Interfacial Dzyaloshinskii-Moriya interaction arising from rare-earth orbital magnetism in insulating magnetic oxides

Abstract

The Dzyaloshinskii-Moriya interaction (DMI) is responsible for exotic chiral and topological magnetic states such as spin spirals and skyrmions. DMI manifests at metallic ferromagnet/heavy-metal interfaces, owing to inversion symmetry breaking and spin-orbit coupling by a heavy metal such as Pt. Moreover, in centrosymmetric magnetic oxides interfaced by Pt, DMI-driven topological spin textures and fast current-driven dynamics have been reported, though the origin of this DMI is unclear. While in metallic systems, spin-orbit coupling arises from a proximate heavy metal, we show that in perpendicularly-magnetized iron garnets, rare-earth orbital magnetism gives rise to an intrinsic spin-orbit coupling generating interfacial DMI at mirror symmetry-breaking interfaces. We show that rare-earth ion substitution and strain engineering can significantly alter the DMI. These results provide critical insights into the origins of chiral magnetism in low-damping magnetic oxides and identify paths toward engineering chiral and topological states in centrosymmetric oxides through rare-earth ion substitution.

Fig. 1. Magnetic and structural characterization of insulating magnetic samples.

a Schematic of the perpendicularly magnetized GGG/TmIG/Pt layer structure. Red (blue) arrows indicate the orientation of Fe³⁺ (Tm³⁺) sublattice ions in ferrimagnetic TmIG. b Omega-2theta (ω−2θ) scans of TmIG films of two different thickness around the GGG(444) substrate peak. c High-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) of the TmIG/GGG interface along the [1$\overline{2}$1] zone axis, with [111] oriented vertically. Scale bar, 2 nm. d Electron energy loss spectroscopy (EELS) maps for metal elements, Tm, Fe, Gd, and Ga. Scale bar, 1 nm. e EELS intensity profile across the interface along horizontal direction at distance d. f Example magnetic hysteresis loop as measured by vibrating sample magnetometry (VSM) of GGG/TmIG (12 nm). g Magnetization per unit area (M/A) as a function of TmIG thickness (t_TmIG) as measured by VSM. The error bars represent the noise of the VSM measurement. M_s saturation magnetization, a.u. arbitrary units. Source data for g are provided as a Source Data file.

Fig. 2. Current-assisted domain wall motion in GGG/TmIG/Pt.

a Schematic of the domain wall track with electrical connections. Red (blue) regions indicate down (up) net magnetization in the TmIG. Yellow regions represent the domain wall nucleation line. Magneto optical Kerr effect laser spot indicated by a turquoise circle. b Exemplary hysteresis loops of GGG/TmIG (6.0 nm)/Pt. Domain wall is nucleated on the positive zero crossing of the magnetic field. Red (blue) loops depict the influence of a positive (negative) current passed through the Pt overlayer. c Propagation field (ΔH_dp) as a function of d.c. current density (J) for various applied in-plane fields of an up-down domain wall. d Schematics illustrating the influence of a longitudinal in-plane field (H_x) on a Néel domain wall. Arrow orientation and color indicates the net magnetization. Gray magnetic field arrows indicate the strength of the in-plane field. a.u., arbitrary units.

Fig. 3. Thickness dependence of the chiral exchange energy in GGG/TmIG/Pt.

a Normalized spin Hall efficiency (χ/χ₀) as a function of in-plane field (H_x) for up-down (open blue squares) and down-up (open red circles) domain walls. Insets are schematics of up-down and down-up domain walls at zero applied field. b χ/χ₀ for down-up domain walls in various thicknesses of GGG/TmIG/Pt films. TmIG thickness (t) dependence of the c Dzyaloshinskii–Moriya interaction energy (D) and d the spin Hall efficiency. Error bars in c are the propagated error of measured M_s, Δ, and H_D at each thickness, while the error bars in d are the standard error of 4–6 measurements at each thickness. Source data for c and d are provided as a Source Data file.

Fig. 4. In-plane field dependence of the spin Hall efficiency in Pt-covered insulating magnetic garnets.

Normalized spin Hall efficiency (χ/χ₀) performed on up-down domain walls in a GGG/TbIG (7.1 nm)/Pt (4.0 nm) and GGG/TbIG (7.1 nm)/Cu (2.0 nm)/Pt (4.0 nm), b GGG/TmIG (6.0 nm)/Pt (4.0 nm) and GSGG/BiYIG (6.9 nm)/Pt (4.0 nm), and c GGG/TmIG (6.0 nm)/Pt (4.0 nm) and SGGG/TmIG (6.0 nm)/Pt (4.0 nm). Insets are layer schematics of each thin film system. d Summary of DMI (D) strengths in each system in a–c.

Fig. 5. X-ray magnetic circular dichroism on GGG/TmIG (6.0 nm).

a Exemplary Tm XMCD spectrum under 10 kOe field at T = 70 K showing positive (μ⁺) and negative (μ⁻) helicity and a difference spectrum (μ⁺–μ⁻). z-component of the b orbital (L_z) and spin (S_z) angular momentum and c magnetization m_z as a function of temperature (T). d Temperature dependence of spin–orbit coupling ($\mathbf{L}\cdot \mathbf{S}$). The inset in d expands the data between 200 and 400 K for clarity. The error bars in b–d are smaller than the data points and represent standard errors estimated from a variation of the sum rule integration boundaries. In addition, there is a systematic measurement uncertainty of 20% on the absolute scale. a.u., arbitrary units. f.u., formula unit.

Fig. 6. Temperature dependence of DMI.

The DMI effective field (H_D) as a function of temperature (T) in a GGG/TmIG (2.4 nm)/Pt (4.0 nm) and b GGG/TmIG (6.0 nm)/Pt (4.0 nm). Error bars are standard error of three measurements. Source data are provided as a Source Data file.