Exchange spin waves in thin films with gradient composition

We report on an investigation of magnetic resonance phenomenon in ferromagnetic thin films with controlled nonuniform composition. An epitaxial Pd-Fe thin film with linear distribution of Fe content across the thickness is used as the model material. Anomalous perpendicular standing spin waves are observed and quantified using the collective dynamic equation. Numerical analysis yields the exchange stiffness constant for the diluted Pd-Fe alloy $D=2A/{\mu }_0{M}_s=15\mathrm{T}·{\mathrm{nm}}^2$ and the ratio of the effective magnetization to the saturation magnetization $M_{\text{eff}}/M_s=1.16$. It is demonstrated that, overall, the engineering of thin films with nonuniform composition across the thickness can be used for high-frequency or low-field magnonic operations using exchange spin waves.

Figure 1

Iron content across the thickness of the studied Pd-Fe film. Red line shows the linear fit.

Figure 2

The dependence of magnetization of the studued Pd-Fe sample on the magnetic field in both the in-plane (red curves, upper $x$-scale) and the out-of-plane (black curve, lower $x$-scale) measurement geometries at $T=5$ K.

Figure 3

Differentiated FMR absorption spectrum $d{S}_{21}(f,H)/dH$ of the Pd-Fe sample at $T=5$ K.

Figure 4

CMR spectrum of the Pd-Fe sample at $T=5$ K.

Figure 5

Experimental $f_r\left(H\right)$ dependencies acquired from the FMR spectrum (Fig. 3) are shown with black circles. Black solid lines show the fit of FMR $f_r\left(H\right)$ lines with Eq. (1). Resonance fields obtained by the CMR measurements at $f_r=9.44$ GHz (Fig. 4) are shown with red crosses. Red dashed lines show extrapolation of CMR using Eq. (1) and the gyromagnetic ratio obtained from the FMR lines.

Figure 6

(a) Dependencies of resonance fields on the mode number ${\mu }_0{H}_r\left(n\right)$ at $f=9.44$ GHz. (b) Normalized dependencies of resonance intensities on the mode numbers $I\left(n\right)/I\left(1\right)$. (c) Dependencies of amplitudes of magnetization precession across the thickness of the film for different modes $n$.

Figure 7

(a) Dependencies of resonance fields on the mode number ${\mu }_0{H}_r\left(n\right)$ at $f=9.44$ GHz. (b) Normalized dependencies of resonance intensities on the mode numbers $I\left(n\right)/I\left(1\right)$. (c) Upper panel: Potential $V\left(z\right)-H$ [see Eq. (2)] in the case of sine distribution of Fe. Lower panel: Dependencies of amplitudes of magnetization precession across the thickness of the film with sine distribution of Fe for different modes $n$. (d) Upper panel: Potential $V\left(z\right)-H$ [see Eq. (2)] in the case of cosine distribution of Fe. Lower panel: Dependencies of amplitudes of magnetization precession across the thickness of the film with cosine distribution of Fe for different modes $n$.