Role of Single-Ion Anisotropy in Stabilizing Higher-Order Skyrmion Crystals in D3d-Symmetric Magnets

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

Zero-field skyrmion, meron, and vortex crystals in centrosymmetric hexagonal magnets

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 noncoplanar triple-$Q$ state regarded as a skyrmion crystal with topological number of two, and coplanar and noncoplanar double-$Q$ states. In an external magnetic field, we find that another noncoplanar triple-$Q$ state, 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. A part of the results, especially for the relatively large biquadratic interaction, qualitatively reproduce those in the Kondo lattice model, which explicitly includes itinerant electrons [S. Hayami and Y. Motome, Phys. Rev. B 99, 094420 (2019)]. We also examine the stability of the field-induced skyrmion crystal by rotating the field direction. As a by-product, we show that a different 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 N\'eel-type skyrmion crystals are selectively realized depending on the sign of the bond-dependent anisotropy, since this anisotropy selects a particular set of the helicity and vorticity. Moreover, we find yet another multiple-$Q$ states with nonzero spin scalar chirality, including two types of meron crystals with the skyrmion numbers of one and two. The systematic investigation of multiple-$Q$ instabilities in triangular itinerant magnets will provide a reference to complex magnetic textures in centrosymmetric magnetic metals.

We report our numerical results for the effect of magnetic anisotropy on a Skyrmion crystal with a high topological number of two, which was recently discovered in an itinerant electron model [R. Ozawa, S. Hayami, and Y. Motome, Phys. Rev. Lett. 118, 147205 (2017)]. By performing numerical simulations based on the kernel polynomial method and the Langevin dynamics for the Kondo lattice model on a triangular lattice, we find that the topological property remains robust against the single-ion anisotropy, while the magnetic texture is deformed continuously. The resultant spin structure is characterized by three wave numbers (triple-$Q$ state), in which the $xy$ component of spins forms a magnetic vortex crystal and the $z$ component of spins behaves a sinusoidal wave. For larger anisotropy, we show that the system exhibits a phase transition from the Skyrmion crystal to topologically trivial phases with vanishing scalar chirality: a single-$Q$ collinear and double-$Q$ noncoplanar states for the easy-axis and easy-plane anisotropy, respectively. We also examine the effect of the single-ion anisotropy in an external magnetic field, and find that the field range of the Skyrmion crystal is rather insensitive to the anisotropy, in contrast to another Skyrmion crystal with the topological number of one whose field range is considerably extended (reduced) by the easy-axis (easy-plane) anisotropy.

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.

Reentrant behaviors in the phase diagram of spin-1 planar ferromagnets with easy-axis single-ion anisotropy via the Devlin two-time Green function framework

A Magnetic Circular Dichroism (MCD) spectroscopic study of the antiferromagnetic ring [Cr₈F₈Piv₁₆] (Piv = pivalate) is reported. From the splitting of the MCD bands, the single ion anisotropy parameters in the cluster spin ground state at different fields were determined to be d(Cr) = -0.33 ± 0.02 cm⁻¹, e(Cr) = 0.11 ± 0.01 cm⁻¹. Analysis of the MCD intensity as a function of field and temperature revealed the influence of spin mixing effects and yielded independent estimates of the single ion anisotropies (d(Cr) = -0.19 cm⁻¹, e(Cr) = 4.3 × 10-4 cm⁻¹), as well as yielding the isotropic exchange interaction strength (J = -6.00 cm⁻¹). Thus it is shown that MCD is a powerful method to unravel the relation between single-ion and cluster anisotropy, furthering the design of molecular magnets with desired properties.

Topological spin textures, such as a skyrmion crystal, are a source of unusual physical phenomena owing to the interplay between magnetism and topology. Since physical phenomena depend on the topological property and the symmetry of underlying spin structures, the search for new topological spin textures and emergent phenomena is one of the challenges in condensed matter physics. In this letter, we theoretically explore new topological spin textures arising from the synergy between spin, charge, and sublattice degrees of freedom in an itinerant magnet. By performing simulated annealing for an effective spin model of the honeycomb Kondo lattice model, we find a plethora of skyrmion crystal instabilities at low temperatures, whose topological spin textures are classified into three types: ferrochiral, antiferrochiral, and ferrichiral skyrmion crystals. We show that the obtained skyrmion crystals are the consequence of the spin-orbit-coupling-free honeycomb structure. Our results reveal the potential for itinerant honeycomb magnets to host a wide variety of SkXs and emergent phenomena.

We theoretically study a stabilization mechanism of the skyrmion crystal in centrosymmetric magnets with a bilayer structure. We show that the interplay between a layer-dependent staggered Dzyaloshinskii-Moriya interaction that arises from the absence of local inversion symmetry and the interlayer exchange interaction gives rise to a plethora of multiple-$Q$ states including the skyrmion crystal with a quantized topological number. By performing the simulated annealing for the bilayer triangular-lattice model under an external magnetic field, we demonstrate that the skyrmion forms the triangular-shaped crystals with different helicities in each layer owing to the staggered Dzyaloshinskii-Moriya interaction. Although the relative positions of the skyrmion core in each layer are different depending on the sign of the interlayer exchange interactions, the skyrmion crystal phases robustly appear under both ferromagnetic and antiferromagnetic interlayer interactions. We also find another two triple-$Q$ states with a uniform scalar chirality but without a quantized topological number in the low- and high-field regions. Especially, the low-field triple-$Q$ state exhibits the opposite sign of the scalar chirality to the skyrmion crystal, which is not found in the single-layer system. Our results indicate that the lack of local inversion symmetry in the lattice structure is another key ingredient to induce topological spin textures in centrosymmetric magnets.

Multiple-[formula omitted] instability under fourth-order inplane single-ion anisotropy

The effect of the biquadratic exchange interaction on the phase diagram of a d-dimensional spin-1 transverse XY model with easy-axis single-ion anisotropy is studied by employing the Devlin-like two-time Green functions framework. The chain of equations of motion is closed adopting the random phase approximation for the exchange higher order Green functions and treating exactly the crystal-field anisotropy terms. For short-range interactions and d > 2, analytical estimates and numerical calculations predict a reentrant behavior of the critical lines close to the magnetic-field-induced quantum critical point for appropriate values of the single-ion anisotropy parameter and suitable combinations of the bilinear and biquadratic exchange couplings. Remarkably, increasing the biquadratic exchange reduces or destroies the reentrant character of the quantum critical lines, in qualitative agreement with the findings of the Anderson-Callen-like strategy. In our formalism, the easy-plane anisotropy case can be studied similarly but the phase diagram and the quantum critical scenario do not present any reentrant phenomena.

The magnetic properties of three-dimensional spin-1 easy-axis single-ion anisotropic antiferromagnets

Effect of biquadratic exchange on the phase diagram of a spin-1 transverse XY model with single-ion anisotropy

For the first time high-temperature series for the susceptibility and heat capacity have been employed to analyze data on ferromagnetic systems with single-ion anisotropy comparable with or greater than the pair interactions between ions. The salts $\mathrm{Ni}M{\mathrm{F}}_{6}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O with $M=\mathrm{S}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{n},\phantom{\rule{0ex}{0ex}}\mathrm{Z}\mathrm{r}$ are spin-one ferromagnetic systems. Each has an easy-axis single-ion anisotropy and long-range dipole-dipole interaction in addition to the more commonly discussed short-range exchange interactions. We show that the same set of interaction parameters can fit simultaneously and quantitatively both susceptibility and heat-capacity data. We also discuss the unusually small deviations of the data from the mean-field predictions for the three large single-ion anisotropy systems ($M=\mathrm{Z}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{T}\mathrm{i},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{n}$).

Reentrant phenomena in a three-dimensional spin-1 planar ferromagnet with easy-axis single-ion anisotropy