Relativistic Spin Research Articles

Probing general relativistic spin–orbit coupling with gravitational waves from hierarchical triple systems

ABSTRACT Wave packets propagating in inhomogeneous media experience a coupling between internal and external degrees of freedom and, as a consequence, follow spin-dependent trajectories. These phenomena, well known in optics and condensed matter physics, are referred to as spin Hall effects. Similarly, the gravitational spin Hall effect is expected to affect the propagation of gravitational waves on curved spacetimes. In this general-relativistic setup, the curvature of spacetime acts as impurities in a semiconductor or inhomogeneities in an optical medium, leading to a frequency- and polarization-dependent propagation of wave packets. In this letter, we study this effect for strong-field lensed gravitational waves generated in hierarchical triple black hole systems in which a stellar-mass binary merges near a more massive black hole. We calculate how the gravitational spin Hall effect modifies the gravitational waveforms and show its potential for experimental observation. If detected, these effects will have profound implications for astrophysics and tests of general relativity.

Giant chiral magnetoelectric oscillations in a van der Waals multiferroic

Helical spin structures are expressions of magnetically induced chirality, entangling the dipolar and magnetic orders in materials1–4. The recent discovery of helical van der Waals multiferroics down to the ultrathin limit raises prospects of large chiral magnetoelectric correlations in two dimensions5,6. However, the exact nature and magnitude of these couplings have remained unknown so far. Here we perform a precision measurement of the dynamical magnetoelectric coupling for an enantiopure domain in an exfoliated van der Waals multiferroic. We evaluate this interaction in resonance with a collective electromagnon mode, capturing the impact of its oscillations on the dipolar and magnetic orders of the material with a suite of ultrafast optical probes. Our data show a giant natural optical activity at terahertz frequencies, characterized by quadrature modulations between the electric polarization and magnetization components. First-principles calculations further show that these chiral couplings originate from the synergy between the non-collinear spin texture and relativistic spin–orbit interactions, resulting in substantial enhancements over lattice-mediated effects. Our findings highlight the potential for intertwined orders to enable unique functionalities in the two-dimensional limit and pave the way for the development of van der Waals magnetoelectric devices operating at terahertz speeds.

Cluster Odd-Parity Multipoles by Staggered Orbital Ordering in Locally Noncentrosymmetric Crystals

Odd-parity multipoles in crystals manifest themselves not only in their peculiar electronic orderings but also in unconventional parity-violating physical phenomena. We here report the emergence of odd-parity multipoles by considering staggered orbital orderings in a locally noncentrosymmetric crystal system with the global inversion center but without the inversion center at each lattice site. We show that various odd-parity multipoles, such as the electric toroidal monopole, electric dipole, and electric toroidal quadrupole, are realized depending on the type of orbital orderings in the one-dimensional zigzag chain. Such odd-parity multipoles give rise to an antisymmetric spin splitting in the electronic band structure with the aid of the relativistic spin–orbit coupling. We also show that similar states with odd-parity multipoles are realized in other locally noncentrosymmetric crystals, such as the two-dimensional honeycomb and three-dimensional diamond structures.

Spin–Orbit Coupling Free Nonlinear Spin Hall Effect in a Triangle-Unit Collinear Antiferromagnet with Magnetic Toroidal Dipole

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena.

Large thermoelectric transport in magnetically coupled CrI3/1T-MoS2 vdW heterostructure via spin–charge interconversion

Low-dimensional materials with prominent thermoelectric (TE) effect play a pivotal role in realizing state-of-the-art nanoscale TE devices. The fusion of TE effect with the magnetism through seamless integration of TE and magnetic materials in the 2D limit offers access to control longitudinal as well as transverse TE properties via magnetic proximity effect. Herein, we design a van der Waals (vdW) heterostructure of metallic 1T-MoS2 with promising TE properties and a layer-dependent magnetic CrI3 material. The result highlights exotic electronic and magnetic configurations of the designed monolayer-CrI3/1T-MoS2 vdW heterostructure, which show magnetically-coupled TE characteristics. The observed remarkable magnetic proximity stems from large magnetic anisotropy energy and spin polarization, which are found to be 2.21 meV Cr−1 and 12.30%, respectively. To this end, the semiconducting CrI3 layer with intrinsic magnetism leads to efficient control and tunability of the observed spin-correlated anomalous Nernst effect. Moreover, a large dimensionless figure of merit of ∼6 and a power factor of ∼3.8×1011/τ∘ Wm−1K−2s−1 near the Fermi level at 300 K endorse the rejuvenated TE effect. The strong relativistic spin–orbit coupling validates the significant correlation of TE properties with intrinsic magnetic configuration. The present study underscores the significance of the magnetic proximity-governed TE effect in vdW heterostructures to engineer low-dimensional TE devices.

The Relativistic Spin Precession in the Compact Double Neutron Star System PSR J1946+2052

Abstract We observe systematic profile changes in the visible pulsar of the compact double neutron star system PSR J1946+2052 using observations with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The interpulse of PSR J1946+2052 changed from a single-peak to a double-peak shape from 2018–2021. We attribute this evolution as the result of the relativistic spin precession of the pulsar. With the high sensitivity of FAST, we also measure significant polarization for the first time, allowing us to model this with the precessional rotating vector model. Assuming, to the first order, a circular hollow-cone-like emission beam pattern and taking the validity of general relativity (GR), we derive the binary’s orbital inclination angle ( 63 ∘ − 3 ∘ + 5 ∘ ) and pulsar’s spin geometry. The pulsar’s spin vector and the orbital angular momentum vector are found to be only slightly misaligned ( 0. ∘ 21 − 0. ∘ 10 + 0. ∘ 28 ). The quoted uncertainties do not reflect the systematic uncertainties introduced by our model assumptions. By simulating future observations of profile and polarization evolution, we estimate that we could constrain the precession rate within a 43% uncertainty in 9 yr. Hence, we suggest that the system’s profile evolution could be combined with precise pulsar timing to test GR in the future.

Foldy–Wouthuysen transformation of Dirac equation in the context of Magueijo–Smolin model of the doubly special relativity

In this paper, in the context of the Magueijo–Smolin (MS) model and using the Foldy–Wouthuysen transformation for relativistic spin-1/2 particles, we study the nonrelativistic limit (NRL) of the Dirac equation within the doubly special relativity. This leads to obtaining a deformed Schrödinger–Pauli equation; there, we test the influence of the MS model on the NRL of the Dirac equation. However, we also examine the efficacy and behavior of the Foldy–Wouthuysen transformation in deriving the NRL in the presence of MS model. Besides, we compute that the energies shift in the context of MS model and check if the deformed Schrödinger–Pauli equation form still shows explicitly the g-factor 2.

Effect of In-Plane Magnetic Field on Skyrmions in a Centrosymmetric Triangular-Lattice System with Symmetric Anisotropic Exchange Interaction

We report our numerical results on the stability of the skyrmion crystal phase in an external magnetic field for both in-plane and out-of-plane directions in a centrosymmetric host. We analyze a spin model with the two-spin symmetric anisotropic exchange interaction that arises from relativistic spin–orbit coupling on a triangular lattice. By performing simulated annealing, we construct magnetic phase diagrams when the magnetic field is tilted from the out-of-plane field direction to the in-plane field direction. We find a different stability tendency of the skyrmion crystal phase according to the directions of the in-plane field, which provides a signal of the two-spin symmetric anisotropic exchange interaction for stabilizing the skyrmion crystal phase. Our results indicate that the mechanism of the skyrmion crystal phase triggered by the two-spin symmetric anisotropic exchange interaction can be experimentally tested by applying the in-plane magnetic field.

Relativistic spin-0 Duffin–Kemmer–Petiau equation in Bonnor–Melvin–Lambda solution

In this paper, we conduct a comprehensive exploration of the relativistic quantum dynamics of spin-0 scalar particles, as described by the Duffin–Kemmer–Petiau (DKP) equation, within the framework of a magnetic space-time. Our focus is on the Bonnor–Melvin–Lambda (BML) solution, a four-dimensional magnetic universe characterized by a magnetic field that varies with axial distance. To initiate this investigation, we derive the radial equation using a suitable wave function ansatz and subsequently employ special functions to solve it. Furthermore, we extend our analysis to include Duffin–Kemmer–Petiau oscillator fields within the same BML space-time background. We derive the corresponding radial equation and solve it using special functions. Significantly, our results show that the geometry’s topology and the cosmological constant (both are related to the magnetic field strength) influence the eigenvalue solution of spin-0 DKP fields and DKP-oscillator fields, leading to substantial modifications in the overall outcomes.

Simultaneous High Charge‐Spin Conversion Efficiency and Large Spin Diffusion Length in Altermagnetic RuO2

AbstractEfficient spin sources with large spin Hall angle (θSH) and long spin diffusion length (λSD) are highly desired in the application of spintronic devices. However, due to strong spin‐orbit coupling, the two targets can hardly be achieved simultaneously in conventional relativistic spin sources, like heavy metals. Here, it is proven that collinear antiferromagnetic RuO2 films are able to address this key issue and break the inverse relationship of θSH versus λSD. Based on spin torque‐ferromagnetic resonance and spin pumping measurements, the authors demonstrate that the θSH of RuO2(100) films is 0.183, and the λSD is over 12 nm being an order of magnitude longer than that of Pt, β‐W, and β‐Ta. Meanwhile, sizable λSD is also obtained in spin current with out‐of‐plane spin polarization generated by RuO2(101) films. By conducting a control experiment, the nonrelativistic altermagnetic spin splitting effect (ASSE) is ascertained to be the crucial mechanism accounting for the simultaneous large θSH and long λSD in RuO2. Besides the fundamental significance, these findings will advance the development of spintronics towards higher efficiency and lower power consumption.

Entropy current and entropy production in relativistic spin hydrodynamics

We use a first-principle quantum-statistical method to derive the expression of the entropy production rate in relativistic spin hydrodynamics. We show that the entropy current is not uniquely defined and can be changed by means of entropy-gauge transformations, similarly as the stress-energy tensor and the spin tensor can be changed with pseudo-gauge transformations. We show that the local thermodynamic relations, which are admittedly educated guesses in relativistic spin hydrodynamics inspired by those at global thermodynamic equilibrium, do not hold in general and they are also non-invariant under entropy-gauge transformations. Notwithstanding, we show that the entropy production rate is independent of those transformations and we provide a universally applicable expression, extending that known in literature, from which the dissipative parts of the energy momentum and spin tensors can be inferred.

Altermagnetic lifting of Kramers spin degeneracy

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids1,2. It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology3–7 to topological quantum matter8–14. Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin15. The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin–orbit coupling (SOC)16–19. A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic20,21, that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization20–23. Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors20,21, that have been either identified recently or perceived for many decades as conventional antiferromagnets21,24,25.

Fractional Laplacian Spinning Particle in External Electromagnetic Field

We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable λ governs the kinetic energy that is non-local in λ. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in λ, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential.

Visualizations and Analyses of Quantum Behavior, Spacetime Curvature, and Metric Relationships in Relativistic Physics

This study aims to investigate essential concepts in quantum mechanics and theoretical physics, with an emphasis on the 1+1 dimension. We examine the Dirac equation for relativistic spin-1/2 particles, the Time-Dependent Schrödinger Equation in 1+1 spacetime with flat conformal metric, and connect them to the Dirac equation. Additionally, we explore the Alcubierre Metric related to warp drive, particle modeling in a harmonic potential using the Schrödinger Equation, and the Gödel Metric Solution to depict the peculiarities of spacetime. The research aims to deepen the understanding of these concepts, identify theoretical implications, and their potential applications. This research aims to enhance the understanding of fundamental physics, assist in the development of future technologies, and provide deeper insights into the universe. Its benefits lie in contributing to theoretical understanding in physics, which can spark the development of new theories. This study is limited to physics concepts in the 1+1 dimensions, without empirical experiments or practical applications. The primary focus is on the theoretical analysis of these concepts. The results of this research have potential theoretical implications in understanding basic physics and spacetime phenomena. The simplification and connections between these concepts can aid in the development of new theories in theoretical physics. The uniqueness of this research lies in its integrative approach to quantum mechanics and theoretical physics concepts in the 1+1 dimension, which may not have been extensively explored previously. Through this research, we have investigated several key concepts in quantum mechanics and theoretical physics in the 1+1 dimension. These findings can make a significant contribution to our understanding of the universe and the potential development of new theories in physics.

Linearly stable and causal relativistic first-order spin hydrodynamics

Linearly stable and causal relativistic first-order spin hydrodynamics

Spin in the Dirac and Schr¨odinger Equations According to the Planck Vacuum Theory

This paper examines the concept of particle spin as it applies to the Dirac and Schr¨odinger equations in the Planck vacuum (PV) theory. Results show: that the reduced Planck constant is equal to the spin coefficient for the Planck particle (PP), the proton, and the electron cores; that the well-known energy and momentum operators can be used to derive the Schr¨odinger equation; that the wavefunctions for both equations are related to the electron Compton radius; and that the relativistic spin operator is derived from the Dirac equation.The spin and mass of the electron or proton cores are created simultaneously within the PV and transmitted into free space.

Space-time origin of gauge symmetry

In this work, by a first principles calculation, we show that quantum states describing massive relativistic free spinning particles obey kinematical conditions whose origin can be traced to parity as a good quantum number. These conditions are at the root of the equations of motion and of the constraints satisfied by the corresponding fields. In the massless limit, well defined parity is lost but a symmetry emerges related to arbitrary changes in the unphysical parity components. It is shown that this emergent symmetry is the celebrated gauge symmetry.

Deep anharmonicity on the relativistic spin-0 particles within the spherical regime

We present an oscillator model of relativistic spin-0 charges moving in quantum states with minimal electromagnetic field coupling. Rather than using a perturbative approach, we implemented anharmonicity directly under the integer-dependent levels. In this way, the rest mass energy is kept at 280[Formula: see text]MeV. Within the extended Pekeris approximation, we have also improved the deep approximation to the third and fourth orders near equilibrium at 7.5[Formula: see text]fm with a width range of [Formula: see text]. By taking into account the Morse potential energy, the improved approximation provides a model for the relativistic quantum states of the spatially independent rest mass without an external magnetic field. We considered an extra-energy addition that results in shifted Morse potentials in the depth range of 80–100[Formula: see text]MeV, yielding positive and negative values for particles and antiparticles, respectively. As a result of the shift, it has been concluded that the potential depth of the charged particle affects the relativistic energy levels, where we have found about 200[Formula: see text]MeV for particles and nearly [Formula: see text]10[Formula: see text]MeV for antiparticles. In addition to the negative energy states, the wave functions ([Formula: see text], [Formula: see text]) and ([Formula: see text], [Formula: see text]), which correspond to the energy levels, have been followed by the typical probability form, which shows charge distribution.

Soft X-ray Fermi surface tomography of palladium and rhodium via momentum microscopy

Fermi surfaces of transition metals, which describe all thermodynamical and transport quantities of solids, often fail to be modeled by one-electron mean-field theory due to strong correlations among the valence electrons. In addition, relativistic spin–orbit coupling pronounced in heavier elements lifts the degeneracy of the energy bands and further modifies the Fermi surface. Palladium and rhodium, two 4d metals attributed to show significant spin–orbit coupling and electron correlations, are ideal for a systematic and fundamental study of the two fundamental physical phenomena and their interplay in the electronic structure. In this study, we explored the Fermi surface of the 4d noble metals palladium and rhodium obtained via high-resolution constant initial state momentum microscopy. The complete 3D-Fermi surfaces of palladium and rhodium were tomographically mapped using soft X-ray photon energies from 34 eV up to 660 eV. To fully capture the orbital angular momentum of states across the Fermi surface, the Fermi surface tomography was performed using p- and s- polarized light. Applicability and limitations of the nearly-free electron final state model in photoemission are discussed using a complex band structure model supported by experimental evidence. The significance of spin–orbit coupling and electron correlations across the Fermi surfaces will be discussed within the context of the photoemission results. State-of-the-art fully relativistic Korringa–Kohn–Rostoker (KKR) calculations within the one-step model of photoemission are used to support the experimental results.

Spin Alignment of Vector Mesons in Heavy-Ion Collisions.

Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element ρ_{00} for ϕ mesons and show that anisotropies of local field correlations with respect to the spin quantization direction lead to ϕ meson's spin alignment. We propose that the local correlation or fluctuation of ϕ fields is the dominant mechanism for the observed ϕ meson's spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of ρ_{00} agrees with STAR's data. We further predict the azimuthal angle dependence of ρ_{00} which can be tested in future experiments.