Broken intrinsic symmetry induced magnon-magnon coupling in synthetic ferrimagnets

TL;DR

Broken intrinsic symmetry in a synthetic ferrimagnet enables strong magnon-magnon coupling between acoustic and optical modes in-plane. Using a CoFe/Ru/NiFe stack with a Ru spacer wedge to tune interlayer exchange, the STFMR spectra exhibit an avoided crossing with gap $g$ up to $3.9$ GHz and a degeneracy field $H_g$, both governed by quadratic and biquadratic exchanges $(J_q,J_{bq})$ as captured by macrospin fits and MuMax3 simulations. The work provides a dynamic-phenomenology-based method to extract interlayer exchange from spin-dynamics spectra and demonstrates a tunable symmetry-breaking mechanism for reconfigurable magnonic devices, such as tunable filters and nonreciprocal components, expanding the design space for on-chip spintronics.

Abstract

Synthetic antiferromagnets offer rich magnon energy spectra in which optical and acoustic magnon branches can hybridize. Here, we demonstrate a broken intrinsic symmetry induced coupling of acoustic and optical magnons in a synthetic ferrimagnet consisting of two dissimilar antiferromagnetically interacting ferromagnetic metals. Two distinct magnon modes hybridize at degeneracy points, as indicated by an avoided level-crossing. The avoided level-crossing gap depends on the interlayer exchange interaction between the magnetic layers, which can be controlled by adjusting the non-magnetic interlayer thickness. A large avoided level crossing gap of 3.9 GHz is revealed, exceeding the coupling strength that is typically found in other magnonic hybrid systems based on a coupling of magnons with photons or magnons with phonons.

Figures (4)

• Figure 1: (a) Schematic illustration of the synthetic ferrimagnet comprising of a CoFe/Ru/NiFe heterostructure. The thickness of Ru is varied from $0$ nm to $1$ nm to tune the coupling strength between CoFe and NiFe. (b) Illustration of the spin-torque ferromagnetic resonance (STFMR) setup, including an inset that shows the relevant torques on the magnetization $\boldsymbol{M}$: $\boldsymbol{\tau}_{||}$ - anti-damping-like torque, $\boldsymbol{\tau}_\alpha$ - damping-like torque, $\boldsymbol{\tau}_\perp$ - field-like torque. The biasing field $\boldsymbol{H}_0$ is applied at an angle of 45 degrees with respect to the microwave field $\boldsymbol{H}_\mathrm{rf}$. (c) Schematic diagram of equilibrium angles of the ferromagnetic layers relative to the external field direction. (d) Vibrating sample magnetometry (VSM) measurement for a sample with Ru thickness of $0.8$ nm. Corresponding macrospin model calculations and micromagnetic simulations (MuMax3) are overlaid. Both the macrospin model and simulations show good agreement with experiment. The arrows indicate the relative alignment of the two exchange-coupled ferromagnetic layers. (e) MuMax3 simulations of the equilibrium angles of the ferromagnetic layers as a function of the applied field during field ramp-down, referenced to the external field direction defined in (c). Note that -180° and 180° correspond to the same magnetization direction. In some regions, the blue data points (magnetization direction of CoFe) are obscured by the overlapping orange data points (magnetization direction of NiFe).
• Figure 2: (a,b) Experimentally measured magnon spectra for Ru thicknesses of 0.8 nm and 0.4 nm, with corresponding macrospin model calculations overlaid. The color scale represents the lock-in amplifier output. (c,d) Corresponding micromagnetic (MuMax3) simulations of the STFMR spectra, with macrospin model results shown for comparison. Here, the color scale represents the FFT amplitude.
• Figure 3: Micromagnetic simulations obtained with MuMax3. (a) Simulated spectrum for a Ru thickness of 0.8 nm. (b–f) Layer-resolved simulations showing the amplitude (top) and phase (bottom) profiles of the magnon modes, extracted from FFTs of the magnetization dynamics at 4, 12, 37, 56, and 100 mT. The two vertical lines in each panel indicate the resonance frequencies at that field. These lines intersect the phase spectra of CoFe (black) and NiFe (red) at the lower-frequency (solid) and higher-frequency (dashed) branches, highlighted by the corresponding horizontal markers in the phase panels. (g) Spatially resolved simulation at 12 mT with X and Y indicating the lateral dimensions of the studied devices. The color wheel represents the magnetization dynamics phase.
• Figure 4: (a) Coupling gap $g$ (blue) and degeneracy field $H_\mathrm{g}$ (green) obtained from macrospin calculations (solid lines) and micromagnetic simulations (dashed lines) as a function of the quadratic exchange constant $J_\mathrm{q}$ at a fixed biquadratic exchange constant of $J_\mathrm{bq} = 2.16~\mathrm{kJ/m^3}$. The degeneracy field $H_\mathrm{g}$ is defined as the magnetic field at which the frequency separation between the high- and low-frequency modes is minimized, yielding the coupling gap $g$. The uncertainty (error bar) in the simulated $H_g$ arises from the finite field resolution, given by the field step size (2 mT in this case). The uncertainty in the simulated $g$ is determined by the finite frequency resolution of the FFT, set by the simulation runtime (100 MHz for 10 ns), and is multiplied by $\sqrt{2}$ to account for error propagation. (b) Same as (a), but shown as a function of the biquadratic exchange constant $J_\mathrm{bq}$ at a fixed quadratic exchange constant of $J_\mathrm{q} = 29.8~\mathrm{kJ/m^3}$. (c--d) The b coefficient in the sublinear power-law dependence on $J_\mathrm{bq}$ and $J_\mathrm{q}$, respectively.