Microscopic origin of the interfacial Dzyaloshinskii–Moriya interaction in amorphous X/CoFeB/MgO heterostructures with heavy-metal underlayers (X = Hf, Ta, TaN, W)

In perpendicularly magnetized X/CoFeB/MgO trilayers, the sign and magnitude of the interfacial Dzyaloshinskii–Moriya interaction (DMI) can be tuned by the choice of heavy-metal underlayer X (chirality reversal between Hf/Ta and W; enhancement by nitriding Ta into TaN; correlation with 5d orbital filling or electronegativity of X), yet the microscopic mechanism responsible remains unidentified and no quantitative theory reproduces the observed underlayer trend for these amorphous stacks. The problem is to determine which mechanism(s) — charge-localization/electronegativity-modified interfacial spin–orbit splitting, 5d–3d orbital hybridization (mixing of the heavy metal's 5d and the ferromagnet's 3d electronic states across the interface), three-site indirect exchange, induced magnetic moments in the heavy metal, or interface atomic arrangement and boron segregation — dominates the interfacial DMI, and to establish a quantitative microscopic account of its sign and relative magnitude including the relative contributions of the X/CoFeB and CoFeB/MgO interfaces.

Background

The Dzyaloshinskii–Moriya interaction (DMI) is the antisymmetric part of the exchange coupling between neighboring spins, $\mathbf{D}_{ij}\cdot(\mathbf{S}_i\times\mathbf{S}_j)$; it appears when spin–orbit coupling coexists with broken inversion symmetry and twists spin structures into a fixed handedness (chirality). In ultrathin magnetic films, inversion symmetry is broken at each interface, so the DMI is a surface effect whose micromagnetic constant $D$ scales inversely with the ferromagnet thickness. An interfacial DMI converts Bloch-type domain walls (magnetization rotating in the wall plane) into Néel-type walls of fixed chirality (magnetization rotating perpendicular to the wall plane), which can be efficiently driven by the spin Hall torque: a charge current in an adjacent heavy metal (a metal with strong spin–orbit coupling, such as Pt, Ta, W, Hf) generates a transverse spin current via the spin Hall effect, and the accumulated spins exert a torque on the adjacent magnetization. This combination underlies current-driven domain-wall 'racetrack' memory and skyrmion (nanoscale chiral bubble) devices.

CoFeB/MgO is the workhorse stack of spin-orbitronics: an ultrathin amorphous CoFeB layer on MgO develops perpendicular magnetic anisotropy (easy axis out of plane) after annealing, and boron is expelled from the CoFeB/MgO region during that anneal. Torrejon et al. (2014) studied stacks substrate/X/1 nm CoFeB/2 nm MgO/1 nm Ta with heavy-metal underlayers X = Hf, Ta, TaN and W. From current-driven domain-wall motion they inferred the DMI constant $D$: the domain-wall chirality reverses when X is changed from Hf or Ta to W, $D$ grows when Ta is nitrided to TaN, and the strength of $D$ tracks the filling of the 5d orbitals, or equivalently the electronegativity, of the underlayer metal. The paper's Discussion explicitly framed the origin as open: the variation might reflect charge localization of the interface atoms (known to reverse Rashba-type spin splittings, the momentum-dependent spin splitting of electronic states at an inversion-asymmetric surface or interface, at alloy surfaces), the local atomic configuration and boron content at the interface, or mechanisms distinct from the Pt-based systems, where induced magnetic moments in the Pt layer had been suggested to generate the large DMI; the three-site indirect-exchange mechanism of Fert and Lévy (a spin–orbit-active non-magnetic atom mediating an antisymmetric exchange between two magnetic neighbors) was cited as a relevant theoretical framework. The proposed correlation with electronegativity was an inference from measured trends, not a demonstrated causal mechanism, and the $D$ extraction carried experimental uncertainties (the true saturation magnetization $M_S$ versus $M/V$ if a magnetic dead layer exists, the unknown current spin polarization $P$ of CoFeB entering the spin-transfer-torque correction, and domain-wall pinning reducing the measured compensation field $H_L^{\star}$); harmonic Hall analysis (extracting current-induced effective fields from the first and second harmonics of the Hall voltage under a small alternating current) failed for W underlayers, the linear thickness dependence of the propagation field $H_P$ for TaN and the drop of the longitudinal effective field for thick Hf underlayers were unexplained, and a $\beta$-W to $\alpha$-W structural phase transition near 5 nm underlayer thickness ($\beta$-W is the metastable, highly resistive phase of tungsten and $\alpha$-W the equilibrium body-centred-cubic phase) was noted as uncharacterized. Candidate mechanisms for interfacial DMI at a heavy-metal/ferromagnet boundary can be grouped as (i) modification of interfacial spin–orbit splitting by charge transfer/localization between the two layers, (ii) hybridization-driven spin–orbit coupling of 3d and 5d states near the Fermi level, (iii) the Fert–Lévy three-site indirect exchange, and (iv) induced magnetic moments in the heavy metal; in the amorphous, sputter-deposited stacks studied here, none had been isolated or quantified.

Problem Statement

Determine the microscopic origin of the interfacial Dzyaloshinskii–Moriya interaction in perpendicularly magnetized amorphous X/CoFeB/MgO heterostructures with heavy-metal underlayers (X = Hf, Ta, TaN, W), as posed by Torrejon et al. (2014): identify which mechanism(s) — charge localization and electronegativity-driven modification of the interfacial spin–orbit splitting, 5d–3d orbital hybridization across the interface, the three-site indirect exchange of Fert and Lévy (a spin–orbit-active non-magnetic atom mediating an antisymmetric exchange between two magnetic neighbors), induced magnetic moments in the heavy-metal layer, or the local atomic arrangement and boron segregation at the interface — produce the observed sign and magnitude of the interfacial DMI constant $D$, and establish whether the correlation of $D$ with the 5d orbital filling or electronegativity of the underlayer is a causal microscopic mechanism. A solution must identify the dominant mechanism(s) and reproduce the sign and relative magnitude of $D$ across the Hf/Ta/TaN/W underlayer series — the chirality reversal between Hf/Ta and W underlayers, the DMI enhancement upon nitriding Ta to TaN, and the magnitude variation across the 5d series — including the separate contributions of the X/CoFeB and CoFeB/MgO interfaces; matching the signs of $D$ alone does not suffice. Refined measurements that remove the stated extraction uncertainties (saturation magnetization $M_S$ versus $M/V$ when a magnetic dead layer is present, the current spin polarization $P$ of CoFeB entering the spin-transfer-torque correction, and domain-wall pinning reducing the compensation field $H_L^{\star}$) and an explanation of the remaining thickness-dependent phenomena (the linear dependence of the propagation field $H_P$ on TaN underlayer thickness, the drop of the longitudinal effective field for thick Hf underlayers, and the $\beta$-W to $\alpha$-W structural transition near 5 nm with its consequences for magnetic and transport properties) are optional extensions, not required to resolve the problem.

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