Voltage-Controlled Dzyaloshinskii-Moriya Interaction

• Voltage-controlled Dzyaloshinskii-Moriya Interaction is a tunable antisymmetric exchange mechanism manipulated by external electric fields to control chiral spin textures.
• It leverages mechanisms like electrical gating, strain transfer, and Rashba spin–orbit interaction to modulate the magnitude and even the sign of DMI.
• This tunability enables dynamic engineering of domain walls, skyrmions, and spiral spin structures, advancing low-power spintronic device applications.

Voltage-controlled Dzyaloshinskii-Moriya interaction (DMI) refers to the tunability or manipulation of DMI—a chiral, antisymmetric exchange term in magnetic systems—by application of external electric fields or voltage bias. DMI is essential for stabilizing chiral spin textures such as skyrmions, domain walls, and spiral ground states, and its controllability enables dynamic engineering of the spin landscape in a broad range of nanomagnetic and spintronic platforms.

1. Fundamental Principles of Voltage-Controlled DMI

The Dzyaloshinskii-Moriya interaction arises in systems with strong spin–orbit coupling and broken inversion symmetry. Its general form in the spin Hamiltonian between sites $m$ and $n$ is

$$\mathcal{H}_{DM} = \sum_{m,n} \mathbf{D}_{mn} \cdot (\mathbf{S}_m \times \mathbf{S}_n)$$

where $\mathbf{D}_{mn}$ is the DMI vector. Voltage control leverages the sensitivity of either the spin–orbit interaction or the inversion symmetry at interfaces, often through mechanisms such as:

• Electrical gating in tunnel junctions, which induces non-equilibrium electronic structure and occupation differences that activate DMI (Fransson et al., 2014).
• Electric-field–driven strain in ferroelectric substrates that modifies lattice symmetry, affecting interfacial DMI magnitude and anisotropy (Udalov et al., 9 Jan 2024).
• Voltage-driven Rashba spin–orbit interaction at magnetic interfaces, resulting in dynamic (time-dependent) DMI terms (Takeuchi et al., 2019).
• Gate-controlled carrier density in itinerant magnetic systems, tuning RKKY exchange and thus DMI (Zheng et al., 2020).

A common feature is that the voltage, either by biasing leads, gate field, or strain transfer, introduces a tunable parameter into the energetic balance dictating DMI.

2. Voltage Modulation Mechanisms and Scaling

Depending on specific system architecture, voltage control can operate through several mechanisms:

System Type	Main Control Mechanism	Scaling of DMI
Tunnel Junctions	Bias–driven nonequilibrium occupation	$D_{mn} \propto V$, with quadratic scaling in coupling (Fransson et al., 2014)
Ferromagnetic Nanowire	Electric field–modified DMI vector	$D \rightarrow D + \delta D$; $\delta D \propto \vec{e}_{ij} \times \vec{E}$ (Sato et al., 2015)
Bilayer/FM/Oxide	Voltage-tuned Rashba SOC	$$D_{1,2} \propto \alpha_R(t),~\partial_t \alpha_R(t)$$ (Takeuchi et al., 2019)
TMD/Multilayer	Gate–modulated carrier density (RKKY)	$D \sim f(k_F(E_g))$ (Zheng et al., 2020)
vdW/Multiferroic	Ferroelectric polarization switching	DMI reversal or anisotropic change (Chen et al., 31 Jul 2024, Udalov et al., 9 Jan 2024)

For tunnel junction molecular magnets, the DM exchange energy between sites $m$ and $n$ has the form:

$$D_{mn} = -\frac{1}{\pi} v_m v_n \mathcal{T}_c^2 (\Gamma^{\uparrow L}\Gamma^{\downarrow R} - \Gamma^{\downarrow L}\Gamma^{\uparrow R}) \times \int_{C.P.} [f_L(\epsilon) - f_R(\epsilon)] (\epsilon - \epsilon_0)^2 \cdots d\epsilon$$

Here, $f_L - f_R$ depends linearly on voltage bias $V$ for small bias; DMI activation relies critically on nonzero $V$ (Fransson et al., 2014). More generally, the magnitude and even sign of the DMI can be tuned, complemented by quadratic dependence on molecule–electrode coupling.

3. Experimental Realizations and Phenomenology

Voltage-controlled DMI has been realized across diverse platforms:

• Interfacial Multiferroics: Films of Pt/Co/Pt on piezoelectric PMN-PT show strong ($-0.2$ up to $0.8$ mJ/m$^2$) and anisotropic DMI variation under electric field via strain transfer, enabling formation control over labyrinth, zig-zag, and skyrmionic domain patterns (Udalov et al., 9 Jan 2024).
• Ultrathin Heterostructures: Ta/FeCoB/TaOx trilayers exhibit up to $130\%$ DMI modulation under gate voltage, permitting skyrmion chirality reversal and dynamic size tuning, measured by Brillouin Light Spectroscopy (Srivastava et al., 2018).
• vdW Multiferroic Structures: Ferroelectric/ferromagnetic CrI$_3$/In$_2$Se$_3$ heterostructures show DMI sign reversal and torque generation driven solely by polarization switching (i.e., voltage), facilitating current-free, energy-efficient domain wall motion and enhanced Walker fields (Chen et al., 31 Jul 2024).
• Molecular Magnets in Junctions: Voltage bias in tunnel junctions activates and controls DMI, with clear scaling trends in lead polarization and coupling, offering direct electrical programming of exchange terms at the molecular level (Fransson et al., 2014).

Common probes include Brillouin Light Spectroscopy for DMI and domain wall dynamics, Magneto-Optical-Kerr microscopy for domain texture, and anomalous Hall effect measurements for interlayer DMI and 3D spin structures (Kammerbauer et al., 2022).

4. Impact on Spin Textures, Domain Wall Physics, and Applications

Tuning DMI via voltage directly impacts spin arrangements and soliton stability:

• Skyrmions: Voltage modulation allows for creation, sizing, and chirality control of skyrmionic bubbles (Srivastava et al., 2018). Alternating DMI across multilayer stacks ([Pt/Co/Ir]/[Ir/Co/Pt]) further enhances effective DMI (+0.6 mJ/m$^{-2}$), stabilizing smaller, robust skyrmions beyond what is possible in additive DMI schemes (Lucassen et al., 2020).
• Domain wall motion: Electric-field–controlled DMI enables precise adjustment of domain wall width and spiral pitch, fine-tuning the transverse magnetization and thus pinning potential. In nanowires, this leads to electrically programmable depinning currents, facilitating ultra-low power device operation (Sato et al., 2015).
• Walker field enhancement: Ferroelectrically induced DMI torque increases critical field for domain wall precession, improving control over domain wall velocity regimes (Chen et al., 31 Jul 2024).

Potential device implications span advanced MRAM, racetrack memories, tunable logic circuits, and energy-efficient computational elements, all leveraging voltage as a dynamic, localized control parameter for chiral spin landscapes.

5. Advanced Theoretical Frameworks for Voltage-Driven DMI

DMI modulation by voltage bias or electric field is described in several theoretical treatments:

• Rashba-Driven Effects: Time-dependent Rashba coefficients under gate voltage lead to dynamic DMI terms, e.g.,

$$H_{DMI} = \frac{D_1 - D_2}{a} \epsilon_{\alpha\beta z} \int m^\alpha \partial_\beta m^z d^2r,$$

with $D_1 \propto \alpha_R(t)$ and $D_2 \propto \partial_t \alpha_R(t)$ (Takeuchi et al., 2019).

• Spin-Current Models: In multiferroics (BiFeO$_3$), voltage-induced polarization modulates internal asymmetric potentials, controlling DM interaction strength and enabling magnon manipulation via the spin-current mechanism (Meyer et al., 2022).
• Hybrid Quantum Systems: Electric-field–driven magnon-plasmon hybridization in 2D crystals utilizes electric field–modified DMI for resonance tuning and magnon–plasmon coupling (Rudziński et al., 13 Jun 2025). The interaction Hamiltonian takes the form:

$$H_{m-pl} = \sum_{k} C_k(a_{-k}b_{-k} - a_{-k}^\dagger b_{-k}) + h.c.,$$

where $C_k$ encodes field- and DMI-dependent coupling.

Time-dependent Anderson impurity models reveal that external fields (voltage via the Peierls phase) can enhance the DM coupling by up to 2 orders of magnitude, making it comparable to Kondo exchange—a route toward voltage-controlled skyrmion stabilization (Yılmaz, 2 Dec 2024).

6. Comparative Context and Device Engineering Implications

Voltage-controlled DMI displays several advantages and distinct engineering pathways compared to alternative methods:

• Additive vs Alternating DMI: While additive DMI relies on fixed material combinations, alternating DMI via voltage or stack design allows a tailored and flexible gain (up to $+0.6$ mJ/m$^2$) not limited by available heavy-metal interfaces (Lucassen et al., 2020).
• Decoupling from Anisotropy: Techniques can target DMI independently of magnetic anisotropy, which is preferable for device optimization (e.g., Ar$^+$ irradiation vs voltage control, (Balk et al., 2016)).
• 3D Spin Texture Management: Electrical current or voltage can manipulate the amplitude and sign of interlayer DMI (IL-DMI), dynamically controlling complex 3D structures such as hopfions (Kammerbauer et al., 2022).
• Low-Power, Nonvolatile Operation: Voltage-controlled DMI enables current-free manipulation of domain walls and skyrmions, significantly reducing Joule heating and fostering energy-efficient, nonvolatile memory and logic architectures (Chen et al., 31 Jul 2024, Takeuchi et al., 2019).

7. Outlook and Future Directions

Research is advancing toward integrating voltage-controlled DMI into practical spintronic platforms by exploring:

• Further exploitation of strain transfer in hybrid multiferroics to program DMI anisotropy and magnitude with in-plane customization (Udalov et al., 9 Jan 2024).
• Expansion into quantum materials and van der Waals systems, leveraging gate-tunability and proximity-induced symmetry breaking.
• Development of magnon–plasmon hybrid systems and quantum logic elements harnessing voltage-tuned DMI–mediated coupling (Rudziński et al., 13 Jun 2025).
• Refinement of theoretical models encompassing time-dependent external fields, non-equilibrium quantum transport, and multi-orbital effects, to predict DMI response under realistic device conditions (Yılmaz, 2 Dec 2024).

Collectively, voltage-controlled DMI is positioned as a central mechanism for the electrical engineering of chiral magnetism, enabling control over spin texture, transport, and dynamics in low-dimensional and heterostructured systems—foundational for advanced information processing with tunable, energy-efficient spintronic devices.