Spin-Hall magnetoresistance and spin Seebeck effect in spin-spiral and paramagnetic phases of multiferroic ${\text{CoCr}}_2{\text{O}}_4$ films

We report on the spin-Hall magnetoresistance (SMR) and spin Seebeck effect (SSE) in multiferroic ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ (CCO) spinel thin films with Pt contacts. We observe a large enhancement of both signals below the spin-spiral ($T_s=28\mathrm{K}$) and the spin lock-in ($T_{\mathrm{lock}\text{−}\mathrm{in}}=14\mathrm{K}$) transitions. The SMR and SSE responses in the spin lock-in phase are one order of magnitude larger than those observed at the ferrimagnetic transition temperature ($T_c=94\mathrm{K}$), which indicates that the interaction between spins at the $\mathrm{Pt}|\mathrm{CCO}$ interface is more efficient in the noncollinear magnetic state. At $T>T_c$, magnetic-field-induced SMR and SSE signals are observed, which can be explained by a high interface susceptibility. Our results show that the spin transport at the $\mathrm{Pt}|\mathrm{CCO}$ interface is sensitive to the magnetic phases but cannot be explained solely by the bulk magnetization.

Figure 1

(a, b) Impression of the types of magnetic order in CCO. (a) Ferrimagnetic state for $T_s<T<T_c$ and (b) transverse conical spiral state for $T<T_s$ with an electrical polarization P. Here, $T_c$ and $T_s$ are the Curie transition temperature to a collinear ferrimagnetic phase and the spin-spiral transition temperature, respectively. (c) Temperature dependence of the zero-field cooled magnetization of the CCO target powder used for film deposition for different applied magnetic fields. $T_{\mathrm{lock}\text{−}\mathrm{in}}$ is the spin lock-in magnetic transition temperature. (d) Device configuration for the transverse resistance (planar Hall effect) measurement of the Pt film on top of CCO.

Figure 2

Illustration of the SMR in $\mathrm{Pt}|\mathrm{CCO}$ bilayers. The charge current $I$ induces a spin current and thereby spin accumulation at the $\mathrm{Pt}|\mathrm{CCO}$ interface by virtue of the SHE. (a) This spin accumulation is absorbed as a spin transfer torque when the magnetization $\vec{M}$ is perpendicular to the current-induced spin polarization in Pt. (b) When $\vec{M}$ is parallel to the spin accumulation, the spin current is reflected back into Pt, where it generates an additional charge current, $J_{\mathrm{refl}}$, by the ISHE. (c) When $\vec{M}$ is at an angle $\alpha$ to $J_c$, the component of the spin accumulation perpendicular to $\vec{M}$ is absorbed and the component parallel is reflected, leading to an extra charge current component normal to $J_c$ that is detected in the Hall configuration. (d) Angular dependence of the first harmonic response in the transverse configuration, $R_1=V_1/I$, for $I=2\mathrm{mA}$ at 5 K in an applied magnetic field of 6 T. The $sin(\alpha +\varphi )$ and $sin2\alpha$ curves illustrate the additive contributions from the ordinary Hall effect and the SMR. (e–g) Temperature dependence of the SMR $R_{1\left(2\alpha \right)}^{\mathrm{ampl}}$ for $J_c=2\mathrm{mA}$ at 6 T (e), 4 T (f), and 2 T (g). Here, $R_{1\left(2\alpha \right)}^{\mathrm{ampl}}$ is the amplitude of the $sin2\alpha$ component from the SMR. $T_c$, $T_s$, and $T_{\mathrm{lock}\text{−}\mathrm{in}}$ are the ferrimagnetic, spin-spiral, and spin lock-in magnetic transition temperatures, respectively. Inset in (e): Zoomed-in image of the SMR signal below $T_s$ and $T_{\mathrm{lock}\text{−}\mathrm{in}}$ at 6 T.

Figure 3

(a) Temperature dependence of $R_{1\left(2\alpha \right)}^{\text{ampl}}$ in a magnetic field of 6 T for $I=2$ mA. The leftward (red) curve shows the fit to the Curie law at low temperatures, below ${\mathrm{T}}_c$, and the rightward (green) curve shows the fit to the Curie-Weiss law in the high-temperature range, above ${\mathrm{T}}_c$ (for ${\theta }_{\mathrm{CW}}=-550K$). (b–d) Field dependence of fitting parameters $A_1$ (b), $A_2$ (c), and $A_3$ (d).

Figure 4

(a) Spin Seebeck effect in $\mathrm{Pt}|\mathrm{CCO}$. A thermal gradient creates magnons at the interface by absorption of a spin current from Pt with polarization $\vec{\sigma }\parallel \vec{M}$, where $\vec{M}$ is the CCO interface magnetization. The spin current generates an electromotive force ${\vec{E}}_{\text{ISHE}}$ by the ISHE. (b) Angular dependence of the second harmonic response, $R_2=\sqrt{2}{V}_2/I^2$, at 5 K for $I=2\mathrm{mA}$ in an applied magnetic field of 6 T. (c–e) Temperature dependence of $R_2^{\mathrm{ampl}}$ at 6 T (c), 4 T (d), and 2 T (e) for $I=2\mathrm{mA}$. Inset in (c): Plot emphasizing the enhancement of the SSE signal below the spin-spiral ($T_s$) and spin lock-in ($T_{\mathrm{lock}\text{−}\mathrm{in}}$) transition temperatures in a magnetic field of 6 T. (f) Temperature dependence of $R_2^{\mathrm{ampl}}$ in the nonlinear current regime ($I=5$ mA). Inset: Magnetic-field dependence of $R_2^{\mathrm{ampl}}$ at $T=130\mathrm{K}$.

Figure 5

In-plane magnetization of a CCO film on a MgO substrate in a magnetic field of 0.01 T after cooling at 1 T.

Figure 6

(a) Dependence of the second harmonic response $V_2$ on $I^2$, due to the SSE, generated by current-induced heating and (b) dependence of the first harmonic contribution $V_{1\left(2\alpha \right)}$, due to SMR, by an ac current $I$ sent through the Pt Hall bar in a magnetic field of 4 T. The SMR scales linearly and the SSE scales quadratically with I in the linear regime ($I\le 2$ mA). (c) Angular dependence of the second harmonic response, $R_2$, for $I=5$ mA, $H=4$ T at $T=140$ and 240 K.

Figure 7

Temperature dependence of (a) the SMR and (b) the SSE in the $\mathrm{Pt}|\mathrm{YIG}$ system for a 2.5-mA current through the Pt Hall-bar in a magnetic field of 0.1 T.