The microscopic origin of DMI in magnetic bilayers and prediction of giant DMI in new bilayers

The study addresses the need for next-generation memory technologies where magnetic skyrmions—topologically protected, nanoscale spin textures moved by very small current densities (~10^6 A/m^2)—are promising candidates. The Dzyaloshinskii–Moriya interaction (DMI) is crucial for creating and stabilizing skyrmions, yet its microscopic origin and the mechanisms by which it generates textures in metallic bilayers are not well understood. Existing theories from magnetic insulators do not explain observed DMI trends in bilayers, and conflicting reports leave open questions about which material parameters control DMI magnitude and sign. The paper aims to fill this gap by developing a first-principles-based theoretical model for metallic HM/FM bilayers, identifying key determinants of DMI strength and sign, and linking spin–orbit coupling (SOC) to the generation of spin textures. Practical motivation includes realizing ≤10 nm skyrmions stable at room temperature: ultrathin HM/FM films host sub-10 nm skyrmions but at low temperatures, whereas multilayers host room-temperature skyrmions but typically >30 nm. Skyrmion size and stability depend on DMI, exchange, anisotropy, and dipolar interactions; thus identifying materials with favorable combinations—especially enhanced DMI—is essential. The authors report new bilayers with giant DMI and propose multilayer designs, aiming to advance controllable skyrmion technologies.

Prior models and experiments provide inconsistent guidance on DMI in HM/FM bilayers. Moriya’s theory for insulators does not capture metallic bilayer trends. One proposal attributes DMI to proximity-induced magnetic moments in HMs, but contradictory results exist. Other studies emphasize HM–FM hybridization as a key factor, which aligns with the present work, but proposed rules linking DMI sign to FM 3d band filling are contradicted by cases such as Ir/Fe (large negative DMI) and varying signs in HM/Co. Similarly, models suggesting DMI is determined solely by spin-polarized HM 5d states in Pt/FM are inconsistent with opposite signs reported for Pt/Co and Pt/Ni. These inconsistencies highlight a gap relating DMI to the electronic structure of both HM and FM layers and the need for a microscopic mechanism connecting SOC to spin texture formation. The present study addresses these gaps with a model where DMI depends on HM–FM hybridization and specific HM orbital contributions that govern SOC-induced spin mixing and ultimately DMI sign.

The authors computed DMI for comprehensive series of HM/FM bilayers via density functional theory (DFT) using VASP with PAW-PBE pseudopotentials. Heavy metals spanned 5d and 6p elements (Hf to Bi), and ferromagnets were γ-Fe(111), Co(0001), and Ni(111). Bilayer supercells comprised one monolayer of FM, one monolayer of HM, and 10 Å of vacuum, appropriate because the DMI in such systems is interfacial. In-plane lattice constants were set by the HM, and the FM was strained <5% to match. K-point meshes and plane-wave cutoffs were converged; structures were relaxed until forces were <0.01 eV/Å. Microscopic interfacial DMI (d, meV/atom) was computed following the method of Yang et al., and converted to micromagnetic D (mJ/m^2). The theoretical analysis employed first-order perturbation theory to derive how SOC generates spin textures: SOC induces spin-mixing transitions between specific HM d orbitals, rotating the magnetic moment of electrons hopping across the HM/FM interface; via exchange, this rotation perturbs FM states and yields DMI. The model identifies three key SOC-induced transitions among HM d orbitals—(d_xz|d_z^2), (d_xy|d_yz), and (d_x^2−y^2|d_xz)—that contribute to the DMI with signs determined by transition directions. An assumption in DMI calculations is that nearest-neighbor (NN) DMI dominates over next-nearest neighbor (NNN) terms, justified by stronger NN hopping via HM in these strained/relaxed interfaces and by reduced NNN importance under nonzero magnetic fields reported in related chiral systems.

- First-principles calculations reveal giant interfacial DMI in six bilayers: Re/Fe, Os/Fe, Re/Co, Os/Co, Os/Ni, and hexagonal Bi (hBi)/Ni. These reach up to roughly twice the previously largest reported values (reference best: ~1.5 meV/atom for Co/Pt, −1.9 meV/atom for Ir/Fe, −1.04 meV/atom for Ir/Co). Authors’ computed benchmarks: Co/Pt d ≈ +2.6 meV/atom; Ir/Fe d ≈ −1.8 meV/atom; Ir/Co d ≈ −1.8 meV/atom. - Newly predicted giant-DMI systems not previously reported include Re/Co, Os/Co, Os/Ni, and hBi/Ni. hBi (a candidate quantum spin Hall material) is notable for potential synergy with large spin Hall currents to drive skyrmions. - Materials design: additive DMI from successive interfaces can be enhanced with simpler stacks such as Pt/Co/Os and Pt/Co/Re, potentially exceeding established designs like Pt/Co/Fe/Ir. - DMI magnitude correlates strongly with HM–FM hybridization, quantified via band overlap (BO) between FM 3d and HM 5d (or HM 6p) states: larger BO generally yields larger |d|. Trends observed: • HM-5d/Fe: |d_W/Fe| < |d_Au/Fe| < |d_Re/Fe| < |d_Os/Fe|, tracking increasing BO. • HM-5d/Co: |d_Hg/Co| ≈ |d_Au/Co| < |d_Pt/Co| < |d_Os/Co| ≈ |d_Re/Co|, consistent with BO. • HM-6p/FM: |d_Tl/Fe| < |d_Pb/Fe| < |d_Bi/Fe| and |d_Tl/Co| < |d_Bi/Co| < |d_Pb/Co|, again tracking BO. Outliers with smaller-than-expected |d| given BO include Ir/Fe, Pt/Co, and Pt/Ni (and hBi/Co among 6p), explained by competing SOC-driven orbital transitions; Hg/Fe and Hg/Co have slightly larger-than-expected DMI, suggesting additional hybridization channels beyond simple 3d–5d BO. - DMI sign is not governed by FM 3d filling; instead, it is controlled by the relative presence of specific HM d orbitals that set the direction and strength of SOC-induced transitions. Analysis of projected band structures around the K point (typically −3 to −1 eV or −4 to −2 eV below EF) shows two dominant competing transitions: (d_yz − d_xy) and (d_xz − d_x^2−y^2). For selected large-DMI bilayers (Re/Fe, Os/Fe, Ir/Fe, Re/Co, Os/Co, Pt/Co, Os/Ni, Pt/Ni): • All exhibit a (d_yz − d_xy) transition contributing a negative DMI term (counter-clockwise spin rotation). • Early HMs (e.g., Re, Os) tend to show (d_xz − d_x^2−y^2) transitions (also negative), leading to additive negative DMI (large |d|) in Re/Fe, Os/Fe, Re/Co. • Late HMs (e.g., Ir, Pt) show reverse tendencies in one channel, causing competing signs and reduced |d| in Ir/Fe, Pt/Co, Pt/Ni. Os/Ni shows competition yet still yields larger-than-expected DMI. - The theoretical framework links DMI to SOC-induced spin mixing and explains the observed correlation between DMI and orbital anisotropy reported in experiments. It provides routes to tune DMI magnitude (via hybridization) and sign (via engineering HM orbital occupations by strain and symmetry breaking).

The work resolves key questions about the microscopic origin of DMI in metallic bilayers. It shows that DMI strength is governed primarily by HM–FM hybridization (3d–5d or 3d–6p band overlap), while the sign is controlled by the relative HM orbital contributions that dictate SOC-induced spin-mixing transitions. The perturbative mechanism clarifies how SOC rotates electron magnetic moments during hopping across the HM/FM interface, with exchange in the FM converting this rotation into an energy change identified as DMI. This framework explains broad material trends and specific outliers where strong hybridization coexists with reduced DMI due to competing orbital-transition channels. The findings reconcile disparate observations in the literature, including the lack of a universal relation to FM 3d filling and the variable DMI signs in similar HM/FM systems. Practically, the identification of giant-DMI bilayers and additive DMI strategies (e.g., Pt/Co/Os, Pt/Co/Re) supports the design of multilayers with stronger chiral interactions, enabling smaller, more stable skyrmions at higher temperatures and improved chiral domain wall dynamics for spintronic devices. The model also rationalizes observed correlations between DMI and orbital anisotropy and suggests that tuning hybridization (via interface engineering, strain, or symmetry breaking) and orbital occupations can control both magnitude and chirality—potentially even via electric fields—advancing skyrmion manipulation in devices.

The paper introduces a microscopic model for DMI in metallic HM/FM bilayers, identifying two decisive factors: (1) HM–FM hybridization that sets DMI magnitude and (2) specific HM orbital contributions that determine SOC-induced spin mixing and thus DMI sign. First-principles calculations predict giant DMI in multiple new bilayers (Re/Fe, Os/Fe, Re/Co, Os/Co, Os/Ni, hBi/Ni), exceeding previous benchmarks, and propose simplified multilayer designs (Pt/Co/Os, Pt/Co/Re) for additive DMI. The theory explains observed trends and outliers across HM/FM combinations, provides a qualitative predictor of DMI sign from orbital contributions, and connects DMI to orbital anisotropy. Future research directions include experimental validation of the predicted giant-DMI systems and multilayers, quantitative control of hybridization through interface engineering, strain and symmetry tuning of HM orbital occupations to set chirality, exploration of electric-field control in device environments, and extending calculations to include beyond-nearest-neighbor DMI contributions where relevant.

- Computational structures use monolayer HM/FM slabs with 10 Å vacuum and fix in-plane lattice constants to the HM, straining the FM (<5%); real interfaces may exhibit additional structural/chemical complexities. - DMI extraction assumes nearest-neighbor (NN) DMI dominance; while justified by stronger NN hopping and by diminished NNN contributions under nonzero fields, NNN terms could be relevant in some systems. - The qualitative use of projected density of states and orbital contributions to infer SOC transition tendencies does not fully capture all k-resolved matrix elements; thus, sign predictions are qualitative. - Temperature effects, defects, intermixing, and capping layers are not explicitly included; these can influence hybridization and DMI in experiments. - Some discrepancies with prior literature (e.g., Re/Fe magnitude relative to Simon et al.) indicate sensitivity to computational details and structural models.