Coexistence of metallic and nonmetallic properties in the pyrochlore Lu$_2$Rh$_2$O$_7$

TL;DR

This study synthesizes and characterizes Lu$_2$Rh$_2$O$_7$, revealing it as a correlated paramagnetic metal with unusual nonmetallic electrical behavior, challenging conventional classifications of metallic and insulating states.

Contribution

It reports the high-pressure synthesis and comprehensive characterization of a new pyrochlore oxide, Lu$_2$Rh$_2$O$_7$, highlighting its unconventional nonmetallic electrical properties despite metallic magnetic signatures.

Findings

Lu$_2$Rh$_2$O$_7$ is a correlated paramagnetic metal.

Electrical resistivity increases with decreasing temperature, indicating nonmetallic behavior.

Resistivity does not follow conventional temperature dependence, suggesting non-Fermi liquid behavior.

Abstract

Transition metal oxides of the $4d$ and $5d$ block have recently become the targets of materials discovery, largely due to their strong spin-orbit coupling that can generate exotic magnetic and electronic states. Here we report the high pressure synthesis of Lu$_2$Rh$_2$O$_7$, a new cubic pyrochlore oxide based on $4d^5$ Rh$^{4+}$ and characterizations via thermodynamic, electrical transport, and muon spin relaxation measurements. Magnetic susceptibility measurements reveal a large temperature-independent Pauli paramagnetic contribution, while heat capacity shows an enhanced Sommerfeld coefficient, $\gamma$ = 21.8(1) mJ/mol-Rh K$^2$. Muon spin relaxation measurements confirm that Lu$_2$Rh$_2$O$_7$ remains paramagnetic down to 2 K. Taken in combination, these three measurements suggest that Lu$_2$Rh$_2$O$_7$ is a correlated paramagnetic metal with a Wilson ratio of $R_W = 2.5$. However, electric transport measurements present a striking contradiction as the resistivity of Lu$_2$Rh$_2$O$_7$ is observed to monotonically increase with decreasing temperature, indicative of a nonmetallic state. Furthermore, although the magnitude of the resistivity is that of a semiconductor, the temperature dependence does not obey any conventional form. Thus, we propose that Lu$_2$Rh$_2$O$_7$ may belong to the same novel class of non-Fermi liquids as the nonmetallic metal FeCrAs.

Tables

Table 1. Table 1: Refined lattice positions and temperature factors for Lu 2 Rh 2 O 7 where the goodness of fit parameters are R p = 7.34, R wp = 10.9, R exp = 6.27 and χ 2 superscript 𝜒 2 \chi^{2} = 3.02

	$x$	$y$	$z$	$B_{iso}$	site
Lu	0.5	0.5	0.5	0.52(4)	$16d$
Rh	0	0	0	0.28(5)	$16c$
O1	0.375	0.375	0.375	0.4(2)	$8b$
O2	0.3296(5)	0.125	0.125	0.4(2)	$48f$

Equations

$$A(t)=A_0\cdot \exp {(-\lambda t)}^{\beta }+A_{BG}$$

Full text

Keywords: Non-Fermi liquid, pyrochlore, high-pressure synthesis, magnetic susceptibility, heat capacity, electrical transport, muon spin relaxation

I Introduction

The electronic and magnetic properties of many transition metal oxides can be understood by considering three energy scales: (i) the on-site Coulomb repulsion, Hubbard $U$, (ii) the band width, $W$ and (iii) the spin-orbit coupling, $\lambda$. The strong-coupling limit of this paradigm occurs for $3d$ oxides where Hubbard repulsion dominates ($U/W\gg 1$) and spin-orbit coupling ($\lambda\propto Z^{4}$) is negligible. As a consequence, Mott insulating states are observed in many materials that one would expect to be metals from band theory, as exemplified by the parent compounds of the high temperature cuprate superconductors Lee et al. (2006). The opposing limit occurs for $5d$ oxides, where the $d$ electron orbitals are far more spatially delocalized such that $U$ decreases while $W$ increases ($U/W\approx 1$). At the same time, the large mass enhancement brings spin-orbit coupling to the forefront, giving rise to remarkable correlated states such as topological insulators, Weyl semi-metals, and spin-orbit assisted Mott insulators Witczak-Krempa et al. (2014). Intermediate to these two limits is the $4d$ oxides, where $U$, $W$, and $\lambda$ can all be comparable in magnitude.

The chemically versatile pyrochlore oxides, $A_{2}B_{2}$O7, are an excellent family of materials to explore the competition between $U$, $W$, and $\lambda$. In this structure, the $A$ site is usually occupied by a rare earth cation, while the $B$ site can be occupied by transition metals from the $3d$, $4d$, or $5d$ block (or a post-transition metal). Consequently, a wide assortment of electronic behaviors are observed, ranging from band insulators to correlated metals. Pyrochlores are also of significant interest for their magnetic properties. The corner-sharing tetrahedral arrangement of the $A$ and $B$ cation sublattices is prone to intense geometric frustration, which has been extensively studied in the insulating families Gardner et al. (2010). The metallic pyrochlore oxides provide an intriguing platform for studying the interplay of geometric frustration and metallic degrees of freedom, an emerging topic that has begun to garner significant attention Nakatsuji et al. (2006); Lacroix (2010); Julian and Kee (2012); Paddison et al. (2013); Billington et al. (2015); Sapkota et al. (2017). Whereas frustration in local moment systems can straightforwardly be identified via the so-called frustration index, $f=\nicefrac{{|\theta_{CW}|}}{{T_{N}}}$ Ramirez (1994), no equivalent metric has yet been established for itinerant magnetic materials. Hence, how to unambiguously identify the presence of frustration in an itinerant system remains an open problem. A recent study broached this topic by using inelastic neutron scattering to extract exchange couplings which were then compared to a local moment picture Sapkota et al. (2017).

In the rare earth pyrochlores, the $4f$ electrons from the $A$-site cation are highly localized and do not participate in electrical conduction. Thus, the electronic properties of pyrochlore materials are largely governed by the choice of $B$-site cation Subramanian et al. (1983). Insulating states are expected and observed in cases where there are no partially filled $d$-electron orbitals, such as when $B=$ Ti4+, Ge4+, Sn4+, and Zr4+. Due to their dominant Hubbard $U$, insulating or semiconducting states are also found in the majority of cases where $B$ has a partially occupied $3d$ shell, such as $B=$ Mn4+ and Cr4+. Semiconducting states are found for a number of pyrochlores with partially filled $4d$ or $5d$-shells, such as those with $B=$ Mo4+, Ru4+, and Pt4+. Pyrochlores with metallic states are fewer in number, with notable examples being found amongst the $B=$ Os5+, Re5+, and Ir4+ families. In these systems, large spin-orbit coupling results in fascinating correlated electron phenomena. For instance, the iridate family of pyrochlores have been lauded as candidates for topological electronic states Wan et al. (2011). Meanwhile, Cd2Re2O7 is a moderately heavy fermion metal, $\gamma$ = 13.3 mJ/mol-Re K2 Blacklock and White (1979), with a superconducting transition at $T_{C}=1.47$ K Sakai et al. (2001). In the case of Cd2Os2O7, the entanglement of spin, orbital, and lattice degrees of freedom drives a metal-to-insulator transition at 226 K concomitant with antiferromagnetic order Sleight et al. (1974); Mandrus et al. (2001); Calder et al. (2016); Sohn et al. (2017). Here, we introduce a new $4d$ pyrochlore, Lu2Rh2O7, where we expect that $U$, $W$, and $\lambda$ are all comparable in magnitude, giving rise to an exotic non-Fermi liquid state.

The magnetism in Lu2Rh2O7 originates from $4d^{5}$ Rh4+ while $4f^{14}$ Lu3+ is non-magnetic. Although several $4d^{5}$ rhodate pyrochlores have been previously reported Sleight and Gillson (1971); Lazarev and Shaplygin (1978), their characterization has been negligible, especially in contrast to their $5d^{5}$ iridate analogs. This can, in part, be attributed to the difficulty in stabilizing rhodium in its 4+ oxidation state, which we overcome using high pressure methods. In the pyrochlore lattice, Rh4+ sits at the center of a trigonally distorted octahedral oxygen environment with $D_{3d}$ point group symmetry. As schematically presented in Figure 1(a), the crystal electric field and moderately strong spin-orbit coupling ($\lambda=0.19$ eV for Rh in contrast with $\lambda=0.40$ eV for Ir Martins et al. (2017)) split the $d$ electron states into a filled $j_{\text{eff}}=3/2$ band and a half-occupied $j_{\text{eff}}=1/2$ band. Thus, akin to the $5d^{5}$ iridates Uematsu et al. (2015), the $4d^{5}$ rhodates can have a $j_{\text{eff}}=1/2$ magnetic degree of freedom, leading to a spin-orbit induced Mott insulating state Rau et al. (2016). Both theoretical calculations and direct spectroscopic measurements have confirmed the applicability of the $j_{\text{eff}}=1/2$ picture in other rhodate materials Birol and Haule (2015); Calder et al. (2016). However, even in cases where $\lambda$ is not large enough to reach the pure $j_{\text{eff}}=1/2$ limit, as is likely the case in Lu2Rh2O7, the influences of spin-orbit coupling are still strongly felt Martins et al. (2011); Luo et al. (2013). We have characterized the magnetic and electronic properties of Lu2Rh2O7 with magnetic susceptibility, heat capacity, resistivity, and muon spin relaxation ($\mu$SR) measurements. These measurements reveal an apparent contradiction: magnetic susceptibility, heat capacity, and $\mu$SR are consistent with a strongly correlated paramagnetic metal. Resistivity data on the other hand suggests an unconventional semiconducting state and hence, a gap in the density of states. Thus, we propose that Lu2Rh2O7 belongs to the class of “nonmetallic metals” a term coined to describe the behavior of FeCrAs Wu et al. (2009); Akrap et al. (2014).

II Results

Under strongly oxidizing conditions, Lu2Rh2O7 crystallizes in the pyrochlore structure (space group $Fd\bar{3}m$). The powder x-ray diffraction pattern, which is presented in Figure 1(b), was analyzed via Rietveld refinement, giving a cubic lattice parameter of $a=10.0265(1)$ Å. The ratio of the ionic radii for Lu3+ (86.1 pm) and Rh4+ (60 pm) is within the stability range for the pyrochlore structure Subramanian et al. (1983). Thus, significant levels of $A/B$ site mixing are neither expected nor observed. The only adjustable coordinate within the pyrochlore structure is the O2 $x$ position, which we refine to $x=0.3296(5)$. When $x=0.3125$, the oxygen environment at the $B$-site is an ideal octahedron (point group $O_{h}$). Deviations from this value induce a compression along the local [111] axis, as shown in Figure 1(a), such that the six equidistant oxygen ions have alternating bond angles of 93.5° and 86.5° with the central Rh4+ cation (point group $D_{3d}$). A small RhO2 impurity, comprising 2.1(2)% of the total sample volume, was included as a second phase in the Rietveld refinements (a tetragonal structure with space group P42/mnm) Muller and Roy (1968); Shannon (1968). RhO2 is a high pressure metallic oxide phase which is insoluble in aqua regia and could not be removed from our samples. The results of the Rietveld refinement, including the goodness-of-fit parameters, are listed in Table I.

The magnetic susceptibility of Lu2Rh2O7 measured in an $H=1$ T field is presented in Figure 2. We have corrected the data for core diamagnetism using the values tabulated in Ref. Bain and Berry (2008), which gives $\chi_{D}=-1.54\cdot 10^{-4}$ emu/F.U. There is no appreciable difference between data collected under zero-field cooled or field cooled conditions. Lu2Rh2O7 is paramagnetic down to the lowest measured temperature, with no evidence for magnetic ordering or spin freezing down to 2 K. The susceptibility is dominated by a large nearly temperature independent Pauli paramagnetic contribution. Below 10 K, the intrinsic susceptibility is obscured by a Curie-tail. We observe a shallow, broad hump in the susceptibility centered near 50 K. As can be seen in Figure 2, the inverse susceptibility between 100 and 300 K is reasonably well-described by a Curie-Weiss equation, $\chi=\frac{C}{T-\theta}$, where we obtain $\theta=-1393(2)$ K and $\mu_{\text{eff}}=\sqrt{8C}=3.1(1)$ $\mu_{B}$. Clearly this magnitude of $\theta$ is not physically meaningful as the susceptibility is dominated by the Pauli paramagnetic contribution. However, attempts to model the susceptibility to a modified Curie-Weiss law, $\chi=\frac{C}{T-\theta}+\chi_{0}$, failed to produce a unique solution. Instead, we proceed by subtracting the Curie-tail contribution, which we fit to $\chi\propto\frac{C}{T}$, allowing us to estimate the low temperature Pauli paramagnetic contribution as $\chi_{P}=7.6\cdot 10^{-4}$ emu/mol-Rh. This value is nearly an order of magnitude larger than in typical metals, signaling strong electron correlation effects. The induced magnetization at 2 K and 7 T is only 0.01 $\mu_{B}$/Rh4+, consistent with an itinerant paramagnetic state (inset of Fig. 2). The susceptibility and magnetization data for Lu2Rh2O7 bear a striking resemblance to that of SrRhO3, another Rh4+-based paramagnetic metal Yamaura and Takayama-Muromachi (2001). The unusual properties of SrRhO3 have been argued to emerge as the result of proximity to a quantum critical point Singh (2003).

The heat capacity of Lu2Rh2O7 is presented in Figure 3, where no phase transitions are observed between 2 and 300 K. For comparison, we plot alongside this data the scaled heat capacity of Lu2Ti2O7, which is an insulating lattice analog with no unpaired $d$ electrons Saha et al. (2008). The heat capacity of Lu2Ti2O7 was scaled by $\mu=\sqrt{\nicefrac{{M_{LRO}}}{{M_{LTO}}}}$ where $M_{LRO}$ and $M_{LTO}$ are the molecular weights of Lu2Rh2O7 and Lu2Ti2O7, respectively. These two data sets are largely consistent, confirming that the high temperature heat capacity of Lu2Rh2O7 can be accounted for by lattice degrees of freedom. The scaled heat capacity of Lu2Ti2O7 is observed to slightly exceed that of Lu2Rh2O7 below 50 K. This difference can be understood to originate from anharmonic effects, which are known to be significant in rare earth pyrochlores Maczka et al. (2008), and will vary between compounds dependent on the details of the phonon interactions. Indeed, the heat capacity of Lu2Ti2O7 is also observed to exceed that of Dy2Ti2O7 in the same temperature interval Saha et al. (2008). At the lowest temperatures, Fermi liquid behavior is observed for Lu2Rh2O7, where $C/T$ is linear with respect to $T^{2}$ up to $T=10$ K (Inset of Fig. 3). The fitted value for the Sommerfeld coefficient is $\gamma$ = 21.8(1) mJ/mol-Rh K2, which is large and comparable to values observed in other strongly correlated rhodates and ruthenates Maeno et al. (1997); Park et al. (2016); Perry et al. (2006).

Enhanced electron masses are most commonly associated with heavy fermion physics in $f$-electron metals Stewart (1984). However, there are several notable examples of $d$-electron systems with anomalously large Sommerfeld coefficients, including Y1-xScxMn2 Shiga et al. (1993) and LiV2O4 Kondo et al. (1997). In both Y1-xScxMn2 (a cubic Laves phase) and LiV2O4 (a spinel), the underlying magnetic sublattice is a pyrochlore-like network of corner-sharing tetrahedra. It has been proposed that geometric frustration plays a central role in their electronic properties. Frustration tends to suppress conventional magnetic order, giving rise to strong spin fluctuations, while the itinerant nature of the electrons results in large spin disorder entropy at low temperatures, which gives rise to an enhanced linear contribution to the specific heat Lacroix (2001). Indeed, the values for $\gamma$ in Y1-xScxMn2 (140 mJ/mol K2 for $x=0.03$ Wada et al. (1987)) and LiV2O4 (420 mJ/mol K2 Kondo et al. (1997)) are comparable to some of the best known examples of $f$-electron heavy fermion systems, such as URu2Si2 (180 mJ/mol K2 Palstra et al. (1985)) and UPt3 (420 mJ/mol K2 Frings et al. (1983)). Given that the magnetic sublattice of Lu2Rh2O7 shares this frustrated architecture, similar mechanisms may be responsible for its enhanced Sommerfeld coefficient.

We have also performed zero field $\mu$SR measurements on Lu2Rh2O7. While the bulk probes employed thus far all indicate the absence of magnetic order, muons as a local probe are highly sensitive to very small ordered moments, even those below 0.1 $\mu_{B}$. Muon decay asymmetry spectra were collected between 2 and 250 K, and several representative data sets are presented in Figure 4(a). The relaxation, which is weak at all measured temperatures, is observed to gradually increase with decreasing temperature. We do not observe any sharp increase in relaxation or spontaneous oscillations, as would be expected in the case of long-range magnetic order. As a function of temperature, the relaxation evolves from more Gaussian-like at high temperatures to Lorentzian at the lowest temperatures. Thus, we fitted the asymmetry spectra to a stretched exponential function

[TABLE]

where $\lambda$ is the relaxation rate and the stretching parameter was constrained to lie between $\beta=1$ (Lorentzian) and $\beta=2$ (Gaussian). The non-relaxing background asymmetry, $A_{BG}$, accounts for muons which land outside the sample. The total asymmetry was constrained by fitting the precessing signal at high temperature in a weak field applied transverse to the muon’s spin. The temperature dependence of both $\lambda$ and $\beta$ are presented in Figure 4(b). The relaxation rate gradually grows below 200 K, reaching a maximum value of 0.15 $\mu s^{-1}$ at 2 K. There is a concomitant decrease of the stretching parameter, which plateaus at $\beta=1$ below 20 K. This can be understood in terms of a crossover, where at high temperatures more Gaussian relaxation is observed due to fluctuating nuclear dipoles whereas at lower temperatures the signal is dominated by slowing spin dynamics. The decrease in $\beta$ may share an origin with the broad hump in the susceptibility in the same temperature interval. Moreover, these $\mu$SR measurements confirm that Lu2Rh2O7 remains paramagnetic, with no evidence for magnetic order or spin freezing down to 2 K.

Electrical resistivity measurements were carried out using a conventional four-terminal method on a cold-pressed pellet Zhou et al. (2003) of Lu2Rh2O7, which was annealed in air at 600 °C for 10 hours to minimize grain boundary effects. X-ray diffraction measurements were performed before and after the annealing protocol to confirm that it did not result in any degradation of the sample. In striking contrast to the magnetic susceptibility and heat capacity, which would both suggest a metallic state, the room temperature resistivity is 0.36 $\ohm$-cm, which is typical of a semiconducting state. Furthermore, the temperature dependence of the resistivity monotonically increases with decreasing temperature (ie. $d\rho/dT<0$). The resistivity is observed to diverge below 10 K. The inset of Figure 5 shows that this resistivity does not obey a thermally activated Arrhenius behavior for a very large range of temperatures. The data can be fit between 200 and 300 K to $\rho\propto\rho_{a}\cdot\exp(-\Delta/2k_{B}T)$, yielding a very small gap of $\Delta=37(1)$ meV. There are several factors worth considering in the quantitative interpretation of this data. First is that this sample is a pressed pellet and thus, scattering from grain boundaries may be expected to uniformly increase the resistivity. However, the cold-pressing and annealing protocol followed here has been demonstrated to provide nearly intrinsic transport measurements in other transition metal oxides, including samples that are far softer and more porous than the one measured here Zhou et al. (2003). Moreover, even without the cold-pressing technique, conventional metallic resistivity (ie. $d\rho/dT>0$) has been measured in numerous polycrystalline samples of rhodates synthesized via the same high-pressure techniques used here Yamaura and Takayama-Muromachi (2001); Yamaura et al. (2002, 2004, 2005); Yamaura and Takayama-Muromachi (2006). It is also worth mentioning that our minor impurity phase, RhO2, is known to be a metal Shannon (1968). Thus, the nonmetallic resistivity is clearly intrinsic to Lu2Rh2O7, a remarkable result in a material that all other probes suggest is metallic.

III Discussion

Our characterizations have revealed that Lu2Rh2O7 possesses a highly unusual non-Fermi liquid state. While both heat capacity and magnetic susceptibility indicate a finite density of states at the Fermi energy, the temperature dependence of the resistivity appears more consistent with a semiconducting gap. Moreover, even for a semiconductor, the temperature dependence of the resistivity is unconventional. It is instructive to consider a comparison with the “nonmetallic metal” FeCrAs. First, an important structural commonality is that in both materials, the magnetic constituent(s) are connected in triangular motifs that can be prone to geometric magnetic frustration. In the case of Lu2Rh2O7 this is the corner-sharing tetrahedral pyrochlore sublattice and in the case of FeCrAs the non-magnetic Fe atoms occupy a triangular network of trimers while the magnetic Cr atoms form a distorted Kagome network. In regards to their electronic properties, the magnetic susceptibility of both materials is dominated by a largely temperature independent Pauli paramagnetic contribution Wu et al. (2009). Secondly, both materials have a Sommerfeld coefficient, as determined by heat capacity measurements, significantly larger than typically expected for a $d$ electron system, $\gamma$ = 21.8(1) mJ/mol-Rh K2 and 31.6 mJ/mol K2 for Lu2Rh2O7 and FeCrAs, respectively. However, the Wilson ratio ($R_{W}=4\pi^{2}k_{B}^{2}\chi_{P}/3(g\mu_{B})^{2}\gamma$) for FeCrAs, $R_{W}=4-5$ Wu et al. (2009) is larger than our computed value of $R_{W}=2.5$ for Lu2Rh2O7. A third commonality is the temperature dependence of the resistivity, where $d\rho/dT$ is negative, nominally indicative of a gap in the density of states. However, the room temperature resistivity for FeCrAs is approximately 0.4 m$\ohm$-cm, approximately three orders of magnitude smaller than our value of 0.4 $\ohm$-cm. Another significant difference between these two materials is that the Cr moments in FeCrAs undergo a long-range antiferromagnetic ordering transition at $T_{N}=125$ K Wu et al. (2009), while no magnetic order is observed in Lu2Rh2O7 down to at least 2 K.

Several compelling explanations have been put forward to explain the nonmetallic metallic state in FeCrAs, which are worth examining in the current context of our results on Lu2Rh2O7. The first proposal, which comes from Rau and Kee, suggests a hidden spin liquid state for the non-magnetic Fe trimers Rau and Kee (2011). They propose that the electrons residing on these trimers are close to a metal-insulator quantum critical point, such that charge fluctuations strongly renormalize the transport behavior while only minimally affecting the thermodynamic properties. A second proposal that does not rely on proximity to a Mott insulating state, but instead attributes the unusual qualities of FeCrAs to it being a Hund’s metal Nevidomskyy and Coleman (2009). In a Hund’s metal, non-Fermi liquid properties emerge due to strong intra-atomic exchange in a multiorbital material, such as ruthenates and iron pnictides Georges et al. (2013). The result of strong Hund’s coupling in these materials is that a subset of the $d$ orbitals are pushed towards the local limit while maintaining strong coupling to other itinerant electrons. Several arguments make this second scenario less favorable in the case of Lu2Rh2O7. First, Hund’s coupling generally plays a weaker role in $4d^{5}$ Rh4+ Georges et al. (2013). Secondly, this model is expected to give a large Wilson ratio Akrap et al. (2014), as indeed observed in FeCrAs where $R_{W}=4-5$ Wu et al. (2009), whereas in Lu2Rh2O7, $R_{W}=2.5$. Recent inelastic neutron scattering experiments have revealed high energy itinerant-like spin excitations, which Plumb et al. propose may account for the nonmetallic resistivity Plumb et al. (2018). Further study of the spin dynamics in Lu2Rh2O7 are called for, a task which would be greatly benefited by the availability of large single crystal samples. While no single crystals of rhodate pyrochlores have been reported to date, a route similar to that used for Sr2RhO4 may prove fruitful Perry et al. (2006).

Using high-pressure methods, we have synthesized a new pyrochlore Lu2Rh2O7, in which $j_{\text{eff}}=1/2$ Rh4+ occupies a frustrated corner-sharing tetrahedral lattice. No magnetic order is observed down to 2 K in $\mu$SR measurements. Heat capacity and magnetic susceptibility measurements both indicate strong electron correlations, with a large temperature independent Pauli paramagnetic response and an enhanced Sommerfeld coefficient, $\gamma$ = 21.8(1) mJ/mol-Rh K2. Resistivity measurements, in contrast, suggest nonmetallic behavior ($d\rho/dT<0$) in the full measured temperature range, 2 - 300 K. Thus, Lu2Rh2O7 has a non-Fermi liquid state, sharing many commonalities with the nonmetallic metal FeCrAs.

IV Methods

High pressure synthetic techniques are often required to stabilize Rh4+ compounds Muller and Roy (1968); Shannon (1968); Sleight and Gillson (1971); Lazarev and Shaplygin (1978); Yamaura and Takayama-Muromachi (2001); Yamaura et al. (2002, 2004), as Rh3+ is the more common oxidation state. The cubic pyrochlore Lu2Rh2O7 was prepared using a belt-type high pressure apparatus at the National Institute for Materials Science in Tsukuba, Japan. Lu2O3 were thoroughly dried prior to the reaction. Rhodium metal was first oxidized to Rh2O3 by reacting under flowing oxygen at 1000 °C for 72 hours. The reaction into the pyrochlore phase was completed using KClO4 as an oxidizing agent to promote the Rh4+ oxidation state. The precursors (Lu2O3, Rh2O3, KClO4 in a 1:1:$\frac{3}{8}$ ratio) were thoroughly ground together and sealed in a platinum capsule. The reaction was completed at 1700 °C and 6 GPa of applied pressure for 2 hours, after which the sample was quenched to room temperature before the pressure was released. The final product was repeatedly washed with water to remove KCl and then dried. The resulting 0.54 gram sample is made up of sub-micron sized black crystallites. Once prepared, this material is stable in air on a timescale of years.

X-ray diffraction measurements were performed using a PANalytical diffractometer with copper Kα1 radiation, $\lambda=1.540560$ Å. Rietveld refinement was performed using FullProf Rodríguez-Carvajal (1993). Magnetic susceptibility, resistivity, and heat capacity measurements between 2 and 300 K were completed using a Quantum Design Physical Property Measurement System. Zero field $\mu$SR measurements were performed at the M20 surface muon channel at TRIUMF in the LAMPF Spectrometer. The $\mu$SR data were fitted over the full measured time interval, up to 9.5 $\mu$s, using the muSRfit software package.

V Data Availability

The crystal structure of Lu2Rh2O7, as determined by Rietveld refinement of the powder x-ray diffraction data, is available at the Cambridge Crystallographic Data Centre with deposition number CSD 1895045. All other data is available from the authors on reasonable request.

VI Acknowledgments

We gratefully acknowledge useful conversations with Yipeng Cai, Jonathan Gaudet, John Greedan, Chien-Lung Huang, and Murray Wilson. We thank Bassam Hitti and Gerald Morris from TRIUMF for their support with the $\mu$SR experiment. A.M.H. thanks the National Institute for Materials Science (NIMS) for their hospitality and support through the NIMS Internship Program. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Canada Foundation for Innovation. C.R.W. is additionally supported by the Canada Research Chair (Tier II) program and the Canadian Institute for Advanced Research. Q.C. and H.D.Z. are supported by the National Science Foundation (NSF-DMR-1350002).

VII Competing Interests

The authors declare no competing interests.

VIII Contributions

The high-pressure synthesis and x-ray diffraction was performed by A.M.H. and M.T. Magnetic susceptibility and electric resistivity measurements, and their analysis, were performed by Q.C., H.D.Z., C.M., P.M.S., J.P.A., A.M.H., and C.R.W. Heat capacity measurements were performed by A.Z.S. and C.R.W. $\mu$SR measurements were performed and analyzed by A.M.H. and G.M.L. with assistance from C.D. and Z.G. The manuscript was written by A.M.H and C.R.W. with input from all authors.