Spin Coupling Research Articles

Salts of vanadyl phthalocyanine {VIVO(Pc•3−)}− anions with decamethylmetallocenium cations (Cp*2M+, M = CrIII and CoIII). Ferromagnetic coupling in the [(Cp*2Cr+){VIVO(Pc•3−)}−]2 assemblies

Vanadyl phthalocyanine {VIVO(Pc2−)}0 was reduced by decamethylchromocene or decamethylcobaltocene (Cp*2MII), and the crystals of the complexes were precipitated by n-hexane. Reduction of this phthalocyanine is centered on the macrocycle providing the formation of the {VIVO(Pc•3−)}− anions containing two paramagnetic VIV and Pc•3− centers with an S = 1/2 spin state. These paramagnetic anions coexist in (Cp*2Cr+){VIVO(Pc•3−)}−·3C6H4Cl2 (1) with the high-spin (S = 3/2) Cp*2Cr+ counter cations. Nearly isolated assemblies in which two Cp*2Cr+ cations are sandwiched between two {VIVO(Pc•3−)}− anions are formed in 1. Effective magnetic moment of 1 of 4.57 μB at 300 K corresponds to the contribution of noninteracting VIV, Pc•3− and CrIII spins. Weiss temperature of +4 K indicates weak ferromagnetic coupling of spins. Effective magnetic moment of 1 increases upon cooling up to 4.78 μB at 8 K and then drastically falls down. Such magnetic behavior is described well by ferromagnetic coupling between the VIV and Pc•3− spins with J1 = + 4.75 cm−1 and weaker ferromagnetic interactions between Pc•3− and CrIII spins through the Cp* ligand with J2 = +1.08 cm−1. Weak antiferromagnetic coupling with J3 = −0.76 cm−1 is also present between the CrIII spins. Complexes (Cp*2Co+){VIVO(Pc•3−)}−·1.5C6H4Cl2 (2) and (Cp*2Co+) {VIVO(Pc•3−)}−·C6H4Cl2 (3) with the diamagnetic Cp*2Co+ counter cations (S = 0) were also obtained allowing to study their crystal structures and optical properties.

Tunable spin-glass optical simulator based on multiple light scattering

The race to heuristically solve nondeterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which represents an archetypal NP problem. However, achieving completely programmable spin couplings in these large-scale optical Ising simulators remains an open challenge. Here, by exploiting the knowledge of the transmission matrix of a random medium, we experimentally demonstrate the possibility of controlling the couplings of a fully connected Ising spin system. By tailoring the input wave front we showcase the possibility of modifying the Ising Hamiltonian both by accounting for an external magnetic field and by controlling the number of degenerate ground states and their properties and probabilities. Our results represent a relevant step toward the realization of fully programmable Ising machines on thin optical-platforms that are capable of solving complex spin-glass Hamiltonians on a large scale.

Dynamic Simulation of the Energy Spectrum of Phonons in the Magnetic BCC Iron


 
 
 We used the symplectic and scalable algorithm for spin lattice dynamics embedded in LAMMPS to model the coupled relaxation processes of the spin and lattice subsystems to investigate the phonon dispersion of bcc Fe at T = 300 K. The atomic interactions were modelled via three semi-empirical many-body potentials within the embedded atom method, while the distance-dependent spin coupling relied on the Heisenberg-type Hamiltonian. In the state of mutual equilibrium of the spin and atom ensembles, we have calculated the dynamical matrix and the phonon spectra in bcc iron. We found that for a small to moderate wavevector absolute values, the phonon dispersion curves agree well with the experimental results obtained from inelastic neutron scattering, while discrepancies between theory and experiment were observed for larger wavevector values, particularly near the zone boundaries. Moreover, the impact of magnons on the phonon spectra is pronounced for all employed potentials.
 
 

The Decisive Role of Spin States and Spin Coupling in Dictating Selective O2 Adsorption in Chromium(II) Metal-Organic Frameworks.

The coordinatively unsaturated chromium(II)-based Cr3 [(Cr4 Cl)3 (BTT)8 ]2 (Cr-BTT; BTT3- =1,3,5-benzenetristetrazolate) metal-organic framework (MOF) has been shown to exhibit exceptional selectivity towards adsorption of O2 over N2 /H2 . Using periodic density functional theory (DFT) calculations, we attempted to decipher the origin of this puzzling selectivity. By computing and analyzing the magnetic exchange coupling, binding energies, the partial density of states (pDOS), and adsorption isotherms for the pristine and gas-bound MOFs [(Cr4 (X)4 Cl)3 (BTT)8 ]3- (X=O2 , N2 , and H2 ), we unequivocally established the role of spin states and spin coupling in controlling the gas selectivity. The computed geometries and gas adsorption isotherms are consistent with the earlier experiments. The binding of O2 to the MOF follows an electron-transfer mechanism resulting in a CrIII superoxo species (O2 .- ) with a very strong antiferromagnetic coupling between the two centers, whereas N2 /H2 are found to weakly interact with the metal center and hence only slightly perturb the associated coupling constants. Although the gas-bound and unbound MOFs have an S=0 ground state (GS), the nature of spin the configurations and the associated magnetic exchanges are dramatically different. The binding energy and the number of oxygen molecules that can favorably bind to the Cr center were found to vary with respect to the spin state, with a significant energy margin (47.6 kJ mol-1 ). This study offers a hitherto unknown strategy of using spin state/spin couplings to control gas adsorption selectivity in MOFs.

Critical behavior of the ferromagnetic metal La3CrAs5 with quasi-one-dimensional spin chains

In this work, we report on the critical properties of ferromagnetic metal La3CrAs5, where the face-sharing CrAs6 octahedral chains are separated by a large distance. Bulk magnetization measurements near the Curie temperature TC are carried out in details. Then we used modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis to analyze the isothermal magnetization curves, and thus obtained a set of precise and self-consistent critical exponents (β, γ and δ), which are close to the theoretical values of chiral XY model. In addition, the scaling equation is followed by the magnetization-field-temperature curves, confirming the reliability of these critical exponents. Furthermore, the magnetic exchange distance, decaying as J(r) ~ r−4.7, indicates the predominant long-range magnetic coupling in La3CrAs5. Furthermore, the magnetic entropy change − ΔSM around the TC reaches a maximum value, such as−ΔSMmax is 1.23 J/kg-K for H = 50 kOe, and the relative cooling power (RCP) is 51.70 J/kg at H = 50 kOe. Our results reveal that the magnetic critical behavior in La3CrAs5 should be attributed to the synergistic action between the direct magnetic exchange and the itinerant electron mediated indirect spin exchange, and the interchain spin coupling should be greatly enhanced via the itinerant electrons and then leads to the increase of the long-range magnetic ordering temperature.

Valley spin polarization in two-dimensional h−MN (M=Nb,Ta) monolayers: Merger of valleytronics with spintronics

The search for new two-dimensional (2D) semiconductors with strong spin-orbit coupling, merging Rashba effect with valley physics, is essential for advancing the emerging fields of spintronics and valleytronics. $h\text{\ensuremath{-}}M\mathrm{N}$ $(M=\mathrm{Nb},\mathrm{Ta})$ monolayers are found to host valley physics together with Rashba effect. $h$-NbN (TaN) monolayers show Zeeman-type valley spin splitting of 32 (112) meV and 130 (406) meV at valence-band and conduction-band edges, respectively, based on density-functional theory calculations. One of the three degenerate valleys around the $K/{K}^{\ensuremath{'}}$ point in the first Brillouin zone (BZ) lies fully enclosed within the first BZ. Berry curvature $\ensuremath{\sim}50(73)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{2}$ shown by h-NbN (TaN) monolayers is much higher than that in ${\mathrm{MoS}}_{2}$ monolayer $(\ensuremath{\sim}11\phantom{\rule{0.16em}{0ex}}{\AA{}}^{2})$, owing to the lower band gap and wave vector magnitude in $h$-NbN (TaN) monolayers. The Rashba energy splitting and Rashba constant induced by strong spin-orbit coupling (SOC) in $h$-NbN (TaN) monolayer is found to be 52 (74) meV and 2.9 (4.23) eV \AA{} respectively, which are amongst the giant Rashba spin-splitting parameters observed so far in 2D materials. The degree of Zeeman-type valley spin splitting and Rashba-type spin splitting is substantially tunable via in-plane biaxial strain and out of-plane electric field. Higher SOC in $h$-TaN monolayer relative to $h$-NbN monolayer caused by the heavier Ta atoms gives rise to a higher Berry curvature, valley-, and Rashba spin splitting in the former as compared to the latter. Valleytronic and spintronic properties in the studied monolayers are found to be superior to that in $h\text{\ensuremath{-}}{\mathrm{MoS}}_{2}$ and Janus MoSSe monolayers and are therefore proposed for an effective coupling of spin and valley physics.

Unconventional interlayer exchange coupling via chiral phonons in synthetic magnetic oxide heterostructures.

Chiral symmetry breaking of phonons plays an essential role in emergent quantum phenomena owing to its strong coupling to spin degree of freedom. However, direct experimental evidence of the chiral phonon–spin coupling is lacking. In this study, we report a chiral phonon–mediated interlayer exchange interaction in atomically controlled ferromagnetic metal (SrRuO3)–nonmagnetic insulator (SrTiO3) heterostructures. Owing to the unconventional interlayer exchange interaction, we have observed rotation of spins as a function of nonmagnetic insulating spacer thickness, resulting in a spin spiral state. The chiral phonon–spin coupling is further confirmed by phonon Zeeman effect. The existence of the chiral phonons and their interplay with spins along with our atomic-scale heterostructure approach unveil the crucial roles of chiral phonons in magnetic materials.

Multi-Messenger Astrophysics of a Millisecond Pulsar Orbiting around a Massive Black Hole

Extreme-mass-ratio and intermediate-mass-ratio binaries with a millisecond pulsar are gravitational-wave sources that emit also electromagnetic radiation. The millisecond pulsars in these binaries have complex orbital and spin dynamics, which are observable because of spin–orbit and spin–spin coupling (through spin–curvature interaction). The strengths of the couplings generally depends on the mass ratio between the pulsar and the black hole. The narrow mass range of neutron stars gives an advantage in parameter extraction as it greatly reduces the search space, in particular, in the determination of the black-hole mass, in gravitational wave experiments and radio pulsar timing observations. Extreme-mass-ratio and intermediate-mass-ratio binaries with a millisecond pulsar will help to resolve the astrophysical problems, concerning the applicability of the M-σ relation for galactic spheroids extending to the very low-mass galaxies and whether or not low-mass dwarf galaxies and globular clusters would harbour a nuclear intermediate-mass black hole. The high-precision that can be achieved in gravitational wave experiments and radio pulsar timing observations will provide an opportunity to directly detect gravitational clock effects that are arisen from spin couplings. Radio monitoring of the orbital and spin evolution of the millisecond pulsar in an extreme-mass-ratio binary can be used as a bootstrap method for correcting the drifts in the phases in the gravitational waves from the extreme-mass-ratio and intermediate-mass-ratio binaries caused by self-force.

Stability of the Discrete Time-Crystalline Order in Spin-Optomechanical and Open Cavity QED Systems

Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body systems out of equilibrium. Recently, it has been proposed that eternal and transient DTC can be present with an open Floquet setup in the thermodynamic limit and in the deep quantum regime with few qubits, respectively. In this work, we consider the effects of spin damping and spin dephasing on the DTC order in spin-optomechanical and open cavity systems in which the spins can be all-to-all coupled. In the thermodynamic limit, it is shown that the existence of dephasing can destroy the coherence of the system and finally lead the system to its trivial steady state. Without dephasing, eternal DTC is displayed in the weak damping regime, which may be destroyed by increasing the all-to-all spin coupling or the spin damping. By contrast, the all-to-all coupling is constructive to the DTC in the moderate damping regime. We also focus on a model which can be experimentally realized by a suspended hexagonal boron nitride (hBN) membrane with a few spin color centers under microwave drive and Floquet magnetic field. Signatures of transient DTC behavior are demonstrated in both weak and moderate dissipation regimes without spin dephasing. Relevant experimental parameters are also discussed for realizing transient DTC order in such an hBN optomechanical system.

Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains.

Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t-J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures.

Radiation modulated spin coupling in a double-stranded DNA model

The spin activity in macromolecules such as DNA and oligopeptides, in the context of the chiral induced spin selectivity has been proposed to be due to the atomic spin–orbit coupling (SOC) and the associated chiral symmetry of the structures. This coupling, associated with carbon, nitrogen and oxygen atoms in biological molecules, albeit small (meV), can be enhanced by the geometry, and strong local polarization effects such as hydrogen bonding. A novel way to manipulate the spin degree of freedom is by modifying the spectrum using a coupling to the appropriate electromagnetic radiation field. Here we use the Floquet formalism in order to show how the half filled band Hamiltonian for DNA, can be modulated by the radiation to produce up to a tenfold increase of the effective SOC once the intrinsic coupling is present. On the other hand, the chiral model, once incorporating the orbital angular momentum of electron motion on the helix, opens a gap for different helicity states (helicity splitting) that chooses spin polarization according to transport direction and chirality, without breaking time reversal symmetry. The observed effects are feasible in physically reasonable parameter ranges for the radiation field amplitude and frequency.

Frustrated magnetic interactions in a cyclacene crystal

We study the emergence of magnetism and its interplay with structural properties in a two-dimensional molecular crystal of cyclacenes, using density functional theory (DFT). Isolated cyclacenes with an even number of fused benzenes host two unpaired electrons in two topological protected zero modes, at the top and bottom carbon rings that form the molecule. We show that, in the gas phase, electron repulsion promotes an open-shell singlet with strong intramolecular antiferromagnetic exchange. We consider a closed packing triangular lattice crystal phase and we find a strong dependence of the band structure and magnetic interactions on the rotation angle of the cyclacenes with respect to the crystal lattice vectors. The orientational ground state maximizes the intermolecular hybridization, yet local moments survive. Intermolecular exchange is computed to be antiferromagnetic, and DFT predicts a broken symmetry ${120}^{\ensuremath{\circ}}$ spin phase reflecting the frustration of the intermolecular spin coupling. Thus, the cyclacene crystal realizes a bilayer of two antiferromagnetically coupled $S=1/2$ triangular lattices. Our results provide a bottom-up route towards carbon based strongly correlated platforms in two dimensions.

Equal-time kinetic equations in a rotational field * *Supported by Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008) and NSFC (11890712, 12005112, 12075129). ZW is also Supported by the Postdoctoral Innovative Talent Support Program of Tsinghua University

We investigate quantum kinetic theory for a massive fermion system under a rotational field. From the Dirac equation in rotating frame we derive the complete set of kinetic equations for the spin components of the 8- and 7-dimensional Wigner functions. While the particles are no longer on a mass shell in the general case due to the rotation–spin coupling, there are always only two independent components, which can be taken as the number and spin densities. With help from the off-shell constraint we obtain the closed transport equations for the two independent components in the classical limit and at the quantum level. The classical rotation–orbital coupling controls the dynamical evolution of the number density, but the quantum rotation–spin coupling explicitly changes the spin density.

Exact ground state and elementary excitations of a competing spin chain with twisted boundary condition

A novel Bethe ansatz scheme is proposed to investigate the exact physical properties of an integrable anisotropic quantum spin chain with competing interactions among the nearest, next nearest neighbor and chiral three spin couplings, where the boundary condition is the twisted one. The eigenvalue of the transfer matrix is characterized by its zero roots instead of the traditional Bethe roots. Based on the exact solution, the conserved momentum and charge operators of this U(1)-symmetry broken system are obtained. The ground state energy and density of rapidities are calculated. It is found that there exist three kinds of elementary excitations and the corresponding dispersion relations are obtained, which gives a different picture from that with periodic boundary condition.

CrTe as a versatile thermoelectromagnetic multi-functional material

Materials with large magnetocaloric effects and high thermoelectric performance are of fundamental interest to all-solid-state refrigeration technology. Herein, we report CrTe-based ferromagnetic semi-metals as an exceptional example showing both desirable magnetic entropy change (−ΔSM) and promising thermoelectric figure of merit (ZT) near room temperature. A proper amount (9 mol. %) of Cr deficiency is found to stabilize the hexagonal structure of CrTe. Cr0.91Te displays a maximum −ΔSM value of ∼2.4 J/Kg·K under an applied magnetic field of 5 T around its Curie temperature (TC) of 332 K and a strikingly large ZT value of 1.2 × 10−2 at 300 K (two to four orders of magnitude larger than any other ferromagnetic compounds reported so far). The exceptional thermoelectric performance in such a semi-metal is believed to originate from the inherently strong electron–phonon–spin interactions: magnon-drag effect mediated Seebeck coefficient enhancement and phonon–spin coupling induced thermal conductivity reduction. The introduction of antiferromagnetic CrSb not only systematically decreases TC of Cr0.91Te down to or even below room temperature but also boosts its thermoelectromagnetic properties. Specifically, Cr0.91Te0.9Sb0.1 obtains a maximum −ΔSM value of ∼2.6 J/Kg·K @ 5 T around TC = 315 K and a ZT value of 2.0 × 10−2 at 300 K, which represent 8% and 75% improvement over pristine Cr0.91Te, respectively. This research highlights the possibility of exploring ferromagnetic semi-metals as advanced thermoelectromagnetic multi-functional materials.

Response of atomic spin-based sensors to magnetic and nonmagnetic perturbations

Searches for pseudo-magnetic spin couplings require implementation of techniques capable of sensitive detection of such interactions. While Spin-Exchange Relaxation Free (SERF) magnetometry is one of the most powerful approaches enabling the searches, it suffers from a strong magnetic coupling, deteriorating the pseudo-magnetic coupling sensitivity. To address this problem, here, we compare, via numerical simulations, the performance of SERF magnetometer and noble-gas-alkali-metal co-magnetometer, operating in a so-called self-compensating regime. We demonstrate that the co-magnetometer allows reduction of the sensitivity to low-frequency magnetic fields without loss of the sensitivity to nonmagnetic couplings. Based on that we investigate the responses of both systems to the oscillating and transient spin perturbations. Our simulations reveal about five orders of magnitude stronger response to the neutron pseudo-magnetic coupling and about three orders of magnitude stronger response to the proton pseudo-magnetic coupling of the co-magnetometer than those of the SERF magnetometer. Different frequency responses of the co-magnetometer to magnetic and nonmagnetic perturbations enables differentiation between these two types of interactions. This outlines the ability to implement the co-magnetometer as an advanced sensor for the Global Network of Optical Magnetometer for Exotic Physics searches (GNOME), aiming at detection of ultra-light bosons (e.g., axion-like particles).

Different types of interactions between fullerene C60 and C70 anions and metal tetraphenylporphyrins in the (PMDAE+)(MIITPP)(Fullerene−)⋅Solvent complexes (M = Co, Mn, Zn) containing coordinating N, N, N, N‘, N‘-pentamethyldiaminoethane cations

Series of anionic salts of fullerenes C60 and C70 with different metal tetraphenylporphyrins, MIITPP, where M = Co, Mn and Zn, and N, N, N, N‘, N‘-pentamethyldiaminoethane cations (PMDAE+) has been obtained in a crystalline form. Composition of the complexes is (PMDAE+)⋅(MIITPP)(C60−)⋅XC6H4Cl2 (M = Co, X = 1.25 (1), M = Mn, X = 0.75 (2) and M = Zn, X = 0.75 (3)) and {(PMDAE+)⋅ZnIITPP}2⋅(C70−)2⋅4C6H4Cl2 (4). Both fullerene anion and nitrogen-containing PMDAE+ cation can coordinate to metal porphyrin competing with each other. Weak Co-C(C60−) coordination bond of 2.426(7) Å length (120 K) is formed in 1 whereas PMDAE+ cation only weakly coordinates to CoIITPP. Dissociation of Co-C(C60−) bond observed at 90–310 K is accompanied by a transition of 1 from singlet to triplet state with an energy gap of 574 ± 3 K. According to the calculations negative charge on C60− is only −0.548 due to electron transfer to the macrocyclic ligand through the cobalt atom. Charge transfer bands are observed in {CoIITPP(C60)}− at 700 and 1240 nm. On the contrary, PMDAE+ cations coordinate to MnIITPP and ZnIITPP in 2 and 3, respectively, with short M−N(PMDAE+) bonds of 2.27–2.33 Å length. In these cases fullerenes are preserved in the non-coordinated radical anion state. Fullerenes are arranged in closely packed π-stacking {C60•−}2 dimers with short interfullerene center-to-center distances of 9.92–9.95 Å. Nevertheless, the C60•− radical anions do not form intercage CC bonds down to 1.9 K. Strong antiferromagnetic coupling of spins is observed in the {C60•−}2 dimers of 3 with exchange interaction of J/kB = -21 K. Both {(PMDAE+)⋅MnIITPP} and C60•− species are paramagnetic in 2 having S = 5/2 and S = 1/2 spin states, respectively. These spins are coupled antiferromagnetically with Weiss temperature of −16 K. It is obvious that magnetic coupling occurs not only in the {C60•−}2 dimers but MnIITPP is also involved in this coupling. The C70•− radical anions are dimerized in 4 forming diamagnetic singly-bonded (C70−)2 dimers which manifest intense NIR absorption. As a result, complex 4 is EPR silent.

Simulating two-dimensional dynamics within a large-size atomic spin

Encoding a dimension in the internal degree of freedom of an atom provides an interesting tool for quantum simulation, facilitating the realization of artificial gauge fields. We propose an extension of the synthetic dimension toolbox, making it possible to encode two dimensions within a large atomic spin. The protocol combines first- and second-order spin couplings, such that the spin projection $m$ and the remainder $r=m$ (mod 3) of its Euclidian division by 3 act as orthogonal coordinates on a synthetic cylinder. It is suited for an implementation with lanthanide atoms, which feature a large electronic spin and narrow optical transitions for applying the required spin couplings. This method is useful for simulating geometries with periodic boundary conditions, and engineering various types of topological systems evolving in high dimensions.

Ising Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks that provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. Here we propose using an electrically coupled array of gigahertz spin Hall nano-oscillators to realize such a network. By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, we explicitly show the mapping between the coupled oscillators' properties and the Ising model. We integrate our analytical model into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillators in circuit simulators. With this abstract model, we analyze the performance of the spin Hall oscillator network at the circuit level using conventional electronic components and considering phase noise and scalability. Our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency.

Enhanced Coupling of Electron and Nuclear Spins by Quantum Tunneling Resonances.

Noble-gas spins feature hours-long coherence times, owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically excited potassium atoms and reveal the formation of quasibound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to 6 orders of magnitude and 2 orders of magnitude enhancement for the thermally averaged, polarization rate coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized.