Perovskite as a spin current generator

We theoretically show that materials with perovskite-type crystal structures provide a platform for spin current generation. Its mechanism is based on spin-split band structures in certain kinds of collinear antiferromagnetic states, requiring neither spin-orbit coupling nor a ferromagnetic moment. By investigating a multiband Hubbard model for transition-metal compounds by means of the Hartree-Fock approximation and the Boltzmann transport theory, we find that a pure spin current is induced by an electric field applied to a $C$-type antiferromagnetic metallic phase. The spin current generation originates from a cooperative effect of spatially anisotropic electron transfer integrals owing to the ${\mathrm{GdFeO}}_3$-type lattice distortion, which is ubiquitous in many perovskites, and the collinear spin configuration. We discuss our finding from the symmetry point of view, in comparison with other spin current generator candidates with collinear antiferromagnetism. We also propose several ways to detect the phenomenon in candidate perovskite materials.

Figure 1

(a) Perovskite structure with the ${\mathrm{GdFeO}}_3$-type distortion. $B_1–B_4$ denote the $B{X}_6$ octahedra contained in the unit cell, connected by symmetry operations and thus crystallographically equivalent. The $abc$ axes are defined for the Pnma space group. The $xyz$ axes represent the local coordinate defined for each octahedron. (b) Two kinds of $B{X}_6$ rotation modes of the ${\mathrm{GdFeO}}_3$-type distortion described in the text. (c) Schematic illustration of the $C$-type AFM spin configuration in the two $ac$ planes. The blue arrows represent up- and down-spin moments of the $d$ orbitals in the TM ions. The green lines denote the glide plane perpendicular to the $ac$ plane. Schematic illustrations of the anisotropies of the $t_{2g}\text{−}{t}_{2g}$ transfer integrals on (d) $B_1\text{−}{B}_2\text{−}{B}_1$ and (e) $B_2\text{−}{B}_1\text{−}{B}_2$ bonds along the [101] and $\left[10\overline{1}\right]$ directions. The magnitudes of the transfer integrals denoted by the solid arrows are larger than those denoted by the dashed arrows in the presence of the distortion.

Figure 2

Spin current conductivity ${\chi }_{ca}$ on the $U\text{−}\varphi$ plane. The black dashed lines on the basal plane indicate the phase boundaries between the different phases. The red solid line stands for the MI transition. The thick orange line represents the region where the $A$-AFM $+ C$-OO phase is stable. The inset shows the $\varphi$ dependences of the charge-spin current conversion rate $\alpha$ in the $C$-AFM metallic phases. The dashed and solid arrows indicate the phase boundaries between the PM and $C$-AFM phases and between the $C$-AFM and $C$-AFM $+ G$-OO1 phases, respectively.

Figure 3

(a) Energy band structure in the $C$-AFM metallic phase at $(U,\varphi )=(0.725\mathrm{eV},{25}^{\circ })$. The Fermi energy is denoted by ${\varepsilon }_{\mathrm{f}}$. The right panel shows the symmetry lines in the first Brillouin zone. (b) and (c) The group velocities of the up- and down-spin electrons, respectively, on the Fermi surfaces at $k_b=0.39$. $k_c$ and $k_a$ stand for the coefficients of the reciprocal vectors ${\mathit{b}}_c$ and ${\mathit{b}}_a$, respectively. The length of the red and blue arrows represents the magnitude of the group velocity on each $\mathit{k}$ point. (d) and (e) are the relative weights of the $t_{2g}$ orbitals on the up- and down-spin Fermi surfaces, respectively. The areas of the red, green, and blue circles represent the magnitudes of the $xy$ (left), $yz$ (middle), and $zx$ (right) components on (b) $(B_1,B_3)$ and (c) $(B_2,B_4)$ sublattices.