In recent years, the skyrmion lattice phase with a short lattice constant has attracted attention due to its high skyrmion density, making it a promising option for achieving high-density storage memory and for observing novel phenomena like the quantized topological Hall effect. Unlike conventional non-centrosymmetric systems where the Dzyaloshinsky-Moriya interaction plays a crucial role, the short pitch skyrmion phase requires a quadratic magnetic interaction $J(q)$ with a peak at finite-$Q$, and weak easy-axis magnetic anisotropy is also critical. Thus, conducting first-principles evaluations is essential for understanding the formation mechanism as well as for promoting the discovery of new skyrmion materials. In this {\it Perspective}, we focus on recent developments of the first-principles evaluations of these properties and apply them to the prototype systems Gd$T_2X_2$ and Eu$T_2X_2$, where $T$ denotes a transition metal and $X$ represents Si or Ge. In particular, based on the spin density functional theory with the Hubbard correction combined with the Liechtenstein method in the Wannier tight-binding model formalism, we first show that the Hubbard $U$ and Hund's coupling is essential to stabilize a skyrmion lattice state by enhancing the easy-axis anisotropy. We then discuss mechanisms of finite-$Q$ instability and show that competition among Gd-5$d$ orbitals determines whether ferromagnetism or a finite-$Q$ structure is favored in Gd$T_2$Si$_2$ with $T=$ Fe and Ru. Our systematic calculations reveal that GdRu$_2$$X_2$, GdOs$_2$$X_2$, and GdRe$_2X_2$ are promising, while GdAg$_2X_2$, GdAu$_2X_2$, and EuAg$_2X_2$ are possible candidates as the skyrmion host materials. Analysis based on a spin spiral calculation for the candidate materials is also presented.
Chiral magnetic phases with an unconventional topological twist in the magnetization are of huge interest due to their potential in spintronics applications. Here, we present a general method to induce such exotic magnetic phases using interfacial phase frustration within artificially grown superlattices. To demonstrate our method, we consider a multilayer with two different chiral magnetic phases as the competing orders at the top and bottom and show, using Monte Carlo calculations, that the interfacial phase frustration is realized at the central layer. In particular, we obtain three unconve…
We present a comprehensive theory of the magnetic phases in monolayer nickel-based Janus dihalides (NiIBr, NiICl, NiBrCl) through a combination of first-principles calculations and atomistic simulations. Phonon band structure calculations and finite temperature molecular dynamics simulations show that Ni-dihalide Janus monolayers are stable. The parameters of the interacting spin Hamiltonian extracted from ab initio calculations show that nickel-dihalide Janus monolayers exhibit varying degrees of magnetic frustration together with a large Dzyaloshinskii-Moriya interaction due to their inheren…
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals in a non-frustrated artificial geometrical lattice as a consequence of the structural con…
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…
Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Recently $β$-Mn structure-type Co-Zn-Mn alloys were identified as a new class of chiral magnet to host such skyrmion crystal phases, while $β$-Mn itself is known as hosting an elemental geometrically frustrated spin liquid. Here we report the intermediate composition system Co$_7$Zn$_7$Mn$_6$ to be a unique host of two disconnected, thermal-equilibrium topological skyrmion phases; one is a conventional s…
We theoretically propose a new stabilization mechanism of a skyrmion crystal (SkX) in a bilayer triangular lattice system consisting of the ferromagnetic and the antiferromagnetic layers. By performing variational calculations and Monte Carlo simulations in a complementary way, we find that a magnetic frustration between the ferromagnetic and antiferromagnetic layers is a source of a finite-Q spiral state and the SkX in the strong interlayer coupling regime. We also show that the degree of frustration is related to the interlayer exchange interaction. The stronger interlayer coupling tends to …
Frustration-driven topological textures on the honeycomb lattice: antiferromagnetic meron-antimeron and skyrmion crystals emerging from spiral spin liquids
The formation of a skyrmion crystal and its phase transition are studied taking into account the Dzyaloshinskii-Moriya (DM) interaction at the interface between a ferroelectric layer and a magnetic layer in a superlattice. The frustration is introduced in both magnetic and ferroelectric films. The films have the simple cubic lattice structure. Spins inside magnetic layers are Heisenberg spins interacting with each other via nearest-neighbor (NN) exchange $J^m$ and next-nearest-neighbor (NNN) exchange $J^{2m}$. Polarizations in the ferroelectric layers are assumed to be of Ising type with NN an…
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…
Geometrically frustrated magnets provide abundant opportunities for discovering complex spin textures, which sometimes yield unconventional electromagnetic responses in correlated electron systems. It is theoretically predicted that magnetic frustration may also promote a topologically nontrivial spin state, i.e., magnetic skyrmions, which are nanometric spin vortices. Empirically, however, skyrmions are essentially concomitant with noncentrosymmetric lattice structures or interfacial-symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustr…
Topological spin structures, such as magnetic skyrmions, hold great promises for data storage applications, thanks to their inherent stability. In most cases, skyrmions are stabilized by magnetic fields in non-centrosymmetric systems displaying the chiral Dzyaloshinskii-Moriya exchange interaction, while spontaneous skyrmion lattices have been reported in centrosymmetric itinerant magnets with long-range interactions. Here, a spontaneous anti-biskyrmion lattice with unique topology and chirality is predicted in the monolayer of a semiconducting and centrosymmetric metal halide, NiI$_2$. Our fi…
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…
The skyrmions generated by frustration in centrosymmetric structures host extra internal degrees of freedom: vorticity and helicity, resulting in distinctive properties and potential functionality, which are not shared by the skyrmions stemming from the Dzyaloshinskii-Moriya interaction in noncentrosymmetric structures. The present work indicates that the magnetism-driven electric polarization carried by skyrmions provides a direct handle for tuning helicity. Especially for the in-plane magnetized skyrmions, the helicity can be continuously rotated and exactly picked by applying an external el…
The experimental realization of magnetic skyrmions in centrosymmetric materials has been driven by theoretical understanding of how a delicate balance of anisotropy and frustration can stabilize topological spin structures in applied magnetic fields. Recently, the centrosymmetric material Gd$_{2}$PdSi$_{3}$ was shown to host a field-induced skyrmion phase, but the skyrmion stabilization mechanism remains unclear. Here, we employ neutron-scattering measurements on an isotopically-enriched polycrystalline Gd$_{2}$PdSi$_{3}$ sample to quantify the interactions that drive skyrmion formation. Our a…
Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu$_2$Si$_2$ and Gd$_2$PdSi$_3$. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5$d$ orbitals is ferromagnetic, but the interaction between the G…
Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity / vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd3Ru4Al12, which materializes a breathing kagomé lattice of Gadolinium moments. The …
The phase diagrams of the frustrated classical spin model with Dzyaloshinskii-Moriya (DM) interaction on the Shastry-Sutherland (S-S) lattice are studied by means of Monte Carlo simulation. For ferromagnetic next-nearest-neighboring (J2) interactions, the introduced exchange frustration enhances the effect of the DM interaction, which enlarges the magnetic field-range with the skyrmion lattice phase and increases the skyrmion density. For antiferromagnetic J2 interactions, the so-called 2q phase (two-sublattice skyrmion crystal) and the spin-flop phase are observed in the simulated phase diagr…
We study the effects of an in-plane Dzyaloshinskii-Moriya interaction under an external magnetic field in the highly frustrated kagome antiferromagnet. We focus on the low-temperature phase diagram, which we obtain through extensive Monte-Carlo simulations. We show that, given the geometric frustration of the lattice, highly non trivial phases emerge. At low fields, lowering the temperature from a cooperative paramagnet phase, the kagome elementary plaquettes form non-coplanar arrangements with non-zero chirality, retaining a partial degeneracy. As the field increases, there is a transition fr…
We study the ordering properties of the isotropic RKKY Heisenberg model on the two-dimensional (2D) triangular lattice by extensive Monte Carlo simulations to get insights into the chiral-degenerate skyrmion crystal (SkX) of metallic magnets. Our Hamiltonian contains only the spin-quadratic RKKY interaction derived from the spherical Fermi surface, containing neither the nesting nor the many-body interaction. The SkX phase is stabilized under applied fields where the frustration associated with the oscillating nature of the RKKY interaction and the emergent many-body interactions generated by …
Motivated by recent experiments in Gd$_3$Ru$_4$Al$_{12}$, we demonstrate the emergence of atomic scale Skyrmions in interacting spins on a breathing kagome lattice with competing nearest neighbor ferromagnetic and next nearest neighbor antiferromagnetic exchange interactions. In the presence of an applied longitudinal magnetic field, the ground state magnetic order evolves from a helical phase at low fields to a Skyrmion phase at intermediate fields before finally entering a polarized phase at high fields. The size of each Skyrmion spans only two unit cells of the lattice, in contrast to tens …
Multi-orbital optical lattices have been attracting rapidly growing research interests in the last several years, providing fascinating opportunities for orbital-based quantum simulations. Here, we consider bosonic atoms loaded in the degenerate $p$-orbital bands of a two-dimensional triangular optical lattice. This system is described by a multi-orbital Bose-Hubbard model. We find the confined atoms in this system develop spontaneous orbital polarization, which forms a chiral Skyrmion lattice pattern in a large regime of the phase diagram. This is in contrast to its spin analogue which largel…
Long-range magnetic interactions in Nd$_2$PdSi$_3$ and the formation of skyrmion phases in centrosymmetric metals
University of Oxford（牛津大学）；ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普顿实验室中子与μ子源）；Zhejiang University（浙江大学）；The University of Tokyo（东京大学）；Institut Laue-Langevin（朗之万研究所）；PSI Center for Neutron and Muon Sciences（瑞士保罗谢勒研究所中子与μ子科学中心）；University of Warwick（华威大学）
Skyrmion and Meron Crystals in Intermetallic Gd$_3$Ru$_4$Al$_{12}$: Microscopic Model Insights into Chiral Phases
University of Science and Technology of China（中国科学技术大学）；University of Tennessee（田纳西大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；The University of Tokyo（东京大学）
Engineering non trivial topological phases in materials, specially skyrmion-like arrangements, has been of great interest in the last decade due to its potential technological applications. In this work, we study a model of electrons coupled to a magnetic texture in the kagome lattice interacting with magnetic moments via Rashba spin orbit coupling in the large Hund interaction limit. We obtain the effective spin Hamiltonian and study the emergent low temperature phases under an external magnetic field using large scale Monte Carlo simulations. We show that strong geometric frustration, charac…
The insulating magnetic material Fe3PO4O3 features a non-centrosymmetric lattice composed of Fe^{3+} triangular units. Frustration, due to competing near neighbor ($J_1$) and next nearest neighbor ($J_2$) antiferromagnetic interactions, was recently suggested to be the origin of an antiferromagnetic helical ground state with unusual needle-like nanoscale magnetic domains in Fe3PO4O3. Magnetic dilution is shown here to tune the ratio of these magnetic interactions, thus providing deeper insight into this unconventional antiferromagnet. Dilution of the Fe^{3+} lattice in Fe3PO4O3 was accomplishe…
We study phase transitions in the two-dimensional Heisenberg model with the Dzyaloshinskii-Moriya interaction, the Ising anisotropy ($η$), and the dipolar interaction under zero and finite magnetic fields ($H$). For three typical strengths (zero, weak, and strong) of the dipolar interaction, we present the $H$-$η$ phase diagrams by estimating order parameters for skyrmion-lattice and helical phases and in-plane magnetization by using a Monte Carlo method with an $O(N)$ algorithm. We find in the phase diagrams three types of skyrmion-lattice phases, i.e., two square lattices and a triangular la…
We investigate the Hubbard model on the anisotropic triangular lattice with two hopping parameters $t$ and $t^\prime$ in different spatial directions, interpolating between decoupled chains ($t=0$) and the isotropic triangular lattice ($t=t^\prime$). Variational wave functions that include both Jastrow and backflow terms are used to compare spin-liquid and magnetic phases with different pitch vectors describing both collinear and coplanar (spiral) order. For relatively large values of the on-site interaction $U/t^\prime \gtrsim 10$ and substantial frustration, i.e., $0.3\lesssim t/t^\prime \le…
We report the results of magnetic, heat-capacity, electrical and magnetoresistance measurements on Ho4RhAl and Er4RhAl, characterized by 3 sites for rare-earths (R). Antiferromagnetic ordering sets in at (T_N =) about 8.8 and 4.0 K respectively. While Ho compound appears to enter into a complex spin-glass phase at T less thanT_N (at nearly 5 K), spin-glass component appears to set in essentially almost at T_N for the Er case. The loss of the spin-disorder contribution in the magnetically ordered state is not pronounced, mimicking that in Gd2PdSi3, a compound which now attracts interest in the …
We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen as to produce frustration. At zero temperature, this system undergoes several quantum phase transitions from both gapped-to-gapless and gapless-to-gapless phases, providing a very rich phase structure with disordered, homogeneous and modulated ordered phases meeting in a quantum Lifshitz point. The gapless phases spontaneously break spatial lattice translations as well as internal symmetries of the form $U(1)^{\mathsf{N}_…
Single-ion anisotropy-stabilized short-period helimagnetism in frustrated chiral Co$_5$TeO$_8$
The University of Tokyo（东京大学）；PSI Center for Neutron and Muon Sciences（瑞士保罗谢勒研究所中子与μ子科学中心）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料能源中心）；Institut Laue–Langevin（朗之万研究所）
