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

Recent NMR experiments have revealed exotic quantum phases in the magnetic Mott insulator with strong spin orbit coupling (SOC) Ba₂NaOsO₆^[1]. To investigate the possible spin and orbital order patterns consistent with the NMR observations, we performed Monte Carlo simulations of a microscopic model for d¹ double perovskites magnetic Mott insulators with multipolar spin interactions^[2] . We obtained the low temperature phase diagram involving both spin and orbital degrees of freedom by magnetic annealing. We found that the zero temperature phase diagram consists of a fluctuating xyAFM, a canted FM[100] and a magnetic quadrupolar state each with distinct corresponding orbital ordering pattern. Furthermore, the xyAFM and the quadrupolar state are also found at intermediate temperatures as a result of enhanced thermal fluctuations. We demonstrate that the ground state evolves from the canted FM[100] state to the quadrupolar state as electric quadrupole-quadrupole interaction increases.

[1] Lu, L., et al. Nature Communications 8 (2017): 14407.
[2] Chen, Gang, Rodrigo Pereira, and Leon Balents. Physical Review B 82.17 (2010): 174440.