Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy

Abstract

We theoretically investigate multiple-$Q$ spin textures, which are composed of superpositions of spin density waves with different wave numbers, for an effective spin model of centrosymmetric itinerant magnets. Our focus is on the interplay between biquadratic interactions arising from the spin-charge coupling and magnetic anisotropy caused by the spin-orbit coupling. Taking into account two types of the magnetic anisotropy, single-ion anisotropy and bond-dependent anisotropy, we elucidate magnetic phase diagrams for an archetypal triangular-lattice system in the absence and presence of an external magnetic field. In the case of the single-ion anisotropy, we find a plethora of multiple-$Q$ instabilities depending on the strength and the sign of the anisotropy (easy plane or easy axis), including a skyrmion crystal with topological number of two. In an external magnetic field, we find that a skyrmion crystal with topological number of one is stabilized by the in-plane (out-of-plane) magnetic field under the easy-plane (easy-axis) anisotropy. We also examine the stability of the field-induced skyrmion crystal by rotating the field direction. As a biproduct, we show that a triple-$Q$ state with nonzero chirality appears in the presence of the biquadratic interaction and the easy-axis anisotropy. Meanwhile, we find that the bond-dependent anisotropy also stabilizes both types of skyrmion crystals. We show that, however, for the skyrmion crystal with topological number of one, Bloch- and Néel-type skyrmion crystals are selectively realized depending on the sign of the bond-dependent anisotropy. Moreover, we find yet another multiple-$Q$ states, including two types of meron crystals with the skyrmion numbers of one and two. The systematic investigation will provide a reference to complex magnetic textures in centrosymmetric magnetic metals.

38 pages, 51 figures

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• Skyrmion crystal and spiral phases in centrosymmetric bilayer magnets with staggered Dzyaloshinskii-Moriya interaction
• Helicity locking of square skyrmion crystal in a centrosymmetric lattice system without vertical mirror symmetry
• Mechanism of antisymmetric spin polarization in centrosymmetric multiple-$Q$ magnets based on bilinear and biquadratic spin cross products
• Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems
• Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet
• Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy
• Charge density waves in multiple-$Q$ spin states
• Anisotropic magnetic interactions in hexagonal AB-stacked kagome lattice structures: Applications to ${\mathrm{Mn}}_3\mathrm{X}$ ($\mathrm{X}$ = $\mathrm{Ge}$, $\mathrm{Sn}$, $\mathrm{Ga}$) compounds
• Ferroaxial moment induced by vortex spin texture
• Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets
• Anisotropic spin model and multiple-$Q$ states in cubic systems
• Hybrid skyrmion and anti-skyrmion phases in polar $C_{4v}$ systems
• Magnetic interactions in AB-stacked kagome lattices: magnetic structure, symmetry, and duality
• Engineering a skyrmion crystal in ferromagnetic/antiferromagnetic bilayers free from the DM interaction
• Tuning of magnetic structures topology via single-ion anisotropy and magnetic field in frustrated 2D semiconductors
• Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice