Quantum Transport and Magnetism of Dirac Electrons in Solids

TL;DR

This paper explores the interplay of electronic and magnetic properties in Dirac electrons within topological insulators, revealing phenomena like magnetoelectric effects and mutual control of electric and magnetic states, relevant for spintronics.

Contribution

It provides a unified theoretical framework for understanding magnetic and electronic coupling in Dirac electron systems, including magnetic topological insulators.

Findings

Magnetic doping induces ferroelectric polarization via spin-orbit coupling.

Electric current can induce uniform magnetization in doped systems.

Oscillating magnetic order can generate electric currents.

Abstract

The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. Topological insulators feature gapless surface states and, moreover, magnetic doping and resultant ferromagnetic ordering break time-reversal symmetry to realize quantum anomalous Hall and Chern insulators. Here we focus on the bulk and investigate the mutual coupling of electronic and magnetic properties of Dirac electrons. Without carrier doping, spiral magnetic orders cause a ferroelectric polarization through the spin-orbit coupling. In a doped metallic state, the anisotropic magnetoresistance arises without uniform magnetization. We find that electric current induces uniform magnetization and conversely an oscillating magnetic order induces electric current. Our model provides a coherent and unified description of all those phenomena. The mutual control of electric and magnetic properties demonstrates implementations of antiferromagnetic spintronics. We also discuss the stoichiometric magnetic topological insulator MnBi$_2$Te$_4$.