Enhanced paramagnetism of the 4d itinerant electrons in the rhodium oxide perovskite SrRhO3

Abstract

Polycrystalline rhodium(IV) oxide perovskite SrRhO3 was obtained by high-pressure synthesis techniques, followed by measurements of the magnetic susceptibility, electrical resistivity, and specific heat. The title compound has five 4d-electrons per perovskite unit and shows Fermi-liquid behavior in its electrical resistivity. The magnetic susceptibility is large [chi(300K) \~1.1*10^{-3} emu/mol-Rh] and proportional to 1/T^2 (< 380 K), while there is no magnetic long-range order above 1.8 K. The specific heat measurements indicate a probable magnetic contribution below ~ 15 K, which is not predicted by the self-consistent renormalization theory of spin fluctuations for both antiferro- and ferromagnetic 3D nearly-ordered metals. Comment: To be published in PRB

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arXiv:cond-mat/0109522v2 [cond-mat.supr-con] 12 Oct 2001
Enhanced paramagnetism of the 4d itinerant electrons in the rhodium oxide
perovskite SrRhO3
K. Yamaura∗
Advanced Materials Laboratory, National Institute for Materials Science,
1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan and
Japan Science and Technology Corporation, Kawaguchi, Saitama 332-0012, Japan
E. Takayama-Muromachi
Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan
Polycrystalline rhodium(IV) oxide perovskite SrRhO3 was obtained by high-pressure synthesis
techniques, followed by measurements of the magnetic susceptibility, electrical resistivity, and spe-
cific heat. The title compound has five 4d-electrons per perovskite unit and shows Fermi-liquid
behavior in its electrical resistivity. The magnetic susceptibility is large [χ(300K) ∼ 1.1 × 10−3
emu/mol-Rh] and proportional to 1/T2(< 380 K), while there is no magnetic long-range order
above 1.8 K. The specific heat measurements indicate a probable magnetic contribution below ∼ 15
K, which is not predicted by the self-consistent renormalization theory of spin fluctuations for both
antiferro- and ferromagnetic 3D nearly-ordered metals.
PACS numbers: 75.50.-y, 75.30.Cr
I. INTRODUCTION
Since p-wave symmetrical pairing of electrons was pro-
posed, driven mainly by ferromagnetic spin fluctuations,
in the 1.5 K superconductor Sr2RuO4[1], further super-
conducting phases have been expected in the vicinity of
the 214 phase. This is probably due to substantial spin
fluctuations found in neighboring compounds, including
ferromagnetic SrRuO3 [2, 3], and nearly ferromagnetic
CaRuO3[3, 4] and Sr3Ru2O7[5]. Although intensive in-
vestigations have been applied to the ruthenium oxide
systems, further ‘p-wave’ superconducting phases have
not been discovered thus far. The current experimental
studies on ferromagnetically induced superconductivity,
then, seem to be tied to a very local variety of materials.
To ameliorate the stagnant situation, we have been ex-
ploring other correlated 4d-metal compounds, not only to
find further superconducting materials in the ruthenium
oxide system, but also to expand the variety of potential
chemical systems for the spin-fluctuations-induced super-
conductors.
The rhodium oxide perovskite SrRhO3 was recently
found, and a pure polycrystalline sample was obtained
by high-pressure synthesis techniques at 60 kbar and
1500◦C, followed by investigations of the magnetic sus-
ceptibility, electrical resistivity, and specific heat. The
compound was fairly metallic and showed enhanced and
thermally activated paramagnetism in the studied tem-
perature range below 380 K. A qualitative fit of the
Curie-Weiss (CW) law to the magnetic susceptibility
data yielded a negative Weiss temperature of -361 K, if
the analysis provided a correct sense of the magnetism.
∗E-mail at:YAMAURA.Kazunari@nims.go.jp
Neither superconductivity nor long range magnetic order
was found above 1.8 K. The magnetic data for SrRhO3
appeared to be qualitatively similar to what was ob-
served for the analogous ruthenium oxide metal CaRuO3
[3, 4].Since then, the self-consistent renormalization
(SCR) theory of spin fluctuations for both antiferro- and
ferromagnetic nearly-ordered magnetic metals was tested
on the observed electronic properties as was done for
CaRuO3 [3, 4]. As a result, all of the present data for
SrRhO3do not meet the quantitative expectations as pre-
dicted by the theory.
II. EXPERIMENTAL
Variable composition precursors were prepared at
Sr:Rh = 1:3, 1:2, and 1:1 as follows. Mixtures of pure
SrCO3(99.9 %) and Rh (99.9 %) powders were heated
in oxygen at 1000◦C overnight, and then ground well
and reheated in oxygen at 1200◦C for two days [6]. One
and two moles of SrO2(>99.9 %) were added to the 1:2
and 1:3 precursors per the formula, respectively, and 8
wt.% of KClO4to the 1:1 precursor. Those were mixed
well, and approximately 0.2 g of each were placed into Pt
capsules. Those were heated at 60 kbar and 1500◦C for 1
hr, then quenched to room temperature before releasing
the pressure [7]. Quality of the finally obtained pellets
was studied by powder x-ray-diffraction techniques in a
regular manner. It was determined from the x-ray read-
ings that the major phase was of perovskite-type. The
position and intensity distribution of the peaks for the
phase were invariable among the patterns for every sam-
ple. The impurity level was 1 % or less in every final
production except KCl. The perovskite-type phase de-
noted SrRhO3, of which no records were found thus far
in the literature.

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Further structural characterization was made for the
selected sample, which was prepared from the 1:2 pre-
cursor and SrO2, by x-ray Rietveld technique (CuKα)
using the program RIETAN-2000 [8]. A distorted per-
ovskite structure model, GdFeO3-type, was tested and
found reasonable to describe the structure of SrRhO3.
The x-ray powder pattern and crystal structure are in-
dicated in Fig.1; Space group was Pnma (no. 62) and
lattice parameters were a = 5.5394(2)˚ A, b = 7.8539 (3)
˚ A, and c = 5.5666(2)˚ A. The estimated positions for the
atoms were Sr(0.0304(1), 0.25, -0.0054(8)), Rh(0, 0, 0.5),
O1(0.4990(23), 0.25, 0.0587(45)), and O2(0.2825(26),
0.0366(24) , 0.7088(26)). During the refinement, the oc-
cupation factors, and the isotropic displacement param-
eters of the metals and oxygen were fixed at 1, 0.3, and
0.7, respectively. The final reliability factors and good-
ness of fit to the analysis were Rwp=20.9 %, Rp=14.41
%, RR=18.57 %, and S = 1.53. Oxygen vacancies in the
perovskite were quantitatively investigated in detail by
thermogravimetric analysis and found to be insignificant
[9].
The same sample was again selected for characteriza-
tion by magnetic, specific heat, and electrical resistivity
measurements. The temperature dependence of magneti-
zation was measured in a Quantum Design MPMS mag-
netometer. The specific heat and the electrical resistivity
data were obtained in a Quantum Design PPMS appa-
ratus. Those measurements were conducted between 1.8
and 400 K. The highest applied magnetic field was 70
kOe.
III. RESULTS AND DISCUSSIONS
Temperature dependence of the electrical resistivity of
polycrystalline SrRhO3is shown in Fig.2. The data were
obtained by a standard 4-terminal dc technique at a cur-
rent of 5 mA on a piece of the sample pellet. The data
clearly reveal the metallic nature of SrRhO3; a metallic
temperature dependence and ∼ 1.3 mΩcm at room tem-
perature are typical for polycrystalline oxide metals. The
low temperature part (<50 K) is expanded and replotted
as ρ vs T2(inset in Fig.2). The observed linear depen-
dence is indicative of Fermi liquid behavior for SrRhO3
[10]. Subsequent fitting studies with standard resistivity
expression for a Fermi liquid (ρ = ρ0+AT2) yielded ρ0=
142 µΩcm and A = 0.062 µΩcm/K2. The unusually large
ρ0probably reflects contributions from extrinsic origins
such as grain boundaries.
constant among the sets of resistivity data for all of the
present pellets (approximately two magnitudes larger for
the pellet containing KCl), while the residual resistivity
ratio, ρ300/ρ0, remained almost constant (∼ 9) among
them. At the magnetic instability point, or in the ex-
treme vicinity of that point, the electrical resistivity is
not expected to obey the famous T2law due to the in-
fluence of spin fluctuations; i.e. T3/2and T5/3law may
be obeyed by antiferro- and ferromagnetically unstable
The parameter ρ0 was not
3D metals, respectively [11, 12, 13]. Detailed analysis
was preliminarily applied for the present resistivity data,
however, the non-Fermi liquid behavior was not clearly
seen. Magnetoresistivity at 1.8 K between -70 and 70
kOe was not observed, and may be due to polycrystalline
nature of the sample. Additional studies using a single
crystal SrRhO3, if it becomes available, could allow us to
exclude the extrinsic contributions and then might help
to reveal the intrinsic nature of electrical resistivity of
SrRhO3. Because the 4d-band in SrRhO3is expected to
be broad, as is the case for SrRuO3, 4d-electrons in the
rhodium oxide should be itinerate by analogy [2]. The ob-
served metallic conductivity is, hence, reflecting mainly
the nature of unlocalized 4d electrons. The perovskite
SrRhO3 could be in a class of the itinerant 4d-electron
systems, such as (Sr,Ca)RuO3[2]. Further investigations
into the electronic transport of SrRhO3, including band
structure calculations, would be of interest.
Magnetic data are summarized in Fig.3.
netic susceptibility of SrRhO3obviously depends on tem-
perature and is approximately 1.1×10−3emu/mol-Rh at
room temperature, in contrast with the properties of the
Pauli paramagnetic rhodium metal (approximately one
magnitude smaller and almost temperature independent)
[14]. A steep rise in the χ vs T plot in low temperature
at 10 kOe was observed, while it was significantly sup-
pressed at 50 kOe. The M vs H curve at 2 K (inset in
Fig.3) indicates a subtle spontaneous magnetic moment
(∼ 0.001 µB per Rh), suggesting SrRhO3 has ordered
magnetic moments. After subtraction of the major part,
1/χupturnvs T plot results in a standard CW line with
an insignificant level of Weiss temperature ∼ -1.5 K [15].
It is therefore reasonable to conclude that the upturn
results from a magnetic impurity origin rather than an
ordered state of SrRhO3. The slightly positive curvature
of the M vs H curve at 2 K is probably due to superim-
posing the small amount of impurity component on the
major part.
To further analyze the major part of the magnetic
data for SrRhO3, two plots of the reciprocal magnetic
susceptibility were prepared in the forms of 1/χ vs T
and 1/χ vs T2without any other manipulations except
subtraction of sample holder contribution (Fig.4). It is
clearly seen in the temperature range that 1/χ is pro-
portional to T2rather than proportional to T as ex-
pected from the standard CW expression. Alternatively,
the CW law with a temperature-independent term, i.e.
1/χ = 1/[C/(T − θ) + χ0] (C and θ are the Curie con-
stant and Weiss temperature, respectively), was applied
to the 1/χ vs T plot. The fit, however, failed to pro-
duce a convincible result [16]. Tentative CW parame-
ters obtained in the calculations were considerably sen-
sitive to least squares fitting conditions, including tem-
perature range width, and stable and reasonable solu-
tions were never found. Further attempts were made to
demonstrate the implied linear relationship between 1/χ
and T2for SrRhO3. Neither the T3/2nor the T4/3fit
(data not shown), however, yielded a linear part, which
The mag-

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was expected, if SrRhO3was just at the magnetic insta-
bility point [12, 13]. The above experimental observa-
tions would suggest that the magnetic susceptibility for
SrRhO3 is rather uncommon among properties of mag-
netic metals, because many antiferro- and ferromagnetic
metals are expected to follow approximately the CW law
above the magnetic ordering temperature or 0 K (in the
case for nearly ordered metals) [11, 12, 13, 17, 18, 19, 20].
The roughly estimated χ(0) ∼ 1 × 10−3cm3/mol for
SrRhO3, and the Sommerfeld constant discussed later
(γ = 7.6 mJ/mol K2), yielded the Wilson ratio (RW) of
∼ 8.6 using the formula [21],
RW=3π2k2
Bχ(0)
µ2
Bγ
. (1)
The preliminary RWfor SrRhO3is clearly out of the ex-
pected range, 1 to 2, for standard Fermi-liquid behavior.
The unreliable RWmight support the presence of pecu-
liar magnetism in SrRhO3.
The most advanced profiling thus far achieved for the
nearly and weakly antiferro- and ferromagnetic 3D met-
als was accomplished by developing the SCR theory of
spin fluctuations in metals [17]. At the paramagnetic re-
gion, 1/χ is expected to be in direct proportion to the
dth power of T, where d =1 to 3/2 and 1 to 4/3 for
antiferro- and ferromagnetic 3D metals, respectively [13].
This is the most notable point to distinguish the progress
of understanding in magnetism of metals achieved by the
SCR studies, and so-far observations, indeed, seem to be
in the range (1/χ ∼ Td) [18]. The rather conventional
Stoner’s model (1/χ ∼ T2) is far beyond the range. The
rhodium oxide metal, however, shows a nearly T2depen-
dence of 1/χ, which ironically matches the Stoner expec-
tation [17]. Although the T2trend in 1/χ was also pre-
dicted by a random phase approximation theory, using
it here to analyze the present data may be problematic,
because it is too limited in temperature range (only ef-
fective within extremely low temperature), due to mainly
a lack of self consistency [17, 22]. Further considerations
with additional studies may be necessary to conclusively
determine the microscopic origin of the 1/χ ∼ T2trend
in SrRhO3.
The specific heat data are presented in Fig.5. A stan-
dard relaxation technique was employed in measurement.
The temperature dependence of the specific heat (Cp)
of SrRhO3 measured between 1.8 and 390 K is plotted
in the inset of the top panel in Fig.5 after subtraction
of a contribution from the addenda. The difference be-
tween Cpand Cvwas assumed insignificant in the tem-
perature range studied.The top main panel shows a
Cp/T vs T2plot of the data below 20 K. As expected
within the Debye approximation, a linear dependence is
clearly seen. The estimated Debye temperature was 190
K and the Sommerfeld constant was 7.6 mJ/mol K2by
a least squares fitting as indicated by the dotted line in
Fig.5. Among Fermi liquid metals, a universality was
found in A/γ2[23]. A tentative calculation of A/γ2with
the obtained parameters for SrRhO3, γ = 7.6 mJ/mol
K2and A = 0.062 µΩcm/K2, produced an incredible re-
sult, a value approximately two magnitudes larger than
the universal constant. The parameter A for SrRhO3
perhaps involves extrinsic contributions somewhat as ρ0
dose. We decided, therefore, not to make further quanti-
tative analysis for A/γ2of SrRhO3. On the other hand,
we found that the Debye temperature of SrRhO3is much
lower than those of the ruthenium oxide perovskites [3].
This fact would indicate the lattice of SrRhO3is much
‘softer’ than that of the ruthenium oxide perovskites. As
expected from the Debye temperature, even within the
studied temperature range, it can be clearly seen that the
specific heat is approaching the roughly expected value ∼
125 mJ/mol K [5(atoms per unit cell)×3 (dimensionality
per atom) ×kBN(Boltzmann and Avogadro’s constants)].
In the low temperature portion of the specific heat
data, an extra contribution (Cm) appears, as Cp/T starts
to part gradually from the linear dependence on cooling.
It is presumably magnetic in origin and is found in a vari-
ety of itinerant magnetic materials [3, 24]. The probable
magnetic term was extracted by subtracting the lattice
contribution and the Sommerfeld constant from the origi-
nal data, which is shown in the bottom panel of Fig.5. At
first, the Cm/T data was quantitatively investigated with
a component for spin fluctuations in the SCR framework
for nearly ferromagnetic metals [3, 20]. The contribution
of the spin fluctuations to the specific heat was approxi-
mated by
Cm
T
∼9N0
T0
?1/K0
0
dxx21
t
?
− u −1
2+ u2Ψ′(u)
?
, (2)
where N0 is the number of magnetic atoms, Ψ′(u) is
the first derivative of the digamma function, T0 and
K0 are the parameters as to spin fluctuations, u =
x(x2+ χ(0)/χ)/t, t = T/T∗, and T∗= T0/K3
expression was then reduced to the following form in the
low temperature limit:
0[20]. The
→3N0
4T0
?
ln(1 + K−2
0) +2
5t2lnt + ···
?
.(3)
For fitting purposes by a least squares method, T0, K0,
and T∗were set as independent variable parameters in
the first two terms in Eq.3, where t was replaced by T/T∗.
The best fitting result is shown in the bottom panel of
Fig.5 as a broken curve. Although the observed data,
Cm/T vs T, were reproduced at a convincible level, all of
the parameters determined here, T0= 0.00305 K, K0=
3.69 and T∗= 26.7 K were, however, incredible [20]. For
example, the tentatively obtained values do not satisfy
the form T∗= T0/K3
0at all. As dictated by Eq.3, there
were no other combinations of the parameters that fit
the data. These facts, therefore, suggest that the con-
tribution from spin fluctuations in nearly ferromagnetic
metals is either unlikely or at least insufficient to account
for the observed Cmin SrRhO3. In 3D nearly antiferro-
magnetic metals, magnetic contributions to the specific
heat in the SCR framework have been studied; an en-
hancement of γ is expected at low temperature instead

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of the parameters in Eq.3 [25]. The 3D nearly antifer-
romagnetic picture is, therefore, unlikely to explain the
observed Cmfor SrRhO3.
IV.CONCLUSIONS
The structure and electronic properties of a polycrys-
talline sample of SrRhO3obtained by high-pressure syn-
thesis techniques was investigated. Although the poly-
crystalline nature of the sample limited quantitatively
detailed analysis of the electrical resistivity properties,
the present data strongly suggests the perovskite is in
the category of a Fermi liquid. The magnetic suscepti-
bility of SrRhO3 was found to follow a rather unusual
temperature dependence, i.e. 1/χ ∼ T2. The tentative
attempt of quantitative analysis using 3D spin fluctua-
tion models resulted in inconvincible results for the mag-
netic susceptibility and the specific heat data. Although
the major contribution to the enhancement of the param-
agnetism of SrRhO3might result from a seizable density
of state at Fermi level, as in (Sr,Ca)RuO3[2, 3, 4], it is
not sufficient to explain the entire magnetic behavior of
SrRhO3, because it is temperature-independent. There
are likely additional factors which account for the tem-
perature dependent portion of the magnetism with the
1/χ ∼ T2trend. The character of the paramagnetism
of SrRhO3seems to be intermediate between that of en-
hanced Pauli- and CW-type paramagnetism. While ex-
tensive studies were made on paramagnon contributions
for the CW paramagnetism in the vicinity of the critical
point, the intermediate paramagnetism was essentially
uninvestigated. Whether the rhodium oxide 3D metal
tends toward either an antiferro- or ferromagnetic insta-
bility point, the imposing appearance of the distinctive
T2term in 1/χ indicates that the magnetic excitation of
4d electrons in SrRhO3remains highly elusive. Further
investigations into SrRhO3, including theoretical consid-
eration, would be of significant interest.
Acknowledgments
We are grateful to Dr. D.P. Young (Louisiana State
Univ.) for helpful discussions. We wish to thank Drs. M.
Akaishi and S. Yamaoka (AML/NIMS) for their advice
on the high-pressure experiments. This research was sup-
ported in part by the Multi-Core Project administrated
by the Ministry of Education, Culture, Sports, Science
and Technology of Japan.
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