Observation of thermal spin-transfer torque via ferromagnetic resonance in magnetic tunnel junctions

The thermal spin-transfer torque (TSTT) in magnetic tunneling junctions (MTJs) was systematically studied using electrical detection of ferromagnetic resonance (FMR). Evidence for the existence of TSTT in MTJs is observed. A temperature difference was applied across an MTJ acting as a TSTT on the free layer of the MTJ. The FMR of the free layer was then excited by a microwave current and electrically detected as a dc voltage. We found that the FMR line shape was changed by the TSTT, indicated by the ratio of dispersive and Lorentz components of the FMR spectra $\left(D/L\right)$. $D/L$ increases by increasing the temperature difference. In addition, we analyze the magnetization orientation dependence of TSTT and provide solid evidence that this dependence differs from the magnetization orientation dependence of spin-transfer torque driven by a dc bias.

Figure 1

Sketch of the thermal spin-transfer torque in an MTJ. $\mathbf{M}$ and $\mathbf{m}$ are the magnetization of the fixed and free layer, respectively. ${\tau }_{t\parallel }$ and ${\tau }_{t\perp }$ are the in-plane and out-of-plane torque generated by the temperature gradient $\nabla T$.

Figure 2

(a) The resistance loops as a function of $H$ of the MTJ at $\varphi =0^{\circ }$ (gray) and $\varphi ={60}^{\circ }$ (red). There are four points marked as A, B, C, and D. (b) Normalized conductance $G_{\text{norm}}$ as a function of dc biased voltage $V_{\text{dc}}$ at AP and P states, corresponding to $\theta =180$ and $0^{\circ }$, respectively. (c) and (d) are the sketches of the configuration of $\mathrm{m}$ and $\mathrm{M}$ corresponding to point B and C, respectively. (e) and (f) are the sketches of the configuration of $\mathrm{m}$ and $\mathrm{M}$ corresponding to point D when $\theta >0$ and $\theta <0$, respectively.

Figure 3

The measurement setup of (a) laser heating, (b) external heating by Peltier device, and (c) dc bias STT.

Figure 4

The coordinates and the magnetization configurations at (a) ${90}^{\circ }$ and (e) $-{101}^{\circ }$. (b)–(d) are results at ${91}^{\circ }$ and (f)–(h) are results at $-{101}^{\circ }$. (b) and (f) are the FMR line-shape evolution with the dc bias in different polarities. The FMR spectrum with no dc bias is in the middle while the FMR spectra with positive and negative dc bias are on the top and bottom, respectively. The gray circles are the measurement results, and the black line is the fittings of the data with the combination of dispersive and Lorentz components. (c) and (g) are the Lorentz (gray) and dispersive (dark cyan) components normalized by $L$. The cases without a dc bias are in the middle, and the cases with positive and negative dc bias are on the top and bottom in each figure. $D/L$ at various dc bias were plotted in (d) and (h), in which the black lines are linear fittings. The insets of (d) and (h) are the resonance positions ${\mu }_0{H}_r$ (left, black) and the linewidth ${\mu }_0\mathrm{\Delta }H$ (right, red) of the FMR at various dc bias.

Figure 5

The coordinates and the magnetization configurations at (a) $90{}^{\circ }$ and (e) $-{101}^{\circ }$. (b)–(d) are results at ${90}^{\circ }$, and (f)–(h) are results at $-{101}^{\circ }$. The top and bottom spectra in (b) and (f) are the FMR line shapes at $\mathrm{\Delta }T=0$ and 3 mK, respectively. The gray circles are the measurement results and the black lines are fittings with a sum of dispersive and Lorentz components. (c) and (g) are the Lorentz (gray) and dispersive (dark cyan) components normalized by the amplitude of $L$. The curves on the top and bottom correspond to $\mathrm{\Delta }T=0$ and 3 mK, respectively. $D/L$ at various $\mathrm{\Delta }T$ were plotted in (d) and (h). The solid gray dots are the values corresponding to $\mathrm{\Delta }T=0$ and $3\mathrm{mK}$. The insets of (d) and (h) are the resonance positions ${\mu }_0{H}_r$ (left, black) and the linewidth ${\mu }_0\mathrm{\Delta }H$ (right, red) of the FMR at various temperature differences.

Figure 6

(a) $D/L$ as a function of (a) $\mathrm{\Delta }T$ and (b) $V_{\text{dc}}$ at various $\theta$. The solid dots correspond to positive $\theta$ and the hollow dots correspond to negative $\theta$. Solid lines in (a) and (b) are linear fittings. (c) $D/L$ as a function of $\theta$ at $\mathrm{\Delta }T=3$ mK and (d) at $I_{\text{dc}}=100\mu \mathrm{A}$. Solid lines in (c) and (d) are guides to the eye.

Figure 7

In the left column, the sketches show that the samples were set into various temperatures or have a temperature difference from the top to the bottom side. (a) The FMR spectra for three different temperatures. (b) $D/L$ of the FMR spectra at various temperatures. The black line is a guide to the eye and the blue, yellow, and red solid dots are $D/L$ at the three temperatures corresponding to the three temperatures in (a). (c) The FMR spectra at different temperature difference $\mathrm{\Delta }T$. (d) $D/L$ at various $\mathrm{\Delta }T$. The black line is a guide to the eye and the blue and solid red dots are the values of $D/L$ at $\mathrm{\Delta }T$ of 0 and 3 mK corresponding to the cases in (c).