Field-Direction Sensitive Skyrmion Crystals in Cubic Chiral Systems: Implication to 4f-Electron Compound EuPtSi

Abstract

We investigate the instability toward a skyrmion crystal (SkX) in noncentrosymmetric cubic magnets with an emphasis on a comparison between point groups (O, T ) and T d . By constructing low-temperature magnetic phase diagrams under an external magnetic field for three directions based on numerically simulated annealing, we find that the system under the point group (O, T ) exhibits different two types of SkXs depending on the field direction, while that under T d does not show such an instability. The difference between them is understood from the difference in the momentum-dependent Dzyaloshinskii-Moriya interaction under each point group. Meanwhile, we show that the system under T d leads to the SkX instability by considering an additional effect of the uniaxial strain, which lowers the symmetry to D 2d . We obtain two different SkXs: Néel-type and anti-type SkXs, the former of which is stabilized in the presence of the interactions at the threedimensional ordering wave vectors. The present results provide rich topological spin textures in the three-dimensional systems, which are sensitive to the magnetic-field direction and point-group symmetry.

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

“…In addition, the model can be extended to include higher-order contributions. For instance, the four-spin biquadratic interactions ∝ (S Qη •S −Qη ) 2 [49,50,58,63,[72][73][74][75][76][77][78][79] and the six-spin bicubic interactions ∝ {S Q1 • (S Q2 × S Q3 )} 2 [61] have also been considered as the origin of stabilization of multiple-Q magnetic orderings.…”

“…In this case, J Qη in the two-spin interaction part does not have to be positive definite. Furthermore, Method II can deal with the generic form of the Hamiltonian expressed by a function of S α Qη , including multiple-spin interactions, such as the biquadratic ones 50,58,63,[72][73][74][75][76][77][78][79] and the bicubic ones…”

“…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.…”

Complex magnetic phase diagram in noncentrosymmetric EuPtAs

“…Subsequently, a series of additional compounds with the B20 structure have also been identified to host magnetic skyrmions, such as Fe 1−x Co x Si [7,8], FeGe [9,10], and Cu 2 OSeO 3 [11,12]. Recently EuPtSi, which also crystallizes in a chiral cubic structure (LaIrSi-type, space group P2 1 3) [13], was shown to be an unusual example of an f -electron system hosting magnetic skyrmions [14][15][16], where the size of a single skyrmion for H [111] is only 18 Å, 10 times smaller than those in MnSi [17]. In addition to these compounds with chiral structures, it was found that compounds with a noncentrosymmetric polar structure are also promising candidates for realizing skyrmions, such as GaV 4 S 8 with a lacunar spinel structure [18], which hosts a Néel-type skyrmion phase.…”

Antiskyrmions and Bloch Skyrmions in Magnetic Dresselhaus Metals

“…On the other hand, antiskyrmions have been observed in bulk materials [15][16][17] but not in thin films. While the early theoretical understanding of these textures was largely based on phenomenological magnetic models, recent years have witnessed efforts towards a microscopic electronic description of these topological textures [18][19][20][21][22][23]. Most of these recent studies focus on identifying the correct electronic model to stabilize one specific type of magnetic textures, such as, Neel-or Bloch-skyrmions or antiskyrmions.…”