from the derivatives, as shown in the figures below.

Figure 17 (a) shows the $M(H)$ data taken at different temperatures, and the
derivatives, $dM/dH$ are shown in Fig. 17 (b). The criteria for determining
the fields corresponding to the transitions are shown in the inset. It can be
seen that the intermediate - field phase gets narrower with increasing
temperatures, and eventually disappears above $T_{mag1}$. The initial steep
increase in $M$ with $H$, persists until higher temperatures, and disappears
above $T_{mag2}$. This is consistent with the interpretation of initial
increase due to alignment of domains, into a state with net ferromagnetic
moment, and with higher fields all the moments getting aligned into a fully
saturated state. The derivatives $dM/dH$ were plotted, and change of slope
determined by drawing straight lines, to obtain the transition points. These
points are plotted in Fig. 19 using solid squares in black and blue.

Figure 18 (a) shows the $M(T)$ data at various applied fields between
$50~{}$Oe to $10~{}$kOe. The inset shows the derivatives $dM/dT$, the minima
of which was used to determine the transition temperatures. The data points
obtained so are plotted as open-crossed symbols in the phase diagram in Fig.
19. Similarly $R(T)$ data taken at various applied fields are shown in Fig. 18
(b), with the inset showing the derivatives $dR/dT$. At low fields, the
resistance curves and their derivatives show two transitions. With applied
field more than $400~{}$Oe, the higher temperature transition is not
resolvable, whereas the lower T transition remains independent of applied
field at low and intermediate fields, and start moving to higher temperatures
at larger fields. This behavior is traced by the extrema in $dR/dT$ curves,
and plotted in Fig. 19 with star shaped symbols, in black and red.

The $H-T$ phase diagram obtained from the measurements mentioned above is
plotted in Fig. 19. At lower field, there appears a dome like region below
$\sim 17~{}$K, which is presumably the phase with a net ferromagnetic moment,
which shows domain formation and alignment. As we go to higher fields, for
temperatures $T\leq T_{mag1}$, there appears another phase (whose boundary is
denoted by the blue symbols), before eventually getting into a fully polarized
state. There is also a nearly-vertical phase line, shown in red colored
symbols, starting at $T_{mag1}$ at zero field. It remains mostly temperature
independent with increasing fields, and crosses the black line around $H\sim
1~{}$kOe. With even higher fields, it seems to meet the blue line, and
eventually moves towards slightly higher temperatures in this regime. This
suggests one of the following possibilities allowed by the phase rules as a
likely scenario to explain the phase diagram: 1. There is a first order
structural transition (or electronic, Lifshitz-like) coinciding with the
magnetic transition around $9~{}$K, which is then weakly magnetic field
dependent, giving rise to the red line. But none of the previous studies have
reported such a transition in the pure compound, which makes this scenario
less likely. 2. The other possibility is that, we are falsely assigning a
transition temperature and field in the Brillouin-like, slowly saturating with
applied field, regime. In this case there is actually no phase transition
happening along the red line but a slow crossover. The low field red points
are likely the extension of the blue line. Thus the interpretation of this
$H-T$ phase diagram remains an open question at this point.

###  IV.5 Magnetization, Magnetoresistance and Magneto optics

A detailed comparison of the anisotropic $M(H)$ and $R/R_{0}(H)$ data,
measured at $1.8~{}$K for magnetization and $2~{}$K for resistance, are shown
for each sample in Figs. 20 \- 25. It can be easily seen that both $M(H)$ and
$R/R_{0}(H)$ data saturate at similar fields, showing the alignment of Eu
moments with the applied filed. Additionally, one can see the feature in
$R/R_{0}(H)$ in the intermediate fields corresponding well with the change in
slope of $M(H)$. For $H\perp c$ direction, $M(H)$ shows a steep increase at
low fields, followed by a slower increase at intermediate fields, and finally
saturates around $5-8~{}$kOe. Corresponding feature in the $R/R_{0}(H)$ data
is subtle and it shows gradual change at low - intermediate fields and
eventually saturates around the same field as $M(H)$ data. On the other hand,
for $H\parallel c$ direction of measurement, $R/R_{0}(H)$ shows a
clearer/stronger feature at the intermediate fields, corresponding to the less
prominent change of slope in $M(H)$ data. This is clearer in the $M(H)$ and
$R/R_{0}(H)$ of the Na-substituted EuCd2As2 samples as shown in Figs. 24 \-
25.

Figure 20: Magnetization as a function of field $M(H)$ measured at $T=1.8~{}$K
and normalized resistivity as a function of field $R/R_{0}(H)$ measured at
$T=2~{}$K for Ag doped EuCd2As2 with $x=0.0008(1)$. (a) Applied field
$H\parallel c$ (b) $H\perp c$ Figure 21: Magnetization as a function of field
$M(H)$ measured at $T=1.8~{}$K and normalized resistivity as a function of
field $R/R_{0}(H)$ measured at $T=2~{}$K for Ag doped EuCd2As2 with
$x=0.0019(3)$. (a) Applied field $H\parallel c$ (b) $H\perp c$ Figure 22:
Magnetization as a function of field $M(H)$ measured at $T=1.8~{}$K and
normalized resistivity as a function of field $R/R_{0}(H)$ measured at
$T=2~{}$K for Ag doped EuCd2As2 with $x=0.0040(3)$. (a) Applied field
$H\parallel c$ (b) $H\perp c$ Figure 23: Magnetization as a function of field
$M(H)$ measured at $T=1.8~{}$K and normalized resistivity as a function of
field $R/R_{0}(H)$ measured at $T=2~{}$K for Ag doped EuCd2As2 with
$x=0.0055(3)$. (a) Applied field $H\parallel c$ (b) $H\perp c$ Figure 24:
Magnetization as a function of field $M(H)$ measured at $T=1.8~{}$K and
normalized resistivity as a function of field $R/R_{0}(H)$ measured at
$T=2~{}$K for Na doped EuCd2As2 with $y=0.005(1)$. (a) Applied field
$H\parallel c$. The line is drawn to show the deviation from linear behavior,
corresponding to the feature in $R/R_{0}(H)$. (b) $H\perp c$ Figure 25:
Magnetization as a function of field $M(H)$ measured at $T=1.8~{}$K and
normalized resistivity as a function of field $R/R_{0}(H)$ measured at
$T=2~{}$K for Ag doped EuCd2As2 with $y=0.008(1)$. (a) Applied field
$H\parallel c$. The line is drawn to show the deviation from linear behavior,
corresponding to the feature in $R/R_{0}(H)$. (b) $H\perp c$

Magneto optical images of $x=0.0055(3)$ Ag-substituted EuCd2As2 with different
applied magnetic fields are shown in Fig. 26. Figure 26 shows images taken at
$T=4~{}$K with (a) zero applied field, (b) $H=880~{}$Oe along $H\parallel c$,
and (c) $H=250~{}$Oe in the $ab-$plane. All three show formation of domains,
which gets modified with applied filed, indicating that the domains are
magnetic in nature. This also shows that the domains change with applied
fields both along $c-$axis and in-plane.

Figure 26: Magneto optical images of EuCd2As2, Ag substituted sample
$x=0.0055$ at $T=4~{}$K (a) with no applied magnetic field (b) with an applied
magnetic field of $H=880~{}$Oe out of plane ($H\parallel c$). (c) with an
applied field of $H=250~{}$Oe in the $ab-$plane. All three show formation of
domains, which gets modified with applied filed.

Figure 27 shows the back scattering images of three Ag-substituted and three
Na-substituted EuCd2As2 samples. There are no clear signatures of contrast
indicating secondary phases, or inclusions, except for the small inclusion
seen in highest doped Ag sample.

Figure 27: Upper panel shows SEM back scattering images of three Ag doped
EuCd2As2 crystals. And lower panel shows three Na doped samples.

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