Dzyaloshinsky–Moriya Interaction in Magnetic Films

• Dzyaloshinsky–Moriya Interaction is an antisymmetric exchange that favors chiral, non-collinear spin textures in materials lacking inversion symmetry.
• It is characterized by asymmetric domain wall expansion and quantifiable effective fields, as demonstrated through MOKE microscopy.
• Understanding DMI enables the design of spintronic devices with robust chiral domain walls and enhanced current-driven dynamics.

The Dzyaloshinsky-Moria Interaction (DMI), also known as the Dzyaloshinskii–Moriya interaction, is an antisymmetric exchange interaction present in magnetic systems lacking inversion symmetry and possessing strong spin–orbit coupling. DMI energetically favors chiral, non-collinear arrangements of magnetic moments, leading to phenomena such as chiral domain walls, spin spirals, and skyrmions. Its characteristic energy term takes the form $$-\mathbf{D}_{ij} \cdot (\mathbf{S}_i \times \mathbf{S}_j)$$, where $\mathbf{D}_{ij}$ is the DMI vector. In ultrathin ferromagnetic layers adjacent to heavy metals (e.g., Pt/Co/Pt), DMI modifies the domain wall energy density and profoundly influences domain-wall dynamics and current-induced effects.

1. Modification of Domain-Wall Energy by DMI

DMI introduces an additional term to the domain-wall (DW) energy density. In ultrathin ferromagnetic films, the total DW energy density is given by

$$\sigma_{\mathrm{DW}}(H_x, \psi) = \sigma_0 + 2K_D \Delta \cos^2\psi - \pi\Delta M_s (H_x + H_{\mathrm{DMI}}) \cos\psi$$

where $\sigma_0$ is the Bloch-type DW energy density, $K_D$ the DW anisotropy density, $\Delta$ the DW width, $M_s$ the saturation magnetization, $H_x$ the applied in-plane field, $H_{\mathrm{DMI}}$ the effective DMI-induced field, and $\psi$ the magnetization angle within the wall. Minimizing this energy with respect to $\psi$ leads to

$$\cos\psi_{\text{eq}} = \frac{\pi M_s (H_x + H_{\mathrm{DMI}})}{4K_D}$$

For moderate field magnitudes, DMI shifts the energy landscape: the energy density and equilibrium DW configuration become functions of $H_{\mathrm{DMI}}$. DMI stabilizes Néel-type walls in otherwise symmetric stacks, in contradiction to expectations of Bloch-type DW in such structures (Je et al., 2013).

2. Asymmetric Domain-Wall Expansion and Its Origin

Experimentally, when a circular domain in a Pt/Co/Pt film expands under an out-of-plane field ($H_z$), the expansion is isotropic in absence of in-plane field. Upon application of an in-plane field ($H_x$), the domain wall displacement becomes directionally asymmetric. This anisotropy results from DMI producing an effective internal field $H_{\mathrm{DMI}}$, combining with $H_x$. The combined field $H_x + H_{\mathrm{DMI}}$ appears in the DW energy density and breaks rotational symmetry. Regions of the wall where $H_x + H_{\mathrm{DMI}}$ is largest experience reduced energy and thus expand more rapidly under $H_z$. This mechanism manifests as a measurable shift of the domain center along $H_x$.

The out-of-plane $H_z$ drives wall motion via DW creep, while $H_x$ biases the internal wall structure but does not generate direct motion. This highlights DMI’s role in modifying static and dynamic energy landscapes that determine DW propagation direction and speed (Je et al., 2013).

3. Quantitative Extraction of DMI Strength

DMI strength in such films is inferred from the asymmetry in the domain wall speed versus applied fields. Two-dimensional contour maps of DW velocity ($V$) as functions of $H_x$ and $H_z$ exhibit inversion symmetry about a finite offset $H_0$, not about $H_x=0$. The DMI-induced field is then $H_{\mathrm{DMI}} = H_0$; experimentally, $H_0 \approx -26.5 \pm 0.5\ \mathrm{mT}$ in Pt/Co/Pt (Je et al., 2013).

The analysis employs a variable separation for equi-speed contours: $H_x^* = H''(V) f(H_x)$ with $V = V_0 \exp\left(-\alpha H_z^{-1/4}\right)$, and $$\alpha(H_x) \propto [\sigma_{\mathrm{DW}}(H_x)]^{1/4}$$. Fitting these models to the measured velocity contours enables extraction of $H_{\mathrm{DMI}}$ and magnetic parameters such as $\sigma_0 \sim 4.7\ \mathrm{mJ/m}^2$, verifying a robust DMI effect consistent with theoretical expectations for these multilayers.

4. Domain-Wall Dynamics and Chiral Effects

DMI qualitatively changes DW dynamics by energetically favoring a specific internal wall structure (Néel-type) and introducing directionality. The domain wall velocity exhibits field dependence governed by the modified creep law, where the energetic scaling parameter now depends on the DMI. Under applied fields, regions with reduced DW energy (as dictated by $H_x + H_{\mathrm{DMI}}$) move faster, resulting in pronounced motion asymmetry. This stabilization of chiral Néel DWs even in symmetric structures alters the physics of current-induced DW motion, spin-transfer torque efficiencies, and Walker breakdown fields.

The resulting dynamics are fundamentally different from systems without DMI, leading to properties such as increased critical current densities for wall motion, directional mobility, and enhanced efficiency and reliability in spintronic devices based on chiral walls (Je et al., 2013).

5. Experimental Techniques and Principal Results

The principal experiment uses polar magneto-optical Kerr effect (MOKE) microscopy to image expansion of nucleated circular domains in ultrathin Pt/Co/Pt. Out-of-plane ($H_z$) and in-plane ($H_x$) fields are applied, and sequential images construct spatially and temporally resolved equi-speed contour maps. The observed symmetry axis shift in these maps directly quantifies $H_{\mathrm{DMI}}$. Quantitative fits yield energy density and DMI values matching theoretical and ab initio predictions.

The observed asymmetry in DW speed is independent of the magnetic polarity, with the DMI effective field always oriented from $+z$ to $-z$ domains, confirming chirality. Such measurements yield a systematic approach to estimating DMI in thin films and demonstrate the reproducibility and robustness of the chiral effect in ultrathin Pt/Co/Pt (Je et al., 2013).

6. Implications for Spin-Transfer Phenomena and Applications

A salient implication is that DMI ensures robust stabilization of chiral Néel walls, modifying both field-driven and current-driven motion in technologically relevant stacks. Since spin-transfer and spin–orbit torque efficiency depend on the DW type, DMI-induced stabilization of Néel walls enhances domain wall velocities, alters effective thresholds for motion, and underpins phenomena such as asymmetric current-induced switching. These features are directly relevant to the design of memory and logic devices that utilize magnetic domain dynamics.

Furthermore, the work challenges the prior expectation that symmetric Pt/Co/Pt interfaces would yield negligible net DMI and Bloch wall stabilization. Rather, the presence of a strong DMI even in such systems necessitates reevaluation of design principles for perpendicularly-magnetized spintronic architectures (Je et al., 2013).

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In conclusion, the Dzyaloshinsky-Moria interaction fundamentally modifies both the statics and dynamics of domain walls in ultrathin ferromagnetic films. By introducing an effective field, DMI creates an energy bias that stabilizes chiral textures, dictates domain-wall dynamics, and enables quantification through magneto-optical measurements of asymmetry. The pronounced effect of DMI on domain-wall energy density and motion has direct consequences for the development of high-speed, robust chiral spintronic devices.