Higher-order Spin Research Articles

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

Spinning waveforms from the Kosower-Maybee-O’Connell formalism at leading order

We provide the analytic waveform in time domain for the scattering of two Kerr black holes at leading order in the post-Minkowskian (weak field, but generic velocity) expansion and up to fourth order in both spins. The result is obtained by the generalization of the Kosower-Maybee-O’Connell formalism to radiative observables, combined with the analytic continuation of the five-point scattering amplitude to complex kinematics. We use analyticity arguments to express the waveform directly in terms of the three-point coupling of the graviton to the spinning particles and the gravitational Compton amplitudes, completely bypassing the need to compute and integrate the five-point amplitude. In particular, this allows us to easily include higher-order spin contributions for any spinning compact body. Finally, in the spinless case, we find a new compact and gauge-invariant representation of the Kovacs-Thorne waveform. Published by the American Physical Society 2024

All-optical photonic switch via the higher-order topological spin Hall effect

All-optical photonic switch via the higher-order topological spin Hall effect

Suppression of Pulsed Dynamic Nuclear Polarization by Many-Body Spin Dynamics.

We study a mechanism by which nuclear hyperpolarization due to the polarization transfer from a microwave-pulse-controlled electron spin is suppressed. From analytical and numerical calculations of the unitary dynamics of multiple nuclear spins, we uncover that, combined with the formation of the dark state within a cluster of nuclei, coherent higher-order nuclear spin dynamics impose limits on the efficiency of the polarization transfer even in the absence of mundane depolarization processes such as nuclear spin diffusion and relaxation. Furthermore, we show that the influence of the dark state can be partly mitigated by introducing a disentangling operation. Our analysis is applied to the nuclear polarizations observed in ^{13}C nuclei coupled with a single nitrogen-vacancy center in diamond [Randall etal., Science 374, 1474 (2021)SCIEAS0036-807510.1126/science.abk0603]. Our Letter sheds light on collective engineering of nuclear spins as well as future designs of pulsed dynamic nuclear polarization protocols.

Resonant inelastic X-ray scattering applications in quantum materials

The essence of quantum materials lies in the intricate coupling among charge, spin, orbital and lattice degrees of freedom. Although X-ray photoemission spectroscopy and inelastic neutron scattering have advantages in detecting fermionic single-particle spectral function and bosonic spin excitations in quantum materials, respectively, probing other bosonic collective excitations especially their coupling is not possible until the establishment of the advanced resonant inelastic X-ray scattering (RIXS). In the past decades, RIXS has flourished with continuously improved energy resolution which made a paradigm shift from measuring crystal-field splitting and the charge-transfer excitation, to probing collective excitations and the order parameters of all degrees of freedom. This review paper summarises the latest research progress of quantum materials studied by the soft X-ray RIXS. For instance, three-dimensional collective charge excitations, plasmons, were discovered experimentally by RIXS in both electron and hole doped cuprate superconductors. The collective orbital excitations and excitons were found in copper and nickel based quantum materials. For the newly discovered nickelate superconductors, RIXS has made substantial contributions to characterising their electronic and magnetic excitations and the related ordering phenomena critical for an in-depth understanding of the underlying superconducting mechanicsm. The RIXS is a unique tool in probing the higher-order spin excitations in quantum materials due to the strong spin-orbit coupling and the core-valence exchange interaction. The RIXS is also found to be superior in probing the Stoner magnetic excitations in magnetic metals and topological magnetic materials. Finally, the development of RIXS technology in Chinese large-scale research facilities is briefly prospected.

High-order optical Hall effect at the tight focus of laser radiation

In this work, by the Richards-Wolf method, which describes the behavior of electromagnetic radiation at the tight focus, it is shown that high-order spin and orbital Hall effects take place in the focal plane. It is shown that when focusing a linearly polarized optical vortex with unit topological charge, four local subwavelength regions are formed in the focal plane, in which directions of the longitudinal projection of the spin angular momentum are opposite in the neighboring regions. That is, photons falling into neighboring regions in the focus have the opposite spin. This is the spin Hall effect of the 2nd order. It is also shown that when tightly focusing of superposition of cylindrical vector beams of the m-th order and zero order, 2m subwavelength regions are formed in the plane of tight focus, in which directions of the longitudinal projection of the orbital angular momentum are opposite in the neighboring regions. That is, photons falling into the neighboring regions at the focus have the opposite-sign on-axis projections of the orbital angular momentum. This is the orbital Hall effect of the m-th order.

Spin evolution of Venus-like planets subjected to gravitational and thermal tides

Context. The arrival of powerful instruments will provide valuable data for the characterization of rocky exoplanets. Rocky planets are mostly found in close-in orbits. They are therefore usually close to the circular-coplanar orbital state and are thus considered to be in a tidally locked synchronous spin state. For planets with larger orbits, however, exoplanets should still have nonzero eccentricities and/or obliquities, and realistic models of tides for rocky planets can allow for higher spin states than the synchronization state in the presence of eccentricities or obliquities. Aims. This work explores the secular evolution of a star–planet system under tidal interactions, both gravitational and thermal, induced by the quadrupolar component of the gravitational potential and the irradiation of the planetary surface, respectively. We show the possible spin–orbit evolution and resonances for eccentric orbits and explore the possibility of spin-orbit resonances raised by the obliquity of the planet. Then, we focus on the additional effect of a thick atmosphere on the possible resulting spin equilibrium states and explore the effect of the evolution of the stellar luminosity. Methods. We implemented the general secular evolution equations of tidal interactions in the secular code called ESPEM. In particular, we focus here on the tides raised by a star on a rocky planet and consider the effect of the presence of an atmosphere, neglecting the contribution of the stellar tide. The solid part of the tides was modeled with an anelastic rheology (Andrade model), while the atmospheric tides were modeled with an analytical formulation that was fit using a global climate model simulation. We focused on a Sun-Venus-like system in terms of stellar parameters, orbital configuration and planet size and mass. The Sun-Venus system is a good laboratory for studying and comparing the possible effect of atmospheric tides, and thus to explore the possible spin state of potential Venus-like exoplanets. Results. The formalism of Kaula associated with an Andrade rheology allows spin orbit resonances on pure rocky worlds. Similarly to the high-order spin–orbit resonances induced by eccentricity, the spin obliquity allows the excitation of high-frequency Fourier modes that allow some spin-orbit resonances to be stable. If the planet has a dense atmosphere, like that of Venus, another mechanism, the thermal tides, can counterbalance the effect of the gravitational tides. We found that thermal tides change the evolution of the spin of the planet, including the capture in spin–orbit resonances. If the spin inclination is high enough, thermal tides can drive the spin toward an anti-synchronization state, that is, a the 1:1 spin–orbit resonance with an obliquity of 180 degrees. Conclusions. Through our improvement of the gravitational and thermal tidal models, we can determine the dynamical state of exo-planets better, especially if they hold a thick atmosphere. In particular, the contribution of the atmospheric tides allows us to reproduce the spin state of Venus at a constant stellar luminosity. Our simulations have shown that the secular evolution of the spin and obliquity can lead to a retrograde spin of the Venus-like planet if the system starts from a high spin obliquity, in agreement with previous studies. The perturbing effect of a third body is still needed to determine the current state of Venus starting from a low initial obliquity. When the luminosity evolution of the Sun is taken into account, the picture changes. We find that the planet never reaches equilibrium: the timescale of the rotation evolution is longer than the luminosity variation timescale, which suggests that Venus may never reach a spin equilibrium state, but may still evolve.

On the higher-order Heisenberg spin system with quintic terms in self-consistent potential

The integrable higher-order Heisenberg spin system with quintic terms in self-consistent potential (HHSQ) is an extension of Heisenberg ferromagnetic equations. In this paper, we calculate the Lax expression of the HHSQ system, then the motioning curves in [Formula: see text] dimension of Heisenberg ferromagnetic equations have been discussed. The Darboux transformation of the HHSQ system is constructed and a set of soliton solutions will be demonstrated by Darboux transformation.

High-Order Orbital and Spin Hall Effects at the Tight Focus of Laser Beams

In this paper, using a Richards–Wolf method, which describes the behavior of electromagnetic waves at the sharp focus, we show that high-order spin and orbital Hall effects take place at the focal plane of tightly focused laser beams. We reveal that four local subwavelength regions are formed at the focus of a linearly polarized optical vortex with unit topological charge, where the spin angular momentum behaves in a special way. Longitudinal projections of the spin angular momentum are oppositely directed in the adjacent regions. We conclude that this is because photons falling into the neighboring regions at the focus have the opposite spin. This newly observed phenomenon may be called a spin Hall effect of the 4-th order. We also show that tightly focusing the superposition of cylindrical vector beams of the m-th and zero-order produces 2m subwavelength regions in the focal plane, such that longitudinal projections of the orbital angular momentum are oppositely directed in the neighboring regions. This occurs because photons falling into the neighboring regions at the focus have the opposite signs of the on-axis projections of the orbital angular momentum. This phenomenon may be termed an orbital Hall effect of the 2m-th order.

Geometric integration of classical spin dynamics via a mean-field Schrödinger equation

The Landau-Lifshitz equation describes the time evolution of magnetic dipoles and can be derived by taking the classical limit of a quantum mechanical spin Hamiltonian. To take this limit, one constrains the many-body quantum state to a tensor product of coherent states, thereby neglecting entanglement between sites. Expectation values of the quantum spin operators produce the usual classical spin dipoles. One may also consider expectation values of polynomials of the spin operators, leading to quadrupole and higher-order spin moments, which satisfy a dynamical equation of motion that generalizes the Landau-Lifshitz dynamics [Zhang and Batista, Phys. Rev. B 104, 104409 (2021)]. Here we reformulate the dynamics of these ${N}^{2}\ensuremath{-}1$ generalized spin components as a mean-field Schr\"odinger equation on the $N$-dimensional coherent state. This viewpoint suggests efficient integration methods that respect the local symplectic structure of the classical spin dynamics.

Stability of the planar synchronous full two-body problem—The approach of periodic orbits

We investigate the dynamical stability of the synchronous state of the planar full two-body problem (PF2BP) by employing the approach of periodic orbit in the primary’s body-fixed frame. Our results indicate that the traditional model to the spin–orbit resonances by neglecting the rotational motion’s influence on the orbital motion is inappropriate in the binary asteroid system because the two asteroids are close to each other, leading to strong coupling between the orbits and rotations. Focusing on the high-order spin–orbit resonance, the family genealogy of periodic orbits in the unperturbed case is broken apart by some resonances in the perturbed case. In the case of no spin–orbit resonances, the periodic orbit is near-circular and is generally but not always stable. In the case of spin–orbit resonances, the periodic orbit can be elliptic, and one branch of the periodic orbits is stable. In contrast, the other branch is unstable for small to moderate orbit eccentricities.

Mode selective excitation of spin waves

Spin waves propagating in a waveguide have eigenmodes depending on the standing waves formed in the perpendicular direction. Although it is functional to excite high order spin wave modes, it has been difficult to excite a high order spin wave mode selectively. In this work, we numerically investigated spin wave excitation in a T-shaped magnetic device, and we consequently found that even high order spin wave modes are selectively excited by optimizing the frequency and the dimension of the T-shaped structure.

Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar–Bernevig–Hughes model

We study the higher-order topological spin phases based on a spin analogue of Benalcazar–Bernevig–Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.

Magnetization of magnetically inhomogeneous Sr2FeMoO6-δ nanoparticles

Magnetization is a key property of magnetic materials. Nevertheless, a satisfactory, analytical description of the temperature dependence of magnetization in double perovskites such as strontium ferromolybdate is still missing. In this work, we develop, for the very first time, a model of the magnetization of nanosized, magnetically inhomogeneous Sr2FeMoO6-δ nanoparticles. The temperature dependence of magnetization was approximated by an equation consisting of a Bloch-law spin wave term, a higher order spin wave correction, both taking into account the temperature dependence of the spin-wave stiffness, and a superparamagnetic term including the Langevin function. In the limit of pure ferromagnetic behavior, the model is applicable also to SFMO ceramics. In the vicinity of the Curie temperature (T/TC > 0.85), the model fails.

Phase transitions of the ferroelectric (ND4)2FeCl5·D2O under magnetic field

Due to the strong coupling between magnetism and ferroelectricity, ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ exhibits several intriguing magnetic and electric phases. In this Letter, we include higher-order onsite anisotropic spin interactions to explain the ferroelectric phase transitions of ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ in a magnetic field and to produce the large weights of high-order harmonic components in the cycloid structure that are observed from neutron diffraction experiments. Moreover, we predict a new ferroelectric phase sandwiched between the FE II and FE III phases in a magnetic field. By emphasizing the importance of the higher-order spin anisotropic interactions, our work provides a framework to understand multiferroic materials with rich phase diagrams.

Dual-polarization topological phases and phase transition in magnetic photonic crystalline insulator

Two-dimensional topological photonic crystals have rapidly emerged as a recent and fascinating branch of photonic research. However, most of them were limited to a specific type of polarization, TE or TM polarization. Here, we explored the dual-polarization topological phases in two-dimensional magnetic photonic crystal (PC) which are composed of ferrite rod clusters in the plasma background. Under the perturbations of the bias magnetic field and/or the cluster distortion in the unit cell, the PC exhibited dual-polarization topological phases, including the quantum Hall (QH) phase, the higher-order quantum spin Hall (HO-QSH) phase and the conventional insulator (CI) phase. We studied the topological nature of these phases by the Wilson loop, Chern number, and unidirectional edge states. Intriguingly, we showed that the HO-QSH phases could present in PC of C 3v symmetry instead of being restricted to C 6v symmetry. The lower symmetry enlarges the gap in the edge states, which helps for the emergence of corner states. By continuously deforming the unit cell configuration, we demonstrated the phase transition in the system was dual-polarization. Our results extend the topological phases in the PCs and pave the way for the dual-polarization topological devices and their applications.

Quantum phases and spin liquid properties of 1T-TaS2

Quantum materials exhibiting magnetic frustration are connected to diverse phenomena, including high Tc superconductivity, topological order, and quantum spin liquids (QSLs). A QSL is a quantum phase (QP) related to a quantum-entangled fluid-like state of matter. Previous experiments on QSL candidate materials are usually interpreted in terms of a single QP, although theories indicate that many distinct QPs are closely competing in typical frustrated spin models. Here we report on combined temperature-dependent muon spin relaxation and specific heat measurements for the triangular-lattice QSL candidate material 1T-TaS2 that provide evidence for competing QPs. The measured properties are assigned to arrays of individual QSL layers within the layered charge density wave structure of 1T-TaS2 and their characteristic parameters can be interpreted as those of distinct Z2 QSL phases. The present results reveal that a QSL description can extend beyond the lowest temperatures, offering an additional perspective in the search for such materials.

Electrical characterisation of higher order spin wave modes in vortex-based magnetic tunnel junctions

NiFe-based vortex spin-torque nano-oscillators (STNO) have been shown to be rich dynamic systems which can operate as efficient frequency generators and detectors, but with a limitation in frequency determined by the gyrotropic frequency, typically sub-GHz. In this report, we present a detailed analysis of the nature of the higher order spin wave modes which exist in the Super High Frequency range (3–30 GHz). This is achieved via micromagnetic simulations and electrical characterisation in magnetic tunnel junctions, both directly via the spin-diode effect and indirectly via the measurement of the coupling with the gyrotropic critical current. The excitation mechanism and spatial profile of the modes are shown to have a complex dependence on the vortex core position. Additionally, the inter-mode coupling between the fundamental gyrotropic mode and the higher order modes is shown to reduce or enhance the effective damping depending upon the sense of propagation of the confined spin wave.

Tidal Dissipation in Dual-body, Highly Eccentric, and Nonsynchronously Rotating Systems: Applications to Pluto–Charon and the Exoplanet TRAPPIST-1e

Abstract Using the Andrade-derived Sundberg–Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto–Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including e 20), we find divergences from the traditionally used e 2 truncation starting around e = 0.1. Order-of-magnitude differences begin to occur for e > 0.6. Critically, higher-order eccentricity terms activate additional spin–orbit resonances. Worlds experiencing nonsynchronous rotation can fall into and out of these resonances, altering their long-term evolution. Nonzero obliquity generally does not generate significantly higher heating; however, it can considerably alter orbital and rotational evolution. Much like eccentricity, obliquity can activate new tidal modes and resonances. Tracking the dual-body dissipation within Pluto and Charon leads to faster evolution and dramatically different orbital outcomes. Based on our findings, we recommend future tidal studies on worlds with e ≥ 0.3 to take into account additional eccentricity terms beyond e 2. This threshold should be lowered to e > 0.1 if nonsynchronous rotation or nonzero obliquity is under consideration. Due to the poor convergence of the eccentricity functions, studies on worlds that may experience very high eccentricity (e ≥ 0.6) should include terms with high powers of eccentricity. We provide these equations up to e 10 for arbitrary obliquity and nonsynchronous rotation. Finally, the assumption that short-period, solid-body exoplanets with e ≳ 0.1 are tidally locked in their 1:1 spin–orbit resonance should be reconsidered. Higher-order spin–orbit resonances can exist even at these relatively modest eccentricities, while previous studies have found such resonances can significantly alter stellar-driven climate.

Tuning thermal expansion by a continuing atomic rearrangement mechanism in a multifunctional titanium alloy

As to multifunctional titanium alloys with high strength and low elastic modulus, thermal training is crucial to tune their thermal expansion from positive to negative, resulting in a novel linear expansion which is stable in a wide temperature range. Aided by the high-order Hooke’s law of elastic solids, a reversible atomic rearrangement mechanism was proposed to explain the novel findings which are unexpected from typical shape memory alloys. To confirm this continuous mechanism, a Ti-Nb based alloy, which possesses a nanoscale spongy microstructure consisting of the interpenetrated Nb-rich and Nb-lean domains produced by spinodal decomposition, was used to trace the crystal structure change by in-situ high energy synchrotron X-ray diffraction analyses. By increasing exposure time, the overlapped diffraction peaks can be separated accurately. The calculated results demonstrate that, in the nanoscale Nb-lean domains, the crystal structure parameters vary linearly with changing temperature along the atomic pathway of the bcc-hcp transition. This linear relationship in a wide temperature range is unusual for first-order martensitic shape memory alloys but is common for Invar alloys with high-order spin transitions. Furthermore, the alloy exhibits smooth DSC curves free of transformation-induced heat peaks observed in shape memory alloys, which is consistent with the proposed mechanism that the reversible transition is of high-order.