Tunable spin-charge conversion through topological phase transitions in zigzag nanoribbons

We study spin-orbit torques and charge pumping in magnetic quasi-one-dimensional zigzag nanoribbons with a hexagonal lattice, in the presence of large intrinsic spin-orbit coupling. Such a system experiences a topological phase transition from a trivial band insulator to a quantum spin Hall insulator by tuning of either the magnetization direction or the intrinsic spin-orbit coupling. We find that the spin-charge conversion efficiency (i.e., spin-orbit torque and charge pumping) is dramatically enhanced at the topological transition, displaying a substantial angular anisotropy.

Figure 1

(a) Top view of zigzag silicene-like nanoribbons switched by a nonmagnetic topological insulator and a magnetic topological insulator. The super unit cell is indicated by the red rectangle. (b) Band structure for different magnetization directions $\mathbf{m}$. (c) Phase diagram as a function of Rashba spin-orbit coupling and magnetic exchange. (d) Density of states for different magnetization directions. The current is directed along the $x$ axis. Parameters are $t_{\mathrm{so}}=36$ meV and $J_{\mathrm{ex}}=10$ meV.

Figure 2

Intraband and interband components of the spin density as a function of the Fermi energy in a nonmagnetic nanoribbon without (a, b) and with (c, d) intrinsic spin-orbit coupling. The electric field is directed along the $x$ axis. Parameters are $t_{\mathrm{so}}=0,J_{\mathrm{ex}}=0,t_{\mathrm{R}}=20$ meV, and $\mathrm{\Gamma }=0.3$ meV.

Figure 3

(a) Intraband spin density, (b, c) interband spin density, and (d) conductance as a function of the Fermi energy without and with intrinsic spin-orbit coupling. The magnetization is directed along the $z$ axis. The exchange coupling is fixed at $J_{\mathrm{ex}}=10$ meV and other parameters are the same as in Fig. 2.

Figure 4

Intraband and interband spin density as a function of the magnetization angle for different Fermi energies: (a–c) without intrinsic spin-orbit coupling and (d–f) with intrinsic spin-orbit coupling.