Anomalous temperature dependence of current-induced torques in $\text{CoFeB}/\text{MgO}$ heterostructures with Ta-based underlayers

We have studied the underlayer thickness and temperature dependencies of the current-induced effective field in $\text{CoFeB}/\text{MgO}$ heterostructures with Ta-based underlayers. The underlayer thickness at which the effective field saturates is found to be different between the two orthogonal components of the effective field; i.e., the dampinglike term tends to saturate at a smaller underlayer thickness than the fieldlike term. For large underlayer thickness films in which the effective field saturates, we find that the measurement temperature significantly influences the size of the effective field. A striking difference is found in the temperature dependence of the two components: the dampinglike term decreases whereas the fieldlike term increases with increasing temperature. Using a simple spin diffusion-spin transfer model, we find that all of these results can be accounted for provided the real and imaginary parts of an effective spin mixing conductance are negative. These results imply that either spin transport in this system is different from conventional metallic interfaces or effects other than spin diffusion into the magnetic layer need to be taken into account in order to model the system accurately.

Figure 1

(a) Schematic illustration of the experimental setup. A definition of the coordinate system is included. Temperature dependence of (b) the longitudinal resistance $R_{XX}$, (c) the anomalous Hall resistance Δ$R_A$, (d) the saturation magnetization $M_S$, and (e) the effective magnetic anisotropy energy $K_{\mathit{EFF}}$, all normalized by their RT value for the Ta and TaN underlayer films. The thickness of the underlayer is indicated. The inset of (e) shows Log${}_{10}$[$K_U$(T)/$K_U$(100 K)] vs Log${}_{10}$[$M_S$(T)/$M_S$(100 K)] to obtain exponent $n$ of $K_U$ vs M${}_S$${}^n$.

Figure 2

(a)–(d) Temperature dependence of (a) the normalized longitudinal resistance $R_{XX}·w/L$, (b) the anomalous Hall resistance Δ$R_A$, (c) the saturation magnetization $M_S$, and (d) the effective magnetic anisotropy energy $K_{\mathit{EFF}}$ for film structure A (Sub.$|$$d$ Ta$|$1 CoFeB$|$2 MgO$|$1 Ta) and film structure B (Sub.$|$$d$ TaN$|$1 CoFeB$|$2 MgO$|$1 Ta).

Figure 3

(a) and (b) Schematic illustration of the Hall resistance measurement setups. External field ($H$) of 20–30 kOe is applied to align the magnetization along the field direction. The sample is rotated along the plane shown by the transparent light blue circle. The angle between the film normal and the external field is defined as ${\phi }_{OOP}$, whereas the angle between the external field and the current flow is set to be ${\phi }_{INP}$. (c) and (d) Hall resistance $R_{XY}$ as a function of (c) angle ${\phi }_{OOP}$ and (d) angle ${\phi }_{INP}$ measured at 100 K. The inset in (d) is a magnified view of the main plot. The solid line in (c) and (d) shows fit to the data to obtain the anomalous Hall resistance Δ$R_A$ and the planar Hall resistance Δ$R_P$, respectively. (e) Δ$R_A$ and Δ$R_P$ plotted as a function of temperature. All data presented in (c)–(e) are from film structure A (Sub.$|$$d$ Ta$|$1 CoFeB$|$2 MgO$|$1 Ta) with $d$ ∼ 1.0 nm. (f) Ratio of the planar Hall resistance to the anomalous Hall resistance ($\xi \equiv \frac{\Delta R_P}{\Delta R_A}$) plotted as a function of temperature for several devices with different Ta underlayer thicknesses for film structure A.

Figure 4

Temperature dependence of (a) Δ$H_T$/$J_N$ and (b) Δ$H_L$/$J_N$ for the Ta underlayer film. Thickness of the Ta underlayer is indicated. Bottom panels show a magnified view of the related upper panels for the thinner Ta underlayer devices. Solid and open symbols correspond to magnetization pointing along +$z$ and −$z$, respectively.

Figure 5

(a) Magnitude $|\Delta H/J_N|\equiv \sqrt{{\left(\Delta H_T/J_N\right)}^2+{\left(\Delta H_L/J_N\right)}^2}$ and (b) angle with respect to the current flow $\phi =arctan\left[\frac{\Delta H_T/J_N}{\Delta H_L/J_N}\right]$ plotted against temperature for film structure A (Sub.$|$$d$ Ta$|$1 CoFeB$|$2 MgO$|$1 Ta) and film structure B (Sub.$|$$d$ TaN$|$1 CoFeB$|$2 MgO$|$1 Ta). The bottom panel of (a) corresponds to a magnified view of the top panel around zero $|\Delta H/J_N|$. Solid and open symbols correspond to magnetization pointing along +$z$ and −$z$, respectively.

Figure 6

Underlayer thickness dependence of (a) and (b) Δ$H_T$/$J_N$ and (c) and (d) Δ$H_L$/$J_N$ for the TaN underlayer film. The measurement temperature is 100 K for (a) and (c) and RT (∼295 K) for (b) and (d). Solid lines are calculated using Eqs. (7) and (8) with the following parameters: $M_S=1200$ emu/cm${}^3$, ${\rho }_N=395$ μΩ·cm, ${\lambda }_N=2.5$ nm, ${\theta }_{SH}=-0.08$, and the real and imaginary parts of the spin mixing conductance ($G_{\mathrm{MIX}}$), which are shown by the solid symbols in Fig. 7.

Figure 7

(a) Temperature dependence of the real and imaginary parts of the spin mixing conductance ($G_{\mathrm{MIX}}$) obtained by the fitting shown in Fig. 6. Linear fit to the data (symbols) is shown by the solid line. Temperature dependence of (b) Δ$H_T$/$J_N$ and (c) Δ$H_L/J_N$ for the TaN underlayer film with $d\sim 8.9$ nm. Solid lines are calculated using Eqs. (7) and (8) with the following parameters: $M_S=1200$ emu/cm${}^3$, ${\rho }_N=395$ μΩ·cm, ${\lambda }_N$ = 2.5 nm, ${\theta }_{SH}=-0.08$, and the interpolated real and imaginary parts of $G_{\mathrm{MIX}}$ shown by the solid lines in (a).

Figure 8

Underlayer thickness ($d$) dependence of (a)–(e) the transverse (Δ$H_T$) and (f)–(j) the longitudinal (Δ$H_L$) components of the current-induced effective field per unit current density ($J_N={10}^8$ A/cm${}^2$) flowing through the TaN underlayer for film structure B (Sub.$|$$d$ TaN$|$1 CoFeB$|$2 MgO$|$1 Ta). The measurement temperature is 100 K for blue symbols and RT (i.e., ∼295 K) for red symbols. Temperature dependence of (k)–(o) the transverse (Δ$H_T$) and (p)–(t) the longitudinal (Δ$H_L$) components of the current-induced effective field per unit current density ($J_N={10}^8$ A/cm${}^2$) flowing through the TaN underlayer for film structure B (Sub.$|$$d$ TaN$|$1 CoFeB$|$2 MgO$|$1 Ta) with $d\sim 8.9$ nm. (a)–(t) Solid and open symbols correspond to magnetization pointing along +$z$ and −$z$, respectively. Solid lines in (a)–(t) are calculated using Eqs. (7) and (8) with the following parameters: $M_S=1200$ emu/cm${}^3$, ${\rho }_N=395$ μΩ·cm, ${\lambda }_N=2.5$ nm, and the real and imaginary parts of the spin mixing conductance $G_{\mathrm{MIX}}$, which are shown in (u)–(y) in the corresponding column. Each column shows calculation results with different ${\theta }_{SH}$; the value used is noted at the top. (u)–(y) Temperature dependence of the real and imaginary parts of $G_{\mathrm{MIX}}$ obtained by the fitting of the underlayer thickness dependence shown in (a)–(j). The linear fit to the data is shown by the solid line.