Anomalous Gilbert damping induced by the coexisting static and dynamic coupling in Fe/Pd/Fe trilayers

Although the magnetic relaxation mechanism in ferromagnetic/nonmagnetic (FM/NM) bilayers has been commendably established, the nonlocal Gilbert damping has been much less addressed in spin valve configurations of FM/NM/FM associated with both the static interlayer exchange coupling and the dynamic coupling. Here, we report the dimensional crossover role of the Pd layer on magnetic relaxation in Fe/Pd/Fe trilayer structures. We identify a pronounced jump of Gilbert damping across the characteristic static interlayer exchange coupling length of Fe/Pd/Fe. The significant enhancement and suppression of Gilbert damping values are ascribed to the entanglement of the dynamics of the two Fe layers mediated by the static exchange coupling and the dynamic exchange coupling. Our work deepens the understanding to manipulate the spin transport and magnetic relaxation via the coherence of spin current.

Figure 1

Illustrations of the stacked bilayers Pd/Fe (a) and trilayers Fe/Pd/Fe (b). Real part of $S_{21}$ vs magnetic field at 14 GHz for Pd(7 nm)/Fe(6 nm) and Fe(7.5 nm)/Pd(7 nm)/Fe (c) at ferromagnetic resonance.

Figure 2

(a) In-plane angular dependent FMR spectra for Fe(7.5 nm)/Pd(7 nm)/Fe(6 nm) at the fixed frequency 14 GHz. (b) In-plane angular dependence of resonance field $H_{\mathrm{r}}$ for Pd(7 nm)/Fe(6 nm) bilayers. (c) The extracted resonance field $H_{\mathrm{r}}$ vs magnetic field angle ${\phi }_H$ from (a). (d) The obtained magnetic anisotropy parameters via fitting the two kinds of the angular relations for Fe(7.5 nm)/Pd($t_{\mathrm{Pd}}$ nm)/Fe(6 nm) trilayers.

Figure 3

$H_{\mathrm{r}}$ vs $f$ (a) and Δ$H$ vs $f$ (b) for Fe(7.5 nm)/Pd(2 nm)/Fe(6 nm). $H_{\mathrm{r}}$ vs $f$ (c) and Δ$H$ vs $f$ (d) for Fe(7.5 nm)/Pd(5 nm)/Fe(6 nm).

Figure 4

(a) Interlayer exchange coupling parameter $A_{\mathrm{ex}}$ vs Pd thickness $t_{\mathrm{Pd}}$ in Fe/Pd/Fe (red lines and squares). The interlayer exchange coupling region is denoted by color code. Spin current density as a function of Pd thickness (Black line). (b) The Gilbert damping vs Pd thickness for the Pd/Fe bilayers and Fe/Pd/Fe trilayers. Sketches of the magnetization precession represent the different excitation modes. The red line is an eye guide.