Twin-boundary-induced nonrelativistic spin splitting

TL;DR

The paper demonstrates that twin boundaries, when coinciding with ferromagnetic domain walls, can induce nonrelativistic spin splitting (NRSS) in compensated magnets even when bulk symmetries forbid altermagnetism. Using density functional theory and tight-binding transport, the authors analyze BiCoO3 with 90-degree ferroelastic walls and CoO2 with 71°, 109°, 135° twins, showing d-wave-like NRSS with two nodal planes dictated by the supercell symmetry. Transport calculations reveal a robust diagonal spin conductance that persists with domain size but decays with increasing domain-wall density due to interfacial scattering, indicating practical limits. The work establishes twin-boundary engineering as a general, SOC-free route to spin-polarized states, tunable via structural motifs, interlayer spacing, or intercalation, and suggests experimental probes such as sARPES and anisotropic magnetotransport.

Abstract

Nonrelativistic spin splitting (NRSS) in compensated magnetic materials is drawing considerable attention due to its potential impact in next-generation spintronic devices. While NRSS is typically restricted to materials with particular symmetry constraints, here we demonstrate, using density functional theory (DFT) and tight-binding transport calculations, that twin boundaries can induce NRSS in magnetic systems where it is otherwise forbidden. We focus on two representative material systems: the tetragonal perovskite oxide BiCoO$_3$ with $90^{\circ}$ ferroelastic domain walls, and the rhombohedral layered delafossite-type oxide CoO$_2$, supporting $71^{\circ}$, $109^{\circ}$, and $135^{\circ}$ twin boundaries. Our results reveal that, if these boundaries coexist with ferromagnetic domain walls, they consistently produce NRSS similar to that of d-wave altermagnets, with nodal surfaces dictated by the underlying symmetry of the supercell containing the twin boundary. Tight-binding models further elucidate how the NRSS and derived transport properties scale with domain size and density. Our results put forward twin boundary engineering as a versatile route to realize and control spin splitting in a broader class of materials.

Figures (5)

• Figure 1: Illustration of nonrelativistic spin splitting induced by twin boundaries. (a) A ferromagnetic domain wall alone does not produce spin splitting. (b) When a ferromagnetic domain wall coincides with a twin boundary, spin splitting can occur.
• Figure 2: (a) Crystal structure of a supercell containing eight formula units of BiCoO3, displaying ferromagnetic, ferroelastic, and ferroelectric domain walls, indicated by thick black vertical lines. Due to periodic boundary conditions, two of each domain wall type are present in the cell. (b) Corresponding Brillouin zone, where the high-symmetry path (T$_1 \rightarrow \Gamma \rightarrow \text{T}_2$) used in the band structure is indicated. (c) Calculated electronic band structure along the Brillouin zone path shown in (b). The solid (pink) and dashed (blue) lines depict the two spin polarizations. The Fermi level is set to 0 eV with the solid black line marking the energy at $-1.0$ eV below the Fermi level. (d) Constant energy cut in the $k_y-k_z$ plane at $-1.0$ eV below the Fermi level. The solid colored lines represent intersections of spin-up and spin-down bands with the energy cut (black line in (c)), and the contour plot shows the broadened bands as calculated using Eq. 1 in SI.
• Figure 3: Calculated dlectronic density of states (DOS) for the d-orbitals of the two Co atoms in BiCoO3: (a) in the primitive unit cell with C-type antiferromagnetic order, and (b) in the minimal engineered cell containing one formula unit per ferroelastic and ferromagnetic domain. The corresponding structures are shown to the left of each DOS plot, along with the axis used for orbital projection. To the right, schematic diagrams illustrate the d-orbital filling.
• Figure 4: Crystal structures and calculated spin-polarized electronic bands of CoO2 (a, d), LiCoO2 (b, e) and NaCoO2 (c, f) for the $135\degree$ (a-d) and $109\degree$ (d-f) twin boundary. The Fermi level is set to 0 eV in all figures.
• Figure 5: (a) $G_s$ as a function of device length for horizontal transport ($G_s^\rightarrow$) and diagonal transport ($G_s^\text{diag} = (G_s^\nearrow - G_s^\searrow)/2$) with (solid) and without (dashed) orbital ordering. Inset shows an schematics of the spin transport anisotropy due to the presence of nonrelativistic spin splitting, where arrows indicate the transport direction. The sketches on the right show the transport setup where half of the device sites have a positive sign of magnetization and orbital ordering (red) and the other half (blue) have a negative sign of magnetization and orbital ordering. Black regions denote the semi-infinite leads. The value and sign of the spin conductance $G_s$ depends on transport direction, dictated by the position of the leads. The device width $W$ is taken as 50 unit cells, the width of the leads as $W_L = W/2$, and the Fermi level $\mu=1.5$. (b) Diagonal spin conductance at a fixed device length as a function of the number of domain walls, $N$. The right schematic shows a device with $N=10$ domains, and the insets show the vector plots of the spin current for $N=6$ and $N=30$. The device size is $L = 200$ and $W = 50$ units cells, and $\mu=1.5$.