Gate tunable spin-orbit coupling and weak antilocalization effect in an epitaxial $\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{S}{\mathrm{r}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ thin film

Epitaxial $\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{S}{\mathrm{r}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ (LSMO) films have been grown on $\mathrm{SrTi}{\mathrm{O}}_3$ (001) substrates via pulsed laser deposition. In a 22-nm-thick LSMO film with a low residual resistivity of ${\rho }_0\approx 59\mu \mathrm{\Omega }\mathrm{cm}$, we found a zero-field dip in the magnetoresistance (MR) below 10 K, manifesting the weak antilocalization (WAL) effect due to strong spin-orbit coupling (SOC). We have analyzed the MR data by including the D’yakonov-Perel’ spin-relaxation mechanism in the WAL theory. We explain that the delocalized spin-down electron sub-band states play a crucial role for facilitating marked SOC in clean LSMO. Moreover, we find that the SOC strength and gate voltage tunability are similar to those in a two-dimensional electron gas at the $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ interface, indicating the presence of an internal electric field near the LSMO/$\mathrm{SrTi}{\mathrm{O}}_3$ interface. In a control measurement on a 5-nm-thick high resistivity $\left({\rho }_0\approx 280\mu \mathrm{\Omega }\mathrm{cm}\right)$ LSMO film, we observe only a small zero-field peak in MR from weak localization effect, indicating negligible SOC.

Figure 1

(a) Schematic energy band structure for a type-$\mathrm{II}{\mathrm{I}}_{\mathrm{A}}$ half metal. $E_{\mathrm{F}}$ denotes the Fermi energy. (b) Temperature dependence of resistivity $\rho \left(T\right)$ for a 22- and a 5-nm-thick epitaxial LSMO film, as indicated.

Figure 2

(a) MR at several $T$ values, as indicated. Black (red) curves correspond to the MR measured with magnetic field sweeping from $+1.2$ to $-1.2\mathrm{T}$ $(-1.2$ to $+1.2\mathrm{T})$. (b) MR at $T=0.36\mathrm{K}$. $H_{\mathrm{c}+}$ and $H_{\mathrm{c}-}$ denote the coercive fields. Inset: Sheet magnetoconductance $G_s\left(H\right)$ plotted in units of conductance quantum $e^2/h$.

Figure 3

(a) Upper panel: A schematic of electrical measurement configuration. Lower panel: A schematic of electron band bending under a positive backgate voltage $V_{\mathrm{bg}}$. (b) $R_{\mathrm{s}}$ as a function of $V_{\mathrm{bg}}$. The black (red) symbols are measured by sweeping $V_{\mathrm{bg}}$ from $+40$ to $-40\mathrm{V}$ $(-40$ to $+40\mathrm{V})$. (c) Symmetrized and normalized MR measured at 0.36 K and at several $V_{\mathrm{bg}}$ values, as indicated. Data are offset for clarity. The solid curves are least-squares fits to Eq. (1). (d) Extracted dephasing length $L_{\phi }$ and spin-orbit scattering length $L_{\mathrm{so}}$ as a function of $V_{\mathrm{bg}}$. The bottom panel shows the variation of SOC spin splitting energy ${\mathrm{\Delta }}_{\mathrm{so}}$ with $V_{\mathrm{bg}}$.

Figure 4

(a) Symmetrized and normalized MR measured at $V_{\mathrm{bg}}=0\mathrm{V}$ and at several $T$ values, as indicated. Data are offset for clarity. The solid curves are least-squares fits to Eq. (1). (b) Extracted dephasing length $L_{\phi }$ as a function of temperature. The dashed straight line indicates $T^{-1/2}$ temperature dependence and is a guide to the eye. The red horizontal line represents the spin-orbit scattering length $L_{\mathrm{so}}$. (c) Dephasing rate ${\tau }_{\phi }^{-1}$ as a function of temperature. The black solid curve is a least-squares fit to ${\tau }_{\phi }^{-1}=2{\tau }_s^{-1}+A_{ee}T$ (see text). The dashed straight line is the theoretical prediction of 2D $e\text{−}e$ scattering rate ${{\tau }_{ee}}^{-1}\left(T\right)$, using the measured $R_s$ value. The red horizontal line represents the spin-orbit scattering rate ${\tau }_{\mathrm{so}}^{-1}$.

Figure 5

(a) MR at $T=0.36\mathrm{K}$ for a 5- and a 22-nm-thick epitaxial LSMO film, as indicated. The MR for the 5-nm-thick film was measured with magnetic field sweeping from $+1.2$ to $-1.2\mathrm{T}$. The data for the 22-nm-thick film are taken from Fig. 2. (b) Low-field MR for the 5-nm-thick LSMO film at several $T$ values, as indicated. The solid curves are least-squares fits to Eq. (1) with ${\tau }_{\mathrm{so}}^{-1}=0$. The inset shows the variation of ${\tau }_{\phi }^{-1}$ with temperature. The solid curve is a least-squares fit to ${\tau }_{\phi }^{-1}=2{\tau }_s^{-1}+A_{ee}T$ (see text).