Quantum Spin Torque Driven Transmutation of an Antiferromagnetic Mott Insulator

The standard model of spin-transfer torque (STT) in antiferromagnetic spintronics considers the exchange of angular momentum between quantum spins of flowing electrons and noncollinear-to-them localized spins treated as classical vectors. These vectors are assumed to realize Néel order in equilibrium, $\uparrow \downarrow \cdots \uparrow \downarrow$, and their STT-driven dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation. However, many experimentally employed materials (such as archetypal NiO) are strongly electron-correlated antiferromagnetic Mott insulators (AFMIs) whose localized spins form a ground state quite different from the unentangled Néel state $|\uparrow \downarrow \cdots \uparrow \downarrow ⟩$. The true ground state is entangled by quantum spin fluctuations, leading to the expectation value of all localized spins being zero, so that LLG dynamics of classical vectors of fixed length rotating due to STT cannot even be initiated. Instead, a fully quantum treatment of both conduction electrons and localized spins is necessary to capture the exchange of spin angular momentum between them, denoted as quantum STT. We use a recently developed time-dependent density matrix renormalization group approach to quantum STT to predict how injection of a spin-polarized current pulse into a normal metal layer coupled to an AFMI overlayer via exchange interaction and possibly small interlayer hopping—mimicking, e.g., topological-insulator/NiO bilayer employed experimentally—will induce a nonzero expectation value of AFMI localized spins. This new nonequilibrium phase is a spatially inhomogeneous ferromagnet with a zigzag profile of localized spins. The total spin absorbed by AFMI increases with electron-electron repulsion in AFMIs, as well as when the two layers do not exchange any charge.

Figure 1

(a) Schematic view of a “bilayer” [10] for TDMRG calculations. The 1D TB chain (blue dots) of $N=N_L+N_{\mathrm{AFMI}}+N_R=92$ sites, with intrachain hopping $\gamma$, models the metallic surface (such as that of topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ in the experiments of Ref. [10]) through which a spin-polarized current pulse is injected. The pulse exerts quantum STT on a Hubbard chain of $N_{\mathrm{AFMI}}=12$ sites with the on-site Coulomb repulsion $U$, modeling the surface of a strongly electron-correlated AFMI (such as that of NiO in Refs. [7, 8, 9, 10]). The electronic spins in two chains interact via interchain exchange interaction $J_v$, and we consider both ${\gamma }_v=0$ and ${\gamma }_v\ne 0$ interchain hopping where the latter mimics possible hybridization of a NM and AFMI via evanescent wave functions [22]. For times $t<0$, $N_e=12$ noninteracting electrons are confined by potential $V$ within $N_{\mathrm{conf}}=25$ sites of the $L$ lead (composed of $N_L=40$ sites), as well as spin-polarized by an external magnetic field ${\mathbf{B}}_e$ along the $z$ axis. Concurrently, $N_e^{\mathrm{AFMI}}=12$ electrons half-fill the AFMI chain. For times $t\ge 0$, $V$ and ${\mathbf{B}}_e$ are removed, so that electrons propagate as a spin-polarized current pulse from the $L$ to the $R$ lead, as animated in the movie in the SM [38]. In panel (c), the AFMI from (a) and (b) is replaced by an AFI modeled as a quantum Heisenberg AF chain whose spin-$\frac{1}{2}$ operators reside on each (orange) site and interact via $J=4{\gamma }^2/U$ in Eq. (1) while no electrons are allowed within this chain.

Figure 2

Spatiotemporal profiles of the $z$ component of spin density within: (a) an AFMI chain with the Coulomb repulsion $U=8\gamma$; and (c) the same chain with $U=0$ (acting then as the second NM chain half-filled with electrons). In both panels $s_i^{\prime z}(t=0)\equiv 0$, so that only the $s_i^{\prime z}(t)\ne 0$ component is induced by a current pulse spin-polarized along the $z$ axis and flowing along the bottom NM chain in Fig. 1 whose $s_i^z$ profiles in panels (b) and (d) are driving the profiles in panels (a) and (c), respectively, via quantum STT. The dotted horizontal lines in (b) and (d) mark the boundaries between the leads and the central region of the NM chain in Fig. 1. The interchain exchange is $J_v=0.5\gamma$ and hopping ${\gamma }_v=0$ in Eq. (5). All four panels, together with the corresponding electron densities, are animated in the movie in the SM [38].

Figure 3

Spatial profile of the $z$ component $s_i^{\prime z}$ of the spin density within the AFMI chain in Fig. 1 driven by quantum STT from the NM chain: (a) at different times using $U=8\gamma$ in Eq. (4); and (b) for different $U$ values at time $t=25\hslash /\gamma$. The interchain exchange is $J_v=0.5\gamma$ and hopping ${\gamma }_v=0$ in Eq. (5).

Figure 4

Time dependence of the total number of electrons within (a) an AFMI and (b) NM chains in the setup of Fig. 1 for two different interchain hoppings ${\gamma }_v=0$ (blue lines) and ${\gamma }_v=0.1\gamma$ (red lines). Panels (c) and (d) show the corresponding time dependence of the sum of the $z$ component of spin densities, ${\sum }_i{s}_i^{\prime z}$ and ${\sum }_i{s}_i^z$, respectively. The on-site Coulomb repulsion is $U=8\gamma$ [Eq. (4)] within the AFMI and the interchain exchange is $J_v=0.5\gamma$.

Figure 5

(a) Time evolution of the sum of spin densities within the NM chain ${\sum }_i{s}_i^z$ (dashed lines) and AFMI chain ${\sum }_i{s}_i^{\prime z}$ (solid lines) in the setup of Fig. 1 for different values of the on-site Coulomb repulsion $U$ within the AFMI chain. For comparison, panel (b) plots the same information for the setup in Fig. 1 where the AFMI is replaced by the AFI, modeled by the quantum spin-$\frac{1}{2}$ Heisenberg AF chain with no electrons, so that solid lines are ${\sum }_i{S}_i^z$ where $S_i^z$ is obtained from Eq. (2). For each $U$ in (a), we set the corresponding intrachain exchange interaction $J$ [Eq. (1)] within the AFI in (b) as $J=4{\gamma }^2/U$. The interchain exchange is $J_v=0.5\gamma$.