Spin transport and dynamics in all-oxide perovskite ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3/{\mathrm{SrRuO}}_3$ bilayers probed by ferromagnetic resonance

Thin films of perovskite oxides offer the possibility of combining emerging concepts of strongly correlated electron phenomena and spin current in magnetic devices. However, spin transport and magnetization dynamics in these complex oxide materials are not well understood. Here, we experimentally quantify spin transport parameters and magnetization damping in epitaxial perovskite ferromagnet/paramagnet bilayers of ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3/{\mathrm{SrRuO}}_3$ (LSMO/SRO) by broadband ferromagnetic resonance spectroscopy. From the SRO thickness dependence of the Gilbert damping, we estimate a short spin diffusion length of $\lesssim 1$ nm in SRO and an interfacial spin-mixing conductance comparable to other ferromagnet/paramagnetic-metal bilayers. Moreover, we find that anisotropic non-Gilbert damping due to two-magnon scattering also increases with the addition of SRO. Our results demonstrate LSMO/SRO as a spin-source/spin-sink system that may be a foundation for examining spin-current transport in various perovskite heterostructures.

Figure 1

$2\theta -\omega$ x-ray diffraction scans of a single-layer LSMO (10 nm) film and LSMO(10 nm)/SRO(18 nm) bilayer.

Figure 2

Exemplary FMR spectra and fitting curves: (a) one mode of Lorentzian derivative and (b) superposition of a main mode and a small secondary mode due to slight sample inhomogeneity.

Figure 3

(a) Out-of-plane resonance field $H_{\mathrm{FMR}}$ versus excitation frequency $f$ for a single-layer LSMO(10 nm) film and a LSMO(10 nm)/SRO(3 nm) bilayer. The solid lines indicate fits to the data using Eq. (1). (b,c) SRO thickness dependence of the out-of-plane Landé $g$ factor (b) and effective saturation magnetization $M_{\mathrm{eff}}$ (c). The dashed lines indicate the values averaged over all the data shown.

Figure 4

(a) Out-of-plane FMR linewidth $\mathrm{\Delta }H$ versus excitation frequency for LSMO(10 nm) and LSMO(10 nm)/SRO(3 nm). The solid lines indicate fits to the data using Eq. (2). (b) Gilbert damping parameter $\alpha$ versus SRO thickness $t_{\mathrm{SRO}}$. The solid curve shows a fit to the diffusive spin-pumping model [Eq. (5)]. (c) Schematic of out-of-plane spin pumping and the equivalent “spin circuit.”

Figure 5

(a) Angular dependence of $H_{\mathrm{FMR}}$ at 9 GHz for LSMO(10 nm) and LSMO(10 nm)/SRO(7 nm). (b) Frequency dependence of $H_{\mathrm{FMR}}$ for LSMO(10 nm)/SRO(7 nm) with field applied in the film plane along the [100] and [110] directions. Inset: Closeup of $H_{\mathrm{FMR}}$ versus frequency around 14–15 GHz. In (a) and (b), the solid curves show fits to the Kittel equation [Eq. (6)]. (c,d) SRO thickness dependence of the in-plane cubic magnetocrystalline anisotropy field (c) and in-plane Landé $g$ factor (d). The dashed lines indicate the values averaged over all the data shown.

Figure 6

(a) In-plane angular dependence of linewidth $\mathrm{\Delta }H$ at 9 GHz for LSMO(10 nm) and LSMO(10 nm)/SRO(7 nm). The solid curves indicate fits to Eq. (8). (b) Frequency dependence of $\mathrm{\Delta }H$ for LSMO(10 nm) and LSMO(10 nm)/SRO(7 nm) with $H$ applied along the [100] direction. The solid curves indicate fits to Eqs. (7) and (8). The dashed and dotted curves indicate estimated two-magnon and Gilbert damping contributions, respectively. (c) Schematic of a spin-wave dispersion curve (when the magnetization is in-plane and has a finite component parallel to the spin-wave wave vector $k$) and two-magnon scattering. (d) Two-magnon scattering coefficient ${\mathrm{\Gamma }}_{2\mathrm{m}}$, estimated for the cases with $H$ applied along the [100] and [110] axes, plotted against SRO thickness $t_{\mathrm{SRO}}$. The dashed curve is the same as that in Fig. 4, scaled to serve as a guide for the eye for ${\mathrm{\Gamma }}_{2\mathrm{m}}$ with $H$ along [100].

Figure 7

(a) Gilbert damping parameter $\alpha$ versus SRO thickness $t_{\mathrm{SRO}}$. The solid curve is a fit taking into account the $t_{\mathrm{SRO}}$ dependence of SRO resistivity, whereas the dotted curve is a fit assuming a constant bulklike SRO resistivity. (b) Resistivity of ${\mathrm{SrRuO}}_3$ films on LSAT(001) as a function of thickness.

Figure 8

Frequency dependence of in-plane FMR linewidth $\mathrm{\Delta }H$ of LSMO(10 nm) on (a) LSAT(001) and (b) ${\mathrm{NdGaO}}_3$(110), with the magnetization along the magnetic easy and hard axes. The solid curves are fits to Eq. (7) with the Gilbert damping parameter $\alpha$ fixed to $0.9\times {10}^{-3}$.