Abstract

Violation of parity symmetry gives rise to various physical phenomena such as nonlinear transport and cross-correlated responses. In particular, the nonlinear conductivity has been attracting a lot of attentions in spin-orbit coupled semiconductors, superconductors, topological materials, and so on. In this paper we present theoretical study of the nonlinear conductivity in odd-parity magnetic multipole ordered systems whose $\mathcal{PT}$-symmetry is essentially distinct from the previously studied acentric systems. Combining microscopic formulation and symmetry analysis, we classify the nonlinear responses in the $\mathcal{PT}$-symmetric systems as well as $\mathcal{T}$-symmetric (non-magnetic) systems, and uncover nonlinear conductivity unique to the odd-parity magnetic multipole systems. A giant nonlinear Hall effect, nematicity-assisted dichroism and magnetically-induced Berry curvature dipole effect are proposed and demonstrated in a model for Mn-based magnets.

Highlights

  • Nonlinear responses have been giving rise to a lot of research interest in condensed matter physics

  • In this paper we present a theoretical study of the nonlinear conductivity in odd-parity magnetic multipole ordered systems whose PT symmetry is essentially distinct from the previously studied acentric systems

  • We find that the nonlinear conductivity (NLC) at H = 0 is a measure of the antisymmetric spin-orbit coupling (ASOC)

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Summary

INTRODUCTION

Nonlinear responses have been giving rise to a lot of research interest in condensed matter physics. A key to the odd-parity magnetic multipole order is locally noncentrosymmetric property of crystals. With such structure of crystals, the local site symmetry of atoms does not have P symmetry the global P symmetry is preserved owing to the sublattice degree of freedom [20,21]. In this work the NLC in odd-parity magnetic multipole metals are investigated. We reveal two types of fieldinduced NLC; the nematicity-assisted dichroism, and Berry curvature dipole effect induced by what we call magnetic ASOC. These phenomena originate from locally noncentrosymmetric crystal structures and magnetic order, and have striking difference from the NLC in noncentrosymmetric (nonmagnetic) crystals.

QUANTUM THEORY AND SYMMETRY ANALYSIS
NLC IN ODD-PARITY MAGNETIC MULTIPOLE SYSTEMS
Field-free nonlinear Hall effect
Nematicity-assisted dichroism
Magnetic ASOC and Berry curvature dipole
CONCLUSION AND DISCUSSIONS
Density matrix formalism
Second-order nonlinear conductivity
Symmetry constraints on nonlinear conductivity tensor
Model Hamiltonian
Nonlinear Hall conductivity at zero magnetic field
Nonlinear Hall conductivity due to Berry curvature dipole
Analytical and numerical results of BCD term

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