Spin-rotation Symmetry Research Articles

Control of spin-wave polarity and velocity using a ferrimagnetic domain wall

We present a theoretical study of the scattering of spin waves by a domain wall (DW) in a ferrimagnetic (FiM) spin chain in which two sublattices carry spins of unequal magnitudes. We find that a narrow but atomically smooth FiM DW exhibits a different behavior in comparison with similarly smooth ferromagnetic and antiferromagnetic DWs due to the inequivalence of the two sublattices. Specifically, for sufficiently weak anisotropy, the smaller spin at the center of the DW is found to become precisely normal to the easy axis, selecting an arbitrary direction in the xy plane and thereby breaking the U(1) spin-rotational symmetry spontaneously. This particular form of a FiM DW does not occur in antiferromagnetic systems and is shown to lead to a strong dependence of spin-wave scattering pattern on the state of polarization of the spin wave, which can be either right-handed or left-handed, suggesting the utilization of such a narrow DW as a spin-wave filter. Moreover, we find that in the case of an atomically sharp DW, where all the spins point either up or down due to strong easy-axis anisotropy and therefore the polarization of the spin wave is conserved upon transmission, the wave vector of the spin-wave changes after passing through the DW leading to a change in the group velocity of the spin wave. This change of the wave vector indicates the acceleration or deceleration of the spin waves and thus a sharp FiM DW could serve as a spin-wave accelerator or decelerator in spintronics devices, offering a functionality absent in a ferromagnetic and an antiferromagnetic counterpart. Our results indicate that FiM spin textures can interact with spin waves distinctly from ferromagnetic and antiferromagnetic counterparts, suggesting that they may offer spin-wave functionalities that are absent in more conventional magnets. Published by the American Physical Society 2024

Projective Spin Adaptation for the Exact Diagonalization of Isotropic Spin Clusters

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for s=12 to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples.

Lieb-Schultz-Mattis Theorem for 1D Quantum Magnets with Antiunitary Translation and Inversion Symmetries.

We study quantum many-body systems in the presence of an exotic antiunitary translation or inversion symmetry involving time reversal. Based on a symmetry-twisting method and spectrum robustness, we propose that a half-integer spin chain that respects any of these two antiunitary crystalline symmetries in addition to the discrete Z_{2}×Z_{2} global spin-rotation symmetry must either be gapless or possess degenerate ground states. This explains the gaplessness of a class of chiral spin models not indicated by the Lieb-Schultz-Mattis theorem and its known extensions. Moreover, we present symmetry classes with minimal sets of generators that give nontrivial Lieb-Schultz-Mattis-type constraints, argued by the bulk-boundary correspondence in 2D symmetry-protected topological phases as well as lattice homotopy. Our results for detecting the ingappability of 1D quantum magnets from the interplay between spin-rotation symmetries and magnetic space groups are applicable to systems with a broader class of spin interactions, including Dzyaloshinskii-Moriya and triple-product interactions.

Persistent spin texture in ferroelectric Hf0.5Zr0.5O2

Persistent spin texture (PST) refers to the unidirectional spin configuration in momentum space and preserves the SU(2) spin rotation symmetry, which protects the spin coherence against the relaxation and renders an ultimately infinite spin lifetime. In this regard, it would be desirable to find high-quality quantum materials sustaining the intrinsic PST. Here, based on density-functional theory calculations, we show that the ferroelectric Hf0.5Zr0.5O2 sustains a PST over large area of Brillouin zone around the conduction band minimum, while the Rashba-type spin texture dominates around the valence band maximum. Based on the group-theoretical analysis, we construct an effective k·p Hamiltonian model and demonstrate that the PST arises from the significant anisotropy of spin splitting, which pins the spin–orbit field to certain direction. In addition, we elucidate the spin SU(2) symmetry for the discovered PST. Given the fact that Hf0.5Zr0.5O2 is compatible with silicon semiconductor technologies, our work discovers a high-quality oxide material sustaining the PST, which holds great promise for spin-orbitronic applications.

Two-dimensional antiferromagnetic nodal-line semimetal and spin Hall effect in MnC4

Nodal-line semimetals, characterized by Dirac-like crossings along one dimensional k-space lines, represent a unique class of topological materials. In this study, we investigate the intriguing properties of room-temperature antiferromagnetic MnC4 and its nodal-line features both with and without spin–orbit coupling (SOC). In the absence of SOC, we identify a doubly degenerate Dirac-nodal line, robustly protected by a combination of time-reversal, mirror, and partial-translation symmetries. Remarkably, this nodal line withstands various external perturbations, including isotropic and anisotropic strain, and torsional deformations, due to the ionic-like bonding between Mn atoms and C clusters. With the inclusion of SOC, we observe a distinctive quasi-Dirac-nodal line that emerges due to the interplay between antiferromagnetism and SOC-induced spin-rotation symmetry breaking. Finally, we observed a robust spin Hall conductivity that aligns with the energy range where the quasi-nodal line appears. This study presents a compelling example of a robust symmetry-protected Dirac-nodal line antiferromagnetic monolayer, which has potential for applications in next-generation spintronic devices.

Plaquette Singlet Transition, Magnetic Barocaloric Effect, and Spin Supersolidity in the Shastry-Sutherland Model.

Inspired by recent experimental measurements [Guo etal., Phys. Rev. Lett. 124, 206602 (2020PRLTAO0031-900710.1103/PhysRevLett.124.206602); Jiménez etal., Nature (London) 592, 370 (2021)NATUAS0028-083610.1038/s41586-021-03411-8] on frustrated quantum magnet SrCu_{2}(BO_{3})_{2} under combined pressure and magnetic fields, we study the related spin-1/2 Shastry-Sutherland model using state-of-the-art tensor network methods. By calculating thermodynamics, correlations, and susceptibilities, we find, in zero magnetic field, not only a line of first-order dimer-singlet to plaquette-singlet phase transition ending with a critical point, but also signatures of the ordered plaquette-singlet transition with its critical end point terminating on this first-order line. Moreover, we uncover prominent magnetic barocaloric responses, a novel type of quantum correlation induced cooling effect, in the strongly fluctuating supercritical regime. Under finite fields, we identify a quantum phase transition from the plaquette-singlet phase to the spin supersolid phase that breaks simultaneously lattice translational and spin rotational symmetries. The present findings on the Shastry-Sutherland model are accessible in current experiments and would shed new light on the critical and supercritical phenomena in the archetypal frustrated quantum magnet SrCu_{2}(BO_{3})_{2}.

Spontaneous dimerization, spin-nematic order, and deconfined quantum critical point in a spin-1 Kitaev chain with tunable single-ion anisotropy

Kitaev-type spin chains have been demonstrated to be fertile playgrounds in which exotic phases and unconventional phase transitions are ready to appear. In this work, we use the density-matrix renormalization-group method to study the quantum phase diagram of a spin-1 Kitaev chain with a tunable negative single-ion anisotropy (SIA). When the strength of the SIA is small, the ground state is revealed to be a spin-nematic phase, which escapes conventional magnetic order but is characterized by a finite spin-nematic correlation because of the breaking spin-rotational symmetry. As the SIA increases, the spin-nematic phase is taken over by either a dimerized phase or an antiferromagnetic phase through an Ising-type phase transition, depending on the direction of the easy axis. For large enough SIA, the dimerized phase and the antiferromagnetic phase undergo a ``Landau-forbidden'' continuous phase transition, suggesting new platform of deconfined quantum critical point in spin-1 Kitaev chain.

Stabilizing Fluctuating Spin-Triplet Superconductivity in Graphene via Induced Spin-Orbit Coupling.

A recent experiment showed that a proximity-induced Ising spin-orbit coupling enhances the spin-triplet superconductivity in Bernal bilayer graphene. Here, we show that, due to the nearly perfect spin rotation symmetry of graphene, the fluctuations of the spin orientation of the triplet order parameter suppress the superconducting transition to nearly zero temperature. Our analysis shows that both an Ising spin-orbit coupling and an in-plane magnetic field can eliminate these low-lying fluctuations and can greatly enhance the transition temperature, consistent with the recent experiment. Our model also suggests the possible existence of a phase at small anisotropy and magnetic field which exhibits quasilong-range ordered spin-singlet charge 4e superconductivity, even while the triplet 2e superconducting order only exhibits short-ranged correlations. Finally, we discuss relevant experimental signatures.

Superfluidlike spin transport in the dynamic states of easy-axis magnets

The existing proposals for superfluidlike spin transport have been based on easy-plane magnets where the U(1) spin-rotational symmetry is spontaneously broken in equilibrium, and this has been limiting material choices for realizing superfluidlike spin transport to restricted classes of magnets. In this work, we lift this limitation by showing that superfluidlike spin transport can also be realized based on easy-axis magnets, where the U(1) spin-rotational symmetry is intact in equilibrium but can be broken in nonequilibrium. Specifically, we find the condition to engender a nonequilibrium easy-cone state by applying a spin torque to easy-axis magnets, which dynamically induces the spontaneous breaking of the U(1) spin-rotational symmetry and thereby can support superfluidlike spin transport. By exploiting this dynamic easy-cone state, we show theoretically that superfluidlike spin transport can be achieved in easy-axis magnets under suitable conditions and confirm the prediction by micromagnetic simulations. We envision that our work broadens the material library for realizing superfluidlike spin transport, showing the potential utility of dynamic states of magnets as venues to look for spin-transport phenomena that do not occur in static magnetic backgrounds.

Interaction-driven spontaneous ferromagnetic insulating states with odd Chern numbers

Motivated by recent experimental work on moiré systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence ± (2N + 1). These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction.

Continuous symmetry breaking in a two-dimensional Rydberg array.

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions1-3. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase4,5. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry6-9.

Anderson localization at the boundary of a two-dimensional topological superconductor

A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a situation when only a given number of channels ($m$) are topologically protected, while others are not and therefore are subject to Anderson localization in the presence of disorder. We study transport properties of such quasi-one-dimensional quantum wires with broken time-reversal and spin-rotational symmetries (class D) and calculate the average conductance, its variance and the third cumulant, as well as the average shot noise power. The results are obtained for arbitrary wire length, tracing a crossover from the diffusive Drude regime to the regime of strong localization where only $m$ protected channels conduct. Our approach is based on the nonperturbative treatment of the nonlinear supersymmetric sigma model of symmetry class D with two replicas developed in our recent publication [D. S. Antonenko et al., Phys. Rev. B 102, 195152 (2020)]. The presence of topologically protected modes results in the appearance of a topological Wess-Zumino-Witten term in the sigma-model action, which leads to an additional subsidiary series of eigenstates of the transfer-matrix Hamiltonian. The developed formalism can be applied to study the interplay of Anderson localization and topological protection in quantum wires of other symmetry classes.

Spin and Orbital Symmetry Breakings Central to the Laser-Induced Ultrafast Demagnetization of Transition Metals

The role of spin and orbital rotational symmetry on the laser-induced magnetization dynamics of itinerant-electron ferromagnets was theoretically investigated. The ultrafast demagnetization of transition metals is shown to be the direct consequence of the fundamental breaking of these conservation laws in the electronic system, an effect that is inherent to the nature of spin-orbit and electron-lattice interactions. A comprehensive symmetry analysis is complemented by exact numerical calculations of the time evolution of optically excited ferromagnetic ground states in the framework of a many-body electronic Hamiltonian. Thus, quantitative relations are established between the strength of the interactions that break the rotational symmetries and the time scales that are relevant for the magnetization dynamics.

Anderson localization transitions in disordered non-Hermitian systems with exceptional points

The critical exponents of continuous phase transitions of a Hermitian system depend on and only on its dimensionality and symmetries. This is the celebrated notion of the universality of continuous phase transitions. Here we numerically study the Anderson localization transitions in non-Hermitian two-dimensional (2D) systems with exceptional points by using the finite-size scaling analysis of the participation ratios. At the exceptional points of either second order or fourth order, two non-Hermitian systems with different symmetries have the same critical exponent $\ensuremath{\nu}\ensuremath{\simeq}2$ of correlation lengths, which differs from all known 2D disordered Hermitian and non-Hermitian systems. These feature is reminiscent of the superuniversality notion of Anderson localization transitions. In the symmetry-preserved and symmetry-broken phases, the non-Hermitian models with time-reversal symmetry and without spin-rotational symmetry, and without both time-reversal and spin-rotational symmetries, are in the same universality class of 2D Hermitian electron systems of Gaussian symplectic and unitary ensembles, where $\ensuremath{\nu}\ensuremath{\simeq}2.7$ and $\ensuremath{\nu}\ensuremath{\simeq}2.3$, respectively. The universality of the transition is further confirmed by showing that the critical exponent $\ensuremath{\nu}$ does not depend on the form of disorders and boundary conditions.

Quantum Hall spin textures far beyond the skyrmion limit

In strongly correlated quantum Hall ferromagnets with noninteger filling factors between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$, evidence of offbeat spin textures is obtained. The platforms for the study are two-dimensional electron systems based on MgZnO/ZnO heterostructures, in which the parameters of Zeeman and exchange energies are inconsistent with ordinary skyrmions. Experimental probing of magnetic order is fulfilled via exploration of the spectra of collective spin excitations by means of inelastic light scattering. In addition to the ferromagnetic spin exciton, a low-energy spin mode is observed, bearing witness to broken spin-rotational symmetry in the ground state. The two spin modes exhibit a pronounced anticrossing behavior, depending on the two-dimensional momentum, electron concentration, filling factor, and magnetic field tilt. The properties of the electron system are simulated using the exact diagonalization technique, showing that Landau level mixing and crossing play a key role in the nontrivial spin configuration. The corresponding spin textures emerging between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$ involve the orbital degree of freedom and are qualitatively different from skyrmions. Experiments at elevated temperatures show the destruction of this orbital spin texture phase with critical temperature far below the Zeeman energy. On the other side of $\ensuremath{\nu}=1$ the textures are absent.

Scaling of the disorder operator at deconfined quantum criticality

We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)d in the J-Q_3J−Q3 model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.

Coexistence of spin-orbit torque and unidirectional magnetoresistance effect induced by spin polarization with spin rotation symmetry in Co/Cu/Co structures

The conventional spin-orbit torque (SOT) and magnetoresistance effect observed in normal-metal (NM)/ferromagnet (FM) bilayers originate from the interaction between magnetic moments and spin with in-plane transverse polarization (${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{y}$). In FM/NM/FM trilayer structures, the presence of an extra FM layer breaks the symmetry, resulting in spin polarization other than ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{y}$ and the corresponding SOT. However, the study on the unidirectional magnetoresistance (UMR) effect induced by the spin polarization with spin rotation (SR) symmetry is still missing. In this work, we investigate the SOT and UMR effect in a Co/Cu/Co structure with crossed anisotropy by utilizing the harmonic longitudinal voltage measurement. We demonstrate that, in addition to the harmonic terms originating from the fieldlike SOT of the spin polarization with spin Hall and SR symmetry, two different unidirectional harmonic signals are observed in the angular and field scan measurements. Further, combining the SOT effective fields results from the harmonic Hall voltage measurement, we successfully separate the contributions of the observed unidirectional harmonic signals, which include the dampinglike SOT contribution through the giant magnetoresistance effect, and the UMR induced by the spin current with different polarization directions through spin-dependent scattering mechanism.

Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na2BaCo(PO4)2

Prototypical models and their material incarnations are cornerstones to the understanding of quantum magnetism. Here we show theoretically that the recently synthesized magnetic compound Na2BaCo(PO4)2 (NBCP) is a rare, nearly ideal material realization of the S = 1/2 triangular-lattice antiferromagnet with significant easy-axis spin exchange anisotropy. By combining the automatic parameter searching and tensor-network simulations, we establish a microscopic model description of this material with realistic model parameters, which can not only fit well the experimental thermodynamic data but also reproduce the measured magnetization curves without further adjustment of parameters. According to the established model, the NBCP hosts a spin supersolid state that breaks both the lattice translation symmetry and the spin rotational symmetry. Such a state is a spin analog of the long-sought supersolid state, thought to exist in solid Helium and optical lattice systems, and share similar traits. The NBCP therefore represents an ideal material-based platform to explore the physics of supersolidity as well as its quantum and thermal melting.

I4/mcm-Si48: An Ideal Topological Nodal-Line Semimetal

Topological semimetals (TSMs) have attracted numerous attention due to their exotic physical properties and great application potentials. Silicon-based TMSs are of particularly importance because of their high abundance, nontoxicity and natural compatibility with current semiconductor industry. In this work, an ideal low-energy topological nodal-line semimetal (TNLSM) silicon (I4/mcm-Si$_{48}$) with a clean band crossing at Fermi level is screened from thousands of silicon allotropes by the transferable tight-binding and DFT-HSE calculations. The results of formation energy, phonon dispersion, ab initio molecular dynamics and elastic constants show that I4/mcm-Si48 possesses good stability and is more stable than several synthetized silicon structures. By analyzing the symmetry, it reveals that the topological nodal-line of I4/mcm-Si48 is protected by mirror symmetry and inversion, time-reversal and SU(2) spin-rotation symmetries, and the nearly flat drumhead-like surface spectrum is observed. Furthermore, I4/mcm-Si48 exhibits exotic photoelectric properties and the Dirac fermions with high Fermi velocity (3.4$\sim$4.36$\times$10$^5$ m/s) can be excited by low energy photons. Our study provides a promising topological nodal-line semimetal for fundamental research and potential practical applications in semiconductor-compatible high-speed photoelectric devices.

Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry

We propose a geometric {approach to Lieb-Schultz-Mattis theorem for} quantum many-body systems with discrete spin-rotation symmetries and lattice inversion or rotation symmetry, but without translation symmetry assumed. Under symmetry-twisting on a $(d-1)$-dimensional plane, we find that any $d$-dimensional inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We also show that any rotation-symmetric generalized spin model with a projective representation at the rotation center has a similar degeneracy under symmetry-twisting. We argue that these degeneracies imply that {a unique symmetric gapped ground state that is smoothly connected to product states} is forbidden in the original untwisted systems -- generalized inversional/rotational Lieb-Schultz-Mattis theorems without lattice translation symmetry imposed. The traditional Lieb-Schultz-Mattis theorems with translations also fit in the proposed framework.