Spin-orbit coupling and the Edelstein effect at conducting ferroelectric domain walls

TL;DR

The paper investigates how conducting ferroelectric domain walls host spin-orbit coupling in a wallbound 2DEG due to inversion symmetry breaking. A symmetry-guided six-band tight-binding framework based on the $t_{2g}$ manifold yields Ising SOC for head-to-head walls and Rashba SOC for head-to-tail walls. Band-structure and Edelstein analyses show spins and orbitals aligned along $\hat{z}$ for Ising textures and in-plane for Rashba textures, with orbital contributions to current-induced magnetization dominating at room temperature in multiorbital systems. An all-electrical measurement of current-induced magnetization at BaTiO$_3$ walls is proposed, suggesting a route to reconfigurable spin-orbitronic devices.

Abstract

Head-to-head ferroelectric domain walls are intrinsically charged, and are typically compensated by a mix of oppositely charged defects and free electrons. The free electrons form a two-dimensional electron gas (2DEG) along the domain wall. In many cases, inversion symmetry is broken at the wall, which implies that the 2DEG is subject to nontrivial spin-orbit coupling. Here, we use symmetry arguments to construct a generic six-band tight-binding electronic Hamiltonian for a $90^\circ$ head-to-head ferroelectric domain wall. The model, which includes spin-orbit physics and has a multi-orbital $t_{2g}$ band structure that is common to transition-metal perovskites, is applied to BaTiO$_3$. We find that the 2DEG develops an Ising spin texture, with spins aligned perpendicular to the domain wall. We contrast this with the Rashba spin texture that should emerge at weakly conducting $90^\circ$ head-to-tail domain walls. We then show that the head-to-head domain walls should have a measurable Edelstein effect (that is, a current-induced magnetization), even in the dilute limit and at room temperature, and describe a simple experiment to measure it.

Figures (5)

• Figure 1: Polarization distributions and corresponding Fermi surfaces for Néel domain walls. Polarization vectors are shown for (a) charged head-to-head and (b) nominally neutral head-to-tail walls. A 2DEG is bound to each domain wall. Their spin-resolved Fermi surfaces, shown in (c) and (d) respectively, are split by SOC, which by symmetry are of (c) Ising and (d) Rashba types. Red and blue contours show the spin-split Fermi surfaces, and arrows indicate the direction of spin polarization at different points on the Fermi surfaces.
• Figure 2: Band structure of the six-band model. (a) Band dispersion and (b) spin splitting for a head-to-head domain wall with Ising SOC; (c) spin-splitting for a head-to-tail domain wall with Rashba SOC. The horizontal dashed line in (a) indicates the energy of the contours in Fig. \ref{['fig:Ising-FS']}. Results are for $\xi=60$ meV and (a),(b) $P_x=0.28$ C/m$^2$ and $t_0^{yz,zx} =t_1^{xy,yz}=t_2^{xy,zx}=40$ meV$\cdot\mathrm{m}^2/\mathrm{C}$ or (c) $P_z=0.28$ C/m$^2$ and $g_0 = 40~\mathrm{meV}\cdot\mathrm{m}^2/\mathrm{C}$. Labels $E_i$ indicate the different bands, and colours have the same meaning in (b) and (c).
• Figure 3: Orbital and spin properties of the (a)-(c) Ising and (d)-(f) Rashba Hamiltonians. The orbital character (a), (d); nonzero components of the electron spin (b), (e); and orbital angular momenta (c), (f) are shown. Parameters are as in Fig. \ref{['fig:Ising-bands']}.
• Figure 4: Spin (blue) and orbital (red) magnetization conversion efficiencies as functions of the the Fermi energy $\varepsilon_F$ for (a) the Ising and (c) the Rashba cases in the degenerate limit ($T\rightarrow 0$). Panel (b) shows the electron filling per unit cell as a function of $\varepsilon_F$. Vertical dashed lines indicate energies of the band bottoms (note that their spin-splitting is too small to resolve). Light grey lines in (a) show the individual band contributions to the orbital conversion efficiency. Here, $\xi=20$ meV and (a) $t_0^{yz,zx} =t_1^{xy,yz}=t_2^{xy,zx}=15$ meV$\cdot\mathrm{m}^2/\mathrm{C}$ or (b) $g_0 = 15~\mathrm{meV}\cdot\mathrm{m}^2/\mathrm{C}$.
• Figure 5: