An energy efficient way for quantitative magnetization switching

Spin‑orbit torque (SOT) offers nonvolatile, fast, and energy‑efficient magnetization control compatible with semiconductor processes. SOT arises predominantly from the spin Hall effect and Rashba effect in FM/heavy‑metal (HM) heterostructures, and manifests as damping‑like torque (DLT) and field‑like torque (FLT). While both torques are critical for switching, their relative contributions depend strongly on device materials and interfaces and remain under debate. Multiferroic heterostructures (artificial multiferroics) provide an interface to couple ferroelectricity and ferromagnetism, enabling electric‑field control of magnetism via strain at room temperature. This work addresses whether and how electric‑field‑induced in‑plane strain in a PMN‑PT (011) substrate can quantitatively and angularly modulate SOT effective fields—and thereby magnetization switching—in Ta/CoFeB‑based devices, with the goal of reducing switching energy and enabling reconfigurable spin logic.

Prior studies established SOT switching in FM/HM systems and techniques for quantifying torques (e.g., ST‑FMR, MOKE, harmonic Hall). The DLT and FLT have been extensively explored in Ta/CoFeB/MgO and related stacks. Multiferroic approaches demonstrated electric‑field control of magnetism (e.g., in BiFeO3 and piezoelectric/ferromagnet hybrids), strain‑mediated domain wall motion, and voltage control of magnetic tunnel junction resistance. Electric‑field control of SOT in perpendicularly magnetized systems and hybrid ferromagnetic/ferroelectric devices has also been reported. However, leveraging localized, orientation‑dependent in‑plane strain to quantitatively tune SOT components (especially DLT vs FLT) in in‑plane magnetized systems for low‑energy logic remains an active area, motivating this study.

Device structure: Ta(5 nm)/CoFeB(3 nm)/Pt(1.5 nm) was deposited by magnetron sputtering on double‑side‑polished (011) PMN‑PT substrates (5 mm × 5 mm × 0.5 mm). PMN‑PT top/bottom electrodes: Pt (50 nm). A 100 nm AlOx layer isolates the magnetic stack from the top PMN‑PT cap. Hall bars (length 50 μm, width 5 μm) were defined by optical lithography and ion milling; Ti(10 nm)/Au(150 nm) pads were deposited by evaporation and liftoff. PMN‑PT was pre‑poled along [011] with polarization up. Under a vertical electric field (top grounded, bottom +0–400 V), PMN‑PT exhibits anisotropic in‑plane strain: compressive along [100] and tensile along [011]. Devices were patterned with four current orientations (0°, 45°, 90°, 135°) to probe angular dependence of strain modulation on SOT. Magnetometry and transport: VSM (Lake Shore 7400) measured magnetic moment from −1 T to 1 T; the CoFeB layer is in‑plane magnetized. Harmonic Hall measurements applied an AC current I(t) = I0 sin(ωt) at f = ω/2π = 133 Hz to generate alternating torques and detect first (Vxy1ω) and second harmonic (Vxy2ω) Hall voltages with a lock‑in amplifier. Hall resistance includes anomalous Hall effect (AHE) and planar Hall effect (PHE). With an in‑plane rotating external field (angle φ) and spin polarization along (0,1,0), analytical expressions separate Vxy1ω ∝ Rp sin 2φ and Vxy2ω containing terms proportional to (RA + HDL/HK) and Rp, enabling extraction of effective fields for DLT (HDL) and FLT (HFL) by fitting measured curves versus field magnitude/angle. Field scans for Vxy1ω and Vxy2ω were performed while varying substrate voltage (0–400 V). Imaging and diffraction: MFM (dynamic lift mode, 30 nm lift) imaged a 5 μm CoFeB dot to visualize switching under four conditions: (1) no current/strain; (2) strain only; (3) strain + current; (4) reversed strain + reversed current. XMCD‑PEEM (Co L2,3 edges, ~5 nm probe depth) imaged magnetic states versus substrate voltage (0–400 V). Laue X‑ray microdiffraction mapped electrically induced deviatoric strain (2D maps with 10 × 10 μm2 pixels) by differencing non‑zero vs zero‑voltage diffraction patterns. Micromagnetic and multiphysics simulation: Strain distribution from a COMSOL Multiphysics model (Structural Mechanics, Piezoelectric, and Magnetostrictive modules) of the FM/PMN‑PT heterostructure was transferred to OOMMF to simulate magnetization dynamics including a magnetoelastic energy term (YY_FixedMEL) derived from the displacement field. The FM layer (300 × 300 × 1 nm3; mesh 3 × 3 × 1 nm3) used parameters representative of CoFeB: saturation magnetization M = 0.86 × 10^6 A/m, exchange constant A = 30 × 10^−12 J/m, anisotropy energy density K = 0.84 MJ/m3, spin polarization p = 0.6, Gilbert damping α = 0.014. Uniaxial anisotropy and initial magnetization were along the bar’s long axis; spin current polarization was perpendicular to the bar (spin Hall effect). Simulations compared cases “on (011) PMN‑PT” (with strain) vs “without strain,” under identical current density (5 × 10^11 A/cm2), tracking magnetization evolution (initial, intermediate under SOT + magnetoelastic energy, and relaxed final states). Logic device concept: A reconfigurable logic unit integrating three inputs and three strain‑control arms on PMN‑PT (011) was proposed. MTJ readouts at inputs/middle/output encode logic as low/high resistance (0/1). Locally applied strain (control arms) selects AND/OR/selector operations (majority gate) and enables cascaded BUFFER and NOT operations by transferring the middle state to the output under identical current and electric‑field magnitudes.

- Electric‑field‑induced in‑plane strain in PMN‑PT (011) quantitatively and anisotropically modulates SOT effective fields in Ta/CoFeB/Pt devices. - Harmonic Hall analysis shows that with increasing substrate voltage (0–400 V): • The DLT effective field (HDL) decreases for 0° devices under compressive strain and increases for 45°, 90°, and 135° devices under tensile strain. • The FLT effective field (HFL) remains approximately constant across all orientations. - Micromagnetic simulations using COMSOL‑derived strain confirm that magnetoelastic energy assists switching for 45°, 90°, and 135° orientations at a current density of 5 × 10^11 A/cm2, while 0° requires additional assistance; snapshots and mx,my(t) traces show deterministic, strain‑assisted switching rather than stochastic behavior. - MFM on a 5 μm CoFeB dot verifies partial switching with strain alone and full switching when current is applied with strain; reversing current and strain restores the initial state, demonstrating rewritability. - Laue X‑ray microdiffraction maps show increased strain magnitude (expanded high‑strain region) with higher applied voltage; XMCD‑PEEM images corroborate voltage‑assisted magnetization switching. - Estimated switching energy is ~200 fJ per operation when using electric‑field‑assisted SOT; the power from the applied electric field itself is negligible. - A reconfigurable logic architecture using locally generated strain implements majority‑gate based AND/OR/selector operations and cascaded BUFFER/NOT, with non‑reciprocal signal flow and potential for complete Boolean logic at ultralow energy.

The study demonstrates that vertical electric fields applied to PMN‑PT (011) substrates generate anisotropic in‑plane strains that are efficiently transferred to the CoFeB layer, selectively modifying the damping‑like SOT while leaving the field‑like component largely unchanged. The strain’s sign and orientation relative to device current direction determine whether HDL is enhanced or suppressed, enabling deterministic, angle‑dependent control of switching thresholds. These findings directly address the goal of energy‑efficient, quantitative modulation of magnetization switching: by boosting HDL via tensile strain in favorable orientations, the required current density for SOT switching is reduced, achieving ~200 fJ energy per operation. The agreement among harmonic Hall fits, micromagnetic simulations, MFM, XMCD‑PEEM, and X‑ray microdiffraction provides a consistent mechanistic picture. This strain‑tunable SOT control is particularly impactful for spin logic, where local, electrically programmable strain fields allow orientation‑selective switching and reconfigurability, enabling majority logic, AND/OR/selector, and robust buffering/negation with minimal overhead and good non‑reciprocity for cascading.

By systematically probing the angular dependence of SOT in Ta/CoFeB devices on PMN‑PT (011), the work establishes an energy‑efficient route to quantitative magnetization switching via electric‑field‑induced in‑plane strain. Compressive strain reduces, while tensile strain increases, the DLT effective field depending on device orientation; FLT remains nearly constant. These effects, validated by transport, imaging, diffraction, and simulation, enable deterministic switching at reduced current density with ~200 fJ energy. The approach supports reconfigurable, low‑power spin logic (majority, AND/OR/selector, BUFFER/NOT) with localized strain control and cascability. Future research could optimize material stacks and device geometries for larger strain transfer and HDL tunability, explore faster voltage actuation and nanoscale scaling, and integrate MTJs for fully functional, dense logic circuits.