Monte Carlo simulation of a strong SOC model for d¹ double perovskite

Recent NMR experiments revealed exotic quantum phases in the magnetic Mott insulator with strong spin-orbit coupling Ba₂NaOsO₆^[1]. In an attempt to associate possible spin and orbital patterns with these NMR findings, we performed Monte Carlo simulations to study a microscopic model for d¹ double perovskites magnetic Mott insulators with strong spin orbit coupling and multipolar spin interactions^[2]. We obtained the low temperature phase diagram, involving both spin and orbital degree of freedoms, by magnetic annealing. We found that the zero temperature phase diagram consists of three phases (a fluctuating xyAFM, a canted FM[100], and a magnetic quadrupolar state), each with distinct corresponding orbital ordering patterns. The xyAFM and the quadrupolar state are also supported at intermediate temperatures by enhanced fluctuations at finite temperature. Furthermore, we reveal that the ground state evolves from canted FM[100] state to the quadrupolar state with increasing electric quadrupole-quadrupole interaction. A phase diagram as a function of the applied magnetic field will also be discussed.

[1] Lu, L., et al. Nature communications 8 (2017): 14407.

[2] Chen, Gang. et al. Physical Review B 82.17 (2010): 174440.