The recent experimental confirmation of a transformation between meron and skyrmion topological spin textures in the chiral magnet Co$_8$Zn$_9$Mn$_3$ [S.-Z. Lin et al., Phys. Rev. B 91, 224407 (2015); X. Z. Yu et al., Nature 564, 95 (2018)] confirms that the skyrmion crystals discovered in 2009 [S. Mühlbauer et al., Science 323, 915 (2009)] are just the tip of the iceberg. Crystals of topological textures, including skyrmions, merons, vortices, and monopoles, can be stabilized by combining simple physical ingredients, such as lattice symmetry, frustration, and spin anisotropy. The current challenge is to find the combinations of these ingredients that produce specific topological spin textures. Here we report a simple mechanism for the stabilization of meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets. In particular, the meron/skyrmion crystals can form even in absence of magnetic field. The application of magnetic field leads to a rich variety of topological spin textures that survive in the long wavelength limit of the theory. When conduction electrons are coupled to the spins, these topological spin textures twist the electronic wave functions to induce Chern insulators and Weyl semimetals for specific band filling fractions.
Fe$_{5-x}$GeTe$_2$ is a centrosymmetric, layered van der Waals (vdW) ferromagnet that displays Curie temperatures $T_c$ (270-330 K) that are within the useful range for spintronic applications. However, little is known about the interplay between its topological spin textures (e.g., merons, skyrmions) with technologically relevant transport properties such as the topological Hall effect (THE), or topological thermal transport. Here, we show via high-resolution Lorentz transmission electron microscopy that merons and anti-meron pairs coexist with Néel skyrmions in Fe$_{5-x}$GeTe$_2$ over a wide…
A skyrmion crystal has internal degrees of freedom in terms of vorticity and helicity, which gives rise to fascinating types of skyrmion phases (Néel, Bloch, and anti-skyrmion). We show how the degeneracy lifting in tetragonal skyrmion crystals occurs in centrosymmetric itinerant magnets by focusing on microscopic interactions through the Fermi surface instability. We demonstrate that four types of skyrmion crystals can be realized according to the signs of the anisotropic Ruderman-Kittel-Kasuya-Yosida interaction, which are sensitive to band structures, electron fillings, atomic orbitals, and…
A skyrmion crystal (SkX) expressed as a multiple number of spiral modulations manifests itself not only in its peculiar magnetic texture but also in nontrivial transport properties originating from an emergent magnetic field. We here report our numerical results for multiple SkXs in a centrosymmetric tetragonal crystal system. By performing simulated annealing for an effective spin model for itinerant magnets, we find that three types of the SkXs with the skyrmion numbers of one and two, which are characterized by different superpositions of helices, are stabilized in the ground state, and are…
We investigate how to engineer an antisymmetric spin-split band structure under spin density waves with finite ordering wave vectors in centrosymmetric systems without the relativistic spin-orbit coupling. On the basis of a perturbative analysis for the spin-charge coupled model in centrosymmetric itinerant magnets, we show that nonzero chiral-type bilinear and biquadratic spin cross products in momentum space under the magnetic orderings are related to an antisymmetric spin polarization in the electronic band structure. We apply the derived formula to the single-$Q$ cycloidal spiral and doubl…
Interplay between itinerant electrons and localized spins in itinerant magnets gives rise to a variety of noncoplanar multiple-$Q$ spin textures, such as the skyrmion, hedgehog, meron, and vortex. We elucidate that another type of multiple-$Q$ state consisting of collinear sinusoidal waves, a magnetic bubble crystal, appears at finite temperatures in a centrosymmetric itinerant electron system. The results are obtained for the classical Kondo lattice model with easy-axis single-ion anisotropy on a triangular lattice by a large-scale numerical simulation. We find that a finite-temperature topol…
We have investigated the non-centrosymmetric tetragonal heavy-fermion compound CeAuAl3 using muon spin rotation (muSR), neutron diffraction (ND) and inelastic neutron scattering (INS) measurements. We have also revisited the magnetic, transport and thermal properties. The magnetic susceptibility reveals an antiferromagnetic transition at 1.1 K with a possibility of another magnetic transition near 0.18 K. The heat capacity shows a sharp lambda-type anomaly at 1.1 K in zero-filed, which broadens and moves to higher temperature in applied magnetic field. Our zero-field muSR and ND measurements c…
We examine static spin susceptibilities $χ_{αβ}({\bf q})$ of spin components $S_α$ and $S_β$ in the non-centrosymmetric tetragonal system. These show anomalous momentum dependences like $χ_{xx}({\bf q})-χ_{yy}({\bf q})\sim q_x^2-q_y^2$ and $χ_{xy}({\bf q})+χ_{yx}({\bf q})\sim q_x q_y$, which vanish in centrosymmetric systems. The magnitudes of the anomalous spin susceptibilities are enhanced by the on-site Coulomb interaction, especially, around an ordering wave vector. The significant and anomalous momentum dependences of these susceptibilities are explained by a group theoretical analysis. A…
PrRu$_4$Sn$_6$ is a tetragonal, non-centrosymmetric structure compound. It is isostructural to the extensively studied Kondo insulator CeRu$_4$Sn$_6$ which crystallizes in the YRu$_4$Sn$_6$-type structure with space group $I$\={4}2$m$. In this structure, the Pr atom fills the void formed by the octahedral Ru$_4$Sn$_6$ units which results in a tetragonal body-centred arrangement. Here we present reports on the physical and magnetic properties of PrRu$_4$Sn$_6$. The temperature dependences of specific heat, $C_p(T)$, electrical resistivity, $ρ(T)$, and magnetic susceptibility, $χ(T)$, reveal the…
We theoretically investigate the stability of a square skyrmion crystal (SkX) in a centrosymmetric tetragonal lattice structure with the emphasis on the role of the magnetic anisotropy arising from the absence of vertical mirror symmetry. Our analysis is based on an effective bilinear and biquadratic model in momentum space, which is a canonical model for itinerant magnets in a weak-coupling regime. By performing the simulated annealing for the model on the two-dimensional square lattice, we find that the off-diagonal spin component in the interaction, which becomes nonzero when the vertical m…
We studied the pressure-induced superconductor CeIrSi$_3$ with the non-centrosymmetric tetragonal structure under high pressure. The electrical resistivity and ac heat capacity were measured in the same run for the same sample. The critical pressure was determined to be $P_{\rm c}$ = 2.25 GPa, where the antiferromagnetic state disappears. The heat capacity $C_{\rm ac}$ shows both antiferromagnetic and superconducting transitions at pressures close to $P_{\rm c}$. On the other hand, the superconducting region is extended to high pressures of up to about 3.5 GPa, with the maximum transition temp…
We report the magnetic properties of two Eu based compounds, single crystalline EuIrGe$_3$ and EuRhGe$_3$, inferred from magnetisation, electrical transport, heat capacity and $^{151}$Eu Mössbauer spectroscopy. These previously known compounds crystallise in the non-centrosymmetric, tetragonal, $I4mm$, BaNiSn$_3$-type structure. Single crystals of EuIrGe$_3$ and EuRhGe$_3$ were grown using high temperature solution growth method using In as flux. EuIrGe$_3$ exhibits two magnetic orderings at $T_{\rm N1}$ = 12.4 K, and $T_{\rm N2}$ = 7.3 K. On the other hand EuRhGe$_3$ presents a single magneti…
Motivated by recent experimental results on GdRu$_2$Si$_2$ [Khanh, N.D., Nakajima, T., Yu, X. et al., \emph{Nat. Nanotechnol.} \textbf{15}, 444-449 (2020)], where nanometric square skyrmion lattice was observed, we propose simple analytical mean-field description of the high-temperature part of the phase diagram of centrosymmetric tetragonal frustrated antiferromagnets with dipolar interaction in the external magnetic field. In the reciprocal space dipolar forces provide momentum dependent biaxial anisotropy. It is shown that in tetragonal lattice in the large part of the Brillouin zone for mu…
Catalog of Altermagnetism in Magnetic Wallpaper/Space Groups and Nonsymmorphic Altermagnets
Hefei National Laboratory（合肥国家实验室）；School of Emerging Technology, University of Science and Technology of China（中国科学技术大学先进技术学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；Department of Physics and Center for Theoretical Physics, National Taiwan University（国立台湾大学物理系暨理论物理中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）
We report the observation of anomalous Hall resistivity in single crystals of EuAl$_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_\mathrm{N} \sim 15.6$ K and $T_\mathrm{CDW} \sim 140$ K, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, EuAl$_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear hump-like anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering dif…
Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their st…
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 ext…
