Switching perpendicular magnets for Processing-in-memory with voltage gated Weyl Semimetals

TL;DR

The paper tackles the challenge of enabling in-memory compute by proposing a SWSM-SOTRAM PIM cell based on a strained Weyl semimetal that gate-tunes a spin-orbit torque. The approach combines an iSGE-driven in-plane spin polarization with a bias-controlled bulk spin Hall effect, facilitated by an exchange field $\Delta_{ex}$, to generate an out-of-plane spin current that can switch a free magnet via the damping-like torque. Using a tight-binding Weyl semimetal model with $D_{2d}$ symmetry and TB-NEGF transport, together with Landau-Lifshitz-Gilbert dynamics, the authors quantify the nonequilibrium transverse spin current $J_{z}^{\sigma_z,neq}$ and extract spin Hall angles $\theta_{SH}$ under different magnet orientations. They demonstrate a strain-gated selector magnet driven by a piezo to switch the exchange field direction, enabling programmable write operations ($0$ vs $1$) and a storage mode, all within a vertically integrated four-terminal bitcell intended for PIM. The work suggests potential energy-latency benefits for PIM by localizing data processing and combining memory and logic in a single material platform, with explicit device physics and switching dynamics backing the proposal. $J_s^{crit}$, $J_z^{\sigma_z}$, and other key quantities are provided to assess feasibility and guiding design parameters for implementing SWSM-SOTRAM in practice.

Abstract

Processing-in-memory (PIM) reduces data transfer latency by rolling memory and logic elements into one compute location. As an emergent material candidate for such an architecture, we propose a strained Weyl semimetal based spin-orbit-torque random-access memory (SWSM-SOTRAM) device. The spin-orbit torque (SOT) originates from two mechanisms: (1) the inverse spin Galvanic effect (iSGE), which generates nonequilibrium in-plane spin accumulation at interfaces, and (2) a bulk spin Hall effect (SHE), which produces a transverse spin current carrying out-of-plane spin angular momentum. The latter is tunable via an exchange Zeeman field. Both effects are evaluated using the tight-binding model coupled with a nonequilibrium Green's function (TB-NEGF) formalism for quantum transport. Information write is achieved through SOT switching of an out-of-plane free magnet. A piezo attached to a magnetostrictive selector modulates the strain in the latter, leading to the rotation of the magnetization and hence the exchange Zeeman field exerted on the Weyl semimetal. This strain-controlled exchange field enables the symmetry tuning of the Weyl semimetal and modulation of its spin Hall effect. The TB-NEGF calculations of SHE and iSGE, combined with Landau-Lifshitz-Gilbert (LLG) simulations of magnetization dynamics, establish the SOT switching mechanism and demonstrate a pathway toward the SWSM-SOTRAM PIM device.

Figures (5)

• Figure 1: Example of a D$_{2d}$ unit cell, in this case CuFeS$_2$ (chalcopyrite, $I\bar{4}2d$). The space group contains: twofold screw-axis-two-fold rotations about $x$ and $y$ axes $C_{2x}$ and $C_{2y}$ combined with a translation of $1/2$ along each axis; S$_{4z}^{+}$ and S$^{-}_{4z}$, improper four-fold rotations about z-axis (90$^\circ$ + reflection); two-fold rotational symmetry $C_{2z}$-product of two improper rotation($C_{2z}=(S_{4z}^{+})^2$); glide mirror $\sigma_d (M_{xy})$ and $\sigma_d (M_{-xy})$ - dihedral mirrors plus translation t = $(1/4, 1/4, 0)$ that contain the $z$-axis and bisect $x$ and $y$.
• Figure 2: Spectrum of the four band model for Weyl semimetals with $D_{2d}$ point group symmetry. Fermi-arc and band plots are computed using the four-band model of Ref. ruan2016ideal. (a) projection of Weyl points in the $k_x-k_y$ plane. The chalcopyrite Weyl semimetal hosts eight symmetry-related Weyl points, grouped into two sets - $(\pm k_{x}^{*},0,\pm k_{z}^{*})$ with chirality $+1$ for each Weyl point and chirality $+2$ for projections in $k_x-k_y$ plane , and $(0,\pm k_{y}^{*},\pm k_{z}^{*})$ with chirality $-1$, where $k_{x}^{*}=k_{y}^{*}$ for each Weyl point and chirality $-2$ for projections in $k_x-k_y$ plane. (b) The top surface of a $50$-layer Weyl semimetal slab without an exchange (Zeeman) field, using low energy model of $\mathrm{CuTlTe_2}$ as an example ruan2016ideal, showing Fermi arcs that connect the Weyl points. (c) The top surface with an exchange (Zeeman) field applied along $+\hat{y}$, of magnitude $\Delta_{\mathrm{ex}} = 0.025 ~\mathrm{eV}$, again showing Fermi arcs that connect the Weyl points. (d) Band structure along the $\Gamma$–Weyl point path, comparing the $\bm k\cdot\bm p$ and tight-binding models. The $k$ path follows the direction from $\Gamma = (0,0,0)$ to the Weyl point at $(k_{x}^{*}, 0, k_{z}^{*})$. (e) Bulk of a $50$-layer Weyl semimetal slab without an exchange (Zeeman) field, showing Fermi arcs that connect the Weyl points. (f) Bulk with an exchange (Zeeman) field applied along $+\hat{y}$, of magnitude $\Delta_{\mathrm{ex}} = 0.025 ~\mathrm{eV}$, again showing Fermi arcs that connect the Weyl points.
• Figure 3: Microscopic features of quantum transport in the Weyl semimetal (WSM) slab of the PIM device during writing mode with in-plane $+\hat{y}$ direction Zeeman field under forward and reverse bias. Under bias voltage, a charge current $J_{y}^{c}$ flows along the $+\hat{y}$ direction within a WSM slab that is infinite in the $x$-direction and biased along $\hat{y}$. Although the system is not translationally invariant in the $y$-direction, the charge current, spin current, and spin density distributions are approximately constant with respect to $y$. Therefore, only depth-dependent ($z$-direction) profiles are shown in the following plots (c)-(f). (a) Inverse spin Galvanic effect (iSGE) mechanism: The spin densities at the top and bottom surfaces (black arrows), have opposite sign for $S_x$ component and the same sign for $S_y$ component, they change sign upon reversing bias. (b) Spin Hall effect (SHE) mechanism: A transverse spin current $J_{z}^{\sigma_{z}}$ (pink arrows), carrying out-of-plane spin angular momentum $+\sigma_z$ (black arrows), flows toward the top surface. There are also non-zero in-plane spin densities $S_x$ and $S_y$ inside the WSM, they change sign upon reversing bias. (c) Depth profile of the charge current density $J_{y}^{c}$ along the $z$-axis, with position measured in units of the lattice constant $c$. (d) Transverse spin current $J_{z}^{\sigma_z}$ carrying $\sigma_z$, plotted between adjacent lattice layers ($i \to i+1$) along $+\hat{z}$-direction. (e) Nonequilibrium component of the transverse spin current that carries out-of-plane spin angular momentum, defined as the antisymmetric part of $J_{z}^{\sigma_z}(V)$ under voltage reversal, i.e., $J^{\sigma_z,\mathrm{neq}}_z(V)=(J_{z}^{\sigma_z}(V)-J_{z}^{\sigma_z}(-V))/2$. (f) In-plane spin densities $S_x$ and $S_y$, versus $z$-position under both forward and reverse bias.
• Figure 4: Dynamical properties for WSM layer, free magnet layer and selector magnet layer: (a) Relation between nonequilibrium spin current and the polar angle of the Zeeman field in the $y-z$ plane relative to the $z$-axis. The azimuthal angle is $90^{\circ}$, while the polar angle runs from $0^{\circ}$ to $90^{\circ}$. Provided by the selector magnet, the exchange Zeeman coupling between the selector magnet and the WSM is $\Delta_{ex} = 0.025~\mathrm{eV}$ and the bias voltage is $V=-0.1~\mathrm{V}$ for writing "0" and $V=0.1~\mathrm{V}$ for writing "1". (b) Relation between charge current and the polar angle of Zeeman field in the $y-z$ plane relative to the $z$-axis. (c) Relation between nonequilibrium spin densities on the surface layer and the polar angle of Zeeman field in the $y-z$ plane relative to the $z$-axis. (d) Writing a "0": switching the magnetization of the magnet from $+\hat{z}$ to $-\hat{z}$. (e) Changing from storage mode to writing mode by applying gate voltage to piezo and rotating the magnet from $+\hat{z}$ to $+\hat{y}$ (f) Changing from writing mode to storage mode, by not applying gate voltage to the piezo and rotating the magnet from $+\hat{y}$ to $+\hat{z}$.
• Figure 5: Device geometry and three modes of the device: (a) Writing "1": When the drain voltage $V_{drain}>0$ and the gate voltage $V_{gate}>0$ such that the magnetization of the selector magnet is in $+\hat{y}$ direction, the charge current (white arrow) flows from drain to source and the WSM generates transverse spin currents (light blue arrow) that carries $+\sigma_z$ spin angular momentum (orange arrow) flowing towards the storage magnet. The magnetization of the storage magnet can be rotated to $+\hat{z}$ direction and write "1". (b) Writing "0": When the drain voltage $V_{drain}<0$ and the gate voltage $V_{gate}>0$ such that the magnetization of the selector magnet is in $+\hat{y}$ direction, the charge current (white arrow) flows from drain to source and the WSM generates transverse spin currents (light blue arrow) that carries $-\sigma_z$ spin angular momentum (orange arrow) flowing towards the storage magnet. The magnetization of the storage magnet can be rotated to $-\hat{z}$ direction and write "0". (c)Storage mode: When no gate voltage is applied to the piezo, i.e., $V_{gate}=0$, the magnetization of the selector magnet is in $\pm \hat{z}$ direction. As a result, the WSM does not generate transverse spin currents that carries out-of-plane spin angular momentum, regardless of what the drain voltage $V_{Drain}$ is and whether there is charge current flowing between source and drain. The storage magnet cannot be rotated and the device is in storage mode. (d) The overall PIM structure, that selects two rows and runs them through a sense amplifier to carry out a bitwise AND or OR logic operation, building thereby one processor locally around a few proximal non-volatile logic elements.