Nonlinear enhancement of coherent magnetization dynamics

Letter

Nonlinear enhancement of coherent magnetization dynamics

Mehrdad Elyasi, Kei Yamamoto, Tomosato Hioki, Takahiko Makiuchi, Hiroki Shimizu, Eiji Saitoh, and Gerrit E. W. Bauer

Phys. Rev. B 109, L180402 – Published 2 May 2024

Abstract

Magnets are interesting materials for classical and quantum information technologies. However, the short decoherence and dephasing times that determine the scale and speed of information networks severely limit the appeal of employing the ferromagnetic resonance. Here we show that the lifetime and coherence of the uniform Kittel mode can be enhanced by three-magnon interaction-induced mixing with the long-lived magnons at the minima of the dispersion relation. Analytical and numerical calculations based on this model explain recent experimental results and predict experimental signatures of quantum coherence.

Received 19 December 2023
Revised 13 March 2024
Accepted 15 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.L180402

Physics Subject Headings (PhySH)

Magnons Quantum coherence & coherence measures

Magnetic systems

Density matrix methods Mean field theory Quantum master equation

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyNonlinear Dynamics

Authors & Affiliations

Mehrdad Elyasi ¹, Kei Yamamoto ², Tomosato Hioki³, Takahiko Makiuchi ^3,4, Hiroki Shimizu³, Eiji Saitoh^5,3,6,2, and Gerrit E. W. Bauer ^5,7,8

¹Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
²Advanced Science Research Center, Japan Atomic Energy Agency, Tokai 319-1195, Japan
³Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
⁴Quantum-Phase Electronics Center, The University of Tokyo, Tokyo 113-8656, Japan
⁵WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
⁶Institute for AI and Beyond, The University of Tokyo, Tokyo 113-8656, Japan
⁷Kavli Institute for Theoretical Sciences, University of the Chinese Academy of Sciences, Beijing 10090, China
⁸Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, Netherlands

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Issue

Vol. 109, Iss. 18 — 1 May 2024

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Images

Figure 1
(a) Schematics of the generic three-state model with frequencies $ω$ and dissipation rates $ξ$ . (b) In a thin film magnet, the Kittel mode interacts with valley magnon pairs with wave vectors $\pm {\vec{k}}_{V}$ . Here we show the dispersion $ω_{\vec{k}}$ of a $d = 1 µ m$ YIG film, for $\vec{k} ∥ \vec{H}$ (bottom curve) and $\vec{k} ⊥ \vec{H}$ (top curve), where $\vec{H}$ is an in-plane magnetic field.
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Figure 2
Numerical calculation of the Kittel mode decay in the presence of a single valley magnon pair mode under resonant excitation $P_{r} = 0.5 ξ_{0} [Θ (t) - Θ (t - t_{s})]$ , $ξ_{0} = 1 MHz$ , $ξ_{{\vec{k}}_{V}} = 0.1 MHz$ , $H^{(4 M S)} = 0$ . (a) $〈 c_{0} 〉 (t)$ for two values of $D_{{\vec{k}}_{V}} / ξ_{0} = 0.05$ and 0 and zero temperature ${\bar{n}}_{0 ({\vec{k}}_{V})} = 0$ . (b) $〈 c_{0} 〉 (t)$ for three different ${\bar{n}}_{{\vec{k}}_{V}} = 0$ , $3.5 f (t)$ , and $3.5 f^{'} (t)$ , where $f (t) = Θ (t - t_{s})$ and $f^{'} (t) = Θ (t - t_{s}) exp [- 2 ξ_{{\vec{k}}_{V}} (t - t_{s})]$ , for a stronger interaction $D_{{\vec{k}}_{V}} / ξ_{0} = 0.25$ . Here, and throughout the paper, $log$ is in basis of 10.
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Figure 3
Decay dynamics for a spectrum of valley magnons and dependence of frequency-dependent interaction parameter $G (ω)$ . (a) The time evolution for $G^{(I)} = 0.1 Θ (ω - ω_{0} / 2)$ and $G^{(II)} = 0.1$ . $P_{r} / ξ_{0} = 10^{5}$ . (b) The dependence of $〈 c_{0} 〉 (t)$ calculated from Eq. (9), on the peak amplitude of $G_{n} (ω)$ , for $G^{(I)}$ (left panel) and $G^{(I I)}$ (right panel). The magenta lines in (b) correspond to $〈 n_{ω} 〉 (t_{s})$ in (a). (c) The minimum decay rate $ξ_{min}$ calculated from the last $2 μ s$ of the dynamics plotted in (b) at each $max [G_{n} (ω)]$ .
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Figure 4
Calculated results for a magnetic thin disk (thickness $d = 1 µ m$ , radius $100 µ m$ ) at an external magnetic field $H = 25 mT$ . (a) Density of states $R (ω)$ and mean value of the 3MS interaction coefficient $\bar{D}$ up to the FMR frequencies $ω_{0}^{YIG (P y)}$ . (b) The dependence of the decay $log [〈 c_{0} 〉 (t)]$ on the detuning $Δ ω^{'} = ω_{0} / 2 - ω_{min}$ for $P_{r} / ξ_{0} = 10^{5}$ . (c) Time evolution for three $Δ ω^{'}$ [indicated by dashed lines colored as in (b)]. In calculations, we used the spectrum of $0.1 GHz$ width centered around $ω_{0} / 2$ and discretization of $0.01 MHz$ . The oscillations in the relatively large $Δ ω^{'}$ are the artifact of limited bandwidth and discretization.
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Figure 5
Decay of quantum coherence. (a) $\tilde{C} (t)$ as a function of time with relatively weak and completely without 3MS interactions. The blue dashed line is our analytical result in the presence of 3MS. (b) $\tilde{C} (t)$ with and without the resonant drive of the Kittel mode, now for weak and strong 3MS interactions. The red dashed line holds for ${\bar{n}}_{{\vec{k}}_{V}} = 2$ for weak 3MS and $P_{r} \neq 0$ .
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