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...
Epitaxial films may be released from growth substrates and transferred to structurally and chemically incompatible substrates, but epitaxial films of transition metal perovskite oxides have not been transferred to electroactive substrates for voltage control of their myriad functional properties. Here we demonstrate good strain transmission at the incoherent interface between a strain-released film of epitaxially grown ferromagnetic La 0.7 Sr 0.3 MnO 3 and an electroactive substrate of ferroelectric 0.68Pb(Mg 1/3 Nb 2/3)O 3-0.32PbTiO 3 in a different crystallographic orientation. Our strain-mediated magnetoelectric coupling compares well with respect to epitaxial heterostructures, where the epitaxy responsible for strong coupling can degrade film magnetization via strain and dislocations. Moreover, the electrical switching of magnetic anisotropy is repeatable and non-volatile. High-resolution magnetic vector maps reveal that micromagnetic behaviour is governed by electrically controlled strain and cracks in the film. Our demonstration should inspire others to control the physical/ chemical properties in strain-released epitaxial oxide films by using electroactive substrates to impart strain via non-epitaxial interfaces.
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