Search Results (27)

Long-range topological objects can exist in many physical systems, and they can tunnel through very wide barriers. Thus, the propagation of long-range kink-like objects through disordered media can be extremely enhanced. When the potential is asymmetric, the long-range kink-like excitations can enter a regime of superpropagation, where, essentially, they can move through almost any disordered medium. We believe these phenomena can find applications in macroscopic quantum technologies (including robust qubits), energy devices for energy harvesting and storage, and high-$T_c$ superconductivity in hydrides. We expect that many of these results can be generalized to other topological objects, e.g., fluxons, domain walls, skyrmions, topological defects, stripes, textures, dislocations in crystals, strings, monopoles, instantons, vortices, and spiral waves. Full article

We theoretically investigate the influence of uniaxial distortion on the stability of square skyrmion crystals, which are described as double-Q spin textures composed of two orthogonal spiral modulations, in noncentrosymmetric magnets. An effective spin model incorporating momentum-resolved frustrated exchange interactions and Dzyaloshinskii–Moriya (DM) interactions is analyzed using simulated-annealing calculations at low temperatures. The results reveal that uniaxial distortion drives a transformation from the double-Q square skyrmion crystal to a single-Q tilted conical spiral or vertical spiral state. The low-temperature phase diagrams further show that the stability region of the skyrmion crystal expands with increasing the magnitude of the DM interaction, making the phase more robust against the uniaxial anisotropy between exchange interactions parallel and perpendicular to the distortion axis. This study provides insight into how uniaxial strain and DM interactions cooperatively influence the formation and stability of skyrmion crystal phases in noncentrosymmetric magnetic systems. Full article

We investigate the role of single-ion anisotropy in stabilizing higher-order skyrmion crystal phases in centrosymmetric magnets under D_3d symmetry. Using a classical spin model that incorporates both a local single-ion anisotropy arising from the two-dimensional crystal symmetry and a D_3d-type magnetic anisotropy originating from the D_3d point-group symmetry, we perform simulated annealing calculations to explore the ground-state spin configurations. We find that a skyrmion crystal with a skyrmion number of two is stabilized over a wide range of parameters of single-ion anisotropy and D_3d-type anisotropy. We also show that the skyrmion core position shifts from an interstitial site to an on-site location as the magnitude of the easy-axis single-ion anisotropy increases. Furthermore, we demonstrate that the magnetic field drives a variety of topological phase transitions depending on the sign and magnitude of the single-ion and D_3d-type anisotropies. These results provide a possible microscopic understanding of how complex topological spin textures can be stabilized in centrosymmetric D_3d magnets, suggesting that multiple phases with topological spin textures could emerge even in the absence of the Dzyaloshinskii–Moriya interaction. Full article

We theoretically investigate multiple-Q instabilities in centrosymmetric hexagonal magnets, formulated as superpositions of independent six ordering wave vectors related by sixfold rotational and mirror symmetries. By employing a spin model that incorporates biquadratic interactions and an external magnetic field, we establish a comprehensive low-temperature phase diagram hosting single-Q, double-Q, triple-Q, and sextuple-Q states, as well as skyrmion crystals with topological charges of one and two. The field evolution of the magnetization, scalar spin chirality, and finite wave-vector magnetic amplitudes reveals a hierarchical buildup of multiple-Q order, accompanied by first-order transitions between topologically distinct and trivial phases. At large biquadratic coupling, all six symmetry-related ordering wave vectors coherently participate, giving rise to two sextuple-Q states under magnetic fields and to another spontaneous sextuple-Q state even at zero field. The latter zero-field sextuple-Q state represents a fully developed sixfold interference pattern stabilized solely by the biquadratic interaction, characterized by alternating skyrmion- and antiskyrmion-like cores with vanishing uniform scalar spin chirality. These findings establish a unified framework for understanding hierarchical multiple-Q ordering and demonstrate that the interplay between bilinear and biquadratic interactions under hexagonal symmetry provides a generic route to complex noncoplanar magnetism in centrosymmetric itinerant systems. Full article

We investigate the stability of higher-order skyrmion crystals with large topological charges in the presence of crystal-dependent magnetic anisotropies. Focusing on the competition between two types of bond-dependent anisotropy allowed by $D_{3\mathrm{d}}$ crystalline symmetry on a two-dimensional triangular lattice, we systematically construct a low-temperature magnetic phase diagram using simulated annealing. Our analysis reveals that the stability of the higher-order skyrmion crystal with skyrmion number of two is strongly controlled by the relative sign of the bond-dependent anisotropy to the $D_{3\mathrm{d}}$-type anisotropy: a positive anisotropy, which favors spin oscillations perpendicular to the ordering wave vector, enhances its stability, whereas a negative anisotropy, favoring oscillations parallel to the ordering wave vector, suppresses it and instead stabilizes a topologically trivial double-Q state. We further examine the field evolution of these phases under an out-of-plane magnetic field and show that distinct types of skyrmion crystals with the skyrmion number of one emerge in the intermediate-field regime. These results highlight that the competition between different magnetic anisotropies in crystalline systems is a key factor governing the stability of both zero-field and field-induced skyrmion crystals. Full article

We theoretically investigate the stability of double-Q square skyrmion crystals under uniaxial distortion. Using an effective spin model with frustrated exchange interactions and bond-dependent anisotropy in momentum space, we construct the low-temperature magnetic phase diagram via simulated annealing. Our results reveal that uniaxial distortion drives a phase transition from the skyrmion crystal to a single-Q conical spiral state when the ratio of exchange interactions parallel and perpendicular to the uniaxial axis is reduced to about 95%. We further find that topologically trivial double-Q states, which emerge in the low- and high-field regimes, are more robust against uniaxial distortion than the skyrmion crystal appearing in the intermediate-field regime. Finally, we examine the role of bond-dependent anisotropy and demonstrate that a finite relative magnitude of this anisotropy is crucial for stabilizing the skyrmion crystal, even under uniaxial distortion. These findings highlight the delicate interplay between lattice distortions and bond-dependent interactions in determining the stability of multiple-Q magnetic textures, and they provide useful guidance for experimental efforts to manipulate skyrmion crystal phases in centrosymmetric magnets. Full article

Multiple-Q magnetic states encompass a broad class of noncollinear and noncoplanar spin textures generated by the superposition of spin density waves. In this study, we theoretically explore the emergence of vortex crystals formed by multiple-Q spin density waves on a two-dimensional triangular lattice with $D_{3\mathrm{h}}$ point group symmetry. Using simulated annealing applied to an effective spin model, we demonstrate that the synergy among the easy-plane single-ion anisotropy, the biquadratic interaction, and the out-of-plane Dzyaloshinsky–Moriya interaction defined in momentum space can give rise to a variety of double-Q and triple-Q vortex crystals. We further examine the role of easy-plane single-ion anisotropy in triple-Q vortex crystals and show that weakening the anisotropy drives topological transitions into skyrmion crystals with skyrmion numbers $\pm 1$ and $\pm 2$. The influence of an external magnetic field is also analyzed, revealing a field-induced phase transition from vortex crystals to single-Q conical spirals. These findings highlight the crucial role of out-of-plane Dzyaloshinskii–Moriya interactions in stabilizing unconventional vortex crystals, which cannot be realized in systems with purely polar or chiral symmetries. Full article

The ferroaxial moment, a time-reversal-even axial dipole degree of freedom, plays a key role not only in conventional quantum states of matter but also in anomalous off-diagonal cross-correlated responses. Here, we theoretically demonstrate that a skyrmion crystal with a swirling non-coplanar spin texture can exhibit ferroaxiality. In particular, we show that a hybrid skyrmion crystal, formed by the superposition of Néel- and Bloch-type vortices, hosts a finite ferroaxial moment. The degree of ferroaxiality is quantified by calculating the expectation value of the electric toroidal dipole within a multi-orbital tight-binding model based on multipole representation theory. We further reveal characteristic off-diagonal responses associated with magnetic and magnetic toroidal multipoles under external magnetic fields. These results establish the hybrid skyrmion crystal as a promising platform for exploring the fundamental nature of ferroaxial moments. Full article

We numerically investigate the effect of multi-spin interactions on the stability of skyrmion crystals and other multiple-Q magnetic states, with a particular emphasis on the momentum-resolved bicubic interaction. By performing simulated annealing for an effective spin model that incorporates bilinear, biquadratic, and bicubic interactions on a two-dimensional triangular lattice, we construct the corresponding low-temperature phase diagram. Our results reveal that a positive bicubic interaction stabilizes a skyrmion crystal with a skyrmion number of two, whereas a negative bicubic interaction favors a single-Q spiral state. Moreover, we demonstrate that the stability region of the field-induced skyrmion crystal with the skyrmion number of one is largely enlarged in the presence of a positive bicubic interaction. Full article

We investigate the role of high-harmonic wave-vector interactions, which affect the stability of the single-Q spiral state and often result in the formation of multiple-Q states. By performing simulated annealing for an effective spin model on a two-dimensional square lattice, we examine the modulation of the single-Q spiral spin configuration by the high-harmonic wave-vector interaction. As a result, we find that the interactions at particular high-harmonic wave vectors affect the stability of the single-Q spiral state. In particular, the incorporation of interactions at high-harmonic wave vectors formed by the sum of two mutually perpendicular ordering wave vectors can lead to the emergence of three double-Q states and a square skyrmion crystal. The present study unveils the importance of high-harmonic wave-vector interactions in order to realize complicated noncoplanar spin textures. Full article

We conduct a numerical investigation into the stability of a quadruple-Q skyrmion crystal, a structure generated by the superposition of four spin density waves traveling in distinct directions within three-dimensional space, hosted on a centrosymmetric body-centered tetragonal lattice. Using simulated annealing applied to an effective spin model that includes momentum-resolved bilinear and biquadratic interactions, we construct a magnetic phase diagram spanning a broad range of model parameters. Our study finds that a quadruple-Q skyrmion crystal does not emerge within the phase diagram when varying the biquadratic interaction and external magnetic field. Instead, three distinct quadruple-Q states with topologically trivial spin textures are stabilized. However, we demonstrate that the quadruple-Q skyrmion crystal can become the ground state when an additional high-harmonic wave–vector interaction is considered. Depending on the magnitude of this interaction, we obtain two types of quadruple-Q skyrmion crystals exhibiting the skyrmion numbers of one and two. These findings highlight the emergence of diverse three-dimensional multiple-Q spin states in centrosymmetric body-centered tetragonal magnets. Full article

I revisit the well-known phase transition between the hexagonal skyrmion lattice and the homogeneous state within the phenomenological Dzyaloshinskii theory for chiral magnets, which includes only the exchange, Dzyaloshinskii–Moriya, and Zeeman energy contributions. I show that, in a narrow field range near the saturation field, the hexagonal skyrmion order gradually transforms into a square arrangement of skyrmions. Then, by the second-order phase transition during which the lattice period diverges, the square skyrmion lattice releases a set of repulsive isolated skyrmions. On decreasing the magnetic field, isolated skyrmions re-condense into the square lattice at the same critical field as soon as their eigen-energy becomes negative with respect to the field-aligned state. The underlying reason for the reorientation transition between two skyrmion orders can be deduced from the energy density distribution within isolated skyrmions surrounded by the homogeneous state. When the negative energy within the ring-shaped area at the skyrmion outskirt outweighs the positive energy amount around the skyrmion axis, skyrmions tend to form the square lattice, in which the overlap of skyrmion profiles results in smaller energy losses as compared with the hexagonal crystal. With the further decreasing field, the hexagonal lattice achieves smaller energy density in comparison with the square one due to the denser packing of individual skyrmions. Full article

We investigate the stability tendency of a magnetic skyrmion crystal in noncentrosymmetric tetragonal systems with the Dzyaloshinskii–Moriya interaction. We show that the stability region of the square skyrmion crystal on a square lattice depends on the Ising-type magnetic anisotropic interaction by performing the simulated annealing for the spin model. The easy-axis anisotropic interaction tends to narrow the region where the square skyrmion crystal is stabilized when the magnetic field is applied in the out-of-plane direction. In contrast, the easy-plane anisotropic interaction tends to enlarge the stability region. Meanwhile, the square skyrmion crystal induced by the easy-axis anisotropic interaction is robust compared with that induced by the easy-plane anisotropic interaction when the magnetic field is tilted from the out-of-plane to the in-plane direction. The results indicate that the instability toward the square skyrmion crystal in noncentrosymmetric crystals is sensitive to both magnetic anisotropy and magnetic fields. Full article

Non-coplanar spin textures such as magnetic vortices and skyrmions manifest themselves in unusual physical phenomena owing to their topologically nontrivial properties. Here, we investigate emergent multipole moments under vortex and skyrmion crystals in the centrosymmetric tetragonal system. Depending on the vorticity and helicity of the vortex or skyrmion, various multipole moments, including magnetic toroidal and electric toroidal multipoles, are induced on the atomic scale. In particular, the vortex and skyrmion spin textures consisting of multiple spin density waves give rise to density waves in terms of other multipole moments. Our results reveal a close relationship between non-coplanar multiple-Q spin textures and multipole moments. Full article

In this study, we investigate the stability of a magnetic skyrmion crystal with short-period magnetic modulations in a centrosymmetric body-centered tetragonal system. By performing the simulated annealing for the spin model, incorporating the effects of the biquadratic interaction and high-harmonic wave–vector interaction in momentum space, we find that the double-Q square skyrmion crystal consisting of two spin density waves is stabilized in an external magnetic field. We also show that double-Q states appear in both low- and high-field regions; the low-field spin configuration is characterized by an anisotropic double-Q modulation consisting of a superposition of the spiral wave and sinusoidal wave, while the high-field spin configuration is characterized by an isotropic double-Q modulation consisting of a superposition of two sinusoidal waves. Furthermore, we show that the obtained multiple-Q instabilities can be realized for various ordering wave vectors. The results provide the possibility of realizing the short-period skyrmion crystals under the body-centered tetragonal lattice structure. Full article