III-2. Atomic & Solid State Physics (Muon)

RIKEN Accel.
(2021)
RIKEN
Accel. Prog.
Prog.Rep.
Rep.5454(2021)

Possible multipolar ordering in spin-orbital-entangled d2 system on aface-centered-cubic lattice
T. Takayama,∗1,∗2 D. P. Sari,∗3,∗4 I. Watanabe,∗4 and H. Takagi∗1,∗2,∗5
The interplay of strong spin-orbit coupling (SOC)and electron correlation in heavy transition-metal compounds containing 4d and 5d elements has been revealed to give rise to unprecedented electronic statesof matter. In such systems, strong SOC produces spinorbit-entangled Jeﬀ states of d-electrons. The interactions between spin-orbital-entangled objects are distinct from those in spin-only systems, and a plethora ofnovel electronic phases has been predicted to emerge.
In d2 conﬁgurations, SOC yields Jeﬀ = 2 quintet states.
When the Jeﬀ = 2 states are placed on a face-centeredcubic (FCC) lattice, multipolar ordering phenomena
such as charge quadrupolar and magnetic octupole orderings are expected to emerge.1,2)
To explore such multipolar orderings of d-electrons,
we focused on cubic tungsten halides A2 WCl6 (A =K, Rb, Cs) with a 5d2 conﬁguration of W4+ ions. The
regular WCl6 octahedra form an FCC lattice. In thesecompounds, the magnetic susceptibility χ(T ) shows aCurie-Weiss behavior at high temperatures, and theeﬀective moments are close to the value expected forJeﬀ = 2 (µeﬀ ∼ 1.22 µB ). K2 WCl6 displays an anomaly
in speciﬁc heat C(T ) at approximately 180 K, whichcorresponds to a structural transition from cubic totetragonal, but no further anomaly was observed atlower temperatures. Rb2 WCl6 and Cs2 WCl6 show nopronounced anomaly in C(T ) and χ(T ) down to 2 K,
although a deviation from the Curie-Weiss behavior
is observed at approximately 100 K. The magnetic
ground state of these materials is thus not clear yet.
One of the possible ground states is the formationof magnetic octupolar ordering, which has been suggested for d2 double-perovskite oxides.3) In those oxides, although any signature of magnetic dipolar ordering was found in χ(T ) and neutron diﬀraction, aclear oscillatory signal was observed in muon spin rotation (µSR) measurements, indicating time-reversalsymmetry breaking. The other possibility, especiallyfor K2 WCl6 , is that the structural transition lifts thedegeneracy of the Jeﬀ = 2 quintet and selects the nonz
= 0 singlet ground state (i.e., chargemagnetic Jeﬀ
quadrupole order), which can be regarded as a spinorbital nematic state in analogy with the S z = 0
spin-nematic state. In this case, the time-reversalsymmetry is retained, and no oscillatory signal is ex∗1∗2∗3∗4∗5Max Planck Institute for Solid State ResearchInstitute for Functional Matter and Quantum Technologies,
University of Stuttgart
Graduate School of Engineering and Science, Shibaura Inst.
of Tech.
RIKEN Nishina Center
Department of Physics, University of Tokyo

Fig. 1. Zero-field time spectra of muon asymmetry for
Cs2 WCl6 at several temperatures.

pected in µSR.
In order to investigate the ground states, we performed a µSR measurement on powder samples ofA2 WCl6 (A = K, Rb, Cs) using ARGUS, ISIS. For all
the samples, the time dependence of muon asymmetry
at low temperatures only shows a monotonic decrease,indicating a nonmagnetic ground state. Figure 1 shows
the result for Cs2 WCl6 . The time dependence of muon
asymmetry at zero magnetic ﬁeld did not show any
pronounced change down to 2 K. For K2 WCl6 , the relaxation rate λ, obtained by ﬁtting with a Lorentzian
curve, shows a kink at approximately 180 K, wherea structural transition occurs. No such anomaly was
found in Cs2 WCl6 or Rb2 WCl6 .
This result excludes the presence of magnetic dipolar or octupolar ordering in A2 WCl6 . The questionof whether the Jeﬀ = 2 moments remain ﬂuctuating orform a quadrupolar ordering with a spin-singlet groundstate remains open. We expect that the ground statesof these compounds can be clariﬁed in combination
with other measurements, especially the analysis of
low-temperature crystal structures.
References

1) G. Chen, L. Balents, Phys. Rev. B 84, 094420 (2011).
2) S. Voleti et al., Phys. Rev. B 101, 155118 (2020).
3) D. Maharaj et al., Phys. Rev. Lett. 124, 087206 (2020).

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