Studies on unusual magnetic properties of 4d and 5d transition metal compounds with the strong spin-orbit coupling

Abstract

We have investigated magnetic properties of various transition metal systems having the strong spin-orbit coupling (SOC), such as Ba2YIrO6, a-RuCl3, and Na2IrO3. It is very interesting that these systems show Mott insulating behavior only after the SOC interaction is included, and exhibit unusual magnetic behaviors. For Ba2YIrO6, the local magnetic moment fluctuation is observed in the susceptibility experiments, despite that Ba2YIrO6 is generally considered to be a non-magnetic system. For a-RuCl3 and Na2IrO3, the quantum fluctuation effects are detected in many experiments. It is believed that the quantum fluctuation effects in these materials are related to their Kitaev-type spin liquid nature. The origin of the magnetic behavior in these systems has been a hot subject of recent interest in the community of strong spin-orbit coupled systems. For systems with four electrons in the d-orbital (d4 system), the large octahedral crystal field and the SOC effects are known to make the system non-magnetic. However, some d4 systems, such as Sr2YIrO6 and Ba2YIrO6, were reported to exhibit magnetic behaviors. The magnetism might arise as a result of the lowered local symmetry from octahedral symmetry and the hopping effect. However, Ba2YIrO6 maintains the perfect octahedral local symmetry at low temperature. Based on the model Hamiltonian with realistic hopping parameters, which are obtained from the density functional theory (DFT) band calculation results, we have shown that no magnetism is induced from the hopping effect. Therefore, we concluded that the experimentally observed magnetic behavior might arise extrinsically from impurities. Indeed, recent experiments have revealed that the magnetism can be generated by impurities or defects. a-RuCl3 is known for as a candidate material that could realize Kitaev spin liquid. To clarify how close the ground state of a-RuCl3 is to Kitaev spin liquid, we have calculated the realistic magnetic exchange interaction parameters between the magnetic ions, employing the DFT for the experimental structure. We have found that, for the DFT calculations, the use of physically reasonable values of Coulomb (U) and Hund's (JH) interactions is essential in the DFT calculation to describe the observed magnetic properties. However, even with proper U and JH, we have found that the extracted magnetic exchange parameters from the DFT results, such as Heisenberg interactions, J1, J2, J3, Kitaev interactions, K1, K2, and other off-diagonal exchange interactions, are overestimated, especially for the transition metal magnetic ions having the strong SOC. To resolve this overestimation, we have taken into account a generalized de Gennes factor. The theoretical model with the magnetic exchange interaction parameters, which are scaled by the generalized de Gennes factor, describes well the observed magnetic properties, such as the spin wave dispersion and the size of the meta-magnetic transition field, of a-RuCl3. To verify the effectiveness of the generalized de Gennes factor, we tested the rescaled exchange parameters for another candidate system of Kitaev spin liquid, Na2IrO3, which is corresponding to a 5d-orbital system, different from a-RuCl3 corresponding to a 4d-orbital system. For Na2IrO3, too, we have resolved the overestimation problem of the magnetic exchange parameters by the adoption of the generalized de Gennes factor. We have suggested the physical meaning of the generalized de Gennes factor, which comes from the anisotropic entanglement of the spin and orbital degrees of freedom due to the strong SOC strength.