Skyrmion crystals in centrosymmetric itinerant magnets without horizontal mirror plane

Abstract

We theoretically investigate a new stabilization mechanism of a skyrmion crystal (SkX) in centrosymmetric itinerant magnets with magnetic anisotropy. By considering a trigonal crystal system without the horizontal mirror plane, we derive an effective spin model with an anisotropic Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction for a multi-band periodic Anderson model. We find that the anisotropic RKKY interaction gives rise to two distinct SkXs with different skyrmion numbers of one and two depending on a magnetic field. We also clarify that a phase arising from the multiple-Q spin density waves becomes a control parameter for a field-induced topological phase transition between the SkXs. The mechanism will be useful not only for understanding the SkXs, such as that in Gd$$_2$$ 2 PdSi$$_3$$ 3 , but also for exploring further skyrmion-hosting materials in trigonal itinerant magnets.

Magnetic field-temperature phase diagrams for multiple-$Q$ magnetic orderings: Exact steepest descent approach to long-range interacting spin systems

“…It can be applied to a generic form of the Hamiltonian, which includes not only two-spin but also multiple-spin interactions with any anisotropy. In recent years, several variations of such effective spin models have been studied for understanding of multiple-Q magnetic orderings in many materials, e.g., the skyrmion lattices in Gd 2 PdSi 3 [85], GdRu 2 Si 2 [73,74,86], Gd 3 Ru 4 Al 12 [78], and EuPtSi [76], and the hedgehog lattices in MnSi 1−x Ge x [62][63][64]. Our framework would be useful to clarify the complete phase diagrams and the nature of the transitions between different multiple-Q phases in a high resolution.…”

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

“…In addition, the multiple-Q spin configuration in Eq. ( 1) can describe other periodic topological spin textures, such as a hedgehog lattice [40][41][42][43][44][45][46], meron-antimeron crystal [47][48][49][50][51][52][53][54][55], and vortex crystal [56][57][58][59][60][61][62].…”

“…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.…”

“…As an example, we demonstrate how to construct the effective spin model in tetragonal, hexagonal, and trigonal crystal systems by applying the rules to 24 gray space groups. Next, we show one of the microscopic origins of the long-range anisotropic exchange interactions by starting from the periodic Anderson model (PAM) incorporating the effect of the SOC [61,96,97]. We present important microscopic model parameters for the anisotropic exchange interactions based on the perturbation analysis.…”

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

“…Although the long-range nature of the interaction like the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction [81,82,83] in itinerant magnets is different from the short-range one in frustrated insulating magnets, an effective multi-spin interaction arising from the Fermi surface instability gives rise to the groundstate SkX even without the DM interaction [78]. Similar to the frustrated magnets, it was shown that the effect of single-ion anisotropy [84,85,86,87], two-ion anisotropy [88,89,90,91,92,93], circularly polarized microwave field [94], and thermal fluctuations [95,96] enhance the stability of the SkX. It was also shown that the introduction of the DM or antisymmetric spin-orbit interaction in itinerant magnets leads to the SkX formation [43,97,98,99,100].…”