Interlayer Dzyaloshinskii-Moriya Interactions

Abstract

Interfacial Dzyaloshinkii-Moriya interaction defines a rotational sense for the magnetization of two-dimensional films and can be used to create chiral magnetic structures like spin-spirals and skyrmions in those films. Here we show by means of atomistic calculations that in heterostructures magnetic layers can be additionally coupled by an interlayer Dzyaloshinskii-Moriya interaction across a spacer. We quantify this interaction in the framework of the Lévy-Fert model for trilayers consisting of two ferromagnets separated by a non-magnetic spacer and show that interlayer Dzyaloshinkii-Moriya interaction yields non-trivial three-dimensional spiral states across the entire trilayer, which evolve within as well between the planes and, hence, combine intra-and inter-plane chiralities. This analysis opens new perspectives for three-dimensional tailoring of the magnetization chirality in magnetic multilayers.The magnetic Dzyaloshinskii-Moriya interaction (DMI) arises in systems with bulk inversion asymmetry [1,2]. Without bulk inversion asymmetry, the DMI arises at interfaces only and couples two magnetic sites both sitting within a surface layer [1,3]. This interaction appeared to be a very important property of interfacial systems, because it is responsible for the unique rotational sense of magnetization and can be used to create topological objects like magnetic skyrmions and chiral domain walls [4][5][6][7], that are attractive candidates for data storage, transfer and processing [8][9][10]. DMI corresponds to an antisymmetric part of the exchange tensor and is described by a vector quantity D. Orientation and strength of D can be estimated using the Moriya symmetry rules [11], the Lévy and Fert model [3] or first-principles calculations [12][13][14]. The Moriya procedure has been created for localized magnetic systems and takes into account two magnetic sites coupled by a Hubbard-type Hamiltonian. The Lévy and Fert model involves an additional third site mediating the DMI via conducting electrons and is more appropriate for itinerant systems. In most cases symmetry rules as well as three-sites model give correct orientation of D. Both of the models have, though, their limitations. The two-sites procedure can often predict only an easy plane, rather than an exact direction of D [15]. DMI from three-sites model applied to systems of low-symmetry like spin chains at interfaces might differ in some cases from ab-initio results [12]. Nontheless, it is broadly accepted that for ultrathin films the Lévy-Fert model provides sound basis for studies on the spin ordering at the interfaces, because majority of experimentally 4d/3d, 5d/3d interfaces or their alloys belong to the class of itinerant systems. Its additional advantage is a clear definition of D in systems with large and complicated unit cell or in disordered systems, which are difficult to treat from the first principles.The typical strength of the DMI at interfaces lies between 0.1 and 2 meV per atomic bond [16][17][18][19], which corresponds to the thermal ene...

Symmetry-breaking interlayer Dzyaloshinskii–Moriya interactions in synthetic antiferromagnets

“…The microscopic intralayer and interlayer DMI vectors Dij are then analytically calculated (10), considering only next nearest neighbor FM and nearest neighbor PM atoms, as detailed in Supplementary 2.1. From these calculations, the IL-DMI strength |Dij (Co/Pt/CoFeB) | is ≈ 0.02-0.03V1, where V1 is the so-called spin-orbit parameter of the material defining the magnitude of the Dij vectors (10,16). For FM/Pt interfaces, V1 (FM/Pt) ≈ 6.4 meV/atom (10), of the same order of magnitude as the direct exchange interaction of Co, J (Co) (22,23).…”

Asymmetric depinning of chiral domain walls in ferromagnetic trilayers

“…The RKKY interaction has been key to the discovery of giant magnetoresistance [19,20] and has remained an active research topic ever since [21][22][23][24][25]. In combination with the Dzyaloshinskii-Moriya interaction (DMI), the RKKY interaction is responsible for chiral interlayer coupling [26,27], which has recently attracted renewed attention [28][29][30]. Other interlayer coupling mechanisms, such as the direct exchange bias between FMs and antiferromagnets [31,32] and interlayer dipolar interactions [33][34][35], are relevant for tuning the response of magnetic tunnel junctions and spin valves to external fields and currents.…”

Spin reorientation transition in an ultrathin Fe film on W(110) induced by Dzyaloshinsky-Moriya interactions

“…Therefore, it is expected that this DMIinduced anisotropy term should have a considerable influence on the design of room-temperature spintronic applications, by affecting the magnon frequencies, the width of domain walls, and the sizes of magnetic skyrmions. The possible competition between intralayer and interlayer contributions to the DMI [26,42,43] should further enrich the variety of observed phenomena in sputtered multilayers, where the growth process typically breaks additional symmetries compared to epitaxial ultrathin films.…”