Magnetic Symmetry Research Articles

Emergent Noninvertible Symmetries in N=4 Supersymmetric Yang-Mills Theory.

One of the simplest examples of noninvertible symmetries in higher dimensions appears in 4D Maxwell theory, where its SL(2,Z) duality group can be combined with gauging subgroups of its electric and magnetic 1-form symmetries to yield such defects at many different values of the coupling. Even though N=4 supersymmetric Yang-Mills (SYM) theory also has an SL(2,Z) duality group, it only seems to share two types of such noninvertible defects with Maxwell theory (known as duality and triality defects). Motivated by this apparent difference, we begin our investigation of the fate of these symmetries by studying the case of 4D N=4 U(1) gauge theory, which contains Maxwell theory in its content. Surprisingly, we find that the noninvertible defects of Maxwell theory give rise, when combined with the standard U(1) symmetry acting on the free fermions, to defects that act on local operators as elements of the U(1) outer automorphism of the N=4 superconformal algebra, an operation that was referred to in the past as the "bonus symmetry." Turning to the non-Abelian case of N=4 SYM theory, the bonus symmetry is not an exact symmetry of the theory, but is known to emerge at the supergravity limit. Based on this observation, we study this limit and show that, if it is taken in a certain way, noninvertible defects that realize different elements of the bonus symmetry emerge as approximate symmetries, in analogy to the Abelian case.

Ultra‐fast finite element analysis of coreless axial flux permanent magnet synchronous machines

AbstractLarge‐scale design optimisation techniques enable the design of high‐performance electric machines. Electromagnetic 3D finite element analysis (FEA) is typically employed in optimisation studies for accurate analysis of axial flux permanent magnet (AFPM) machines, which require extensive computational resources. To reduce the computational burden, a FEA‐based mathematical method relying on the geometric and magnetic symmetry of coreless AFPM machines is proposed to estimate the machine performance indicators using the least number of FEA solutions, thereby significantly lowering the running time. This method is generally applicable to AFPM machines with low saturation effects and cogging torque as exemplified for a printed circuit board (PCB) stator coreless AFPM machine. To further reduce the computation time, a systematically simplified equivalent 3D FEA model for planar PCB coils integrated with this machine is also proposed. The practical implementation of the introduced method is elaborated based on an example optimisation study, and an analytical method for fast design scaling is also discussed. The results of the proposed approach are compared with detailed transient FEA results, and a prototype 26‐pole PCB stator coreless AFPM machine was also used to validate the results experimentally.

X-Ray Magnetic Circular Dichroism in Altermagnetic α-MnTe.

Altermagnetism is a recently identified magnetic symmetry class combining characteristics of conventional collinear ferromagnets and antiferromagnets, that were regarded as mutually exclusive, and enabling phenomena and functionalities unparalleled in either of the two traditional elementary magnetic classes. In this work we use symmetry, abinitio theory, and experiments to explore x-ray magnetic circular dichroism (XMCD) in the altermagnetic class. As a representative material for our XMCD study we choose α-MnTe with compensated antiparallel magnetic order in which an anomalous Hall effect has been already demonstrated. We predict and experimentally confirm a characteristic XMCD line shape for compensated moments lying in a plane perpendicular to the light propagation vector. Our results highlight the distinct phenomenology in altermagnets of this time-reversal symmetry breaking response, and its potential utility for element-specific spectroscopy and microscopy.

Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry

Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average C2zT, m, and C4zT and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups Pm,P2′,P4′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Pm,P{2}^{{\\prime} },P{4}^{{\\prime} }$$\\end{document}, and P6′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P{6}^{{\\prime} }$$\\end{document} with and without spin-orbit coupling, most of which can support CMP.

Excitonic instability towards a Potts-nematic quantum paramagnet

Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we focus on frustrated quantum magnets and study the nature of the quantum phase transition between a paramagnet and a magnetically ordered state with broken threefold (Z3) crystal rotation symmetry. We show that the transition can occur in two stages, giving rise to an intermediate nematic phase in which rotation symmetry is broken but the system remains magnetically disordered. Since the nematic transition is described by the three-state Potts model, the intermediate phase is a Z3 Potts-nematic phase. Our prediction of the existence of a Potts-nematic phase is based on an analysis of bound states formed from two-magnon excitations in the paramagnet, which become gapless while single-magnon excitations remain gapped. By considering three different lattice models, we demonstrate a generic instability towards two-magnon bound state formation in the Potts-nematic channel. We present both numerical results and a general analytical perturbative formula for the bound state binding energy similar to BCS theory. We further discuss a number of different materials that realize key features of the model considered, and thus provide promising venues for possible experimental observation. Published by the American Physical Society 2024

Noninvertible symmetries and anomalies from gauging 1-form electric centers

We devise a general method for obtaining 0-form noninvertible discrete chiral symmetries in 4-dimensional SU(N)/ℤp and SU(N) × U(1)/ℤp gauge theories with matter in arbitrary representations, where ℤp is a subgroup of the electric 1-form center symmetry. Our approach involves placing the theory on a three-torus and utilizing the Hamiltonian formalism to construct noninvertible operators by introducing twists compatible with the gauging of ℤp. These theories exhibit electric 1-form and magnetic 1-form global symmetries, and their generators play a crucial role in constructing the corresponding Hilbert space. The noninvertible operators are demonstrated to project onto specific Hilbert space sectors characterized by particular magnetic fluxes. Furthermore, when subjected to twists by the electric 1-form global symmetry, these surviving sectors reveal an anomaly between the noninvertible and the 1-form symmetries. We argue that an anomaly implies that certain sectors, characterized by the eigenvalues of the electric symmetry generators, exhibit multi-fold degeneracies. When we couple these theories to axions, infrared axionic noninvertible operators inherit the ultraviolet structure of the theory, including the projective nature of the operators and their anomalies. We discuss various examples of vector and chiral gauge theories that showcase the versatility of our approach.

Chirality-selective topological magnon phase transition induced by interplay of anisotropic exchange interactions in honeycomb ferromagnet

A variety of distinct anisotropic exchange interactions commonly exist in one magnetic material due to complex crystal, magnetic and orbital symmetries. Here we investigate the effects of multiple anisotropic exchange interactions on topological magnon in a honeycomb ferromagnet, and find a chirality-selective topological magnon phase transition induced by a complicated interplay of Dzyaloshinsky–Moriya interaction and pseudo-dipolar interaction, accompanied by the bulk gap close and reopen with chiral inversion. Moreover, this novel topological phase transition involves band inversion at high symmetry points K and K′, which can be regarded as a pseudo-orbital reversal, i.e. magnon valley degree of freedom, implying a new manipulation corresponding to a sign change of the magnon thermal Hall conductivity. Indeed, it can be realized in 4d or 5d correlated materials with both spin–orbit coupling and orbital localized states, such as iridates and ruthenates, etc. This novel regulation may have potential applications on magnon devices and topological magnonics.

A Magnetic-Geared Machine With Improved Magnetic Circuit Symmetry for Hybrid Electric Vehicle Applications

Magnetic-geared machine (MGM) has been widely investigated as the power split device for hybrid electric vehicles with the inherently high-integration of multi-mechanical ports. It is revealed that the magnetic circuits of armature winding in MGM are essentially asymmetrical for different phases under the magnetic field modulation effect. This inevitably results in unbalanced phase back electromotive force (EMF) waveforms, severe torque ripples, acoustic noise, and difficulty for precise control. To alleviate the asymmetry problem, a generic winding design model is presented for MGMs in this paper, which allows for consideration of all potential winding configurations. Firstly, a novel back EMF harmonic factor is proposed to account for both the harmonic content and asymmetric level in MGM. The genetic algorithm (GA) is further employed to optimize the winding in terms of minimizing the back EMF harmonic factor, armature magnetomotive force harmonic contents, and phase winding resistance. The proposed winding layout exhibits superior filtering capability for three-phase asymmetric magnetic field harmonics. As compared with the conventional integral-slot distributed winding, the MGM with the proposed winding exhibits improved back EMF waveform symmetry, suppressed torque ripple, and reduced core losses. Finally, an experimental prototype is manufactured to validate the effectiveness of asymmetric magnetic field suppression for MGMs. The results show the investigated winding design method is an effective solution to the asymmetric issue of MGMs, paving the way to research opportunities for further improvements.

A symmetry principle for gauge theories with fractons

Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

The central role of tilted anisotropy for field-free spin–orbit torque switching of perpendicular magnetization

The discovery of efficient magnetization switching upon device activation by spin Hall effect (SHE)-induced spin–orbit torque (SOT) changed the course of magnetic random-access memory (MRAM) research and development. However, for electronic systems with perpendicular magnetic anisotropy (PMA), the use of SOT is still hampered by the necessity of a longitudinal magnetic field to break magnetic symmetry and achieve deterministic switching. In this work, we demonstrate that robust and tunable field-free current-driven SOT switching of perpendicular magnetization can be controlled by the growth protocol in Pt-based magnetic heterostructures. We further elucidate that such growth-dependent symmetry breaking originates from the laterally tilted magnetic anisotropy of the ferromagnetic layer with PMA, a phenomenon that has been largely neglected in previous studies. We show experimentally and in simulation that in a PMA system with tilted anisotropy, the deterministic field-free switching exhibits a conventional SHE-induced damping-like torque feature, and the resulting current-induced effective field shows a nonlinear dependence on the applied current density. This relationship could be potentially misattributed to an unconventional SOT origin.

Realizing altermagnetism in two-dimensional metal-organic framework semiconductors with electric-field-controlled anisotropic spin current.

Altermagnets exhibit momentum-dependent spin-splitting in a collinear antiferromagnetic order due to their peculiar crystallographic and magnetic symmetry, resulting in the creation of spin currents with light elements. Here, we report two two-dimensional (2D) metal-organic framework (MOF) semiconductors, M(pyz)2 (M = Ca and Sr, pyz = pyrazine), which exhibit both altermagnetism and topological nodal point and line by using first-principles calculations and group theory. The altermagnetic 2D MOFs exhibit unconventional spin-splitting and macroscopic zero magnetization caused by 4-fold rotation in crystalline real space and 2-fold rotation in spin space, leading to the generation and control of anisotropic spin currents when an in-plane electric field ( E ) is applied. In particular, pure spin current with the spin Hall effect occurs when E is applied along the angular bisector of the two spin arrangements. Our work indicates the existence of altermagnetic MOF systems and a universal approach to generate electric-field-controlled spin currents for potential applications in antiferromagnetic spintronics.

Metamagnetic phase transition induced large magnetocaloric effect in a Dy0.5Ho0.5MnO3 single crystal.

Magnetic refrigeration based on the magnetocaloric effect is gaining interest in orthogonal or hexagonal rare-earth manganite. However, a more comprehensive understanding of the underlying mechanism is still required. We grew a high-quality single crystal of Dy0.5Ho0.5MnO3 using the optical floating zone method, since the parent crystals DyMnO3 and HoMnO3 have orthogonal and hexagonal structures, respectively. The magnetic and magnetocaloric properties and refrigeration mechanisms are thoroughly investigated. Doping modifies the magnetism according to the results obtained from the investigation of magnetic and dielectric properties and heat capacity. The spin reorientation transition shifts towards low temperature in comparison to HoMnO3. Near the Néel temperature of rare-earth sublattices (5 K), the highest changes in negative magnetic entropy under 0-70 kOe are 18 J kg-1 K-1 and 13 J kg-1 K-1 along the a- and c-axes, respectively. The low-temperature metamagnetic phase transition caused by the alterations in the magnetic symmetry of Ho3+ contributes to an increased magnetocaloric effect in comparison to the parent crystals, rendering it a promising choice for magnetic refrigeration applications. Dy0.5Ho0.5MnO3 exhibits a clear magnetocrystalline anisotropy with enhanced refrigeration capacity and negative magnetic entropy change along the a-axis. The adiabatic temperature change of Dy0.5Ho0.5MnO3 is 8.5 K, larger than that of HoMnO3, rendering it a promising choice for low-temperature magnetic refrigeration applications.

Detection of Inter-turn Short Circuit in Stator Windings of Electric Machines using Magnetic Symmetry Index and Machine Learning Methods

Detection of Inter-turn Short Circuit in Stator Windings of Electric Machines using Magnetic Symmetry Index and Machine Learning Methods

QSym2: A Quantum Symbolic Symmetry Analysis Program for Electronic Structure.

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, and they are not able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym2 that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym2 is able to address all of these shortcomings. To illustrate these capabilities of QSym2, four sets of case studies are examined in detail in this article: (i) high-symmetry C84H64, C60, and B9- to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral Fe(CN)63- to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral H3+ to demonstrate the analysis of density symmetries.

Shift Current with Gaussian Basis Sets and General Prescription for Maximally Symmetric Summations in the Irreducible Brillouin Zone.

The bulk photovoltaic effect is an experimentally verified phenomenon by which a direct charge current is induced within a non-centrosymmetric material by light illumination. Calculations of its intrinsic contribution, the shift current, are nowadays amenable from first-principles employing plane-wave bases. In this work, we present a general method for evaluating the shift conductivity in the framework of localized Gaussian basis sets that can be employed in both the length and velocity gauges, carrying the idiosyncrasies of the quantum-chemistry approach. The (possibly magnetic) symmetry of the system is exploited in order to fold the reciprocal space summations to the representation domain, allowing us to reduce computation time and unveiling the complete symmetry properties of the conductivity tensor under general light polarization.

Multistep magnetization switching in orthogonally twisted ferromagnetic monolayers.

The advent of twist engineering in two-dimensional crystals enables the design of van der Waals heterostructures with emergent properties. In the case of magnets, this approach can afford artificial antiferromagnets with tailored spin arrangements. Here we fabricate an orthogonally twisted bilayer by twisting two CrSBr ferromagnetic monolayers with an easy-axis in-plane spin anisotropy by 90°. The magnetotransport properties reveal multistep magnetization switching with a magnetic hysteresis opening, which is absent in the pristine case. By tuning the magnetic field, we modulate the remanent state and coercivity and select between hysteretic and non-hysteretic magnetoresistance scenarios. This complexity pinpoints spin anisotropy as a key aspect in twisted magnetic superlattices. Our results highlight control over the magnetic properties in van der Waals heterostructures, leading to a variety of field-induced phenomena and opening a fruitful playground for creating desired magnetic symmetries and manipulating non-collinear magnetic configurations.

Templates for magnetic symmetry and altermagnetism in hexagonal MnTe

Templates for magnetic symmetry and altermagnetism in hexagonal MnTe

First-principles investigation of the magnetoelectric properties of Ba7Mn4O15

Type-II multiferroics, in which the magnetic order breaks inversion symmetry, are appealing for both fundamental and applied research due their intrinsic coupling between magnetic and electrical orders. Using first-principles calculations we study the ground state magnetic behaviour of Ba7Mn4O15 which has been classified as a type-II multiferroic in recent experiments. Our constrained moment calculations with the proposed experimental magnetic structure shows the spontaneous emergence of a polar mode giving rise to an electrical polarisation comparable to other known type-II multiferroics. When the constraints on the magnetic moments are removed, the spins self-consistently relax into a canted antiferromagnetic ground state configuration where two magnetic modes transforming as distinct irreducible representations coexist. While the dominant magnetic mode matches well with the previous experimental observations, the second mode is found to possess a different character resulting in a non-polar ground state. Interestingly, the non-polar magnetic ground state exhibits a significantly strong linear magnetoelectric (ME) coupling comparable to the well-known multiferroic BiFeO3, suggesting strategies to design new linear MEs.

No superconductivity in Pb$_9$Cu$_1$(PO$_4$)$_6$O found in orbital and spin fluctuation exchange calculations

Finding a material that turns superconducting under ambient conditions has been the goal of over a century of research, and recently Pb_{10-x}10−xCu_xx(PO_44)_66O aka LK-99 has been put forward as a possible contestant. In this work, we study the possibility of electronically driven superconductivity in LK-99 also allowing for electron or hole doping. We use an ab initio derived two-band model of the Cu e_geg orbitals for which we determine interaction values from the constrained random phase approximation (cRPA). For this two-band model we perform calculations in the fluctuation exchange (FLEX) approach to assess the strength of orbital and spin fluctuations. We scan over a broad range of parameters and enforce no magnetic or orbital symmetry breaking. Even under optimized conditions for superconductivity, spin and orbital fluctuations turn out to be too weak for superconductivity anywhere near to room-temperature. We contrast this finding to non-self-consistent RPA, where it is possible to induce spin singlet d-wave superconductivity at T_cTc ≥300K if the system is put close enough to a magnetic instability.

Chirality-dependent energy induced by spin-orbit torque-driven artificial spin texture

Recently, vast research has been under investigation on the role of chirality in magnetization dynamics, an area that currently lacks a comprehensive understanding. To gain further insight into the importance of chirality, we explore the effects of varying the degree of chirality. To investigate these effects, we have fabricated samples with perpendicular magnetic anisotropy symmetry breaking through local helium ion irradiation with various azimuthal angles and degrees of irradiation. In this system, the spin-orbit torque can induce artificial spin texture, and our azimuthal angle and degree of chirality dependent results reveal a clear cosine dependence and a nonlinear increase, respectively. It implies the system not only follows the energy contribution of interfacial Dzyaloshinskii-Moriya interaction but also has a nonlinear impact depending on anisotropy asymmetry induced chirality differences. These experimental observations are consistent with our theoretical model and micromagnetic simulations, supporting our experimental results. Overall, our findings provide further insights into the role of chirality in magnetization dynamics and may have important implications for the development of future magnetic devices.