A Unified Theory of Deterministic Magnetic Switching

Abstract

The deterministic switching of magnetic order parameters is critically important, as it forms the fundamental basis for manipulating information states in magnetic memory devices. This work presents a general theoretical framework that unifies the mechanisms of magnetic switching by introducing the concept of switching symmetry and establishing that the necessary condition for deterministic switching is the breaking of all switching symmetries, which can be achieved through asymmetric states, asymmetric barriers, and asymmetric torques. Our theory can successfully and universally explain all reported experimental cases of deterministic magnetic switching and provides unified and simple design principles for new switching devices of all magnetic materials without the need of complicated simulations.

Figures (4)

• Figure 1: Schematic illustration of symmetry operations and their effects on ground states. (a) In a magnetic system with n-fold degenerate ground states, the switching symmetry $g_\mathrm{S}^{\nu\mu}$ maps the ground state $\psi_\mu$ to $\psi_\nu$, thereby transforming the order parameter from $\mathbf{O}_\mu$ to $\mathbf{O}_\nu$. In contrast, the magnetic space group symmetry $g_\mathrm{M}^{\mu}$ leaves $\psi_\mu$ and $\mathbf{O}_\mu$ invariant. (b) Left: In a FM with a single sublattice, the identity $E$ preserves the ground state, whereas the time-reversal $\mathcal{T}$ reverses the net magnetization $\mathbf{M} = \mathbf{m}_1$. Right: In an AFM with two sublattices, the Néel vector $\mathbf{N} = (\mathbf{m}_1 - \mathbf{m}_2)/2$ is reversed under either $\mathcal{T}$ or the translation $t$. The four-fold rotation $C_4$ rotates both $\mathbf{M}$ (FM) and $\mathbf{N}$ (AFM) by 90$^\circ$.
• Figure 2: (a) Phase diagram of transition between ground states $\psi_1,\psi_2,...,\psi_l$, with switching symmetry $g_\mathrm{S}$ connecting intermediate states $\mathbf{m}(t)$ (green points) and $\mathbf{\widetilde{m}}(t)$ (yellow points). (b)-(e) Transition in magnetic systems with: (b) unbroken $g_\mathrm{S}$, (c) asymmetric states, (d) asymmetric barriers, and (e) asymmetric torques. In (b)-(e), the curve enclosing the gray region represents the energy profile along the path; solid curves with arrowheads denote allowed paths, while dashed curves with red crosses mark forbidden paths; black arrows indicate driving torques.
• Figure 3: Switching cases in FMs and A$l$Ms. (a),(b) Schematic diagrams of net magnetization ($\mathbf{M} \parallel\pm\hat{\mathbf{z}}$) reversal in a FM driven by (a) a magnetic field $\mathbf{H}\parallel\pm\hat{\mathbf{z}}$ or (b) a charge current $\mathbf{J}_\mathrm{C}\parallel\mp\hat{\mathbf{z}}$ passing through a fixed FM layer with magnetization $\mathbf{M}_\mathrm{fix}\parallel+\hat{\mathbf{z}}$, where $\mathbf{H}$ and $\mathbf{M}_\mathrm{fix}$ are slightly tilted to initiate the dynamical process. (c) Switching symmetries ($C_{2,[100]}$ and $C_{2,[010]}$) for a single magnetic moment $\mathbf{m}_1$ in an orthorhombic cell. (d),(e) Atomistic simulations of $\mathbf{M}$ reversal between $\mathbf{M}_\pm\parallel\pm[001]$ driven by (d) $\mathbf{H}\parallel\pm[001]$ and (e) a current-induced polarization $\mathbf{p}\parallel\pm[001]$, each with a slight tilt. (f),(g) Schematic diagrams of (f) field-free and (g) field-assisted switching of Néel vector ($\mathbf{N} \parallel\pm\hat{\mathbf{x}}$) in A$l$M CrSb films (top layers), achieved by $\mathbf{J}_\mathrm{C}\parallel\pm\hat{\mathbf{x}}$ passing through the bottom heavy metal layers. (h) Switching symmetries ($C_{2,[100]}$ and $C_{2,[001]} t_{1/2}$, where $t_{1/2}$ is a half-translation along [001]) for a CrSb thin film with $\mathbf{m}_1$ and $\mathbf{m}_2$. (i),(j) Atomistic simulations of $\mathbf{N}$ reversal between $\mathbf{N}_\pm\parallel\pm[001]$ with DM vector $\mathbf{d}\parallel[100]$ in (i) field-free ($\mathbf{p}\parallel\mp[120]$) and (j) field-assisted ($\mathbf{p}\parallel\pm[100]$ and $\mathbf{H}\parallel[001]$) modes.
• Figure 4: Current-induced 90$^\circ$ and 120$^\circ$ switching of the Néel vector. (a) A charge current $\mathbf{J}_\mathrm{C}$ ($\mathbf{J}_\mathrm{C}\parallel\pm[100]$ or $\mathbf{J}_\mathrm{C}\parallel\pm[010]$) rotates the Néel vector $\mathbf{N}$ to be perpendicular to $\mathbf{J}_\mathrm{C}$. (b) A charge current $\mathbf{J}_\mathrm{C}$ ($\mathbf{J}_\mathrm{C}\parallel\pm[210]$, $\mathbf{J}_\mathrm{C}\parallel\pm[120]$, or $\mathbf{J}_\mathrm{C}\parallel\pm[1\bar{1}0]$) rotates the Néel vector $\mathbf{N}$ to be parallel or antiparallel to $\mathbf{J}_\mathrm{C}$.