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Register a new userTheoretical evidence of spin-orbital-entangled $J_{mathbf{eff}}$=1/2 state in the 3$d$ transition metal oxide CuAl$_2$O$_4$
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Transition metal oxides exhibit various competing phases and exotic phenomena depending on how their reaction to the rich degeneracy of the $d$-orbital. Large spin-orbit coupling (SOC) reduces this degeneracy in a unique way by providing a spin-orbital-entangled ground state for 4$d$ and 5$d$ transition metal compounds. In particular, the spin-orbital-entangled Kramers doublet, known as the $J_{mathbf{eff}}$=1/2 pseudospin, appears in layered iridates and $alpha$-RuCl$_3$, manifesting a relativistic Mott insulating phase. Such entanglement, however, seems barely attainable in 3$d$ transition metal oxides, where the SOC is small and the orbital angular momentum is easily quenched. From experimental and theoretical evidence, here we report on the CuAl$_2$O$_4$ spinel as the first example of a $J_{mathbf{eff}}$=1/2 Mott insulator in 3$d$ transition metal compounds. Based on the experimental study, including synthesis of the cubic CuAl$_2$O$_4$ single crystal, density functional theory and dynamical mean field theory calculations reveal that the $J_{mathbf{eff}}$=1/2 state survives the competition with an orbital-momentum-quenched $S$=1/2 state. The electron-addition spectra probing unoccupied states are well described by the $j_{mathbf{eff}}$=1/2 hole state, whereas electron-removal spectra have a rich multiplet structure. The fully relativistic entity found in CuAl$_2$O$_4$ provides new insight into the untapped regime where the spin-orbital-entangled Kramers pair coexists with strong electron correlation.
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Structure with orbital degeneracy is unstable toward spontaneous distortion. Such orbital correlation usually has a much higher energy scale than spins, and therefore, magnetic transition takes place at a much lower temperature, almost independently from orbital ordering. However, when the energy scales of orbitals and spins meet, there is a possibility of spin-orbital entanglement that would stabilize novel ground state such as spin-orbital liquid and random singlet state. Here we review on such a novel spin-orbital magnetism found in the hexagonal perovskite oxide Ba$_3$CuSb$_2$O$_9$, which hosts a self-organized honeycomblike short-range order of a strong Jahn-Teller ion Cu$^{2+}$. Comprehensive structural and magnetic measurements have revealed that the system has neither magnetic nor Jahn-Teller transition down to the lowest temperatures, and Cu spins and orbitals retain the hexagonal symmetry and paramagnetic state. Various macroscopic and microscopic measurements all indicate that spins and orbitals remain fluctuating down to low temperatures without freezing, forming a spin-orbital entangled liquid state.
The pyrochlore iridate In$_2$Ir$_2$O$_7$ is a strong $J_{mathrm{eff}} = 1/2$ Mott insulator with frustrated magnetism. Despite the large trigonal crystal field, a small admixture of $J_{mathrm{eff}} = 3/2$ component in the $J_{mathrm{eff}} = 1/2$ bands and a small splitting of $J_{mathrm{eff}} = 3/2$ bands are observed as compared with other pyrochlore iridates A$_2$Ir$_2$O$_7$ (A: trivalent cation). We argue that the reduced inter-site hopping between the $J_{mathrm{eff}} = 1/2$ and the $J_{mathrm{eff}} = 3/2$ manifold plays a predominant role in the distinct behavior of In$_2$Ir$_2$O$_7$ compared with other A$_2$Ir$_2$O$_7$. The effect of the intersite hopping should not be dismissed in the local physics of spin-orbital-entangled $J_{mathrm{eff}} = 1/2$ Mott insulators.
We present AC and DC magnetometry, heat capacity, muon spin relaxation ($mu$SR) and resonant inelastic X-ray scattering (RIXS) studies of the pyrochlore osmate Y$_2$Os$_2$O$_7$. We observe a non-zero effective moment governed by $sqrt{f}mu_{rm{eff}} = 0.417(1),mu_{rm{B}}$ where $f$ is the fraction of Os sites which exhibit a spin, and spin freezing at temperature $T_{rm f} simeq 5,$K, consistent with previous results. The field dependence of magnetisation data shows that the paramagnetic moment is most likely due to large moments $mu_{rm eff} simeq 3,mu_{rm B}$ on only a small fraction $f simeq 0.02$ of Os sites. Comparison of single-ion energy level calculations with the RIXS data yields a non-magnetic $J_{rm eff} = 0$ ground state on the Os$^{4+}$ sites. The spin-orbit interaction, Hunds coupling and trigonal distortion of OsO$_{6}$ octahedra are all important in modelling the experimentally observed spectra. We are able to rule out impurity effects, leaving disorder-related effects such as oxygen non-stoichiometry or site interchange between Os and Y ions as the most plausible explanation for the magnetic response in this material.
Polycrystalline samples of NaYbO$_2$ are investigated by bulk magnetization and specific-heat measurements, as well as by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) as local probes. No signatures of long-range magnetic order are found down to 0.3~K, evidencing a highly frustrated spin-liquid-like ground state in zero field. Above 2,T, signatures of magnetic order are observed in thermodynamic measurements, suggesting the possibility of a field-induced quantum phase transition. The $^{23}$Na NMR relaxation rates reveal the absence of magnetic order and persistent fluctuations down to 0.3~K at very low fields and confirm the bulk magnetic order above 2~T. The $H$-$T$ phase diagram is obtained and discussed along with the existing theoretical concepts for layered spin-$frac{1}{2}$ triangular-lattice antiferromagnets
By means of density functional theory plus dynamical mean-field theory (DFT+DMFT) calculations and resonant inelastic x-ray scattering (RIXS) experiments, we investigate the high-pressure phases of the spin-orbit-coupled $J_{rm{eff}}=3/2$ insulator GaTa$_4$Se$_8$. Its metallic phase, derived from the Mott state by applying pressure, is found to carry $J_{rm{eff}}=3/2$ moments. The characteristic excitation peak in the RIXS spectrum maintains its destructive quantum interference of $J_{rm{eff}}$ at the Ta $L_2$-edge up to 10.4 GPa. Our exact diagonalization based DFT+DMFT calculations including spin-orbit coupling also reveal that the $J_{rm{eff}}=3/2$ character can be clearly identified under high pressure. These results establish the intriguing nature of the correlated metallic magnetic phase, which represents the first confirmed example of $J_{rm{eff}}$=3/2 moments residing in a metal. They also indicate that the pressure-induced superconductivity is likely unconventional and influenced by these $J_{rm{eff}}=3/2$ moments. Based on a self-energy analysis, we furthermore propose the possibility of doping-induced superconductivity related to a spin-freezing crossover.
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