Intrinsic Gyrotropic Magnetic Current of Orbital Origin

TL;DR

The paper addresses the origin of intrinsic gyrotropic magnetic currents (IGMC) in gyrotropic materials, emphasizing an orbital counterpart to the previously identified spin-driven magnetic displacement current. It develops a density-matrix formalism that couples both orbital minimal coupling and spin-Zeeman interactions, introducing the magnetic Berry connection polarizability (MBCP) and its orbital variant, which drive an intrinsic, Fermi-sea–driven GMC. The GMC is decomposed into Fermi-surface oscillations, dynamic charge polarization, and chiral magnetic velocity, with IGMC comprising the polarization and velocity channels; in ${\mathcal{PT}}$-symmetric CuMnAs, the CMV channel is symmetry-forbidden, making IGMC purely dispersion-driven and orbital-dominated. The study demonstrates that IGMC in CuMnAs is tunable via the Néel vector orientation and reverses sign with Néel-vector reversal, establishing IGMC as a direct probe of antiferromagnetic order and highlighting the dominant role of orbital mechanisms in gyrotropic responses. Overall, the work provides a unified, symmetry-aware framework linking orbital magnetism, Berry connection corrections, and gyrotropic transport with potential experimental observables such as measurable voltages in CuMnAs.

Abstract

In gyrotropic crystals, an oscillating magnetic field induces a charge response known as the gyrotropic magnetic current. While its conventional origin is attributed to magnetic field modified band energy and shift in the Fermi-surface, a recent study identified an additional spin-driven magnetic displacement contribution. Here, we complete the picture by identifying the orbital counterpart of the magnetic displacement current. Using a density-matrix formulation that incorporates both minimal coupling and spin-Zeeman interactions, we derive the electronic equations of motion in the presence of an oscillating magnetic field and uncover a previously unexplored orbital contribution to the wavepacket velocity. Physically, this contribution arises from the time variation of the magnetic-field induced charge polarization. In the low frequency transport regime, this mechanism becomes purely intrinsic. We illustrate this intrinsic gyrotropic current of orbital origin in the ${\cal P}{\cal T}$-symmetric antiferromagnet CuMnAs. We show that the intrinsic gyrotropic magnetic current reverses sign upon Néel vector reversal, establishing it as a direct probe of antiferromagnetic order in CuMnAs and other $\mathcal{PT}$-symmetric antiferromagnets.

Figures (3)

• Figure 1: Schematic of the intrinsic gyrotropic magnetic current (IGMC) of orbital origin. A time-varying magnetic field $\bm{B}(t)$ couples to the electronic orbital magnetic moment, inducing an orbital contribution to the oscillatory positional shift of the wave packet and dynamic charge polarization. The time variation of this polarization gives rise to the IGMC response.
• Figure 2: (a) Crystallographic and magnetic structure of tetragonal $\ce{CuMnAs}$. The red arrows indicate the direction of magnetic moments. The projected Brillouin zone in the $x-y$ plane, along with high-symmetry points, is also shown. (b) The band dispersion for three different orientations of the Néel vector, $\phi = \{\pi/12, \pi/6,\pi/4\}$. Here, $\phi$ is the angle made by the Néel vector $(\hat{\bm n})$ with $\hat{\bm x}$ ([100]) axis. (c), (d) The momentum space distribution of spin-MBCP ($\tilde{\mathcal{G}}_{1\bm{k};S}^{B;xz}$) and orbital-MBCP ($\tilde{\mathcal{G}}_{1\bm{k};L}^{B;xz}$) for the first conduction band for Néel angle $\phi = \pi/4$.
• Figure 3: (a), (b): Intrinsic gyrotropic magnetic conductivities $\chi_{x;z}^{\mathrm{IGMC}}$ and $\chi_{y;z}^{\mathrm{IGMC}}$ as functions of the Néel vector angle $\phi$ and chemical potential $\mu$. The polar angle $\phi$ is measured from the $\hat{\bm{x}}$ axis, parallel to the crystallographic [100] direction. (c) Chemical potential dependence of $\chi_{x;z}^{\mathrm{IGMC}}$ for three representative Néel orientations. (d) orbital- and Spin-MBCP contributions to $\chi_{x;z}^{\mathrm{IGMC}}$ at $\phi = \pi/12$. For all plots, the magnetic driving frequency is assumed to be $\hbar \omega = 1 ~ \mu \text{eV}$. The orbital response dominates the spin contribution by almost an order of magnitude. The IGMC response in the band gap highlights that it is a Fermi sea response, and it measures the total 'magnetic polarizability' of all the filled bands.