Hf thickness dependence of perpendicular magnetic anisotropy, damping and interfacial Dzyaloshinskii-Moriya interaction in $\mathrm{Pt}/\mathrm{CoFe}/\mathrm{Hf}/{\mathrm{HfO}}_2$

Vibrating sample magnetometery (VSM) combined with Brillouin light scattering (BLS) were used to investigate the Dzyaloshinskii-Moriya interaction (iDMI), the perpendicular magnetic anisotropy (PMA) and the damping in ${\mathrm{Co}}_{0.5}{\mathrm{Fe}}_{0.5}$-based systems grown by sputtering on $\mathrm{Si}/{\mathrm{SiO}}_2$ substrates, using Pt or Cu buffer layers and Hf capping layer of variable thickness $(0\le t_{\mathrm{Hf}}\le 2\mathrm{nm})$. VSM measurements revealed a significant decrease of the areal magnetic moment at saturation as $t_{\mathrm{Hf}}$ increases, most likely due to the increase of the magnetic dead layer thickness at CoFe/Hf interface up to $0.73\pm 0.06\mathrm{nm}$ for $t_{\mathrm{Hf}}=2\mathrm{nm}$. Damping measurements allowed concluding to the weaker spin pumping contribution by the CoFe/Hf interface compared to Pt/CoFe. The analysis of the $t_{\mathrm{Hf}}$ dependence of damping within a model considering the contribution of each interface allowed us to determine the spin diffusion length of Hf, found to be 1.7 nm. The Hf thickness dependence of iDMI and PMA constants revealed significant (weak) contribution of the CoFe/Hf interface to PMA (iDMI). The surface iDMI constant of CoFe/Hf interface was estimated to be $(-0.37\pm 0.12)\times {10}^{–7}\mathrm{erg}/\mathrm{cm}$. This suggests that the iDMI sign of Hf and Pt are opposite, and an additive behavior can be obtained when they are placed in opposite sides of the CoFe layer, allowing thus to strengthen the iDMI, needed for some applications. Quadratic correlations between PMA and iDMI constants and linear dependence of damping versus PMA constant were obtained confirming their relationship with the spin-orbit coupling.

Figure 1

(a) $2\theta /\omega$ diffraction patterns recorded for samples S1-Ta(2.5)/Pt(4)/CoFe(1.4)/Hf(6)/${\mathrm{HfO}}_2$(4), S2-Ta(2.5)/Pt(4)/CoFe(10)/Hf(6)/${\mathrm{HfO}}_2$(4), S3-Ta(2.5)/Hf(6)/CoFe(1.4)/${\mathrm{HfO}}_2$(4) and S4-Ta(2.5)/Hf(6)/CoFe(10)/${\mathrm{HfO}}_2$(4). (b) X-ray reflectivity patterns on samples S5-Ta(2.5)/Pt(4)/CoFe(1.4)/${\mathrm{HfO}}_2$(2)/Ta(2.5) and S6-Ta(2.5)/Pt(4)/CoFe(1.4)/Hf(1.5)/${\mathrm{HfO}}_2$(2)/Ta(2.5). Symbols are experimental data, while the continuous lines are theoretical fits within the Parratt formalism.

Figure 2

(a) Variations of the nominal magnetization at saturation ($M_{\mathrm{sn}}$), calculated by dividing the measured VSM magnetic moment at saturation to the nominal volume ($\mathrm{surface}\times \mathrm{nominal}$ thickness of CoFe) of the CoFe film for Pt/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$) and Pt/Cu/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$), versus the Hf thickness ($t_{\mathrm{Hf}}$). (b) Magnetic dead thickness ($t_d$), deduced from the measured $M_{\mathrm{sn}}$ by considering that $M_{\mathrm{sn}}$ is given by $M_{\mathrm{sn}}\times t_{\mathrm{CoFe}}=M_s\times \left(t_{\mathrm{CoFe}}-t_d\right)$ and (c) effective CoFe thickness $\left(t_{\mathrm{eff}}=t_{\mathrm{CoFe}}-t_d\right)$, where $t_{\mathrm{CoFe}}=1.4$, 1, or 0.6 nm, versus the Hf thickness ($t_{\mathrm{Hf}}$). (d) Saturation magnetic moment per unit area versus CoFe thickness of Pt/CoFe($t_{\mathrm{CoFe}}$)/${\mathrm{HfO}}_2$, Pt/CoFe($t_{\mathrm{CoFe}}$)/Hf(0.4 nm) and Hf/CoFe($t_{\mathrm{CoFe}}$)/${\mathrm{HfO}}_2$. Symbols refer to the VSM measurements and solid lines are the linear fits.

Figure 3

Variations of the (a) the mean frequency $\left[F=\left(F_S+F_{aS}\right)/2\right]$ and (b) the mean $\delta F[\delta F=(\delta F_S+\delta F_{aS})/2]$, determined from the fit of the recorded BLS spectra at fixed spin wave vector of $8.08\mu {\mathrm{m}}^{–1}$ (incident angle of 20°) to obtained the Stokes (S) and anti-Stokes (aS) line frequencies and their full width at half maximum ($\delta F_S$ and $\delta F_{aS}$), for Pt/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$). Symbols refer to the experimental data and solid lines are fits using Eqs. (1) and (2).

Figure 4

Variations of the (a) effective magnetization $\left(4\pi M_{\mathrm{eff}}\right)$ versus the Hf thickness and (b) the effective perpendicular anisotropy constant ($K_{\mathrm{eff}}$) times the effective thickness $K_{\mathrm{eff}}\times t_{\mathrm{eff}}$ versus the effective thickness of the CoFe layers ($t_{\mathrm{eff}}$) for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ and Pt/Cu/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$) systems. $4\pi M_{\mathrm{eff}}$ values were extracted from the fit of similar measurements of Fig. 2. The inset in (b) shows the effective perpendicular anisotropy constant versus the inverse of the effective thickness of the CoFe layers for Pt/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$), Pt/Cu/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$) and Hf/CoFe($t_{\mathrm{CoFe}}$)/${\mathrm{HfO}}_2$ (blue triangles) systems. The effective CoFe thickness defined as $t_{\mathrm{eff}}=t_{\mathrm{CoFe}}-t_d$, where $t_{\mathrm{CoFe}}=1.4\mathrm{nm}$ and $t_d$ is presented in Fig. 2 for each $t_{\mathrm{Hf}}$, in the case of Pt/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$) and Pt/Cu/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$). Symbols refer to experimental data while solid lines are the linear fits.

Figure 5

(a) Variations of the Gilbert effective damping (α) versus the Hf thickness for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ system. The inset shows α versus the inverse of the effective thickness of the CoFe layers for Pt/CoFe($t_{\mathrm{CoFe}}$)/${\mathrm{HfO}}_2$, Pt/CoFe($t_{\mathrm{CoFe}}$)/Hf(0.4 nm) and Hf/CoFe($t_{\mathrm{CoFe}}$)/${\mathrm{HfO}}_2$ systems. Symbols are experimental data and solid lines are linear fits whereas dashed line refers to fit using Eq. (4). (b) Variations of the Gilbert effective damping (α) versus $1/(M_s\times t_{\mathrm{eff}})$ for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ system. Symbols are experimental data and dashed line is the fit using Eq. (4).

Figure 6

(a) Hf thickness dependence of the experimental frequency mismatch $\mathrm{\Delta }F$ measured at $k_{\mathrm{sw}}=20.45\mu {\mathrm{m}}^{–1}$ for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ and Pt/Cu/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$) systems. Symbols refer to experimental data and dashed lines are used for eye guide. Variation of the (b) effective iDMI constant ($D_{\mathrm{eff}}$) versus the inverse effective thickness of CoFe and (c) iDMI surface constant ($D_s$) versus the Hf thickness for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ and Pt/Cu/CoFe(1.4 nm)/Hf($t_{\mathrm{Hf}}$) systems.

Figure 7

(a) Variations of the perpendicular effective magnetic anisotropy constant ($K_{\mathrm{eff}}$) as a function of the effective iDMI constant ($D_{\mathrm{eff}}$) for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ and Pt/Cu/CoFe(1.4nm)/Hf($t_{\mathrm{Hf}}$) systems with a variable Hf thickness. Symbols refer to experimental data, dashed lines are linear fits and the solid lines are fits with equations:$K_{\mathrm{eff}}=1.08\times {10}^7+0.16\times {10}^6{D}_{\mathrm{eff}}^2$ (violet line) and $K_{\mathrm{eff}}=0.66\times {10}^6+2.59\times {10}^7{D}_{\mathrm{eff}}^2$ (green line). (b) Variations of the damping constant (α) as a function of the effective PMA constant $\left(K_{\mathrm{eff}}\right)$ for $\mathrm{Pt}/\mathrm{CoFe}\left(t_{\mathrm{CoFe}}\right)/\mathrm{Hf}\left(t_{\mathrm{Hf}}\right)$ system with a variable Hf thickness. Symbols refer to experimental data and solid lines are linear fits.