Magnon-mediated electric current drag and nonlocal spin-Peltier effect in the ac regime

TL;DR

The paper develops a comprehensive linear-response theory for magnon-mediated spin and heat transport in N|F|N trilayers under ac driving up to THz frequencies. Using a magneto-electric circuit framework, it treats coherent and incoherent magnons as parallel transport channels connected through interfacial and bulk impedances, yielding explicit expressions for local and nonlocal conductivities $\sigma^{xx}_{kj}(\omega)$, $\sigma^{yx}_{kj}(\omega)$ and spin-Peltier coefficients $\eta^{x}_{kj}(\omega)$. Numerical analysis for Pt|YIG|Pt shows strong freq-dependent behavior: at low frequencies the nonlocal drag is comparable to dc SMR, while at higher frequencies the drag is suppressed except near magnon resonances, with the nonlocal effect generally smaller than the local SMR. The framework also captures the spin-Peltier effect, including nonlocal cooling and Joule-heating competition, highlighting the potential for ultrafast spintronic cooling and energy transport applications. Overall, the work provides a unified, extensible description that links incoherent and coherent magnon transport to a broad set of spintronic and spin-caloritronic phenomena in nanoscale multilayers.

Abstract

Electron-magnon coupling at the interface between a normal metal and a magnetically ordered insulator modifies the electrical conductivity of the normal metal, an effect known as spin-Hall magnetoresistance. It can also facilitate magnon-mediated electric current drag, the nonlocal electric current response of two normal metal layers separated by a magnetic insulator. Additionally, spin and heat transport are coupled both in the magnetic insulator and across the interfaces to normal metals. In this article, we present a theory of these spintronic and spin-caloritronic effects for time-dependent applied electric fields $E(ω)$, with driving frequencies $ω$ up to the THz regime. Our model describes how the dominant transport mechanism, coherent or incoherent magnons, evolves with the driving frequency $ω$.

Figures (7)

• Figure 1: Geometry of the N$|$F$|$N trilayer consisting of two normal metals N1 and N2 and a magnetically ordered insulator F. Via the spin-Hall effect (SHE), an in-plane electric field $\mathbf{E}_1(t) = E(t) \mathbf{e}_x$ in N1 causes a spin current through the F$|$N interfaces, which, via the inverse spin-Hall effect (ISHE), causes a correction to the charge current in N1 (not shown here). This correction to the charge conductivity is the spin-Hall magnetoresistance (SMR). In addition, a nonlocal current response arises in the N2 layer, which is referred to as magnon-mediated current drag. In the magnetic insulator F, the component $j_{{\rm s}\perp}$ of the spin current polarized perpendicular to the equilibrium magnetization direction $\mathbf{m}_{\rm eq}$ is carried by coherent magnons, whereas the collinear component $j_{{\rm s}\parallel}$ is carried by incoherent, thermal magnons. The coherent magnons couple at the F$|$N interfaces via spin-transfer torque (STT) to the electronic spin accumulation in N. Incoherent magnons are excited by spin-flip scattering of electrons in N at the F$|$N interfaces. In this article, we calculate the charge currents $\mathbf{i}_k$ linear in $E_j$ for driving fields $E_j(t) \propto \cos(\omega t)$ with driving frequencies ranging from the dc limit $\omega = 0$ to the THz regime.
• Figure 2: Real part (solid line) and imaginary part (dashed line) of local linear response coefficients $s_{11}(\omega)$ (blue), $s_{11}'(\omega)$ (orange), and $s_{11}"(\omega)$ (green), see Eq. \ref{['eq:sji']}. The three dimensionless coefficients have a different dependence on the direction of the magnetization in F and characterize the local conductivity correction from the coupling of N to F$|$N. We note that the coefficient $s_{11}(\omega)$ is directly proportional to the SMR response calculated in Ref. Reiss2021-em, while $s_{11}"(\omega)$ describes the anomalous Hall effect (AHE).
• Figure 3: Magnon-mediated electric current drag. Real part (solid line) and imaginary part (dashed line) of nonlocal linear response coefficients $s_{21}(\omega)$ (blue), $s_{21}'(\omega)$ (orange), and $s_{21}"(\omega)$ (green), see Eq. \ref{['eq:sji']}. At low frequency, the nonlocal conductivity is mediated by thermal magnons, but coherent spin waves dominate at GHz to THz frequencies.
• Figure 4: Eigenvalues $l_1$ and $l_2$ of $\Lambda$, Eq. \ref{['eq:capitallambda']}. The eigenvalues at zero frequency correspond to the characteristic decay lengths $l_{\mu}$, Eq. \ref{['eq:approxlmu']}, and $l_{\rm T}$, Eq. \ref{['eq:approxlT']}, for magnon or heat transport, respectively. Their numerical values are given in Tab. \ref{['tab:derivedparameters']}. We refer to Sec. \ref{['sec:numericalestimates']} for an estimate of $l_{\rm m} (\omega)$, $m=1,2$, in the large-frequency limit.
• Figure 5: Local and nonlocal spin Peltier effect in an N$|$F$|$N trilayer. Since longitudinal spin and heat currents are coupled inside F and at the two N$|$F interfaces, the flow of a spin current linear in the applied electric field also implies the flow of a heat current and, hence, the generation of a temperature gradient.