Dynamical Stabilization of Inverted Magnetization and Antimagnons by Spin Injection in an Extended Magnetic System

TL;DR

The paper addresses stabilizing a magnetization state inverted with respect to an applied field in an extended magnetic film. It demonstrates dynamical stabilization by continuous spin injection from Pt, driving a nonequilibrium, multi-magnon population that shortens $\mathbf{M}$ and locks it opposite to $\mathbf{H}$, with antimagnons emerging as the elementary excitations. Micromagnetic simulations reveal a field- and size-dependent transition from incoherent multi-magnon dynamics to coherent single-magnon switching, governed by damping and anisotropy compensation. The work establishes a dissipative phase transition in macroscopic magnonics and points to applications in spin-wave amplification, magnon lasing, and bosonic-relativistic analogues in solid-state systems.

Abstract

Dynamical perturbations can modify the energy landscape of a physical system, such that unstable equilibrium configurations become stable when subject to an external drive. The magnetic analog of such dynamical stabilization corresponds to saturation of the magnetization against an external field. Here we report dynamical stabilization of the magnetization in thin film bismuth-substituted yttrium iron garnet by spin current injection from an adjacent Pt layer. Magneto-optical Kerr effect measurements demonstrate magnetization reversal against magnetic fields up to 3000 times larger than the film's coercivity once the spin injection surpasses a critical threshold associated with negative damping. Micromagnetic simulations reveal that this process is mediated by the excitation of a large population of incoherent magnons with non-zero wave vector, leading to a transient shortening and subsequent stabilization of the inverted magnetization. The elementary excitations of the high-energy inverted magnetization state are shown to be antimagnons, quasi-particles carrying opposite energy and spin relative to magnons. Our results further reveal how the system's size and minimization of nonlinear magnon scattering processes play a key role in dynamical stabilization, opening new avenues for magnetic state control beyond conventional magnetization switching. Dissipation-driven phase transitions in large-area magnetic systems provide a solid-state platform to study magnonic analogs of relativistic phenomena, such as Klein tunneling and black holes, as well as spin-wave amplification and lasing.

Figures (6)

• Figure 1: Schematic of the experiment and MOKE measurements. (a) An electric current $I$ flowing in Pt generates an in-plane spin accumulation at the Pt/Bi:YIG interface via the spin Hall effect. Angular momentum is then injected into the Bi:YIG film via spin-flip scattering, resulting in magnon creation when the spin moment $\bm{\upsigma} \parallel \mathbf{M}$ (i.e., spin magnetic moment antiparallel to $\mathbf{M}$). (b) In-plane reorientation of $\mathbf{M}$ driven by strong spin injection from Pt, which generates a large population of magnons. (c) Illustration of the longitudinal MOKE geometry, spin injection, and Bi:YIG/Pt bilayer grown on a GSGG substrate. (d,e) Field-dependent MOKE measurements under different alternating currents with $\mathbf{H}$ applied along $\mathbf{x}$ and $\mathbf{y}$, respectively. $\bar{\theta}_{\mathrm{K}}$ is the time-average of the Kerr rotation during current injection.
• Figure 2: Dynamical stabilization of the magnetization by longitudinal spin--orbit torques. (a) Time-domain Kerr rotation at different external magnetic fields within one period of the alternating current (gray dashed curve). (b) Maximum excursion of the Kerr rotation per current cycle as a function of applied field and current after subtraction of the Joule heating contribution. Blue and red shading indicate positive and negative current polarity, respectively. The inset shows linecuts at $I=\pm6.5~\mathrm{mA}$, solid lines are guides for the eye. (c) Reference Kerr rotation measurement showing full reversal of $\mathbf{M}$ in an external field. (d,e) Time-domain Kerr rotation traces within one current cycle at $(-50,-100,-210)~\mathrm{mT}$ (d) and $(50, 100, 210)~\mathrm{mT}$ (e). The thermal background due to Joule heating was subtracted from every curve. Arrows indicate the relative orientation between $\mathbf{M}$ and $\mathbf{H}$. Negative (positive) $\mathbf{H}$ favors $\mathbf{M}\parallel -\mathbf{y}$ ($+\mathbf{y}$). Positive (negative) $\Delta\theta_{\mathrm{K}}$ indicates $\mathbf{M}\parallel +\mathbf{y}$ ($-\mathbf{y}$).
• Figure 3: Evolution of the dynamic stabilization threshold with magnetic field and current. (a) Current-dependent harmonic Kerr rotation measurements at different magnetic fields. Black arrows indicate the critical current above which the system transits into the nonlinear regime. (b) Critical current vs applied magnetic field. (c) Field-dependent harmonic Kerr rotation measurements for different applied currents. (d) Schematics of thermal magnon dispersion (left) and population (right). The magnon dispersion is parabolic, $\hbar\omega_\mathrm{0}$ indicates the energy of Kittel's mode. The inset shows the magnon chirality relative to $\mathbf{M}$. The right panel shows the Bose-Einstein distribution $n(\hbar \omega, \mu)$ (solid line) for the indicated magnon chemical potential $\mu$ (dashed line); the red shaded area corresponds to the magnon population $N$. (e) Free energy of the magnetic system. The curvature of the free energy is proportional to the excitation frequency of magnons (red) and antimagnons (blue). $\varphi$ denotes the angle between static $\mathbf{M}$ and $\mathbf{H}$. (f) Schematics of magnon dispersion (left) and population (right) in the nonequilibrium state. Negative frequency excitations correspond to antimagnons with left-handed chirality. The right panel shows $n(\hbar \omega, \mu)$, $\mu$, and the magnon (red shaded area) and antimagnon (blue-shaded area) populations.
• Figure 4: Micromagnetic simulations of the longitudinal magnetization switching and (anti-)magnon distributions. (a) Time-domain evolution of the spatially averaged magnetization components $M_{\mathrm{x}}$, $M_{\mathrm{y}}$, and $M_{\mathrm{z}}$ during the switching process at $H_{\mathrm{y}}=100$ mT. The curves are shown normalized by the saturation magnetization $M_{\mathrm{s}}$. Gray shaded lines indicate the magnon thermal background at 300 K. (b) Three-dimensional representation of the switching trajectory. (c) Spatial maps of $M_{\mathrm{y}}$ at four time snapshots: $t = 2.5$, $6.3$, $8.8$, and $20.0~\mathrm{ns}$. (d) Wavevector distributions of the magnonic excitations in (c) shown on a logarithmic scale. (e) Dispersion of thermal magnons and their population (right panel) prior to spin injection. The inset illustrates the chirality of magnons with respect to $\mathbf{M}$. (f) Dispersion and population of magnons (red) and antimagnons (blue) in the nonequilibrium state. Here the energy of antimagnons is flipped from negative to positive relative to Fig. \ref{['fig3']}(f) for comparison with theoretical results Harms2024.
• Figure 5: Simulated field dependence of dynamical stabilization. (a) Time-domain evolution of the spatially averaged $M_{\mathrm{y}}$ under $\mathbf{H}$ applied along $\mathbf{y}$, ranging from 100 to 1000 mT in 100 mT steps. These simulations were performed with a device width of 1 $\upmu$m to reduce computational costs. The applied current density was $0.8\times10^{11}$ A/m$^{2}$. (b) Time-domain evolution of the spatially averaged $M_{\mathrm{y}}$ at $H_{\mathrm{y}}=1$ T, showing that the magnetization requires about 800 ns to stabilize against a high field due to enhanced dissipation. (c) Field dependence of the dynamical stabilization studied by continuously running the simulation and changing the field every 200 ns. Each field configuration evolves from the stabilized state of the previous one, reducing the time required to reach a steady state at high magnetic fields. For $\mu_0H_{\mathrm{y}}>1$ T ($t>2000$ ns), the applied current density is insufficient to stabilize $\mathbf{M}$ opposite to $\mathbf{H}$. The simulations are shown for uncompensated magnetic anisotropy ($\mu_0M_{\rm eff}=\mu_0M_{\mathrm{s}}$, blue) and nearly compensated anisotropy ($\mu_0M_{\rm eff}=40$ mT, red). (d) Average $M_{\mathrm{y}}$ extracted within the time window where the magnetization is dynamically stabilized by the applied current as a function of magnetic field, showing the same trend as observed experimentally [Fig. \ref{['fig3']}(c)].