Broadband ferromagnetic resonance characterization of anisotropies and relaxation in exchange-biased IrMn/CoFe bilayers

The magnetization dynamics of exchange-biased IrMn/CoFe bilayers have been investigated using broadband and in-plane angle-dependent ferromagnetic resonance spectroscopy. The interface energy of the exchange bias effect in these bilayers exceeds values previously reported for metallic antiferromagnets. A strong perpendicular magnetic anisotropy and a small in-plane uniaxial anisotropy are also observed in these films. The magnetization relaxation of the bilayers has a strong unidirectional contribution, which is in part caused by two-magnon scattering. However, a detailed analysis of in-plane angle– and thickness-dependent linewidth data strongly suggests the presence of a previously undescribed unidirectional relaxation mechanism.

Figure 1

Sketch of the geometry, where the exchange bias field ${\vec{H}}_{\mathrm{eb}}$ serves as a reference direction. The static external magnetic field $\vec{H}$ is applied in the film plane at an angle ${\varphi }_H,$ with the microwave field ${\overleftrightarrow{h}}_{\mathrm{mw}}$ also applied in the film plane, but perpendicular to $\vec{H}$. Also shown is the magnetization $\vec{M}$ with equilibrium orientation $\left({\theta }_0,{\varphi }_0\right)$ and the easy axis of the (in-plane) uniaxial anisotropy field ${\vec{H}}_u$, which is shown at an angle ${\varphi }_u$ relative to the exchange bias direction.

Figure 2

Microwave frequency $f$ versus resonance field $H_{\mathrm{res}}$ (Kittel plot) for a 6 nm CoFe exchange-biased layer. Black (red) symbols show broadband FMR data with the external magnetic field applied parallel (antiparallel) to the exchange bias direction. The corresponding solid lines are the result of a simulataneous fit to the Kittel Eq. (6) for both orientations.

Figure 3

Effective magnetization $M_{\mathrm{eff}}$, determined using broadband ferromagnetic resonance data, as a function of the inverse CoFe film thickness $t_{\mathrm{CoFe}}$. The red line is a linear fit to the experimental data.

Figure 4

Dependence on the in-plane angle of the applied field ${\varphi }_H$ of (a) the resonance field $H_{\mathrm{res}}$ of a 6 nm CoFe exchange-biased layer, where the figure includes the experimental data (blue symbols), a fit using the analytic model (green line), and a fit using the full model (red line), (b) the residuals of the fit using the analytical model (green line and symbols) and the full model (red line & symbols), and (c) the misalignment of the in-plane angle of the magnetization ${\varphi }_0$ from the direction of the applied field ${\varphi }_H$ calculated using the full model.

Figure 5

Dependence on the in-plane angle of the applied field ${\varphi }_H$ of (a) the resonance field $H_{\mathrm{res}}$, where the red line is the result of the full model for $H_{\mathrm{eb}}=500\left(\mathrm{Oe}\right)$ and $H_u=200\left(\mathrm{Oe}\right)$, and the green line is a fit of this data using Eq. (6), (b) the residuals of the fit, and (c) the misalignment of the equilibrium direction of the magnetization ${\varphi }_0$ from the direction of the applied field ${\varphi }_H$.

Figure 6

Field shift $H_{\mathrm{shift}}$ of the magnetization reversal curves as a function of the in-plane angle ${\varphi }_H$ of the applied field. Experimental data determined using the magneto-optic Kerr effect are shown as blue symbols, whereas the red line is a fit using $H_{\mathrm{shift}}\left({\varphi }_H\right)=H_{\mathrm{eb}}\cos \left({\varphi }_H\right)$.

Figure 7

Exchange bias field $H_{\mathrm{eb}}$ as a function of the inverse of the CoFe thickness $t_{\mathrm{CoFe}}$ as determined from ferromagnetic resonance data (black solid symbols) and magneto-optic Kerr effect data (blue open symbols). The red line shows a linear fit of the data. The inset shows the in-plane uniaxial anisotropy field as determined from ferromagnetic resonance data as a function of the CoFe thickness.

Figure 8

Ferromagnetic resonance linewidth $\mathrm{\Delta }H$ as a function of the microwave frequency $f$ for a CoFe sample with a thickness of (a) $t_{\mathrm{CoFe}}=4\left(\mathrm{nm}\right)$ and (b) $t_{\mathrm{CoFe}}=6\left(\mathrm{nm}\right)$. The black (red) symbols represent broadband ferromagnetic resonance data measured with the field parallel (antiparallel) to the exchange bias direction. The solid lines show a fit of the data assuming Gilbert-type damping, Eq. (8), and the dashed line in (a) shows a fit of the data assuming two-magnon scattering as described by Eq. (9).

Figure 9

Effective Gilbert-type damping parameter ${\alpha }_{\mathrm{eff}}$ as a function of the square of the inverse CoFe thickness $t_{\mathrm{CoFe}}$. The black (red) symbols represent damping parameters determined from broadband ferromagnetic resonance data measured with the field parallel (antiparallel) to the exchange bias direction. The solid lines show linear fits of the data.

Figure 10

(a) Peak-to-peak ferromagnetic resonance linewidth $\mathrm{\Delta }H$ as a function of the in-plane angle ${\varphi }_H$ of the applied field measured for a 6-nm-thick exchange-biased CoFe film at a microwave frequency of $f=20\left(\mathrm{GHz}\right)$. Experimental data are shown as blue symbols, where the red and green lines represent fits using a unidirectional relaxation described by Eq. (11) using the full model and assuming ${\varphi }_0={\varphi }_H$ respectively. (b) Residuals of the two different fits.

Figure 11

Unidirectional linewidth contribution $\mathrm{\Delta }{H}_{\mathrm{eb}}$ determined from in-plane angle–dependent ferromagnetic resonance measurements. (a) Contribution is plotted as a function of $1/t_{\mathrm{CoFe}}^2$, where the blue line is a linear fit of the data with a vanishing unidirectional linewidth contribution for the bulk. (b) The same data shown as a function of the inverse CoFe thickness $t_{\mathrm{CoFe}}$. The red line is a fit including a linear contribution (dashed green line) and quadratic contribution (dashed blue line) in the inverse film thickness. The red shaded area indicates the $95\%$ confidence bands of the fit.