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Terahertz spin-orbit torque as a drive of spin dynamics in the insulating antiferromagnet Cr$_{2}$O$_{3}$

R. M. Dubrovin, Z. V. Gareeva, A. V. Kimel, A. K. Zvezdin

Abstract

Contrary to conventional wisdom that spin dynamics induced by current are exclusive to metallic magnets, we theoretically predict that such phenomena can also be realized in magnetic insulators, specifically in the magnetoelectric antiferromagnet $\mathrm{Cr}_{2}\mathrm{O}_{3}$. We reveal that the displacement current driven by the THz electric field is able to generate a N{é}el spin-orbit torque in this insulating system. By introducing an alternative electric dipole order parameter arising from the dipole moment at $\mathrm{Cr}^{3+}$ sites, we combine symmetry analysis with a Lagrangian approach and uncover that the displacement current couples to the antiferromagnetic spins and enables ultrafast control of antiferromagnetic order. The derived equations of motion show that this effect competes with the linear magnetoelectric response, offering a novel pathway for manipulating antiferromagnetic order in insulators. Our findings establish insulator antiferromagnets as a viable platform for electric field driven antiferromagnetic spintronics and provide general design principles for non-metallic spin-orbit torque materials.

Terahertz spin-orbit torque as a drive of spin dynamics in the insulating antiferromagnet Cr$_{2}$O$_{3}$

Abstract

Contrary to conventional wisdom that spin dynamics induced by current are exclusive to metallic magnets, we theoretically predict that such phenomena can also be realized in magnetic insulators, specifically in the magnetoelectric antiferromagnet . We reveal that the displacement current driven by the THz electric field is able to generate a N{é}el spin-orbit torque in this insulating system. By introducing an alternative electric dipole order parameter arising from the dipole moment at sites, we combine symmetry analysis with a Lagrangian approach and uncover that the displacement current couples to the antiferromagnetic spins and enables ultrafast control of antiferromagnetic order. The derived equations of motion show that this effect competes with the linear magnetoelectric response, offering a novel pathway for manipulating antiferromagnetic order in insulators. Our findings establish insulator antiferromagnets as a viable platform for electric field driven antiferromagnetic spintronics and provide general design principles for non-metallic spin-orbit torque materials.

Paper Structure

This paper contains 6 sections, 31 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Material
  3. Results and Discussion
  4. Symmetry analysis
  5. Spin Dynamics
  6. Conclusions

Figures (3)

  • Figure 1: Crystal and magnetic structures of antiferromanget $\mathrm{Cr}_{2}\mathrm{O}_{3}$ with oppositely directed antiferromagnetic vectors (a) $\mathbf{l}_{\downarrow}$ and (b) $\mathbf{l}_{\uparrow}$. Green arrows denote the orientation of magnetic moments $\mathbf{m}_{1}$--$\mathbf{m}_{4}$ of $\mathrm{Cr}^{3+}$ ions (labelled 1--4). Positions of the symmetry elements $\overline{1}$, $3_{z}$, and $2_{x}$ in the unit cells are given in panel (a). (c) Electric dipole moments $\mathbf{d}_{1}$--$\mathbf{d}_{4}$ (blue arrows) in the unit cell in the vicinity of magnetic $\mathrm{Cr}^{3+}$ ions. The nominal charges of $\mathrm{Cr}^{3+}$ and $\mathrm{O}^{2-}$ ions in $e$ are given. (d) The nearest $\mathrm{O}^{2-}$ cations are located at two different distances $r_{1}$ and $r_{2}$ from the $\mathrm{Cr}^{3+}$ ions as marked in light and dark blue.
  • Figure 2: (a) Geometry of the considered THz experiment, in which dynamics of the antiferromagnetic vector $\mathbf{l} = \mathbf{m}_{\mathrm{A}} - \mathbf{m}_{\mathrm{B}}$ in $\mathrm{Cr}_{2}\mathrm{O}_{3}$ is driven by a THz nearly single cycle pulse. Time traces of (b) the THz electric field $\mathbf{E}^{\mathrm{THz}}$ and (c) the resulting displacement current $\mathbf{j}_{\mathrm{D}} \propto \dot{\mathbf{E}}$ along with the time derivative $\dot{\mathbf{E}}$.
  • Figure 3: Temporal oscillations of (a) magnetization $m_{x}$ and (b) antiferromagnetic vector $l_{y}$ components driven by the THz electric field $\mathbf{E}^{\mathrm{THz}} \parallel x$ in a single antiferromagnetic domain of $\mathrm{Cr_{2}}\mathrm{O_{3}}$. (c) Normalized Fourier spectra of spin dynamics from (a) and (b) compared to the spectrum of the THz pump pulse. (d) Polar diagram of the amplitude of oscillations $m_{x}$ and $l_{y}$ as a function of the THz polarization angle for two opposite antiferromagnetic domain with $\mathbf{l} \parallel z$ (blue) and $\mathbf{l} \parallel \overline{z}$ (red).