Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility

  title={Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility},
  author={Atsuo Shitade and Hikaru Watanabe and Youichi Yanase},
  journal={Physical Review B},
We derive a quantum-mechanical formula of the orbital magnetic quadrupole moment (MQM) in periodic systems by using the gauge-covariant gradient expansion. This formula is valid for insulators and metals at zero and finite temperature. We also prove a direct relation between the MQM and magnetoelectric (ME) susceptibility for insulators at zero temperature. It indicates that the MQM is a microscopic origin of the ME effect. Using the formula, we quantitatively estimate these quantities for room… 
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