Bulk properties of single crystals of the valence-unstable compound SmRh$_2$Si$_2$

TL;DR

This study reports the synthesis and comprehensive characterization of SmRh₂Si₂ single crystals, revealing antiferromagnetic order at 64 K and discussing valence and electronic properties with implications for Kondo physics.

Contribution

The paper provides new insights into the bulk properties and valence state of SmRh₂Si₂, including crystal growth, structural analysis, and thermodynamic measurements, highlighting its antiferromagnetic ground state.

Findings

Antiferromagnetic order at T_N = 64 K

Small Sommerfeld coefficient similar to LuRh₂Si₂

No evidence of Kondo screening in thermodynamic data

Abstract

We present the crystal growth as well as the structural, chemical and physical chracterization of SmRh$_2$Si$_2$ single crystals. Their ground state is antiferromagnetic, as indicated by the behaviour of the magnetic susceptibility and the specific heat at the second order phase transition observed at T$_{\rm N}$ = 64 K. The Sommerfeld coefficient is small and similar to that of LuRh$_2$Si$_2$ with $\gamma_0\approx$ J/(molK$^2$). Susceptibility measurements show no Curie-Weiss behaviour at high temperatures which is a consequence of the large Van-Vleck contribution of the excited multiplets of Sm$^{3+}$. Previous angle-resolved photoemission studies showed that at 10 K, the valence of the Sm ions is smaller than three at the surface as well as in the bulk, suggesting a possible Kondo screening of the Sm$^{3+}$ ions. This could not be observed in our thermodynamic and transport measurements.

Full text

I Introduction

Sm-based compounds have been studied rarely in the past compared to compounds containing lanthanide ions like Ce, Eu, Gd, Ho or Yb, but the recent discovery of topologically insulating behaviour in SmB6 Takimoto2011 ; Lu2013 ; Kim2014 renewed the interest in the community in Sm-based compounds. Some Sm compounds exhibit strongly correlated electron behaviour like the heavy-fermion compounds SmOs4Sb12 Sanada2005 or SmT2Al20 Higashinaka2011 , which have a complex crystallographic structure and the characterization of systems with lower structural complexity is highly desired. Recently, the valence of the Sm ions in SmRh2Si2 single crystals was studied by angle resolved photoemission spectroscopy (ARPES). Contributions from the bulk as well as from the surface to the photoemission spectrum have been determined Chikina2017 . Divalent Sm $4f$ contributions to the photoemission spectrum are expected close to the Fermi level and have been observed experimentally in the past for Sm metal Wertheim1978 and a number of Sm compounds Allen1980 ; Yamaoka2012 . Such emissions from divalent Sm were mostly identified as surface valence transitions in trivalent bulk systems. ARPES revealed that for Sm ions in SmRh2Si2, the electronic properties of bulk and surface are rather similar and the Sm ions behave in both cases slightly mixed valent. The mean valence of the Sm ions in SmRh2Si2 was estimated to be about $2.94$ at $T=10\,\rm K$ Chikina2017 . Usually, the valence of Sm ions at the surface of a single crystal is $2+$ and the observed deviation is quite unusual. In the bulk, small deviations from the $3+$ valence usually occur in Ce or Yb compounds which show the Kondo effect. This motivated the study of the bulk properties to see, if these small deviations influence the thermodynamic and transport properties of SmRh2Si2.

The crystallographic ThCr2Si2-type structure of SmRh2Si2, Fig. 1 (a), was reported by Felner and Nowik Felner1983a ; Felner1984 and an isothermal section ($T=870\,\rm K$) of the ternary Sm-Rh-Si phase diagram was explored by Morozkin et al. Morozkin1996 ; Morozkin1996a . Susceptibility as well as electrical resistivity measurements on polycrystalline samples were reported by different authors: Signatures of magnetic transitions in the susceptibility at $62$, $35$ and $10\,\rm K$ and a kink in the resistivity at $60.5\,\rm K$ were observed by Kochetkov et al. Kochetkov1997 . Felner and Nowik reported about peaks in the susceptibility at $8\pm 2\,\rm K$ and $46\pm 2\,\rm K$ Felner1984 . These conflicting results in literature, call for a precise determination of the magnetic and thermodynamic properties in high-quality single crystals.

II Experiment

Single crystals of SmRh2Si2 were grown in In flux. The high purity starting materials Sm (99.99%, REP), Rh (99.9%, Heraeus), Si (99.9999%, Wacker), with the molar ratio of 1:2:2, and In (99.9995%, Schuckard) were weighed in a graphite crucible with a volume of 10 ml and sealed in a niobium crucible under argon atmosphere (99.999%). The stoichiometric composition of the elements was used with 96 at.% indium as flux. Indium was put at the bottom of the crucible covered by the high-melting elements Rh and Si covered again by indium pieces. Subsequently, the crucible was transfered to the Ar-filled glove-box, where Sm was placed on top, covered once more by indium. Finally, the Nb-crucible was closed using arc-welding. The filled Nb-crucible was put under a stream of Ar in a resistive furnace (GERO HTRV 70-250/18) and the elements were heated up to 1550*∘C. The melt was homogenized for 1 hr and then cooled by slow moving the whole furnace with 1 mm/hrs leading to a cooling rate in the range of 0.5 - 4 K/hrs down to 1000∘*C, while the position of the crucible stayed fixed. The growth parameters have been chosen similarily as reported for the growth of GdRh2Si2 Kliemt2015 .

Until now, the successful single crystal growth was not reported, which probably is due to the incongruent melting of this material at approximately 1760*∘C Morozkin1997 . We therefore employed the flux-growth technique as described above, which allows to perform the crystal growth at temperatures below the high melting points of the elements (Sm 1072∘C, Rh 1964∘C, and Si 1414∘*C). So far, it was not possible to determine the accurate crystallization temperature of SmRh2Si2 in 96  at.% In, but a systematic optimization of the temperature profile revealed that the largest crystals could be grown when starting the crystal growth at Tstart= 1520∘C, compared to growths starting below 1500∘C. After cooling, the excess In was dissolved by hydrochloric acid until phase pure SmRh2Si2 was obtained. Although, not everything of the starting material crystallized in the SmRh2Si2 phase, the resulting single crystals of SmRh2Si2 are large enough to carry out several physical characterization measurements. Typical single crystals as the one shown in inset Fig. 1 (c) have a platelet habit with the shortest dimension, $100-400\,\mu$m, along the crystallographic $c$-direction and $1-2\,\rm mm$ perpendicular to that direction. Few single crystals had an extension in $c$-direction of about $1\,\rm mm$ and thus were suitable for transport measurements along this direction.

The chemical composition determined by energy-dispersive X-ray spectroscopy (EDX) revealed (20$\pm$1)at.$\%$ Sm, (40$\pm$1)at.$\%$ Rh and (40$\pm$2)at.$\%$ Si. We cannot exclude some Rh-Si site exchange within these error bars; however, for the related compound YbRh2Si2 a detailed structural and chemical analysis was conducted by highly accurate X-ray diffraction and wavelength dispersive X-ray spectroscopy measurements wirth2012 . There, it turned out that the structure accepts some Rh-Si site exchange, with a rather small homogeneity range for Rh, which was found to be 40.0 - 40.2  at.%.

The crystal structure was characterized by powder X-ray diffraction (PXRD) on crushed single crystals, using Cu-Kα radiation. PXRD confirmed the $I4/mmm$ tetragonal structure with lattice parameters a = 4.0555(2) Å  and c =10.0402(4) Å, which is in agreement with the data published for polycrystalline samples Felner1983a .

The orientation of the single crystals was determined using a Laue camera with X-ray radiation from a tungsten anode. The high quality of the single crystals is evident also from a Laue back scattering image, presented in Fig. 1 (b). The central point can be indexed as the (001) reflex, proving that the direction perpendicular to the surface of the platelets corresponds to the $c$-direction. Four-point resistivity, magnetization, and heat-capacity measurements were performed using the commercial measurements options of a Quantum Design Physical Properties Measurement System.

III Results and discussion

Heat capacity and entropy

In Fig. 2 (a) specific-heat data are shown for the two related materials SmRh2Si2 and LuRh2Si2. The latter serves as a non-magnetic reference system with a completely filled $4f-$shell. The LuRh2Si2 data were taken from Ref. Ferstl2007 . For SmRh2Si2 a pronounced and sharp $\lambda$-type anomaly is observed at $T_{\rm N}=64\,\rm K$, establishing a second order phase transition into the antiferromagnetically (AFM) ordered phase. Inset (b) in Fig. 2 displays $C/T$ versus $T^{2}$. Between $20\,{\rm K}^{2}<T^{2}<60\,{\rm K}^{2}$, $C/T$ of SmRh2Si2 is nearly equal to $C/T$ of LuRh2Si2 which shows that magnetic excitations are frozen out indicating the presence of a gap in the magnon spectra. Above $T^{2}=60\,{\rm K}^{2}$, $C/T$ of SmRh2Si2 increases much stronger than $C/T$ of LuRh2Si2 which exhibits a nearly linear behavior. This much stronger increase corresponds to the exponential thermal activation of magnetic excitations across the gap. This gap very likely results from the magnetic anisotropy not only between the $c$ and the in-plane direction, but also within the plane as evidenced by magnetization data (see below discussion of Fig. 4). While both LuRh2Si2 and LaRh2Si2 show a linear behavior in $C/T(T)$ versus $T^{2}$ for $T^{2}<60\,{\rm K}^{2}$, SmRh2Si2 still present a small positive curvature resulting in slightly larger values of $C/T$ than in LuRh2Si2 at lowest $T$. This indicate the onset of an additional contribution to $C/T$ at lowest $T$, which is likely connected with the nuclear contribution, but might also origin from magnetic defects. The presence of this additional low $T$ contribution prevents a direct determination of the Sommerfeld coefficient $\gamma_{0}$ and of the low $T$ Debye temperature $\Theta_{D}$. However, the observation that for $T^{2}<80\,\rm K^{2}$ SmRh2Si2 presents nearly the same $C/T$ as LuRh2Si2 indicate that $\gamma_{0}$ and $\Theta_{D}$ of SmRh2Si2 are very close to those of LuRh2Si2, $\gamma_{0}\approx 7\rm mJ/(molK^{2})$ and $\Theta_{D}=380\,\rm K$.

By subtracting the heat capacity of the non-magnetic reference compound LuRh2Si2 Ferstl2007 we obtained the magnetic part of the specific heat $C^{\rm 4f}$ and by integrating $C^{\rm 4f}/T$ the entropy $S^{\rm 4f}$. Fig. 2 inset (c) shows that $S^{\rm 4f}$ increases up to the phase transition and increases further towards higher temperature. The Sm ion with $J=5/2$ has 6 possible states and the entropy of the full crystalline electric field (CEF) multiplet would amount to $S^{\rm 4f}=R\,\rm ln\,6$ at the phase transition. We find that the entropy is strongly influenced by the CEF. It is smaller than $R\,\rm ln\,6$ and larger than $R\,\rm ln\,2$ at the phase transition which shows that besides the ground state doublet also the occupation of higher levels contributes to the entropy.

Electrical resistivity

Electrical transport data shown in Fig. 1, indicate an anisotropic behaviour for current flowing parallel and perpendicular to the $[001]$-direction below $T_{\rm N}$. We determined $RR^{j\parallel c}_{1.8\,\rm K}=10$ and $RR^{j\perp c}_{1.8\,\rm K}=25$. The absolute value of $\rho(T)$ at room temperature for the in-plane resistivity was about $80\,\mu\Omega\rm cm$. For better comparison of the data with $j\parallel c$ and $j\perp c$, we present the normalized resistivity $\rho(T)/\rho_{300\,\rm K}$. For both directions, the resistivity shows a quasi-linear-in-$T$ behaviour from $300\,\rm K$ to the AFM phase transition. Upon cooling, at $T_{\rm N}$ a change of the slope of the resistivity curves occurs and the decrease of the resistivity becomes stronger. In previous work, $\rho_{200K}/\rho_{0}\sim 5$ was determined for polycrystalline material Kochetkov1997 . The residual resistivity ratios $\rm RRR=\rho_{300K}/\rho_{0}\sim 25$ (corresponding to $\rho_{200K}/\rho_{0}\sim 17.5$) determined on our samples for $j\perp c$ shows that we succeeded in growing high-quality crystals using the indium-flux method.

Magnetization

The magnetic moment of the Sm ions in SmRh2Si2 is small and great care needs to be taken to subtract the background contribution. We therefore studied this material by using large single crystals with a mass of about $30\,\rm mg$. In Fig. 3, the temperature dependence of the susceptibility for a field of $B=5\,\rm T$ along two main symmetry directions is shown. Upon cooling, the transition into the AFM-ordered state appears at the Néel temperature $T_{\rm N}=65\,\rm K$. For $B\perp c$, the susceptibility decreases strongly below $T_{\rm N}$ and shows a small increase at lowest temperatures. This feature varies from sample to sample and is probably caused by a paramagnetic defect contribution. The comparison of the susceptibility curves for both field directions suggests that below $T_{\rm N}$ the magnetic moments are ordered within the basal plane of the tetragonal lattice. Additionally, our data shows the absence of further magnetic transitions which were proposed by Ref. Felner1983a and Ref. Kochetkov1997 in previous works. Above $T_{\rm N}$, the $T$ dependence of the susceptibility is typical for a Sm3+ system, cf. Fig. 3. It first shows in a small $T$ range a Curie-Weiss like decrease, then evolves towards a large $T$ independent susceptibility, and for field along the $c$ axis even show a slight increase towards higher temperatures. This peculiar $T$ dependence which significantly differs from the Curie-Weiss behaviour observed for most other rare earth can easily be accounted for by the specific properties of the $4f$ state of Sm3+. In the $J=L-S=5/2$ ground state multiplet of the $4f^{5}$ state of Sm3+ the almost cancellation of the orbital part of the moment with $L=5$, $g_{\rm orb}=1$ by the spin part with $S=5/2$, $g_{\rm spi}=2$ results in a tiny Landé factor $g_{L}=0.286$. This leads to a quite small value of the effective moment, $\mu_{\rm eff}=0.84\mu_{\rm B}$ and, accordingly, to a small Curie-Weiss contribution. In contrast, the first excited multiplet $J=7/2$ being at a comparatively low energy $E_{7/2}\approx 1500\,\rm K$ Osborn1991 results in a large $T$-independent Van-Vleck type susceptibility which overwhelms the Curie contribution at $T>200\,\rm K$. Further on the increase of the susceptibility for $T>400\,\rm K$ is due to thermal excitation of the $J=7/2$ multiplet, because it has a much larger Landé factor $g_{L}=0.825$, and thus a much larger effective moment $\mu_{\rm eff}=3.28\mu_{\rm B}$. Therefore the prefactor of its Curie contribution is a factor of 15 larger than that of the $J=5/2$ ground state multiplet. The further excited $J$ multiplets enhance this behaviour. The observed susceptibility, cf. Fig. 3, qualitatively agrees with that calculated for an isolated Sm3+ ion using the standard expression for Sm3+ and Eu3+ systems, see e.g. Ref. Takikawa2010 (Fig. 3, grey dots), but presents a number of differences, e.g a clear anisotropy. This anisotropy is likely dominated by the effect of the crystal electric field which affects both, the Curie contribution of the different multiplet states as well as the Van-Vleck contribution. But especially at low temperatures it is also affected by the exchange interaction, which also seems to be anisotropic. Due to the low susceptibility of the Sm3+ ions, contributions of the conduction electrons namely Pauli, orbital and diamagnetic susceptibility need to be taken into account. At high temperatures, the difference between the calculated curve (grey dots) and the measured susceptibility is about $2.0\cdot 10^{-9}{\rm m}^{3}/{\rm mol}$. This is in perfect agreement with the susceptibility of the non-$4f$ electrons determined for LaRh2Si2 by Ref. Sekizawa1987 .

The field dependence of the magnetization was investigated at $T=2.15\,\rm K$ in fields up to $B=9\,\rm T$. In the upper panel of Fig. 4, the magnetization for fields applied along the main symmetry directions is shown. Here, the magnetization shows anisotropic hystereses effects. While the slope of $M$ is nearly constant for field $B$ along the $[001]$ direction, red curve in Fig. 4, for $B\perp 001$, it is smaller and shows hysteresis effects, black and blue curves. This field dependent behaviour is consistent with a moment orientation in the basal plane of the tetragonal lattice. The occurence and size of the hystereses effects is strongly sample dependent.

IV Summary

We have grown SmRh2Si2 single crystals for the first time which enables us not only to determine precisely the phase transition temperature but also to study the anisotropic behaviour of this compound via electrical transport and magnetization measurements. In this work, single crystals of SmRh2Si2 have been grown by a modified Bridgman method from indium flux. After an optimization of the temperature-time profile of the growth experiment, we obtained millimetre-sized single crystals with a platelet habit with the $c$ axis perpendicular to the platelet. PXRD measurements on crushed single crystals confirmed the $I4/mmm$ tetragonal structure. The lattice parameters are in agreement with the data published for polycrystalline samples. The specific heat of SmRh2Si2 shows only one sharp $\lambda$-type anomaly at $T_{\rm N}=64\,\rm K$, establishing a second order phase transition into the AFM ordered phase. Magnetic measurements on the single crystals show the ordering of the Sm3+ moments at $T_{\rm N}$ as well as the reorientation of magnetic domains for an external field applied in the basal plane of the tetragonal lattice. Above $T_{\rm N}$, the susceptibility presents the typical behavior of a Sm3+ system. It shows a small Curie-Weiss contribution below $100\,\rm K$ due to the tiny Landé factor of the $J=5/2$ ground state multiplet, but a large $T$-independent Van-Vleck contribution which dominates the susceptibility above $200\,\rm K$ and results from low lying excited $J$ multiplets of Sm3+. Below $T_{\rm N}$, electrical transport data show an anisotropy between the resistivity measured with current parallel and perpendicular to the $c$ axis. The residual resistivity ratio $\rm RRR=\rho_{300K}/\rho_{0}\sim 25$ indicates that we succeeded in growing high-quality single crystals from a high-temperature indium flux. Recently, the single crystals enabled the investigation of their bulk and surface properties by ARPES. It turned out that at $T=10\,\rm K$ the valence of the Sm ions is smaller than three at the surface as well as in the bulk Chikina2017 . This hints to a possible Kondo screening of the Sm3+ ions but we could not detect any effect in the transport and thermodynamic properties.

Acknowledgements.

We are indebted to B. Schmidt for useful discussions. KK, CK and MB grateful acknowledge support by the German Research Foundation (DFG) by Grants No. KR 3831/4-1 and No. BR 4110/1-1.