Chiral Spin States Research Articles

Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models

Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models

Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions

The triangular-lattice Fermi-Hubbard model has been extensively investigated in the literature due to its connection to chiral spin states and unconventional superconductivity. Previous simulations of the ground state of the doped system rely on quasi-one-dimensional lattices where true long-range order is forbidden. Here we simulate two-dimensional and quasi-one-dimensional triangular lattices using state-of-the-art Auxiliary-Field Quantum Monte Carlo. Upon doping a non-magnetic chiral spin state, we observe evidence of chiral superconductivity supported by long-range order in Cooper-pair correlation and a finite value of the chiral order parameter. With this aim, we first locate the transition from the metallic to the non-magnetic insulating phase and the onset of magnetic order. Our results pave the way towards a better understanding of strongly correlated lattice systems with magnetic frustration.

Chirality reversal of magnetic solitons in chiral Cr1/3TaS2

Ferromagnetism in two-dimensional (2D) materials provides an ideal platform to study emergent electromagnetic phenomena in low dimensions for future spintronics. In magnetic-element intercalated transition metal dichalcogenides, topologically nontrivial spin textures, such as chiral helimagnetic spin states and chiral soliton lattices, are realized due to the chiral lattice distortions induced by intercalated magnetic ions. Consequently, the magnetic chirality is predictably determined by the sign of antisymmetric exchange interaction (or Dzyaloshinskii–Moriya interaction, DMI) vector that is coupled to the underlying crystal chirality. Here, using cryogenic Lorentz phase microscopy, we directly observed the chirality reversal behavior of the chiral soliton lattices in Cr1/3TaS2 across the structural defects. We show that a partial 1 T stacking in 2H-TaS2 locally reduces DMI, leading to magnetic chirality reversal with direct atomic resolution imaging. Our experimental results show that manipulation of stacking sequence provides a viable way to control the chirality of topologically nontrivial soliton lattices in 2D magnets.

Two-dimensional short-range spin-spin correlations in the layered spin- 32 maple leaf lattice antiferromagnet Na2Mn3O7 with crystal stacking disorder

We report the nature of magnetic structure, and microscopic spin-spin correlations and their dependence on the underlying crystal structure of the geometrically frustrated layered spin-$\frac{3}{2}$ maple leaf lattice (MLL) antiferromagnet ${\mathrm{Na}}_{2}{\mathrm{Mn}}_{3}{\mathrm{O}}_{7}$ by a comprehensive neutron diffraction study. Crystal structural studies by x-ray and neutron diffraction reveal that the MLL layers (constituted by ${\mathrm{Mn}}_{3}{\mathrm{O}}_{7}{}^{2\ensuremath{-}}$ units) are well separated by nonmagnetic Na layers. The studies also conclude the presence of stacking faults (in-plane sliding of magnetic MLL layers) as well as a distortion in the MLL of ${\mathrm{Mn}}^{4+}$. Temperature dependent magnetic susceptibility, heat capacity, and neutron diffraction data yield a short-range antiferromagnetic (AFM) ordering below $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ without a long-range magnetic ordering down to 1.5 K. The analysis of the diffuse magnetic neutron scattering patterns by the reverse Monte Carlo method reveals two-dimensional (2D) spin-spin correlations within the MLL layers. Additionally, we establish a relation between the correlation length of the short-range magnetic ordering with the stacking faults through a varying synthesis condition. The present study, therefore, explores a microscopic picture of the crystal and spin structures, as well as their correlation; hence it provides experimental insight of the magnetic ordering in a MLL AFM. Further, we have outlined the formation of several 2D frustrated lattice geometries having triangular plaquettes, including the MLL, by crystal engineering of the triangular lattice, and their role in the stabilization of multiple unique chiral spin states which opens up the door for study of unique chiral spin states.

Large Dzyaloshinskii-Moriya interaction and field-free topological chiral spin states in two-dimensional alkali-based chromium chalcogenides

Noncentrosymmetric ferromagnetic systems with large Dzylochinskii-Moriya interaction (DMI) have gained intensive attention for hosting topologically protected solitons such as skyrmions and bimerons. Recently, a series of two-dimensional (2D) Li- and Na-based chromium chalcogenides has been theoretically predicted to be a new family of intrinsic inversion asymmetric ferromagnets. Here, by combining first-principles calculations and atomistic spin model simulations, we unveil that there is very large DMI in these series of 2D alkali-based chromium chalcogenides, which enables a variety of filed-free topological spin textures in these structures. Furthermore, we find robust hole-doping tunable DMI in the ${\mathrm{LiCrSe}}_{2}$ and ${\mathrm{NaCrSe}}_{2}$ monolayers. Our finding opens up further possibilities toward 2D materials in spintronic devices.

Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions

Quantum spin systems can break time reversal symmetry by developing spontaneous magnetization or spin chirality. However, collinear magnets and chiral spin states are invariant under different symmetries, implying that the order parameter of one phase vanishes in the other. We show how to construct one-dimensional anisotropic spin models that exhibit a "Landau-forbidden" continuous phase transition between such states. As a concrete example, we focus on a zigzag chain with bond-dependent exchange and six-spin interactions. Using a combination of exact solutions, effective field theories, and numerical simulations, we show that the transition between the chiral and magnetic phases has an emergent U(1) symmetry. The excitations governing the transition from the chiral phase can be pictured as mobile defects in a $\mathbb Z_2$ flux configuration which bind fermionic modes. We briefly discuss extensions to two dimensions and analogies with deconfined quantum criticality. Our results suggest new prospects for unconventional phase transitions involving chiral spin states.

Curved Magnetism in CrI_{3}.

Curved magnets attract considerable interest for their unusually rich phase diagram, often encompassing exotic (e.g., topological or chiral) spin states. Micromagnetic simulations are playing a central role in the theoretical understanding of such phenomena; their predictive power, however, rests on the availability of reliable model parameters to describe a given material or nanostructure. Here we demonstrate how noncollinear-spin polarized density-functional theory can be used to determine the flexomagnetic coupling coefficients in real systems. By focusing on monolayer CrI_{3}, we find a crossover as a function of curvature between a magnetization normal to the surface to a cycloidal state, which we rationalize in terms of effective anisotropy and Dzyaloshinskii-Moriya contributions to the magnetic energy. Our results reveal an unexpectedly large impact of spin-orbit interactions on the curvature-induced anisotropy, which we discuss in the context of existing phenomenological models.

Spin interactions and topological magnonics in chromium trihalide CrClBrI

The discovery of spontaneous magnetism in van der Waal (vdW) magnetic monolayers has opened up an unprecedented platform for investigating magnetism in purely two-dimensional systems. Recently, it has been shown that the magnetic properties of vdW magnets can be easily tuned by adjusting the relative composition of halides. Motivated by these experimental advances, here we derive a model for a trihalide CrClBrI monolayer from symmetry principles and we find that, in contrast to its single-halide counterparts, it can display highly anisotropic nearest- and next-to-nearest neighbor Dzyaloshinskii-Moriya and Heisenberg interactions. Depending on the parameters, the DM interactions are responsible for the formation of exotic chiral spin states, such as skyrmions and spin cycloids, as shown by our Monte Carlo simulations. Focusing on a ground state with a two-sublattice unit cell, we find spin-wave bands with nonvanishing Chern numbers. The resulting magnon edge states yield a magnon thermal Hall conductivity that changes sign as function of temperature and magnetic field, suggesting chromium trihalides as a candidate for testing topological magnon transport in two-dimensional noncollinear spin systems.

Magnetically Induced Terahertz Birefringence and Chirality Manipulation in Transverse‐Magnetized Metasurface

AbstractActive manipulation of photonic spin state and optical chirality leads to some key applications, such as in multichannel communication, polarization‐sensitive imaging, chiral spectroscopy, and chiral sensing. Magneto‐optical materials have unique advantages in the intrinsic transmission and magnetic control of photonic chiral spin states. Here, a scheme for dynamic terahertz (THz) anisotropy and chirality manipulations in the transversely magnetized InSb and its hybrid magneto‐optical metasurface structure is presented. A special transverse photonic spin state in the InSb and a transverse−longitudinal spin coupling effect in the hybrid magneto‐optical metasurface are revealed by the eigenmode analysis and numerical simulations. The strong magnetic birefringence effect induced by this spin mode is demonstrated in the experiment. Moreover, the symmetry‐breaking mechanism in this magneto‐optical structure leads to strong intrinsic chirality and polarization conversion. The experimental results confirm the magnetically active manipulation of spin states and their asymmetric transmission in this hybrid magneto‐optical metasurface, which achieve a polarization conversion rate of near 100% and an induced intrinsic chirality of over 15 dB. This work opens a new development for active THz polarization control and chiral manipulation in the magneto‐optical microstructure.

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials.

ConspectusQuantum materials refers to a class of materials with exotic properties that arise from the quantum mechanical nature of their constituent electrons, exhibiting, for example, high-temperature superconductivity, colossal magnetoresistivity, multiferroicity, and topological behavior. Quantum materials often have incompletely filled d- or f-electron shells with narrow energy bands, and the conduct of their electrons is strongly correlated. One distinct characteristic of the materials is that their electronic states are often spatially inhomogeneous and thus well suited for study using a spatially resolved electron beam with its great scattering power and sensitivity to atomic ionicity. Furthermore, most of these exotic properties only manifest at very low temperatures, posing a challenge to modern electron microscopy. It requires extraordinarily instrument stabilities at cryogenic temperatures with critical spatial, temporal, and energy resolutions in both static and dynamic manner to probe these materials. On the other hand, the ability to directly visualize the atomic, electronic and spin structures and inhomogeneities of quantum materials and correlate them to their functionalities creates enormous opportunities. At the most elementary levels of condensed matter physics, understanding the competing order of electron, spin, orbital, and lattice and their degrees of freedom, the impacts of defects and interfaces, and the site-specific quantum phenomena and phase transitions that give rise to the emergent behaviors allows us to discover and control novel materials for quantum information science and technologies.In this Account, several of our research examples are selected to highlight the use of cryogenic electron microscopy (cryo-EM) to study strongly correlated quantum materials. We focus on the critical roles of heterogeneity, interfaces, defects, and disorder in crystal structure, magnetic structure, and electronic structure to understand the physical properties of the materials that cryo-EM enables. We show how electron crystallography coupled with Bragg diffraction and diffuse scattering analysis empowers us to reveal the nature of structural modulations, lattice distortion, and phonons and how quantitative electron diffraction can be used to map the distributions of the valence electrons that bond atoms together. We exploit transformative advances in imaging capabilities including the use of femtosecond laser and ultrafast electron diffraction to probe electron-lattice interactions and photoinduced transitions beyond equilibrium of matter. We review our Lorentz phase microscopy studies to illustrate the intriguing transformations among various topological chiral spin states under applied magnetic field at various cryogenic temperatures. Finally, we show that atomically resolved imaging and electron energy-loss spectroscopy at 10 K can be used to understand interface-enhanced superconductivity. The wide range of research and progress on quantum materials at low temperature reported here may inspire and attract more researchers in this ever-expanding field of cryo-EM.

Mixed topology ring states for Hall effect and orbital magnetism in skyrmions of Weyl semimetals

Skyrmion lattices as a novel type of chiral spin states are attracting increasing attention, owing to their peculiar properties stemming from real-space topological properties. At the same time, the properties of magnetic Weyl semimetals with complex $k$-space topology are moving into the focus of research in spintronics. We consider the Hall transport properties and orbital magnetism of skyrmion lattices imprinted in topological semimetals, by employing a minimal model of a 2D mixed Weyl semimetal which, as a function of the magnetization direction, exhibits two Chern insulator phases separated by a Weyl state for an an in-plane magnetization direction. We find that while the orbital magnetization is topologically robust and Hall transport properties are very sensitive to the details of the spin distribution in accordance to the behavior expected from the recently discovered chiral Hall effect[1], their behavior in the region of the Chern insulator gap is largely determined by the properties of the so-called mixed topology ring states, emerging in domain walls that separate the skyrmion core from the ferromagnetic background. In particular, we show that these localized ring states possess a given orbital chirality which reverses sign as a function of the skyrmion radius, thereby mediating a smooth switching dynamics of the orbital magnetization of the skyrmion lattice. We speculate that while the emergent ring states can possibly play a role in the physics of Majorana states, probing their properties experimentally can provide insights into the details of skyrmionic spin structures.

Artificial Double-Helix for Geometrical Control of Magnetic Chirality.

Chirality plays a major role in nature, from particle physics to DNA, and its control is much sought-after due to the scientific and technological opportunities it unlocks. For magnetic materials, chiral interactions between spins promote the formation of sophisticated swirling magnetic states such as skyrmions, with rich topological properties and great potential for future technologies. Currently, chiral magnetism requires either a restricted group of natural materials or synthetic thin-film systems that exploit interfacial effects. Here, using state-of-the-art nanofabrication and magnetic X-ray microscopy, we demonstrate the imprinting of complex chiral spin states via three-dimensional geometric effects at the nanoscale. By balancing dipolar and exchange interactions in an artificial ferromagnetic double-helix nanostructure, we create magnetic domains and domain walls with a well-defined spin chirality, determined solely by the chiral geometry. We further demonstrate the ability to create confined 3D spin textures and topological defects by locally interfacing geometries of opposite chirality. The ability to create chiral spin textures via 3D nanopatterning alone enables exquisite control over the properties and location of complex topological magnetic states, of great importance for the development of future metamaterials and devices in which chirality provides enhanced functionality.

Controlling Chiral Spin States of a Triangular‐Lattice Magnet by Cooling in a Magnetic Field

AbstractMagnetic materials with a non‐collinear and non‐coplanar arrangement of magnetic moments hosting a nonzero scalar spin‐chirality exhibit unique magnetic and spin‐dependent electronic transport properties. The spin chirality often occurs in materials where competing exchange interactions lead to geometrical frustrations between magnetic moments and to a strong coupling between the crystal lattice and the magnetic structure. These characteristics are particularly strong in Mn‐based antiperovskites where the interactions and chirality can be tuned by substitutional modifications of the crystalline lattice. This study presents evidence for the formation of two unequal chiral spin states in magnetically ordered Mn3.338Ni0.651N antiperovskite based on density functional theory calculations and supported by magnetization measurements after cooling in a magnetic field. The existence of two scalar spin‐chiralities of opposite sign and different magnitude is demonstrated by a vertical shift of the magnetic‐field dependent magnetization and Hall effect at low fields and from an asymmetrical magnetoresistivity when the applied magnetic field is oriented parallel or antiparallel to the direction of the cooling field. This opens up the possibility of manipulating the spin chirality for potential use in the emerging field of chiral spintronics.

Symmetry-breaking interlayer Dzyaloshinskii-Moriya interactions in synthetic antiferromagnets.

The magnetic interfacial Dzyaloshinskii-Moriya interaction (DMI) in multilayered thin films can lead to chiral spin states, which are of paramount importance for future spintronic technologies1,2. Interfacial DMI typically manifests as an intralayer interaction, mediated via a paramagnetic heavy metal in systems lacking inversion symmetry3. Here we show that, by designing synthetic antiferromagnets with canted magnetization states4,5, it is also possible to observe direct evidence of the interfacial interlayer DMI at room temperature. The interlayer DMI breaks the symmetry of the magnetic reversal process via the emergence of non-collinear spin states, which results in chiral exchange-biased hysteresis loops. The spin chiral interlayer interactions reported here are expected to manifest in a range of multilayered thin-film systems, opening up as yet unexplored avenues for the development and exploitation of chiral effects in magnetic heterostructures6-8.

Synthesis of antisymmetric spin exchange interaction and chiral spin clusters in superconducting circuits

We have synthesized the anti-symmetric spin exchange interaction (ASI), which is also called the Dzyaloshinskii-Moriya interaction, in a superconducting circuit containing five superconducting qubits connected to a bus resonator, by periodically modulating the transition frequencies of the qubits with different modulation phases. This allows us to show the chiral spin dynamics in three-, four- and five-spin clusters. We also demonstrate a three-spin chiral logic gate and entangle up to five qubits in Greenberger-Horne-Zeilinger states. Our results pave the way for quantum simulation of magnetism with ASI and quantum computation with chiral spin states.

Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model.

Recently, the frustrated XY model for spins 1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

Generation of chiral spin state by quantum simulation

Chirality of materials in nature appears when there are asymmetries in their lattice structures or interactions in a certain environment. Recent development of quantum simulation technology has enabled the manipulation of qubits. Accordingly, chirality can be realized intentionally rather than passively observed. Here we theoretically provide simple methods to create a chiral spin state in a spin-1/2 qubit system on a square lattice. First, we show that switching ON/OFF the Heisenberg and $XY$ interactions produces the chiral interaction directly in the effective Hamiltonian without controlling local fields. Moreover, when initial states of spin-qubits are appropriately prepared, we prove that the chirality with desirable phase is dynamically obtained. Finally, even for the case where switching ON/OFF the interactions is infeasible and the interactions are always-on, we show that, by preparing an asymmetric initial qubit state, the chirality whose phase is $\pi/2$ is dynamically generated.

Pressure-induced inhomogeneous chiral-spin ground state in FeGe.

(57)Fe nuclear forward scattering on the chiral magnet FeGe reveals an extremely large precursor phase region above the helimagnetic ordering temperature T(C)(p) and beyond the pressure-induced quantum phase transition at 19 GPa. The decrease of the magnetic hyperfine field ⟨B(hf)⟩ with pressure is accompanied by a large increase of the width of the distribution of ⟨B(hf)⟩, indicating a strong quasistatic inhomogeneity of the magnetic states in the precursor region. Hyperfine fields of the order of 4 T (equivalent to a magnetic moment μ(Fe)≈0.4μ(B)) persist up to 28.5 GPa. No signatures of magnetic order have been found at about 31 GPa. The results, supported by ab initio calculations, suggest that chiral magnetic precursor phenomena, such as an inhomogeneous chiral-spin state, are vastly enlarged due to increasing spin fluctuations as FeGe is tuned to its quantum phase transition.

Cotunneling signatures of spin-electric coupling in frustrated triangular molecular magnets

The ground state of frustrated (antiferromagnetic) triangular molecular magnets is characterized by two total-spin $S=1/2$ doublets with opposite chirality. According to a group theory analysis [M. Trif et al., Phys. Rev. Lett. 101, 217201 (2008)], an external electric field can efficiently couple these two chiral spin states, even when the spin-orbit interaction (SOI) is absent. The strength of this coupling, $d$, is determined by an off-diagonal matrix element of the dipole operator, which can be calculated by ab initio methods [M. F. Islam et al., Phys. Rev. B 82, 155446 (2010)]. In this work, we propose that Coulomb-blockade transport experiments in the cotunneling regime can provide a direct way to determine the spin-electric coupling strength. Indeed, an electric field generates a $d$-dependent splitting of the ground-state manifold, which can be detected in the inelastic cotunneling conductance. Our theoretical analysis is supported by master-equation calculations of quantum transport in the cotunneling regime. We employ a Hubbard-model approach to elucidate the relationship between the Hubbard parameters $t$ and $U$, and the spin-electric coupling constant $d$. This allows us to predict the regime in which the coupling constant $d$ can be extracted from experiment.

First-principles studies of spin-orbit and Dzyaloshinskii-Moriya interactions in the {Cu3} single-molecule magnet

Frustrated triangular molecule magnets such as \{Cu$_3$\} are characterized by two degenerate S=1/2 ground-states with opposite chirality. Recently it has been proposed theoretically [PRL {\bf 101}, 217201 (2008)] and verified by {\it ab-initio} calculations [PRB {\bf 82}, 155446 (2010)] that an external electric field can efficiently couple these two chiral spin states, even in the absence of spin-orbit interaction (SOI). The SOI is nevertheless important, since it introduces a splitting in the ground-state manifold via the Dzyaloshinskii-Moriya interaction. In this paper we present a theoretical study of the effect of the SOI on the chiral states within spin density functional theory. We employ a recently-introduced Hubbard model approach to elucidate the connection between the SOI and the Dzyaloshinskii-Moriya interaction. This allows us to express the Dzyaloshinskii-Moriya interaction constant $D$ in terms of the microscopic Hubbard model parameters, which we calculate from first-principles. The small splitting that we find for the \{Cu$_3$\} chiral state energies ($\Delta \approx 0.02$ meV) is consistent with experimental results. The Hubbard model approach adopted here also yields a better estimate of the isotropic exchange constant than the ones obtained by comparing total energies of different spin configurations. The method used here for calculating the DM interaction unmasks its simple fundamental origin which is the off-diagonal spin-orbit interaction between the generally multireference vacuum state and single-electron excitations out of those states.