# Valence and magnetism in $\rm EuPd_{3}S_{4}$ and
$\rm(Y,La)_{x}Eu_{1-x}Pd_{3}S_{4}$

D. H. Ryan  Physics Department and Centre for the Physics of Materials, McGill
University, 3600 University Street, Montreal, Quebec, H3A 2T8, Canada  Sergey
L. Bud’ko  Brinda Kuthanazhi  Paul C. Canfield  Ames National Laboratory, and
Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011,
USA

###### Abstract

151Eu Mössbauer spectroscopy shows that yttrium substitution in mixed-valent
$\rm EuPd_{3}S_{4}$ drives the initial 50:50 mix of Eu3+ and Eu2+ towards pure
Eu2+, whereas lanthanum substitution has the opposite effect, but only for
substitution levels above 50%. We find that total valence electron count and
chemical pressure effects cannot account for the observed behaviour, however
conserving the cell volume provides a consistent description of the changes in
the Eu2+:Eu3+ ratio. Remarkably, lanthanum substitution also leads to a clear
transition from static mixed-valent behavior at lower temperatures to dynamic
mixed valent behavior at higher temperatures, with the onset temperature
monotonically increasing with Eu content and extrapolating to a value of
$\sim$340 K for the pure $\rm EuPd_{3}S_{4}$ compound. Magnetic order persists
at least as far as x=0.875 in both series, despite the drastic reduction in
the amount of moment-carrying Eu2+ ions.

##  I Introduction

The rare earth palladium sulphides $\rm RPd_{3}S_{4}$ have been reported for
the majority of the rare earths, including yttrium Keszler  _et al._ (1985);
Wakeshima  _et al._ (1997); Wakeshima and Hinatsu (1999); Bonville  _et al._
(2003). They all crystallise in the cubic $\rm NaPt_{3}O_{4}$ structure
($Pm\overline{3}n$ #223) with the rare earth occupying the 2$a$ site forming a
bcc sublattice, the palladium on the 6$d$ site and the sulphur on the 8$e$
site. Remarkably, although the $\rm RPd_{3}S_{4}$ phases exist for the
trivalent rare earths, but apparently not for the divalent alkaline earths (Ca
and Sr), when prepared with europium Wakeshima  _et al._ (2001) or ytterbium
Bonville  _et al._ (2003) a roughly 50:50 mix of divalent and trivalent rare
earth is found.

Here we will use chemical substitution of yttrium and lanthanum for europium
to investigate the stability of the valence distribution and its effects on
magnetic ordering. Although both 170Yb and 151Eu Mössbauer spectroscopy can
generally be used to identify the valence of their respective target ions, for
170Yb Mössbauer spectroscopy, the isomer shift between the two valence states
is extremely small so the technique is almost totally dependent on the
presence of an electric field gradient (efg) at the Yb3+ ions to identify
trivalent ytterbium. Unfortunately the high symmetry of the 2$a$ site makes
the efg contribution effectively zero and the presence of the Yb3+ ions is
only apparent in the magnetically ordered state well below T${}_{N}\sim$2 K
Bonville  _et al._ (2003). We will therefore only study $\rm EuPd_{3}S_{4}$
using 151Eu Mössbauer spectroscopy where the two valence states are clearly
isolated by a large difference in isomer shift, even at ambient temperatures.

We find that, by substituting Y for Eu, the remaining Eu sites become more and
more divalent. In contrast, by substituting La for Eu we find that, initially,
the remaining Eu sites stay roughly a 50:50 mixture of di- and tri-valent Eu,
but for higher La substitution levels the remaining Eu rapidly becomes more
trivalent. La substitution also leads to a transition from statically mixed
valent behavior at lower temperatures to dynamically mixed valent behavior at
higher temperatures with the onset temperature (Tonset) monotonically
increasing with Eu content and passing through room temperature as pure $\rm
EuPd_{3}S_{4}$ is approached. Despite the decreasing fraction of moment-
carrying Eu2+ ions, both $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ and $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ continue to exhibit some form of magnetic order at
least as far as x=0.875, with transition temperatures of $\sim$3 K (Y) and
$\sim$6 K (La).

##  II Experimental methods

Polycrystalline samples of $\rm EuPd_{3}S_{4}$ and
$\rm(Y,La)_{x}Eu_{1-x}Pd_{3}S_{4}$ were prepared from stoichiometric mixtures
of EuS (99.9% – American Elements) $\rm Y_{2}S_{3}$ (99.9%), $\rm La_{2}S_{3}$
(99%), Pd (99.95%) and S (99.5%), all from Alfa-Aesar. The powders were mixed
and then pressed to form a dense pellet. This was loaded into an alumina
crucible and sealed under a partial pressure of helium in a fused silica tube.
The sample was heated to 650∘C over three hours, held for an hour and then
taken to 900∘C over a further three hours. After 75 hours at 900∘C the sample
was furnace cooled and removed once it reached ambient temperature. In most
cases this single thermal cycle was found to yield a single-phased product,
however when an impurity was found (typically PdS seen by x-ray diffraction or
EuS seen in susceptibility vs. temperature) the sample was crushed, pressed
and subjected to a second 75 hr annealing cycle to 900∘C to remove the
impurity.

X-ray diffraction measurements were made on a Rigaku Miniflex-II
diffractometer using a Cu-Kα source. The instrument calibration was checked
using NIST 676a $\rm Al_{2}O_{3}$ and found to be consistent within fitted
uncertainties. Full Rietveld refinement of the diffraction pattens was carried
out using the GSAS/EXPGUI packages Larson and Von Dreele (2000); Toby (2001).
As all three species occupy special sites in the $Pm\overline{3}n$ structure,
no positional parameters were adjusted during the fits. For the yttrium and
lanthanum substituted samples only random occupation of the Eu(2$a$) site was
considered.

151Eu Mössbauer spectroscopy measurements were carried out using a 4 GBq
151SmF3 source, driven in sinusoidal mode. The drive motion was calibrated
using a standard 57CoRh/$\alpha$-Fe foil. Isomer shifts are quoted relative to
EuF3 at ambient temperature. The 21.6 keV gamma rays were recorded using a
thin NaI scintillation detector. For temperatures above 5 K, the samples were
cooled in a vibration-isolated closed-cycle helium refrigerator with the
sample in a helium exchange gas. Temperatures below 5 K were achieved using a
helium flow cryostat while pumping on the sample space and using a needle
valve to throttle the flow. The spectra were fitted to a sum of Lorentzian
lines with the positions and intensities derived from a full solution to the
nuclear Hamiltonian Voyer and Ryan (2006).

Temperature- and magnetic field- dependent magnetization measurements ($\rm
1.8~{}K\leq T\leq 300~{}K$, $\rm 0~{}T\leq\mu_{0}H\leq 7~{}T$) were performed
using a Quantum Design MPMS-3 SQUID magnetometer. The sample was confined in a
#4 gelatin capsule and a transparent drinking straw was used as a sample
holder. Low-temperature heat capacity measurements were made using
semiadiabatic thermal relaxation technique as implemented in the heat capacity
option of a Quantum Design Physical Property Measurement System (PPMS). For
selected samples, the 3He option was used to cool to $\sim$0.4 K. Sintered
samples of 20–70 mg mass with at least one flat surface were mounted on a
micro-calorimeter platform using Apiezon N grease. The addenda (platform +
grease) heat capacity was measured separately for each sample and subtracted
from the total heat capacity using the PPMS software. Although the samples
possibly had reduced density, the measured sample coupling parameter took
reasonable values of more than 97%.

##  III Results

###  III.1 $\rm EuPd_{3}S_{4}$

Figure 1: Cu-Kα x-ray diffraction pattern for $\rm EuPd_{3}S_{4}$. Solid line
is a full Rietveld refinement using the GSAS/EXPGIU packages Larson and Von
Dreele (2000); Toby (2001). The line below the data shows the residuals. Tick
marks between the data and residual lines show the calculated positions of the
Bragg peaks. The inset shows the low-angle range. The diffraction pattern was
collected in two overlapping blocks with a longer counting time at higher
angles to compensate for the loss of intensity due to the effects of the x-ray
form factor.

Fitting the x-ray diffraction pattern of the $\rm EuPd_{3}S_{4}$ sample showed
it to be single phased with the expected cubic $\rm NaPt_{3}O_{4}$ structure
Wakeshima  _et al._ (1997) and a lattice parameter of $a=6.6786(1)$ Å (Fig.
1). The room temperature 151Eu Mössbauer spectrum showed two distinct
contributions from Eu3+ and Eu2+ in the ratio 50.4(4):49.6(4), with the
linewidth of the Eu2+ component being slightly broader, in complete agreement
with previous reports Wakeshima  _et al._ (2001). On cooling to 5 K the ratio
becomes 46.2(5):53.8(5) (Fig. 2) as the Debye temperature of the Eu3+
component is slightly higher than that of the Eu2+ component. Fitting the
temperature dependence of the two component areas to a simple Debye model, as
shown in Fig. 3, yields Debye temperatures of 227(3) K (Eu3+) and 204(3) K
(Eu2+). It is important to emphasise that any apparent changes in the
Eu2+:Eu3+ ratio with temperature in Fig. 3 do not reflect actual changes in
the ratio, rather they are the result of the different temperature dependences
of the recoil-free-fractions (often denoted f) for the two species. In order
to minimise the impacts of this effect, all valence ratios will be taken from
low-temperature spectra.

Figure 2: 151Eu Mössbauer spectra of $\rm EuPd_{3}S_{4}$ at RT (top), 5 K
(middle), and 1.8 K (bottom). Between RT and 5K the primary changes are a
significant increase in the absorption due to conventional thermal effects and
a slight change in the 2+:3+ area ratio due to differences in the Debye
temperatures of the two components. At 5 K the two valence contributions are
almost equal in area and fully resolved, with the Eu2+ at $-10.91$(2) mm/s and
Eu3+ at $+0.07$(1) mm/s. At 1.8 K only the Eu2+ component is ordered and shows
a hyperfine field (Bhf) of 29.9(2) T, while the Eu3+ component is unchanged.
The solid red lines are fits as desribed in the text. For the 1.8 K spectrum
we also show the magnetically split Eu2+ and unchanged Eu3+ components. Figure
3: Temperature dependence of the normalised (adjusted for total counting time)
area of both the total spectrum and the two valence components in the 151Eu
Mössbauer spectra of $\rm EuPd_{3}S_{4}$. Solid lines in each case are fits to
a simple Debye model yielding Debye temperatures of 227(3) K (Eu3+) and 204(3)
K (Eu2+). Fitting the total spectral area yields an average Debye temperature
of 212(3) K.

On cooling to 1.8 K, the Eu2+ component develops a clear magnetic splitting
whereas the Eu3+ component is unchanged, consistent with trivalent europium
being non-magnetic (Fig. 2). In principle one might anticipate a small
transferred field at the Eu3+ sites from the ordered Eu2+ moments, however
none was observed and no increase in the width of the Eu3+ component was
detected (B${}_{hf}\ll$1 T), perhaps as a result of cancellations arising from
the antiferromagnetic ordering of the Eu2+ moments. The hyperfine field (Bhf)
for the Eu2+ component at 1.8 K is 29.9(2) T, typical for ordered Eu2+, and
fitting the temperature dependence shown in Fig. 4 to the expected
$J=\frac{7}{2}$ Brillouin function yields a T=0 Bhf=37.9(6) T and an ordering
temperature of TN=2.90(1) K in good agreement with both previous work
Wakeshima  _et al._ (2001) and our own susceptibility and Cp data (Fig. 5).
The clear cusp in the susceptibility vs. temperature is consistent with
antiferromagnetic (AF) ordering and it is accompanied by a sharp peak in the
heat capacity. The high-field magnetisation curve taken at 1.8 K (inset to
Fig. 5) shows that the system is readily saturated despite the AF order,
consistent with the low ordering temperature as well as the low anisotropy
typically associated with the Eu2+ ion. Furthermore, the maximum moment
observed in the applied field of 7 T suggests a Eu2+ fraction of 50% (assuming
a moment of 7 $\mu_{B}$/Eu2+) consistent with the 53.8(5)% derived above from
the 151Eu Mössbauer spectrum at 5 K, and with earlier results Abe  _et al._
(1999); Wakeshima  _et al._ (2001).

Figure 4: Temperature dependence of hyperfine field (Bhf) for $\rm
EuPd_{3}S_{4}$ fitted using the expected $J=\frac{7}{2}$ Brillouin function to
obtain the ordering temperature of TN=2.90(1) K.  Figure 5: Top: DC
susceptibility vs. temperature for $\rm EuPd_{3}S_{4}$ showing a cusp at
TN$\sim$3 K. Inset shows M vs. $\mu_{0}$H at 1.8 K confirming that half of the
europium is divalent. Bottom: Temperature dependence of the heat capacity
(black points) revealing the corresponding cusp associated with the AF
transition, with d(T$\cdot$M/H)/dT (red line) showing that Cp(T) and the
temperature derivative of T$\cdot$M/H take the same form around the
transition.

The unusual and apparently stable valence mix in $\rm EuPd_{3}S_{4}$ leads to
the question: “why?”. What makes europium (and ytterbium) “special”? How
robust is the valence distribution? Can we change it?

As the Eu3+ ion is smaller than the Eu2+ ion, one might expect hydrostatic
pressure to promote Eu2+ $\rightarrow$ Eu3+ conversion. Alternatively, if we
force some fraction of the R sites to be unambiguously trivalent, by replacing
some of the europium with a formally trivalent ion, will this cause more of
the remaining europium to become divalent to preserve the average electron
count?

Although the driving that can be achieved by chemical substitution is not as
clean as that generated by direct hydrostatic pressure, it is much easier to
make direct measurements of the valence distribution, magnetisation and
transition temperatures in doped samples at ambient pressures. We turn
therefore to an investigation of the impacts of chemical substitution on $\rm
EuPd_{3}S_{4}$ using the non-moment bearing, trivalent La and Y ions with
$r_{ionic}\rm(Eu^{2+}$) $\gtrsim$ $r_{ionic}\rm(La^{3+}$) $>$
$r_{ionic}\rm(Eu^{3+}$) $>$ $r_{ionic}\rm(Y^{3+}$). If, on the one hand, the
total valence electron count is a dominant factor, then partially replacing
the europium with an unambiguously trivalent ion should lead to a compensating
increase in the Eu2+ fraction. On the other hand, if preserving the cell
volume is critical, then the lattice expansion that would be caused by
introducing the $r_{ionic}\rm(La^{3+}$) $\lesssim$ $r_{ionic}\rm(Eu^{2+}$)
lanthanum ion could be compensated by some Eu2+ $\rightarrow$ Eu3+ conversion
(the reverse being expected for the $r_{ionic}\rm(Y^{3+}$) $<$
$r_{ionic}\rm(Eu^{3+}$) yttrium ion). Alternatively, if the substitutions act
as chemical pressures, then expanding the cell using lanthanum substitution
should lead to Eu3+ $\rightarrow$ Eu2+ conversion (again, the reverse process
being expected for yttrium substitution). As we show below, we can clearly
distinguish between these three options.

###  III.2 Valence impacts

Figure 6: (top) Lattice parameters for $\rm(Y,La)_{x}Eu_{1-x}Pd_{3}S_{4}$
showing the expansion associated with La-substitution and the contraction when
yttrium is substituted. We note that whereas the values for the La-substituted
series lie on the line connecting the pure La and Eu compounds, those for the
Y-substituted samples lie significantly above the corresponding line between
the pure Eu and Y compounds.
(bottom) The Eu2+ fractions in the pure and Y,La-substituted compounds showing
that Y-substitution leads to a significant shift towards more Eu2+, while La-
substitution initially appears to have no effect, but for $x>0.5$ there is a
marked shift towards Eu3+. Open circles show values taken from 151Eu Mössbauer
spectroscopy at 5 K(Y-substituted) or 10 K(La-substituted); solid symbols show
values derived from bulk magnetisation data: high-temperature Curie-Weiss fits
(red squares), saturation magnetisation (blue circles). The deviation of the
Curie-Weiss values for the La-rich compounds reflects the development of
dynamic effects discussed in the text.

Fitting the x-ray diffraction data for the yttrium and lanthanum substituted
compounds showed that they all retained the expected $\rm NaPt_{3}O_{4}$
structure but with progressively smaller (Y) or larger (La) lattice parameters
(Fig. 6). There is a clear, and significant, change in lattice parameters for
both Y and La substitution. We detect no indication of phase separation in the
powder x-ray diffraction data, i.e. no broadening or splitting of peaks that
would suggest segregation of the samples into Eu-richer and Eu-poorer phases.

For the Y-substituted series, the fitted lattice parameters all lie visibly
above the line connecting the Eu and Y compounds, suggesting that a shift
towards more of the larger Eu2+ ion occurs, as the yttrium content is
increased. This valence shift is confirmed directly by the 5 K 151Eu Mössbauer
spectra shown in Fig. 7, where the line near 0 mm/s associated with the
trivalent europium decreases rapidly in intensity as the level of yttrium
substitution increases. (All valence ratios for the Y-substituted series were
taken from 5 K spectra to minimise the impacts of f-factor differences for the
two species, as noted above.) Both magnetisation measurements in the ordered
state at 1.8 K (Fig. 8) and Curie-Weiss fits to the temperature dependence of
the susceptibility above 10 K, further support these observations (see below).
The Eu2+ fractions derived from all three measurements are summarised in the
lower panel of Fig. 6.

Figure 7: 151Eu Mössbauer spectra of $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ at 5 K
showing the loss of the Eu3+ component (the line at $\sim$0 mm/s) as the level
of yttrium substitution increases. The spectrum for x=0.875 has been rescaled
by a factor of 2.5 to compensate for the low Eu content. Figure 8: High-field
magnetisation curves measured at 1.8 K for $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$
showing the increase in moment/mol-Eu with increasing yttrium content as the
substitution promotes Eu3+ $\rightarrow$ Eu2+ conversion. All of the curves
appear to saturate in about 3–4 T, reflecting the low anisotropy associated
with the Eu2+ ion.

By contrast with the yttrium-substituted series, the effects of lanthanum
substitution are more complex and nuanced. The lattice parameters of the La-
substituted compounds lie much closer to the line connecting the two end
members (upper panel of Fig. 6) for all substitution levels, and the Eu2+
fraction derived from 151Eu Mössbauer spectroscopy at 10 K (Fig. 9) is
essentially constant (lower panel of Fig. 6) for x$\leq$0.5. This is
consistent with the fact that $r_{ionic}\rm(Eu^{2+}$) $\gtrsim$
$r_{ionic}\rm(La^{3+}$) $>$ $r_{ionic}\rm(Eu^{3+}$) and initial La
substitution does not force any significant change in the Eu2+:Eu3+ ratio.
However, once about half of the europium has been replaced by lanthanum,
further substitution leads to a marked change in behaviour, again consistent
with the fact that $r_{ionic}\rm(La^{3+}$) is ultimately somewhat closer to
$r_{ionic}\rm(Eu^{2+}$) rather than $r_{ionic}\rm(Eu^{3+}$). It is readily
apparent from Fig. 9 that the line near $-$11 mm/s that corresponds to Eu2+
decreases in relative intensity and this rapid loss of the divalent fraction
is confirmed by the magnetisation measurements shown in Fig. 10. We use 10 K
Mössbauer data for the La-substituted series, rather than the 5 K data as was
used for the Y-substituted series, to avoid complications due to the onset of
magnetic ordering (see below).

Figure 9: 151Eu Mössbauer spectra of $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ at 10 K
showing an essentially constant Eu2+:Eu3+ distribution up to x=0.50 followed
by a marked drop in the Eu2+ fraction above that point. Spectra taken at 10 K
are used here to avoid complications associated with the magnetic ordering of
the Eu2+ component at 6 K.

Finally, as is clear in Fig. 6, the Eu2+ fraction derived from Curie-Weiss
fits (data shown below) to the temperature dependence of the susceptibility,
for $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ with $\rm x\gg 0.5$ (measured on the same
sample as part of the run used to obtain the saturation magnetisation) appears
to show the opposite behaviour – a marked growth in the effective moment and
hence the derived Eu2+ fraction. As we show below, this is most likely due to
dynamic effects that lead to intermediate valence behaviour of the europium
ions and makes a simple Curie-Weiss analysis intractable over the temperature
range available to us.

Figure 10: High-field magnetisation curves measured at 1.8 K for $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ showing an approximately constant moment/mol-Eu
with increasing lanthanum content up to $x=0.5$ as the Eu2+:Eu3+ ratio remains
largely independent of the lanthanum content, then there is a marked drop as
rapid Eu${}^{2+}\rightarrow$Eu3+ occurs.  Figure 11: Room temperature 151Eu
Mössbauer spectra of $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ showing minimal changes
from the 5 K spectra shown in Fig. 7 beyond the expected impacts of the
differing Debye temperatures of the two valence components. Figure 12: Room
temperature 151Eu Mössbauer spectra of $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ showing
the development of a new, intermediate valence feature with increasing
lanthanum content.

###  III.3 Dynamics in the Yttrium and Lanthanum substituted series

Figure 13: Isomer shifts of the three components seen in the RT 151Eu
Mössbauer spectra of $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ (shown in Fig. 12)
showing that the values are relatively constant for all three, and that the
dynamic, intermediate valence component lies between the Eu2+ and Eu3+
component, suggesting a composition-independent valence of $\sim$Eu2.5+.
Figure 14: Temperature dependence of the fitted area of the intermediate
valence feature for $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ showing both the greater
extent and earlier onset associated with increasing lanthanum substitution.
Dashed lines are guides to the eye.

We have presented low-temperature Mössbauer data for the yttrium- (5 K) and
lanthanum- (10 K) substituted series in order to minimise the impacts of the
differing Debye temperatures of the two valence components in the spectra.
Figures 11 and 12 present the room temperature Mössbauer spectra for the $\rm
Y_{x}Eu_{1-x}Pd_{3}S_{4}$ and $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ series. As can
be seen, the differences between the room temperature and 5 K yttrium data are
minimal and certainly not qualitative. However, for the $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ series, the changes in the spectra on warming go
far beyond the simple, and expected, slight reduction in the apparent Eu2+
fraction with increasing temperature. As is clear from the RT spectra of $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ shown in Fig. 12, an entirely new feature appears
in the spectra and eventually dominates the pattern by x=0.875. This feature
is a line located midway beween the lines associated with Eu2+ and Eu3+. As
Fig. 13 shows, the position of this line is essentially composition
independent, appearing for all compositions 0.25$\leq$x$<$1.00, and lying
almost precisely midway between the Eu2+ and Eu3+ lines, leading us to
identify it as being due to intermediate-valence europium: “Eu2.5+”. In many
other intermediate-valence europium compounds such as $\rm EuCu_{2}Si_{2}$
Bauminger  _et al._ (1973); Palenzona  _et al._ (1986) and $\rm
EuPd_{2}Si_{2}$ Abd-Elmeguid  _et al._ (1985), where the electron exchange is
between the europium and the conduction band, Röhler  _et al._ (1982); Hossain
_et al._ (2004) the isomer shift of the intermediate valence component is
strongly temperature dependent Bauminger  _et al._ (1973) as electrons
initially associated with the Eu2+ ions spend more time in the conduction band
so that the average europium valence (and hence isomer shift) changes. That is
not the case here as the electron exchange is between Eu2+ and Eu3+ ions, and
as long as the residence time on each ion is roughly the same, then the time-
averaged valence is constant, even if the residence time (or equivalently, the
hopping rate) changes.

The area of the intermediate valence feature is strongly dependent on both
temperature and composition (Fig. 14). At base temperature the area of the
intermediate valence feature is zero, but as temperature increases beyond
Tonset it starts to increase, with Tonset decreasing with increasing x, i.e.
increasing with increasing Eu concentration. Fig 15 plots Tonset versus x; the
extrapolation of the data to x=0, i.e. pure $\rm EuPd_{3}S_{4}$, suggests that
Tonset should occur near T$\sim$340 K. The inset to Fig 15 shows the
intermediate valence area data presented in Fig. 14, plotted versus effective
temperature, T/Tonset. The data scale well and this suggests that temperatures
well above 340 K will need to be measures for pure $\rm EuPd_{3}S_{4}$ in
order to see the intermediate valence signal. The progressive decrease in
Tonset apparent in Fig 15 for the La-substituted series suggests that
lanthanum substitution reduces the barrier for electron hopping in $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$.

Figure 15: Composition dependence of the temperature at which the intermediate
valence feature first appears in the 151Eu Mössbauer spectra of $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ (see Fig. 14). The dashed line is a guide to the
eye showing an extrapolation to x=0 that suggests a similar transition for
pure $\rm EuPd_{3}S_{4}$ near 340 K. The inset shows how the composition and
temperature dependences from Fig. 14 collapse when scaled to Tonset.

Finally, although the position of the Eu2.5+ line appears to be both
composition and temperature independent, its width is not. As is clear from
Fig. 16, the Eu2.5+ line becomes progressively sharper with increasing
temperature while the widths of the Eu2+ and Eu3+ lines remain unchanged. This
sharpening is characteristic of motional narrowing.

Thermally driven conversion of Eu2+ and Eu3+ to an average Eu2.5+ is
consistent with rapid electron hopping between the two species. Clearly, the
two valence states are equally stable in $\rm EuPd_{3}S_{4}$ and in the
absence of evidence for charge ordering, it would appear that the spatial
distribution of the two species on the 2a site is essentially random. If a
given site is randomly $2+$ or $3+$, there would appear to be no reason to
expect that selection to be time-independent, and given sufficient thermal
energy an electron might be expected to jump from a Eu2+ site to a
neighbouring Eu3+ site, exchanging the valence of the two sites in the
process. If the residence time of the electron is much longer than the
characteristic measuring time used to detect the valence ($\sim$10–100 ns for
Mössbauer spectroscopy) then the system appears static and two distinct
valence states are seen. If the residence time is much shorter, then an
averaged valence is seen. Intermediate residence times (“slow relaxation”) can
lead to more complex behaviour in the spectrum, but in the current case where
the two components are single lines with no significant quadrupole or magnetic
splittings, slow relaxation simply leads to a broad dynamic component. Raising
the temperature generally leads to faster hopping and a shorter residence time
and the system evolves from fully static, through the slow relaxation regime,
to dynamically averaged (or motionally narrowed). As can be seen for x=0.75 in
Fig. 14, a weak broad line appears, it becomes stronger and sharper (Fig. 16)
as more europium sites become dynamic and motional narrowing occurs, finally
developing into a natural-width line as the hopping rate increases and moves
up out of the Mössbauer window.

Figure 16: Temperature dependence of the spectral linewidths for the three
components seen in the 151Eu Mössbauer spectra of $\rm
La_{0.75}Eu_{0.25}Pd_{3}S_{4}$. The Eu2+ and Eu3+ features have constant
linewidths, as expected. However, the dynamic feature associated with the
appearance of the Eu2.5+ component clearly sharpens with increasing
temperature reflecting motional narrowing associated with an increasing
relaxation rate.

It is likely that the Eu2+/Eu3+ dynamics and the development of intermediate
valence europium are the cause of the difference between the estimate of
percentage of Eu2+ between the Mössbauer, M(H) and M(T) data for the lanthanum
substituted samples shown in Fig. 6. The 151Eu Mössbauer and the saturation
magnetisation measuerements were made at 10 K and 1.8 K respectively, well
below Tonset, and the valence ratios derived from them are in agreement.
However, the Curie-Weiss analysis relies on measurements made at much higher
temperature ranges where the intermediate valence behaviour is both pronounced
and temperature dependent. Indeed, as the intermediate valence fraction
becomes larger (Fig. 14), the Curie-Weiss-derived Eu2+ fraction deviates more
strongly from the Mössbauer and saturation magnetisation values (Fig. 6). A
simple Curie-Weiss analysis of temperature-dependent susceptibility is not
valid where the valence and hence europium moment is strongly temperature
dependent.

Finally, we note that if the same intermediate valence behaviour is present in
$\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ at RT it accounts for less than 10% of the
total area (Fig. 11). The difference between the yttrium- and lanthanum-
substituted series may reflect stabilisation of Eu2+ by yttrium substitution,
but there is also a very rapid loss of Eu3+ as yttrium is added, so as we
approach the substitution levels where the Eu2.5+ component dominated in $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$, there is almost no Eu3+ left in $\rm
Y_{x}Eu_{1-x}Pd_{3}S_{4}$ to exchange electrons with the majority Eu2+, so the
absence of intermediate valence europium may simply be the result of limited
supply.

###  III.4 Magnetic ordering

Although the Eu2+ fraction does increase as yttrium is added, there is a
steady decline in the net moment-bearing rare-earth content of the $\rm
Y_{x}Eu_{1-x}Pd_{3}S_{4}$ series with increasing x. This decline is even
stronger in the $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ series as the Eu2+ fraction is
either constant (up to x$\sim$0.5) or decreases with increasing x. Despite
these monotonic reductions in the moment-bearing fraction, Fig. 17 shows that
both series continue to exhibit some form of magnetic order, at least as far
as x=0.875. Furthermore, it is apparent from both the high-field magnetisation
curves (Figs. 8 and 10) and low-field dc susceptibility (Figs. A.2 and A.4 in
the appendix) that both series develop some ferromagnetic character to their
ordering. Heat capacity measurements (Figs. A.1 and A.3 in the appendix)
confirm the persistence of magnetic ordering. With increasing dilution, the
signature of the ordering becomes progressively weaker, with a softer onset,
but it is never lost.

Figure 17: Estimated transition temperatures for (top) $\rm
Y_{x}Eu_{1-x}Pd_{3}S_{4}$ and (bottom) $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$. Open
symbols show estimates derived from dc susceptibility while solid symbols are
based on Cp data.

For $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ the onset of magnetic order appears to be
largely insensitive to the level of substitution, remaining near 3 K for all
x. However the Y-substituted samples also exhibit a secondary feature around 2
K in the heat capacity data, and it too is largely independent of the
composition.

For $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$, heat capacity (Fig. A.3 in the appendix)
and dc susceptibility (Fig. A.4 in the appendix) measurements show that the
ordering behaviour is more complex in the lanthanum substituted series.
Whereas the $\sim$3 K feature from the parent compound persists for all finite
x, but becomes progressively less distinct, a new feature develops at $\sim$6
K as lanthanum is added. This is despite the steady dilution of the moment
bearing component: by $x=$0.875 only $\sim$4% of the rare earth atoms are
moment-bearing Eu2+, yet the 6 K magnetic feature is still apparent in both
heat capacity and susceptibility. 151Eu Mössbauer spectroscopy confirms that
the 6 K feature at x=0.75 is indeed magnetic and associated with the Eu2+ in
the material. Although the $\sim$5 K limit of the closed-cycle fridge was not
low enough to yield a fully resolved magnetic splitting, Fig. A.5 (in the
appendix) shows that it is possible to observe the initial line broadening
that occurs as order develops. Fitting the broad Eu2+ line at 5.3 K yields a
hyperfine field of 11(1) T. Fig. 17 summarises the composition dependence of
the transition temperatures observed for $\rm(Y,La)_{x}Eu_{1-x}Pd_{3}S_{4}$.

The form of Cp(T) for $\rm La_{0.25}Eu_{0.75}Pd_{3}S_{4}$, and to a lesser
extent $\rm La_{0.375}Eu_{0.625}Pd_{3}S_{4}$, might lead one to suspect that
either an impurity phase is present, or that the sample has perhaps separated
into La-rich and La-poor regions, yielding distinct $\sim$6 K and $\sim$3 K
transitions respectively. The magnitude of the Cp signal would require a
rather significant impurity content to account for it. None was detected by
x-ray diffraction, as noted earlier. Furthermore, the change in lattice
parameter with x in the La-substituted series is quite strong (see Fig. 6) so
any phase separation would yield broadened, or more likely split, diffraction
lines. These were not seen in any sample studied here. Finally, the $\rm
NaPt_{3}O_{4}$ form of $\rm RPd_{3}S_{4}$ appears to be stable across the
entire rare-earth series and for both the Y- and La- substituted series
studied here, giving us no reason to expect phase separation. The monotonic
composition and temperature evolution of the intermediate valence component
apparent in Figs. 12 and 14 also argues for homogeneous, rather than phase
separated samples. The 151Eu Mössbauer spectra in Fig. A.6 (in the appendix)
reveal a progressive development of magnetic order on cooling: The Eu2+
component near $-$11 mm/s first broadens below 6 K, then a full magnetic
pattern appears (more apparent on the low-velocity side of the Eu2+ component)
on further cooling. Even at 1.8 K the magnetic component is extremely broad
(compare the 1.8 K spectrum in Fig. A.6 (in the appendix) with that of $\rm
EuPd_{3}S_{4}$ at the same temperature in Fig. 2). A simple parametrisation of
the spectra was obtained by using three components to fit the Eu2+
contribution: zero field, low-field and high-field. Fewer components gave a
poor fit while using more led to instabilities. Following the areas of the
magnetic and non-magnetic Eu2+ components (Fig. A.7 in the appendix) shows a
gradual shift from non-magnetic to magnetic starting below 6 K with no
apparent break near 3 K. The average magnetic field shown in Fig. A.8 (in the
appendix) shows similar behaviour, again with no break near 3 K. We conclude
that although the Eu2+ experiences a very broad range of magnetic
environments, there is no evidence for phase separation.

##  IV Discussion

Given that the $\rm RPd_{3}S_{4}$ compound series exists for most, if not all
of the trivalent rare earths (R) and yttrium Keszler  _et al._ (1985);
Wakeshima  _et al._ (1997); Wakeshima and Hinatsu (1999); Bonville  _et al._
(2003), but not, apparently, for the divalent alkaline earths, it is
remarkable that $\rm EuPd_{3}S_{4}$ not only accommodates such a large
fraction of divalent europium, but that the fraction of Eu2+ is so robust
against substitution by other trivalent rare earths: Substituting yttrium
actually promotes the divalent state, whereas substituting lanthanum has
little impact on the europium valence until at least half of the europium has
been replaced.

It is clear that band filling or average valence electron count does not
control the Eu2+:Eu3+ ratio in $\rm R_{x}Eu_{1-x}Pd_{3}S_{4}$ as both yttrium
and lanthanum are trivalent yet act on the Eu2+:Eu3+ ratio in opposite
directions. Similarly, chemical pressure arguments fail as lattice compression
using yttrium substitution favours the larger Eu2+ ion, and lattice expansion
using lanthanum leads to more of the smaller Eu3+ ion – the reverse of what
would be predicted.

We are left with preservation of the average rare-earth size as the dominant
factor controlling the Eu2+:Eu3+ valence ratio. Since $r_{ionic}\rm(Y^{3+}$)
is both smaller than $r_{ionic}\rm(Eu^{3+}$) and much smaller than
$r_{ionic}\rm(Eu^{2+}$), converting Eu3+ into the larger Eu2+ as yttrium is
added acts to maintain the average rare-earth size. By the same token,
$r_{ionic}\rm(La^{3+}$) lies between those of Eu2+ and Eu3+, so lanthanum
substitution initially has very little effect on the Eu2+:Eu3+ ratio. Only
after half of the europium has been replaced do we see a shift in the balance
towards Eu3+.

Hydrostatic pressure would provide a complementary window on how pure changes
in volume affect the Eu2+:Eu3+ ratio, and synchrotron Mössbauer spectroscopy
under pressure would be a useful extension of this study.

Remarkably, La-substitution also appears to reduce the barrier for electron
hopping between the Eu2+ and Eu3+ ions in $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$, and
a temperature dependent intermediate valence component develops at
progressively lower temperatures with increasing lanthanum content.
Extrapolating the composition trend in the onset temperature leads to the
prediction that electron hopping should start around 340 K in un-doped $\rm
EuPd_{3}S_{4}$. The much weaker dynamic behaviour in the Y-substituted series
may reflect a stronger bias towards Eu2+ in $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$
which may in turn stabilise the valence of the two europium components.
Alternatively, the much lower availabilty of Eu3+ for electron exchange may be
the limiting factor.

The evolution of low temperature magnetism, as seen by Mössbauer spectroscopy,
heat capacity and low field magnetic susceptibility also differs between
yttrium and lanthanum. Remarkably, suppression of the ordering by the dilution
of the magnetic Eu2+ is not the primary impact in either series. Magnetic
order persists in $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ even as far as x=0.875, with
the onset temperature essentially unchanged, despite only about 12% of the
europium sites being occupied by a moment-bearing ion (Fig. 17). However the
behaviour of the La-substituted series is perhaps more surprising. Not only
does the magnetic order also persist to x=0.875 (where the moment-bearing
fraction is only $\sim$4% because of the much lower Eu2+:Eu3+ ratio in the La-
substituted series), but the onset temperature jumps from $\sim$3 K to $\sim$6
K for low x and remains near 6 K at least as far as x=0.875 (Fig. 17). We
emphasise that our data do not provide access to the specific magnetic
structures of the Y- and La- substituted materials. The behaviour of $\chi$(T)
and Cp(T) in Fig. 5 strongly suggests that the parent compound orders
antiferromagnetically, however it is unlikely that this survives the
substitutional disorder introduced when we replace the europium. The form of
$\chi$(T) clearly changes in both series (Figs. A.2 and A.4 in the appendix)
and the magnetic order appears to develop at least some ferromagnetic
character, although it is probably dominated by short ranged order. The
extremely broad hyperfine field distributions and the presence of significant
zero field components well below the onset of magnetic order in both $\rm
La_{0.25}Eu_{0.75}Pd_{3}S_{4}$ and $\rm Y_{0.25}Eu_{0.75}Pd_{3}S_{4}$ (Fig.
A.9) point to inhomogeneous ordering in both of these magnetically diluted
materials.

##  V Conclusions

The impact of yttrium and lanthanum substitution on mixed-valence $\rm
EuPd_{3}S_{4}$ has been studied using 151Eu Mössbauer spectroscopy, bulk
magnetisation and heat capacity measurements. Average valence electron count
clearly does not control the europium valence distribution as trivalent
yttrium and lanthanum substitutions have opposite effects. Similarly, chemical
pressure arguments fail as lattice compression using yttrium substitution
favours the larger Eu2+ ion, with the reverse effect seen with lanthanum. It
appears that preservation of the average rare-earth size is the dominant
factor controlling the Eu2+:Eu3+ valence ratio.

Lanthanum substitution was also found to promote electron hopping between the
Eu2+ and Eu3+ ions, leading to the formation of intermediate valence europium.
Increasing lanthanum substitution both increases the amount of intermediate
valence europium seen at ambient temperatures and reduces the temperature at
which hopping starts to appear. An onset temperature of $\sim$340 K is
predicted for undoped $\rm EuPd_{3}S_{4}$.

Inhomogeneous magnetic order is seen at all levels of substitution, with the
onset temperature in the Y-substituted series being essentially unchanged at 3
K, while for the La-substituted series the onset temperature is seen to
increase to 6 K despite the low concentration of magnetic ions.

###### Acknowledgements.

Financial support for this work was provided by Fonds Québécois de la
Recherche sur la Nature et les Technologies, and the Natural Sciences and
Engineering Research Council (NSERC) Canada. Work at the Ames Laboratory was
supported by the U.S. Department of Energy, Office of Science, Basic Energy
Sciences, Materials Sciences and Engineering Division. The Ames Laboratory is
operated for the U.S. Department of Energy by Iowa State University under
contract No. DE-AC02-07CH11358. BK is supported by the Center for the
Advancement of Topological Semimetals (CATS), an Energy Frontier Research
Center funded by the US DOE, Office of Basic Energy Sciences. Much of this
work was carried out while DHR was on sabbatical at Iowa State University and
their generous support during this visit is gratefully acknowledged.

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##  Appendix A Additional figures and tables

This appendix contains additional figures showing heat capacity and
susceptibility data for $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ and $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$.

We also present low temperature 151Eu Mössbauer data for $\rm
La_{0.5}Eu_{0.5}Pd_{3}S_{4}$ showing the onset of magnetic broadening near 6
K, and spectra for $\rm La_{0.25}Eu_{0.75}Pd_{3}S_{4}$ showing the
inhomogeneous magnetic order that develops below the transition temperature.
The temperature dependence of some fitting parameters for the $\rm
La_{0.25}Eu_{0.75}Pd_{3}S_{4}$ spectra is also shown.

The fitted lattice parameters and Eu2+ fractions used to construct Fig. 6 in
the main body of the text are also tabulated here.

Figure A.1: Heat capacity measurements for $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$
showing the persistence of the magnetic transition near 3 K despite the
significant dilution of the magnetic Eu2+. At x=1 there is no transition
observed as the system contains no magnetic species and so is paramagnetic.
The vertical dashed lines mark 3 K.  Figure A.2: Field-cooled (FC) and zero-
field-cooled (ZFC) dc susceptibility for $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$
confirming the persistence of the magnetic transition seen near 3 K in the
heat capacity data (Fig. A.1) despite the significant dilution of the magnetic
Eu2+. The vertical dashed lines mark 3 K.  Figure A.3: Heat capacity
measurements for $\rm La_{x}Eu_{1-x}Pd_{3}S_{4}$ showing the gradual
replacement of the 3 K transition by a new feature at 6 K, despite the
significant dilution of the magnetic Eu2+ component. The inset in (f) shows
the region between 2 K and 8 K on an expanded vertical scale. At x=1 there is
no transition observed as the system contains no magnetic species and so is
paramagnetic. The vertical dashed lines mark 3 K and 6 K. Figure A.4: Field-
cooled (FC) and zero-field-cooled (ZFC) dc susceptibility for $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ confirming the gradual replacement of the 3 K
transition by a new feature at 6 K, seen in the heat capacity data (Fig. A.3)
despite the significant dilution of the magnetic Eu2+. The vertical dashed
lines mark 3 K.  Figure A.5: Temperature dependence of the Eu2+ line width in
$\rm La_{0.5}Eu_{0.5}Pd_{3}S_{4}$ showing the onset of ordering at 6.1(1) K.
Figure A.6: 151Eu Mössbauer spectra of $\rm La_{0.25}Eu_{0.75}Pd_{3}S_{4}$
showing the progressive development of magnetic order in the Eu2+ component.
The solid lines are fits using a single line for the Eu3+ line near 0 mm/s,
and three components to fit the Eu2+: an unsplit line, and two magnetic
contributions with a “small” and “large” field used to reproduce the gross
behaviour of the system. Figure A.7: Temperature dependence of the magnetic
and non-magnetic Eu2+ compoents in the 151Eu Mössbauer spectra of $\rm
La_{0.25}Eu_{0.75}Pd_{3}S_{4}$ showing the gradual onset of magnetic order
below 6 K but no evidence for a break at 3 K that might suggest the presence
of a second phase. Figure A.8: Temperature dependence of the average Eu2+
magnetic hyperfine field (Bhf) in the 151Eu Mössbauer spectra of $\rm
La_{0.25}Eu_{0.75}Pd_{3}S_{4}$ showing the gradual onset of magnetic order
below 6 K. Two averages are shown: (i) $\rm<Eu^{2+}>$ (blue circles) is
calculated for all three Eu2+ components used in the fits; (ii) $\rm<mag>$
(red squares) is calculated omitting the Eu2+ component that exhibits no
magnetic splitting. See text for details of the model used to fit the spectra.
Figure A.9: 151Eu Mössbauer spectra of $\rm EuPd_{3}S_{4}$ (top), $\rm
La_{0.25}Eu_{0.75}Pd_{3}S_{4}$ (middle) and $\rm Y_{0.25}Eu_{0.75}Pd_{3}S_{4}$
(bottom) measured at 1.8 K showing that while the substituted materials do
appear to exhibit magnetic ordering of the Eu2+ component, the lines are not
sharp, reflecting a broad distribution of hyperfine fields.

x |  a (Å) | Eu2+ fraction (%)
---|---|---
|  |  Mössbauer |  Curie-Weiss | M(H)
|  |  |  $\pm$5% |  $\pm$5%
0.00 | 6.67858(8) | 53.8(5) | 57 | 49
0.125 | 6.67637(9) | 56.3(8) | 59 | 56
0.25 | 6.67371(13) | 61.5(5) | 66 | 63
0.375 | 6.66983(12) | 68.4(5) | 72 | 68
0.500 | 6.66527(20) | 73.3(9) | 71 | 69
0.625 | 6.66148(10) | 83.2(7) | 92 | 89
0.750 | 6.65514(12) | 87.3(8) | 85 | 86
0.875 | 6.64921(11) | 93(2) | 95 | 94
1.00 | 6.64193(17) | – | – | –
Table A.1: Measured lattice parameters and Eu2+ fractions for the $\rm Y_{x}Eu_{1-x}Pd_{3}S_{4}$ compound series. x |  a (Å) | Eu2+ fraction (%)
---|---|---
|  |  Mössbauer |  Curie-Weiss | M(H)
|  |  |  $\pm$5% |  $\pm$5%
0.00 | 6.67858(8) | 53.8(5) | 57 | 49
0.25 | 6.69217(18) | 53.1(6) | 55 | 52
0.375 | 6.70125(17) | 51.1(9) | 53 | 49
0.50 | 6.70871(17) | 51.5(8) | 54 | 49
0.625 | 6.71763(12) | 47(2) | 53 | 46
0.75 | 6.72490(14) | 46(2) | 56 | 43
0.8125 | 6.72981(12) | 39(1) | 57 | 40
0.875 | 6.73316(14) | 32(1) | 61 | 36
0.9375 | 6.73557(6) | 25(3) | 86 | 34
1.00 | 6.73948(9) | – | – | –
Table A.2: Measured lattice parameters and Eu2+ fractions for the $\rm
La_{x}Eu_{1-x}Pd_{3}S_{4}$ compound series.