Interplay between Single-Ion and Two-Ion Anisotropies in Frustrated 2D Semiconductors and Tuning of Magnetic Structures Topology

Abstract

The effects of competing magnetic interactions in stabilizing different spin configurations are drawing renewed attention in order to unveil emerging topological spin textures and to highlight microscopic mechanisms leading to their stabilization. The possible key role of the two-site exchange anisotropy in selecting specific helicity and vorticity of skyrmionic lattices has only recently been proposed. In this work, we explore the phase diagram of a frustrated localized magnet characterized by a two-dimensional centrosymmetric triangular lattice, focusing on the interplay between the two-ion anisotropy and the single-ion anisotropy. The effects of an external magnetic field applied perpendicularly to the magnetic layer, are also investigated. By means of Monte Carlo simulations, we find an abundance of different spin configurations, going from trivial to high-order Q skyrmionic and meronic lattices. In closer detail, we find that a dominant role is played by the two-ion over the single-ion anisotropy in determining the planar spin texture; the strength and the sign of single ion anisotropy, together with the magnitude of the magnetic field, tune the perpendicular spin components, mostly affecting the polarity (and, in turn, the topology) of the spin texture. Our analysis confirms the crucial role of the anisotropic symmetric exchange in systems with dominant short-range interactions; at the same time, we predict a rich variety of complex magnetic textures, which may arise from a fine tuning of competing anisotropic mechanisms.

Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry

“…This bond-dependent interaction often plays a similar role to the dipole-dipole interaction in the stabilization of the SkXs [87,88]. Besides, bond-dependent anisotropic exchange interaction originating from the breaking of the horizontal mirror symmetry also leads to the SkXs in the trigonal system [84,86,89]. More recently, it was shown that the staggered DM interaction that originates form the breaking of the local inversion symmetry becomes the origin of the SkX in centrosymmetric magnets [90,91].…”

“…Although the form of the spin interactions depends on a way of breakings of the lattice symmetry, such an effect can appear in any discrete lattice systems via the spin-orbit coupling. For instance, the bond-dependent anisotropic exchange interaction owing to the discrete rotational symmetry gives rise to the square-shaped SkXs in the tetragonal system [80][81][82][83] and the triangular-shaped SkXs in the hexagonal system [84][85][86]. This bond-dependent interaction often plays a similar role to the dipole-dipole interaction in the stabilization of the SkXs [87,88].…”

“…In addition, magnetic anisotropy plays an important role in lifting the degeneracy between the helicity and the vorticity of the centorsymmetric SkXs. For example, the bond-dependent anisotropic interaction in the hexagonal systems lifts the degeneracy between the Néel, Bloch, and anti SkXs [84][85][86]. Similarly, their degeneracy is lifted in the tetragonal [80][81][82]93] and trigonal systems [84,86,89].…”

Effective spin model in momentum space: Toward a systematic understanding of multiple-$Q$ instability by momentum-resolved anisotropic exchange interactions

“…In contrast to the early studies based on the antisymmetric DM interaction, recent discoveries of SkX and hedgehog lattices in centrosymmetric magnets [14,15,18,28] open up the possibility that various multiple-Q states can emerge by symmetric anisotropic exchange interactions. In fact, some model calculations have clarified that such a symmetric anisotropic exchange interaction stabilizes the multiple-Q states including the SkXs in centrosymmetric crystals with the space group P 4/mmm [51,52,88,89] P 6/mmm [54,[90][91][92], and P 3m1 [61,85,93]. However, there have been few studies focusing on the symmetric anisotropic exchange interactions in spite of various types of them depending on the crystal symmetry classified by the space group.…”

Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy

“…The pioneering work by Okubo, Chung, and Kawamura has clarified that the SkX appears at finite temperatures in the triangular-lattice Heisenberg model with the competing ferromagnetic and antiferromagnetic exchange interactions but without the DM interaction [65]. Then, the ground-state SkX has been clarified by additionally taking into account the uniaxial single-ion anisotropy [66,67,68,69,70], two-ion magnetic anisotropy [71,72,73], dipolar interaction [74,75] and nonmagnetic impurity [76]. Furthermore, another mechanism to stabilize the SkX has been established based on the spin-charge coupling in itinerant magnets [77,78,6,79,80].…”