Theory of orbital magnetic quadrupole moment and magnetoelectric susceptibility

Abstract

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-temperature antiferromagnetic semiconductors BaMn${}_2$As${}_2$ and CeMn${}_2$Ge${}_{2-x}$Si${}_x$. We find that the orbital contribution to the ME susceptibility is comparable with or even dominant over the spin contribution.

arXiv comment6 pages, 1 figure, Supplemental Material is available in the source

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• Analysis of model parameter dependences on the second-order nonlinear conductivity in $\mathcal{P}\mathcal{T}$-symmetric collinear antiferromagnetic metals with magnetic toroidal moment on zigzag chains
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• Berry-phase effects in dipole density and Mott relation
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• Thermodynamic approach to electric quadrupole moments
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• Charge density waves in multiple-$Q$ spin states
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• Towards a theory of surface orbital magnetization
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• Efficient Method for Prediction of Meta-stable/Ground Multipolar Ordered States and its Application in Monolayer $\alpha$-\ce{RuX3} (X=Cl,I)
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• Lattice excitations with finite polarization and magnetization
• Quantum Geometric Origin of Orbital Magnetization
• Vector Potential and Surface Magnetic Field in Magnetoelectric Antiferromagnetic Materials
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• Intrinsic spin accumulation in the magnetic spin Hall effect