Domain-wall profiles in Co/Irn /Pt(111) ultrathin films: Influence of the Dzyaloshinskii-Moriya interaction

Abstract

We perform a study of domain walls in Co/Irn/Pt(111) (n = 0, . . . , 6) films by a combined approach of first-principles calculations and spin dynamics simulations. We determine the tensorial exchange interactions and the magnetic anisotropies for the Co overlayer in both FCC and HCP geometries, depending on the number of Ir buffer layers. We find strong ferromagnetic nearest-neighbor isotropic exchange interactions between the Co atoms and an out-of-plane magnetic anisotropy for the films in FCC geometry. Our simulations show that the magnetic domain walls are of Néel type, and their rotational sense (chirality) is changed upon the insertion of an Ir buffer layer as compared to the pristine Co/Pt(111) system. Our spin dynamics simulations indicate a twisting of the spins with respect to the planar domain wall profile on the triangular lattice. We discuss this domain wall twisting using symmetry arguments and in terms of an appropriate micromagnetic continuum model considering extra energy terms compared to the available literature. I. INTRODUCTIONEffective spin models are widely used to investigate the magnetic properties of solids. The breaking of inversion symmetry in noncentrosymmetric crystals, at surfaces or interfaces and the presence of the spin-orbit coupling lead to the appearance of an anisotropic exchange term beyond the isotropic Heisenberg interaction, which is known as the Dzyaloshinskii-Moriya (DM) interaction [1,2]. In collinear ferromagnetic systems, this type of interaction provides domain walls (DWs) with a chiral character [3][4][5][6][7][8], plays a key role in DW dynamics [9][10][11][12], and leads to the stabilization of isolated chiral skyrmions [13][14][15][16]. It may also cause the formation of noncollinear magnetic states [7,17] such as spin spirals [18,19] and condensated skyrmionic phases [16,[20][21][22][23][24]. Furthermore, the DM interaction induces an asymmetry in the spin wave spectrum of thin ferromagnetic films [25,26]. Based on this asymmetry, recently extensive experimental efforts have been directed towards the measurement of the interfacial DM interaction by using inelastic light scattering [27][28][29], highly resolved spinpolarized electron energy loss [30] or propagating spin wave spectroscopy [31].The current-driven motion of domain walls is mainly investigated in ultrathin films and multilayers, paving the way for future applications in spintronic and logic devices [32,33]. In these systems, heavy nonmagnetic elements provide the strong spin-orbit coupling necessary for the appearance of the DM interaction in the adjacent magnetic layers. Using the micromagnetic energy functional determined by Dzyaloshinskii[34], it has been demonstrated [3,35,36] that the DM interaction prefers a cycloidal or Néel-type rotation of spins within a domain wall in the C nv symmetry class to which the majority of these systems belong. The rotational plane of domain walls is determined by the competition between the DM interaction and the magnetostatic dipolar interaction preferring a h...

Magnetism of a Co monolayer on Pt(111) capped by overlayers of 5d elements: A spin-model study

“…As an example, in Table I we present the comparison between DMI values obtained for the Co monolayer on Pt(111) without a capping layer using different ab initio calculation methods in Refs. [12,22,31,43], similarly to the summary given in Ref. [45].…”

Magnetic structure of monatomic Fe chains on Re(0001): Emergence of chiral multispin interactions

“…[9] how Heisenberg exchange interactions between pairs of spins may be determined based on the derivatives of the energy, that is, the torque acting on * laszloffy@phy.bme.hu the spin directions. The torque method has been generalized to tensorial two-spin interactions appearing in the presence of spin-orbit coupling [10,11], and it was validated for various systems over the last decade [12][13][14]. A fully real-space calculation of the interactions in a magnetic cluster is presented in Ref.…”

Spin-spiral formalism based on the multiple-scattering Green's function technique with applications to ultrathin magnetic films and multilayers

“…Due to the large ferromagnetic isotropic coupling, the energy gain from the formation of spin-spiral states is negligible and the easyaxis MAE of 0.57 meV (see in Ref. [35] ) clearly stabilizes an out-of-plane ferromagnetic ground state. Table III.…”

“…The interactions derived from the RTM were previously reported in Ref. [35] for hcp stacking of the Co monolayer. For comparison, the corresponding values for J 1 and J 2 , as well as for the effective and micromagnetic parameters are also presented in Table II.…”

“…We also derived these parameters based on the previously reported in-plane DM interactions calculated in terms of the RTM [35] and summarized them in Table III. Most likely again due to the strong interaction between the Co and Pt moments, the effective DM parameters turned out to be by about 50 % larger in case of the spin-spiral calculations as compared to the torque method and in both calculations the rotational direction of the DM vectors is left-handed (counterclockwise) in agreement with other theoretical results [23,34,35,53]. Due to the large ferromagnetic isotropic coupling, the energy gain from the formation of spin-spiral states is negligible and the easyaxis MAE of 0.57 meV (see in Ref.…”