Voltage-Controlled Magnetic Anisotropy

• Voltage-controlled magnetic anisotropy is the electric field tuning of magnetic anisotropy at material interfaces, enabling reversible, low-power control of magnetic states.
• Advanced measurement techniques like the anomalous Hall effect, ferromagnetic resonance, and micromagnetic simulations quantify VCMA coefficients from tens of fJ/V·m to pJ/V·m.
• VCMA supports scalable applications in MRAM, skyrmion logic, and magnonic devices by offering deterministic switching and minimal energy dissipation.

Voltage-controlled magnetic anisotropy (VCMA) is the electric-field tuning of magnetocrystalline or interfacial anisotropy in magnetic materials, enabling reversible, low-power, and non-volatile manipulation of magnetic states at nanoscale dimensions. VCMA fundamentally relies on electric-field–induced modification of orbital occupancies, hybridization, or strain at interfaces involving ferromagnetic metals, oxides, antiferromagnets, or 2D materials, and has direct applications in spintronic memory, logic, magnonics, and topological magnetism. The following sections systematize the physics, materials systems, measurement protocols, operational metrics, and device applications of VCMA, with explicit references to quantitative results from arXiv sources.

1. Microscopic Mechanisms and Theoretical Basis

VCMA arises primarily from two microscopic channels: (1) direct electric-field modification of the electronic structure (charge-driven), and (2) indirect strain transfer (magnetoelastic effects) in multiferroic or piezoelectric hybrids. Most commonly, VCMA refers to the interfacial charge-mechanisms predominant at transition metal/oxide boundaries, such as Fe(Co)/MgO (Zhang et al., 2016), CoFeB/MgO (Wen et al., 2016), and emergent platforms such as 2D systems (Shukla et al., 5 Jul 2025).

At the atomic scale, the key effect is the electric-field–induced redistribution of d-orbital occupation at a ferromagnet/oxide interface, where the change in occupancy modifies the spin–orbit–mediated terms in the local magnetocrystalline anisotropy energy. This can be formalized in second-order perturbation theory as: $$E_{\text{MCA}} \approx \sum_{o,u,\sigma} \frac{|\langle u, \sigma | H_{\text{SO}} | o, \sigma \rangle |^2}{\epsilon_{u,\sigma} - \epsilon_{o,\sigma}}$$ Here, variation in occupancy (Δn) and energetic proximity of occupied and unoccupied minority-spin states determines the VCMA coefficient ξ (Zhang et al., 2016).

In piezoelectric and strain-mediated systems, an applied voltage generates a mechanical strain, which, via the magnetostriction coefficient λ, couples to the magnetic energy and thus the anisotropy constant K. In FM/FE systems, the total change in anisotropy is a sum of these two effects: $$\Delta K_u(V) = \frac{\Delta K_s(V)}{d} + \frac{1}{2} B_{\text{eff}} \varepsilon_p(V)$$ where ΔK_s(V) is the interface-charge VCMA (∝1/d), and the second term is the strain-mediated contribution (d-independent) (Hu et al., 2010). There is a sharp crossover thickness $d_{\rm tr}$ between the two regimes, e.g. $d_{\rm tr}\sim 0.5$ nm for Fe/BaTiO₃.

2. Quantitative VCMA Metrics and Material Dependencies

The VCMA coefficient ξ (units fJ/V·m or pJ/V·m) is defined as: $\xi = \frac{\partial K_{\text{eff}}}{\partial E}$ and typically ranges from ≈10–100 fJ/V·m in state-of-the-art Fe(Co)/MgO or CoFeB/MgO systems (Zhang et al., 2016, Wen et al., 2016). Notably, the Pt-porphyrin/graphene/NiFe system achieves β ≈ 376 fJ/V·m (Shukla et al., 5 Jul 2025), while strain-mediated multiferroic stacks may deliver much larger effective coupling—e.g., α_CE ≈ 1.43 μs/m in Ni₉₀Fe₁₀/BaTiO₃(001) (Begué et al., 21 Mar 2025), exceeding earlier perovskite or transition-metal systems by an order of magnitude.

In antiferromagnetic systems such as MnPt/MgO, direct DFT calculations yield voltage-control coefficients β up to ±1.5 pJ/V·m, depending on termination and thickness (Chang et al., 2020). Quantum confinement in ultrathin Fe quantum wells produces nontrivial, even “A-shaped” (bipolar) VCMA curves, controlled by layer parity and resonance location (Xiang et al., 2020).

A summary of representative VCMA coefficients is provided:

Material/Stack	ξ (VCMA Coefficient)	Reference
Fe(Co)/MgO	20–100 fJ/V·m	(Zhang et al., 2016Walker et al., 2021)
Co₂FeAl/MgO/Ru	108 fJ/V·m @ RT	(Wen et al., 2016)
Ni₉₀Fe₁₀/BaTiO₃(001)	α_CE=1.43 μs/m (strain-driven)	(Begué et al., 21 Mar 2025)
MnPt/MgO	±1.5 pJ/V·m	(Chang et al., 2020)
Graphene/Pt-porphyrin/NiFe	376 fJ/V·m	(Shukla et al., 5 Jul 2025)

3. Experimental Methodologies and Modeling

Quantitative extraction of VCMA is achieved through:

• Magneto-Transport: Anomalous Hall effect and magnetoresistance loops under variable gate voltage, used to measure anisotropy fields, coercive field, and switching times (Zayets et al., 2018).
• Ferromagnetic Resonance (FMR): Microstrip FMR (MS-FMR) and spin-torque FMR quantify voltage-induced shifts in resonance field H_res and linewidths, providing direct access to K_u(V) and effective fields (Shukla et al., 5 Jul 2025, Zighem et al., 2013, Wen et al., 2016).
• X-ray and Kerr Microscopy: Domain structure and anisotropy orientation under gating are visualized using XMCD-PEEM and Kerr effect (Begué et al., 21 Mar 2025).
• Micromagnetic Simulation: Landau–Lifshitz–Gilbert (LLG) equation, with voltage-dependent anisotropy term H_K(V) = (2K_u(V))/(μ₀M_s), forms the basis of dynamical simulation in Skyrmion logic (Walker et al., 2021), magnonic crystals (Wang et al., 2016), and switching/logic (Yang et al., 2022).

The dependence of K_eff on electric field or gate voltage is almost universally linear in the “charge-driven” regime, and can become quadratic or exhibit nonlinear (hysteretic) behavior in strain-mediated or quantum-confined systems (Xiang et al., 2020, Hu et al., 2010). Device-level VCMA exploits this for deterministic switching, clocking, or reconfiguration.

4. Device Applications and Non-Volatile Control

VCMA enables compelling low-energy switching modalities for both digital and analog spintronic devices.

MRAM and Memory Elements

Electrostatic reduction of the anisotropy barrier in CoFeB/MgO p-MTJs (using ξ ≈ 200 fJ/(V·m), t_ox ~1–2 nm) reduces the switching energy per bit to O(10 fJ), and allows precessional or toggle switching with sub-ns pulses (Yang et al., 2022, Drobitch et al., 2017, Wen et al., 2016). Negative-capacitance amplification has been proposed to further enhance VCMA response to >500 fJ/(V·m) for sub-100 nm devices (Zeng et al., 2016).

Skyrmion Logic and Topological Memory

VCMA can localize and clock skyrmions for pipelined, synchronized logic without current-driven notches, leading to ~3 fJ per stage and high reliability in sub-50 nm tracks (Walker et al., 2021). Voltage pulses can also reversibly create/annihilate skyrmions in MTJ-like cells (writing/erasing ~fJ per operation, non-volatile retention), avoiding external fields or high current densities (Bhattacharya et al., 2019).

Magnonic and Spin-Wave Devices

Periodic or localized gating—modulating VCMA in Co(MgO) nanowires—can produce and tune magnon bandgaps (band gap width Δf_gap ∝ ΔK_u, frequencies 10–40 GHz), implement phase shifters (Δφ up to 0.25 π for ξ~500 fJ/V·m, 1 μm gate), and route spin waves at energy cost < 10 fJ per operation (Petrillo et al., 5 Feb 2024, Wang et al., 2016).

Antiferromagnetic Resonance and Terahertz Control

Voltage-modulated anisotropy in AFM/MgO enables parametric and forced resonance of the Néel vector, with exchange-enhanced coupling efficiency—1–2 orders higher than microwave or spin-orbit torques, and operation at zero bias field; this establishes VCMA as a promising control knob for terahertz AFM oscillators (Tomasello et al., 2022).

5. Materials Platform Engineering and Scalability

Material choice, interface termination, layer thickness, and dielectric selection are critical for maximizing VCMA coefficient and operational reliability:

• Transition thickness d_tr marks the point where interface-charge VCMA (∝1/d) dominates in nm-thin FMs, while strain effects dominate beyond d_tr (Hu et al., 2010).
• Interface chemistry, quantum well tailoring, and work-function engineering allow for inversion (“inverse VCMA sign”) and even enhancement of the coefficient beyond 1 pJ/V·m (Xiang et al., 2020, Zhang et al., 2016).
• Use of high-SOC ligand functionalization (Pt-porphyrins), 2D graphene interfaces, and GdOₓ dielectrics have yielded record interface β, broadening device opportunities (Shukla et al., 5 Jul 2025, Petrillo et al., 5 Feb 2024).
• The sign and linearity of VCMA, as well as temperature and cycling stability, depend sensitively on coding of interface states and dielectric/oxide character (Wen et al., 2016, Zayets et al., 2018).

6. Operational Trade-offs, Energy, and Endurance

The VCMA approach is distinguished by vanishing static power consumption (off-state) and avoidance of Joule heating, with energy switching cost in the few-fJ regime for sub-100 nm² devices and up to 10× reduced energy per logic operation in dynamic pipelines (Walker et al., 2021, Petrillo et al., 5 Feb 2024). VCMA-based write can sharply suppress sneak paths in crossbar arrays, due to non-linear thresholding of the in-plane precessional trajectory (Yang et al., 2022).

Scalability and endurance are provided by the interface-electronic (charge) nature of the effect, with >10⁵ cycles demonstrated without decay or drift; magneto-ionic approaches enable non-volatile state retention at larger β but slower speed (Petrillo et al., 5 Feb 2024). Thermal, voltage-window, and oxide reliability considerations require careful stack engineering and process control, especially for high-β and sub-1 V operation (Wen et al., 2016, Zeng et al., 2016).

7. Emerging Directions and Multiferroic Coupling

VCMA in strain-mediated multiferroic heterostructures (Ni₉₀Fe₁₀/BaTiO₃, FM/FE) offers voltage-driven 90° easy-axis reorientation, giant converse magnetoelectric coupling, and reconfigurability for logic, domain-wall, and magnonic devices, with device-level engineering for toggled memory functionality and reversible anisotropy control (Begué et al., 21 Mar 2025, Zighem et al., 2013). Dual tuning via charge and strain, and negative-capacitance amplification to achieve giant VCMA at low voltage, are active areas of research (Zeng et al., 2016, Qurat-ul-Ain et al., 2020). VCMA concepts are expanding into resonant control of antiferromagnets, dynamic patterning of uniaxial anisotropy by resistive switching, and quantum-confined film design for nontrivial field response (Tomasello et al., 2022, Salev et al., 2021, Xiang et al., 2020).

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In summary, voltage-controlled magnetic anisotropy offers a universal and energy-efficient route to electrostatic control of magnetism via engineered interfaces, orbital tuning, and hybrid strain-charge couplings. Quantitative benchmark coefficients, diverse materials platforms, rigorous measurement protocols, and robust device demonstrations position VCMA as a cornerstone of beyond-CMOS, spin-based and wave-based information technologies.