Role of higher-order exchange interactions for skyrmion stability

Role of isotropic and anisotropic Dzyaloshinskii-Moriya interaction on skyrmions, merons and antiskyrmions in theCnvsymmetric system

The lattice Hamiltonian with the presence of a chiral magnetic isotropic Dzyaloshinskii-Moriya interaction (DMI) in a square and hexagonal lattice is numerically solved to give the full phase diagram consisting of skyrmions and merons in different parameter planes. The phase diagram provides the actual regions of analytically unresolved asymmetric skyrmions and merons, and it is found that these regions are substantially larger than those of symmetric skyrmions and merons. With magnetic field, a change from meron or spin spiral (SS) to skyrmion is seen. The complete phase diagram for theCnvsymmetric system with anisotropic DMI is drawn and it is shown that this DMI helps to change the SS propagation direction. Finally, the well-defined region of a thermodynamically stable antiskyrmion phase in theCnvsymmetric system is shown.

Constructing temporal networks with bursty activity patterns

Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One of the key statistics to summarize temporal patterns is the inter-event time, namely the duration between successive pairwise interactions. Empirical studies have found inter-event time distributions that are heavy-tailed, for both physical and digital interactions. But it is difficult to construct theoretical models of time-varying activity on a network that reproduce the burstiness seen in empirical data. Here we develop a spanning-tree method to construct temporal networks and activity patterns with bursty behavior. Our method ensures any desired target inter-event time distributions for individual nodes and links, provided the distributions fulfill a consistency condition, regardless of whether the underlying topology is static or time-varying. We show that this model can reproduce burstiness found in empirical datasets, and so it may serve as a basis for studying dynamic processes in real-world bursty interactions.

Laser-induced topological spin switching in a 2D van der Waals magnet

Two-dimensional (2D) van der Waals (vdW) magnets represent one of the most promising horizons for energy-efficient spintronic applications because their broad range of electronic, magnetic and topological properties. However, little is known about the interplay between light and spin properties in vdW layers. Here we show that ultrafast laser excitation can not only generate different type of spin textures in CrGeTe₃ vdW magnets but also induce a reversible transformation between them in a topological toggle switch mechanism. Our atomistic spin dynamics simulations and wide-field Kerr microscopy measurements show that different textures can be generated via high-intense laser pulses within the picosecond regime. The phase transformation between the different topological spin textures is obtained as additional laser pulses are applied to the system where the polarisation and final state of the spins can be controlled by external magnetic fields. Our results indicate laser-driven spin textures on 2D magnets as a pathway towards reconfigurable topological architectures at the atomistic level.

Two-dimensional magnetic Janus monolayers and their van der Waals heterostructures: a review on recent progress

A magnetic Janus monolayer, a special type of material which has asymmetric arrangements of its surface at the nanoscale, has been shown to present rather exotic properties for applications in spintronics and its intersections. This review aims to offer a comprehensive review of the emergent physical properties of magnetic Janus monolayers and their van der Waals heterostructures from a theoretical point of view. The review starts by introducing the theoretical methodologies composed of the state-of-the-art methods and the challenges and limitations in validations for the descriptions of the magnetic ground states and thermodynamic properties in magnetic materials. The built-in polarization field induced physical phenomena of magnetic Janus monolayers are then presented. The tunable electronic and magnetic properties of magnetic Janus monolayer-based van der Waals heterostructures are discussed. Finally, the conclusions and future challenges in this field are prospected. This review serves as a complete summary of the two-dimensional magnetic Janus library and emergent electronic and magnetic properties in magnetic Janus monolayers and their heterostructures, and provides guidelines for the design of electronic and spintronic devices based on Janus materials.

Nano-scale collinear multi-Q states driven by higher-order interactions

Complex magnetic order arises due to the competition of different interactions between the magnetic moments. Recently, there has been an increased interest in such states not only to unravel the fundamental physics involved, but also with regards to applications exploiting their unique interplay with moving electrons. Whereas it is the Dzyaloshinskii-Moriya interaction (DMI) that has attracted much attention because of its nature to induce non-collinear magnetic order including magnetic-field stabilized skyrmions, it is the frustration of exchange interactions that can drive magnetic order down to the nano-scale. On top of that, interactions between multiple spins can stabilize two-dimensional magnetic textures as zero-field ground states, known as multi-Q states. Here, we introduce a two-dimensional itinerant magnet with various competing atomic-scale magnetic phases. Using spin-polarized scanning tunneling microscopy we observe several zero-field uniaxial or hexagonal nano-scale magnetic states. First-principles calculations together with an atomistic spin model reveal that these states are stabilized by the interplay of frustrated exchange and higher-order interactions while the DMI is weak. Unexpectedly, it is found that not only non-collinear magnetic states arise, but that higher-order interactions can also lead to collinear nano-scale multi-Q states.

Multi-Q states are 2D typically non-collinear spin textures that can be stabilized at the nanoscale and at zero magnetic field by interactions between multiple spins. Gutzeit et al. uncover a variety of multi-Q states in Fe/Rh atomic bilayers on the Ir(111) surface, including unexpected 2D collinear states.

Square skyrmion crystal in centrosymmetric systems with locally inversion-asymmetric layers

We investigate an instability toward a square-lattice formation of magnetic skyrmions in centrosymmetric layered systems. By focusing on a bilayer square-lattice structure with the inversion center at the interlayer bond instead of the atomic site, we numerically examine the stability of the square skyrmion crystal (SkX) based on an effective spin model with the momentum-resolved interaction in the ground state through the simulated annealing. As a result, we find that a layer-dependent staggered Dzyaloshinskii-Moriya (DM) interaction built in the lattice structure becomes the origin of the square SkX in an external magnetic field irrespective of the sign of the interlayer exchange interaction. The obtained square SkX is constituted of the SkXs with different helicities in each layer due to the staggered DM interaction. Furthermore, we show that the interplay between the staggered DM interaction and the interlayer exchange interaction gives rise to a double-Qstate with a uniform component of the scalar chirality in the low-field region. The present results provide another way of stabilizing the square SkX in centrosymmetric magnets, which will be useful to explore further exotic topological spin textures.

Assembling Diverse Skyrmionic Phases in Fe3 GeTe2 Monolayers

Skyrmionic magnetic states are promising in advanced spintronics. This topic is experiencing recent progress in 2D magnets, with, for example, a near 300 K Curie temperature observed in Fe₃ GeTe₂ . However, despite previous studies reporting skyrmions in Fe₃ GeTe₂ , such a system remains elusive, since it has been reported to host either Néel-type or Bloch-type textures, while a net Dzyaloshinskii-Moriya interaction (DMI) cannot occur in this compound for symmetry reasons. It is thus desirable to develop an accurate model to deeply understand Fe₃ GeTe₂ . Here, a newly developed method adopting spin invariants is applied to build a first-principle-based Hamiltonian, which predicts colorful topological defects assembled from the unit of Bloch lines, and reveals the critical role of specific forms of fourth-order interactions in Fe₃ GeTe₂ . Rather than the DMI, it is the multiple fourth-order interactions, with symmetry and spin-orbit couplings considered, that stabilize both Néel-type and Bloch-type skyrmions, as well as antiskyrmions, without any preference for clockwise versus counterclockwise spin rotation. This study also demonstrates that spin invariants can be used as a general approach to study complex magnetic interactions.

A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI3

The first magnetic 2D material discovered, monolayer (ML) CrI₃, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI₃'s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI₃. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI₃'s ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements-an accomplishment given the ∼10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI₃'s magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI₃ are 3.62 μ_B per chromium and -0.145 μ_B per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin-orbit coupling of CrI₃'s I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI₃, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI₃ exhibits a substantial spin-phonon coupling of ∼3.32 cm^-1. Our work, thus, establishes many of ML CrI₃'s key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.

Phase shift in skyrmion crystals

The magnetic skyrmion crystal is a periodic array of a swirling topological spin texture. Since it is regarded as an interference pattern by multiple helical spin density waves, the texture changes with the relative phase shifts among the constituent waves. Although such a phase degree of freedom is relevant to not only magnetism but also transport properties, its effect has not been elucidated thus far. We here theoretically show that a phase shift in the skyrmion crystals leads to a tetra-axial vortex crystal and a meron-antimeron crystal, both of which show a staggered pattern of the scalar spin chirality and give rise to nonreciprocal transport phenomena without the spin-orbit coupling. We demonstrate that such a phase shift can be driven by exchange interactions between the localized spins, thermal fluctuations, and long-range chirality interactions in spin-charge coupled systems. Our results provide a further diversity of topological spin textures and open a new field of emergent electromagnetism by the phase shift engineering.

Skyrmions are a type of topological spin texture, which can exist as both an isolated state, and as a skyrmion crystal. Here, Hayami et al present a theoretical study of phase shifts in skyrmion crystals, showing how such phase shifts can lead to other crystalline topological spin textures.

Strain driven phase transition and mechanism for Fe/Ir(111) films

By way of introducing heterogeneous interfaces, the stabilization of crystallographic phases is critical to a viable strategy for developing materials with novel characteristics, such as occurrence of new structure phase, anomalous enhancement in magnetic moment, enhancement of efficiency as nanoportals. Because of the different lattice structures at the interface, heterogeneous interfaces serve as a platform for controlling pseudomorphic growth, nanostructure evolution and formation of strained clusters. However, our knowledge related to the strain accumulation phenomenon in ultrathin Fe layers on face-centered cubic (fcc) substrates remains limited. For Fe deposited on Ir(111), here we found the existence of strain accumulation at the interface and demonstrate a strain driven phase transition in which fcc-Fe is transformed to a bcc phase. By substituting the bulk modulus and the shear modulus and the experimental results of lattice parameters in cubic geometry, we obtain the strain energy density for different Fe thicknesses. A limited distortion mechanism is proposed for correlating the increasing interfacial strain energy, the surface energy, and a critical thickness. The calculation shows that the strained layers undergo a phase transition to the bulk structure above the critical thickness. The results are well consistent with experimental measurements. The strain driven phase transition and mechanism presented herein provide a fundamental understanding of strain accumulation at the bcc/fcc interface.

Spin Vortex Crystal Order in Organic Triangular Lattice Compound

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.

Topological spin crystals by itinerant frustration

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 stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

Spin Hamiltonians in Magnets: Theories and Computations

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, spin interactions, for short) that may be used in effective spin Hamiltonians as well as the various methods of computing the interaction parameters. A detailed discussion about the merits and possible pitfalls of each technique of computing interaction parameters is provided.

Stacking-Dependent Spin Interactions in Pd/Fe Bilayers on Re(0001)

Using spin-polarized scanning tunneling microscopy and density functional theory, we have studied the magnetic properties of Pd/Fe atomic bilayers on Re(0001). Two kinds of magnetic ground states are discovered due to different types of stacking of the Pd adlayer on Fe/Re(0001). For fcc stacking of Pd on Fe/Re(0001), it is a spin spiral propagating along the close-packed (ΓK[over ¯]) direction with a period of about 0.9 nm, driven by frustrated exchange and Dzyaloshinskii-Moriya interactions. For the hcp stacking, the four-site four-spin interaction stabilizes an up-up-down-down state propagating perpendicular to the close-packed direction (along ΓM[over ¯]) with a period of about 1.0 nm. Our work shows how higher-order exchange interactions can be tuned at interfaces.