Dzyaloshinskii-Moriya interaction accounting for the orientation of magnetic domains in ultrathin films: Fe/W(110)

Abstract

Combining relativistic first-principles calculations with a micromagnetic model, we establish the Dzyaloshinskii-Moriya interaction as an important mechanism in thin-film magnetism, determining the orientation of magnetic domains relative to the lattice, the type of domain wall, and the rotational direction of the magnetization in the wall. Applying the analysis to two monolayers Fe on W͑110͒, we provide an explanation for puzzling experimental data obtained by spin-polarized scanning tunneling microscopy. DOI: 10.1103/PhysRevB.78.140403 PACS number͑s͒: 75.70.Ak, 71.15.Mb, 75.60.Ch Understanding the nature of domains and domain walls in magnetic nanostructures has become an important issue in the field of spintronics as the controlled motion of domain walls opens up vistas for new types of memory and logic devices ͑e.g., Refs. 1 and 2͒. Domain walls in nanostructures and thin films are known to originate from the interplay of the quantum-mechanical exchange interaction ͑also expressed as spin stiffness͒, the magnetocrystalline anisotropy caused by the relativistic spin-orbit coupling ͑SOC͒, and the classical long-ranged magnetostatic contribution. Usually, the shape of the domains is at random or depends on the size and geometry of the sample. [3][4][5] In these instances there is no correlation between the relative orientation of the domains and the crystal lattice. For a few systems, however, the orientation and anisotropy of the crystal lattice matter. To explain the shape and orientation of the domains, in some of these cases the anisotropy of the spin stiffness must be taken into account, 6,7 while in others only certain spatial orientations of the domain walls minimize the sum of the magnetostatic stray-field energy and the magnetocrystalline anisotropy energy. 8 In this Rapid Communication we report on a different mechanism on how the domain-wall orientation is linked to the crystal lattice. For an ultrathin Fe film, we found out that the Dzyaloshinskii-Moriya interaction ͑DMI͒ plays the crucial role accounting for the orientation of the walls and further for the type of the wall and the rotational direction of the magnetization in the wall. The DMI is an antisymmetric exchange interaction that favors spatially rotating magnetic structures of a specific rotational direction.9,10 It vanishes in inversion-symmetric crystal structures; therefore, it can be excluded for most simple bulk materials. In surface or interface geometries, however, the inversion symmetry is broken and the DMI may become relevant.11 In a recent work 12 it was demonstrated for the first time that on some surfaces the DMI is so strong that it even dominates over the symmetric exchange interactions and induces a spatially rotating magnetic ground state.In this study, we describe the domain walls by a micromagnetic model in which the DMI is included. In contrast to earlier work, we determine all model parameters quantitatively from their electronic origin by first-principles calculations and thus we are able to draw conclusions on th...

Unlocking Bloch-type chirality in ultrathin magnets through uniaxial strain

“…The sign of the average chiralities g B and g N reflects rotational sense and, following the conventions used by Heide et al 30 , the Bloch-type component is called left-handed (right-handed) for positive (negative) g B , and the Néel-type component is lefthanded (right-handed) for positive (negative) g N . Figure 4c plots the dependence of g B and g N on f, the angle between the DW normal and K u .…”

Breathing modes of confined skyrmions in ultrathin magnetic dots

“…In these cases, the experimental results suggest that the domain wall structure involves a Néel profile, rather than a Bloch form, which is possible in these strong ferromagnets if a sufficiently large DMI is present. 25,31 From the strength of the DMI obtained in these experiments, theoretical studies suggest that isolated skyrmions should at least be metastable in these systems. 32 In this article, we explore the dynamics of individual skyrmions confined geometrically in ultrathin circular dots.…”

First-Principles Evaluation of the Dzyaloshinskii–Moriya Interaction

“…One way to compute E(q) in the first-principles calculations is to employ the generalized Bloch theorem, that is, apply different boundary conditions for up and down spins to simulate twisted magnetic structures. 21,23) Calculations of energies for actual twisted magnetic structures with supercells have also been performed. 32) …”

“…For quantitative analysis, several techniques have been developed to calculate the DM interaction from first-principles calculations. [17][18][19][20][21][22][23][24][25][26] Most of these approaches consider the energy difference by twisting the magnetic structures in various ways. One of the most direct approaches is to calculate the energies of spirals with the finite vector q as E(q) and extract the q-linear term, [21][22][23] although this approach is sometimes time-consuming.…”

“…[17][18][19][20][21][22][23][24][25][26] Most of these approaches consider the energy difference by twisting the magnetic structures in various ways. One of the most direct approaches is to calculate the energies of spirals with the finite vector q as E(q) and extract the q-linear term, [21][22][23] although this approach is sometimes time-consuming. When the twisting angle is small, the energy change can be evaluated from the information of the uniform magnetic structures by utilizing, for example, the magnetic force theorem, [17][18][19] Berry phase, 24) or spin gauge field transformation.…”