Spin pumping and interlayer exchange coupling through palladium

The magnetic behavior of ultrathin ferromagnetic films deposited on substrates is strongly affected by the properties of the substrate. We investigate the spin pumping rate, interlayer exchange coupling, and dynamic exchange coupling between ultrathin ferromagnetic films through palladium, a nonmagnetic substrate that displays strong Stoner enhancement. We find that the interlayer exchange coupling, both in the static and dynamic versions, is qualitatively affected by the electron-electron interaction within the substrate. For instance, the oscillatory behavior that is a hallmark property of the RKKY exchange coupling is strongly suppressed by the induced moment in Pd. Although the spin pumping rate of ferromagnetic films atop palladium is only mildly changed by the electron-electron interaction in Pd, the change is large enough to be detected experimentally. The qualitative aspects of our results for palladium are expected to remain valid for any nonmagnetic substrate where Coulomb repulsion is large.

Figure 1

Magnetic moment per atom for 8Co/Pd(001) at each atomic layer from the surface of the Co ultrathin-film (layer 0) to the 10th layer of Pd (layer 17). The green dashed line marks the interface between the ferromagnetic film (Co, black solid circles, and Ni, red solid squares) and the Pd substrate. The inset shows the results of a DFT-based calculation for 8Co/Pd(001).

Figure 2

Magnetic moment per atom at each atomic layer of Co${}_2$/Pd${}_{10}$/Co${}_2$/Pd(001) (solid circles). The vertical dashed lines mark the interfaces between Co and Pd. Only the two layers of the substrate closest to the second Co film are shown. The triangles represent the magnetizations obtained from a DFT calculation on the same system [Co${}_2$/Pd${}_{10}$/Co${}_2$/Pd(001)].

Figure 3

Spin pumping rate for $N$Co/Pd(001) (solid black circles) and $N$Ni/Pd(001) (solid red squares). The effective Coulomb interaction in Pd has been turned off. The dashed lines are fittings to power laws $N^{-\alpha }$ with exponents ${\alpha }_{\mathrm{Co}}\sim 0.83$ and ${\alpha }_{\mathrm{Ni}}\sim 1.2$.

Figure 4

Damping rate for $N$Co/Pd(001) as a function of the Co film thickness $N$ for interacting Pd (solid circles) and noninteracting Pd (open triangles) substrates. The solid line is a $1/(N+N_0)$ fitting of the results for the enhanced substrate (see text). The (red) dashed line is a $1/N^{\alpha }$ fitting of the results for the enhanced substrate, with $\alpha \approx 0.74$. The dot-dashed line is a $1/N^{\alpha }$ fitting of the results for the nonenhanced substrate with $\alpha \approx 0.83$ (also shown in Fig. 3).

Figure 5

Damping rate for $N$Ni/Pd(001) as a function of the Ni film thickness $N$ for interacting Pd (solid circles) and noninteracting Pd (solid triangles) substrates. The solid curve is a $1/(N+N_0)$ fitting of the results for the enhanced substrate (solid circles).

Figure 6

Interlayer exchange coupling between two Co films (with two atomic layers each) separated by $N_{\mathrm{Pd}}$ Pd atomic layers measured by the frequency of the optical FMR mode (squares). For comparison we show the same IEC calculated without exchange enhancement within the Pd spacer (open circles). For clarity, due to the magnitude mismatch between the two results, we repeat the IEC with the Coulomb repulsion turned off in Pd and show the results in the inset.

Figure 7

Frequency of the optical (out-of-phase) precession mode of two Ni films (with two atomic layers each) separated by $N_{\mathrm{Pd}}$ atomic layers.

Figure 8

Dynamic coupling between two Co films (with two atomic layers each) separated by $N_{\mathrm{Pd}}$ atomic layers. The results represented by solid circles where obtained with Coulomb repulsion turned off within the Pd spacer. The dashed and dot-dashed lines are meant as guides to the eye only. The absolute value of the static IEC (solid triangles) is also shown for comparison (scale on the right).

Figure 9

Dynamic coupling between two Co films (with two atomic layers each) separated by $N_{\mathrm{Pd}}$ atomic layers for a finite wave vector of the pumping field, ${\vec{Q}}_{\parallel }=\frac{0.44}{a_0}\widehat{i}$. The results represented by solid circles where obtained with Coulomb interaction turned off within the Pd spacer. The dashed and dot-dashed lines are meant as guides to the eye only.