Interfacial Dzyaloshinskii-Moriya Interactions

• Interfacial DMI is an antisymmetric exchange interaction emerging at heavy metal/ferromagnet interfaces with strong spin-orbit coupling and broken inversion symmetry, crucial for chiral magnetic textures.
• The interaction is quantitatively measured via techniques like spin-wave spectroscopy and domain-wall dynamics, allowing extraction of the DMI constant from nonreciprocal spin behavior.
• Careful material engineering, including optimal heavy metal selection and interface quality control, enables tunable DMI values, advancing the design of chiral spintronic and magnonic devices.

Interfacial Dzyaloshinskii-Moriya Interactions (DMI) are antisymmetric exchange interactions that arise at interfaces where inversion symmetry is broken and spin-orbit coupling (SOC) is strong, typically in heterostructures containing heavy metals interfaced with magnetic layers. These interfacial DMIs play a foundational role in stabilizing chiral spin textures such as Néel-type domain walls (DWs), magnetic skyrmions, and influence spin-wave (SW) nonreciprocity, underpinning current developments in nonvolatile spintronic devices, magnonic technologies, and chiral magnetism.

1. Theoretical Framework and Continuum Description

Interfacial DMI emerges at atomically sharp interfaces, notably heavy-metal/ferromagnet boundaries, via the SOC provided by the heavy metal and broken inversion symmetry at the interface. The generic form of the interfacial DMI Hamiltonian, for normalized spin vectors $\mathbf{S}_i$, $\mathbf{S}_j$ at sites $i$ and $j$, is: $$H_{\rm DMI} = \sum_{\langle i,j\rangle} \mathbf{D}_{ij} \cdot (\mathbf{S}_i \times \mathbf{S}_j)$$ Here $\mathbf{D}_{ij}$ is the Dzyaloshinskii-Moriya vector determined by the local symmetry and bonding environment. In the continuum micromagnetic limit, the energy density is typically expressed as: $$w_{\rm DMI} = D\, [\,m_z \nabla \cdot \mathbf{m} - (\mathbf{m} \cdot \nabla) m_z\,]$$ or equivalently in vector notation: $$w_{\rm DMI} = D\,\mathbf{m} \cdot (\nabla \times \mathbf{m})$$ where $\mathbf{m}(\mathbf{r})$ is the unit magnetization vector and $D$ is the interfacial DMI constant (J/m$^2$). Symmetry analysis (Moriya's rules) dictates that $\mathbf{D}_{ij}$ lies in the interface plane and is perpendicular to the bond direction for ideal systems such as fcc(111) or fcc(001) interfaces (Robertson et al., 2020, Yang et al., 2015, Robertson et al., 2020).

The atomistic origin is a three-site mechanism in which SOC on the heavy metal atom modifies the electronic hybridization between neighboring magnetic atoms through inversion-asymmetric hopping (Kim et al., 2017, Yang et al., 2015).

2. Quantitative Measurement Techniques

Multiple experimental protocols probe interfacial DMI with high precision:

• Spin-Wave Spectroscopy (e.g., BLS): BLS measures the nonreciprocal frequency shift $\Delta f$ between counter-propagating spin waves. The sign and slope of $\Delta f$ versus wavevector $k$ yield $D$ via:

$$\Delta f(k) = \frac{2\gamma}{\pi M_s} D k \implies D = \frac{\pi M_s \Delta f}{2\gamma k}$$

This is broadly validated across materials classes, including Co-based ultrathin films (Kim et al., 2018), oxide heterostructures (Yang et al., 9 Aug 2024), and ferrimagnetic alloys (Quessab et al., 2019).

• Domain-Wall Methods: The DMI induces an effective in-plane magnetic field $H_{\rm DMI}$ that reorients DW internal magnetization, extracted via current-driven depinning or creep-regime expansion. The DMI constant is then:

$D = \mu_0 M_s \Delta H_{\rm DMI}$

with $\Delta = \sqrt{A/K_{\rm eff}}$ the DW width determined by exchange stiffness $A$ and anisotropy $K_{\rm eff}$ (Kim et al., 2018, Khan et al., 2016).

• NV Magnetometry: Direct nanoscale mapping of stray fields above DWs allows local resolution of D$($nm-scale inhomogeneities in $D$ inaccessible to integral methods (Gross et al., 2016).
• FMR-Based Schemes: While interfacial DMI does not shift the $k=0$ uniform FMR frequency, interlayer DMI (IL-DMI) does, discernible in coupled magnetic bilayers (Vedmedenko et al., 22 Nov 2024).

Crucially, DW-based and SW-based methods have been shown to yield quantitatively consistent values for $D$ within a given material stack (Kim et al., 2018).

3. Microscopic Mechanisms and Material Dependence

Quantitative DMI strengths and their microscopic origin exhibit pronounced sensitivity to interfacial chemistry, lattice symmetry, electronic structure, and local coordination:

• Heavy-Metal SOC: Interfacial DMI is maximized with high-Z metals (Pt, Ir, W) possessing strong $d$-band SOC at the Fermi level (Yang et al., 2015, Dutta et al., 2023). Substitution of the adjacent nonmagnetic layer tunes both magnitude and sign, with the electric dipole moment and electronegativity serving as predictive descriptors in materials screening (Jia et al., 2019).
• Interface Engineering: Structural factors including underlayer/capping composition, intermixing, interface sharpness, and polar terminations strongly influence $D$ (Vedmedenko et al., 22 Nov 2024, Yang et al., 9 Aug 2024). For example, interface-stabilized spin–orbit coupling channels (e.g., via Nd 4$f$–6$s$–3$d$ coupling in LSMO/NGO) can produce record-high DMI, outperforming metallic benchmarks (Yang et al., 9 Aug 2024).
• Symmetry and Lattice Configurations: DMI tensors are symmetry-constrained. In fcc(111) and fcc(001) epitaxy, the DMI vector lies in-plane, with the out-of-plane DMI component negligible within experimental detection limits. Manipulation of stacking sequence, vicinal step density, or breaking of additional symmetries (through lateral patterning, miscut substrates) can introduce new vector components (Robertson et al., 2020).
• Dipole/Orbital Anisotropy Correlations: Experimental and DFT evidence ties the DMI magnitude to anisotropies in orbital moment and intra-atomic magnetic dipole terms in the magnetic layer (Kim et al., 2017). Tight-binding and ab initio models demonstrate that asymmetric orbital occupation and hybridization, modulated by interface strain, SOC, and orbital filling, directly control the emergent DMI (Kim et al., 2017, Jia et al., 2019).

4. Systems and Scalings: Metal, Oxide, Ferrimagnet, and Antiferromagnet Interfaces

Systematic studies reveal the following key trends in measured and computed interfacial DMI coefficients, $D_s$:

System	$D_s$ (pJ/m)	Noteworthy Mechanism or Feature	Reference
W/Co/Pt	1.83—1.7	Epitaxial, additive interface Co contributions	(Jena et al., 2023)
La$_{0.7}$Sr$_{0.3}$MnO$_3$/NdGaO$_3$	1.96	Nd 4$f$–6$s$–3$d$ hybridization at perovskite interface	(Yang et al., 9 Aug 2024)
Pt/Fe/Au	0.43	OOP Fe spins, enhanced hyperfine field at Fe-Pt boundary	(Longo et al., 1 Dec 2025)
Ta/CoFeB/MgO	0.057	Anneal-tuned interface crystallinity and B expulsion	(Khan et al., 2016)
Pt/CoGd/W	0.23 (0.09—0.23)	Interfacial scaling in amorphous ferrimagnet	(Quessab et al., 2019)
Pt/TmIG (insulating garnet)	$\sim$0.001	Chiral DMI with long decay length, low $M_s$	(Ding et al., 2019)

DMI is invariably interfacial (scaling $D\sim1/t$), decays within a few nanometers into the magnetic material, and can be strongly modulated by interface alloying, stacking asymmetry, or capping layers.

5. Physical Manifestations: Chiral Textures and Nonreciprocal Spin Transport

The key consequence of interfacial DMI is stabilization of homochiral Néel-type DWs, skyrmions, spiral ground states, and nonreciprocal spin-wave propagation.

• Domain Walls and Skyrmions: The sign and magnitude of $D$ select the wall chirality and domain wall type. DMI constants exceeding the threshold $D_c=4\sqrt{A K_{\rm eff}}/\pi$ stabilize chiral Neél DWs and sub-100 nm skyrmions. Additive DMI effects in multilayer stacks support robust, high-density skyrmion lattices (Jena et al., 2023, Quessab et al., 2019).
• Spin Wave Propagation: DMI introduces a linear-in-$k$ shift in spin-wave dispersion (Doppler-like nonreciprocity). The group velocity nonreciprocity $\Delta v_g$ is linear in $D$, permitting unidirectional magnonics and minigap engineering (Xia et al., 2021, Yang et al., 9 Aug 2024).
• Chiral Magnetization Dynamics: In synthetic antiferromagnets and noncollinear antiferromagnetic/metal bilayers, both interfacial DMI and its interlayer analog can generate anisotropy, bias hysteresis loops with chiral exchange fields, and modify resonance spectra (Fernández-Pacheco et al., 2018, Vedmedenko et al., 22 Nov 2024, Yamane et al., 16 Feb 2025).

6. Interface Design and Materials Engineering

Optimizing interfacial DMI requires precise control of atomic structure, composition, and electronic environment:

• Heavy Metal Selection and Layer Engineering: Maximizing heavy metal atomic number and d-band occupancy yields maximal $D$ (e.g., Pt, Ir, W outperform Au, Pd) (Yang et al., 2015).
• Electrochemical and Dipolar Descriptor Engineering: The magnitude and sign of DMI at, e.g., Co/Pt interfaces depends on electronegativity differences across the interface and atomic-scale charge redistribution (quantified by electric dipole moments) (Jia et al., 2019).
• Interface Quality: High crystalline quality and minimal intermixing enable constructive DMI additivity and record values approaching or exceeding 2 pJ/m (as in MBE-grown W/Co/Pt and LSMO/NGO) (Jena et al., 2023, Yang et al., 9 Aug 2024).
• Termination/Polarity Control: Polar termination and strain state are decisive: switching substrate termination (e.g., SrO versus TiO$_2$ in STO) can modulate but not eliminate DMI, while perovskite symmetry breaking can yield 'giant' values via f–s–d interactions (Yang et al., 9 Aug 2024).

7. Outlook and Implications for Spintronics and Magnonics

The ability to engineer and tune interfacial DMI in oxide, metallic, and insulating systems has established DMI as a primary route for designing next-generation chiral spintronic architectures, for both room-temperature skyrmionics and reconfigurable magnonic devices (Yang et al., 9 Aug 2024, Jena et al., 2023, Ding et al., 2019). The latest developments extend interfacial DMI concepts to noncollinear antiferromagnets and polycrystalline systems, where DMI can endow nanoscale disorder with finite macroscopic chiral responses (Yamane et al., 16 Feb 2025, Erokhin et al., 2022).

Detailed mapping of atomic-scale mechanisms, scaling behaviors, and interfacial descriptors (e.g., electric dipole moment) enables predictive design of materials with targeted DMI. This positions interfacial DMI at the nexus of condensed matter physics, high-speed spintronics, and topological magnetism.

Key References:

(Jena et al., 2023) Interfacial Dzyaloshinskii-Moriya interaction in epitaxial W/Co/Pt multilayers (Yang et al., 9 Aug 2024) Giant interfacial Dzyaloshinskii-Moriya Interaction in perovskite La₀.₇Sr₀.₃MnO₃ films (Yang et al., 2015) Anatomy of Dzyaloshinskii-Moriya Interaction at Co/Pt Interfaces (Kim et al., 2017) Microscopic Origin of Interfacial Dzyaloshinskii-Moriya Interaction (Jia et al., 2019) Electric dipole moment as descriptor for interfacial Dzyaloshinskii-Moriya interaction (Ding et al., 2019) Interfacial Dzyaloshinskii-Moriya interaction and chiral magnetic textures in a ferrimagnetic insulator (Kim et al., 2018) Quantitative agreement of Dzyaloshinskii-Moriya interactions for domain-wall motion and spin-wave propagation