Quadrupolar Spin Research Articles

Electric and elastic characteristics of the orthorhombic paramagnet after the quantum quench

Quantum quench (the sudden change) of the magnetic field in the orthorhombic and monoclinic paramagnets yields the renormalization of the spin quadrupole moment of the system. In the closed system, the renormalized spin quadrupole moment oscillates with the frequency, determined by the final value of the magnetic field. In the open system, these oscillations are damped in the steady-state regime. The renormalization of the electric permittivity, piezoelectric modulus, and elastic modulus of the system are dependent on both initial and finite values of the magnetic field via the spin quadrupole susceptibility demonstrating features at the critical values of the magnetic field, at which crossover of the energy levels of the paramagnet takes place.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets.

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Quantum spin nematic phase in a square-lattice iridate.

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3-5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit6-9. Upon cooling, the transition into the spin nematic phase at TC ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.

Let’s Sweep: The Effect of Evolving J 2 on the Resonant Structure of a Three-planet System

Short and ultrashort period planets are peculiar types of exoplanets with periods as short as a few days or less. Although it is challenging to detect them, already several have been observed, with many additional candidates. If these planets have formation pathways similar to their longer-period counterparts, they are predicted to reside in multiplanet systems. Thus, gravitational perturbation from potential planetary neighbors may affect their orbital configuration. However, due to their close proximity to their host star, they are also subject to general relativity precession and torques from the stellar spin quadrupole moment (J 2). Here we show that an evolving J 2 due to magnetic braking affects the magnitude and location of secular resonances of the short-period planet in a multiplanet system, thus driving the short-period planet into and out of a secular resonance, exciting the planet’s eccentricity and inclination. The high inclination can hinder transit observation and, in some cases, the high eccentricity may result in an unstable configuration. We propose that evolving J 2 in a multiplanet system can be critical to understanding the detectability and stability of short-period planets.

Quantum coherence resourced by the strong nuclear quadrupolar interaction

We propose a setup for studying the quantum coherence properties of a quadrupolar nucleus using the nuclear magnetic resonance platforms We consider powder samples labeled with 23Na and oriented with respect to the static magnetic field. By using the l 1-norm of coherence, we examine the quantum coherence in the Zeeman basis at thermal equilibrium. Non-zero coherence is found to result from the strong nuclear quadrupolar spin interactions. It is also shown that higher coherence is created as the quadrupolar interaction coefficient increases. We also discuss the stability of coherence in a possible measurement process in order to use it as a potential resource in any quantum computation protocol.

Dynamical electric characteristics of a quantum paramagnet

We consider the quantum paramagnet with the coupling between spin and electric degrees of freedom. The dynamical electric characteristics of the system under the action of the ac electric field are calculated. It is shown that for the closed system the quadrupole spin moment oscillates with the frequency of the ac field. The oscillations are modulated by the Rabi-like frequency, while the amplitude of the modulation is minimal at resonance, at which the frequency of the electric field is equal to the double energy of spin excitation of the paramagnet. The open system in the steady-state regime manifests only oscillations with the frequency of the ac field. The calculated dynamical electric susceptibility is nonzero only for nonzero dc magnetic field, and, depending on the values of the single-ion magnetic anisotropy, can manifest nonmonotonic dependence on temperature, dc electric and magnetic fields.

Multiple quantum filtered nuclear magnetic resonance of 23Na+ in uniformly stretched and compressed hydrogels.

Stretching or compressing hydrogels creates anisotropic environments that lead to motionally averaged alignment of embedded guest quadrupolar nuclear spins such as 23Na+. These distorted hydrogels can elicit a residual quadrupolar coupling that gives an oscillation in the trajectories of single quantum coherences (SQCs) as a function of the evolution time during a spin-echo experiment. We present solutions to equations of motion derived with a Liouvillian superoperator approach, which encompass the coherent quadrupolar interaction in conjunction with relaxation, to give a full analytical description of the evolution trajectories of rank-1 (T^1±1), rank-2 (T^2±1), and rank-3 (T^3±1) SQCs. We performed simultaneous numerical fitting of the experimental 23Na nuclear magnetic resonance (NMR) spectra and rank-2 (T^2±1) and rank-3 (T^3±1) SQC evolution trajectories measured in double and triple quantum filtered experiments, respectively. We estimated values of the quadrupolar coupling constant CQ, rotational correlation time τC, and 3 × 3 Saupe order matrix. We performed simultaneous fitting of the analytical expressions to the experimental data to estimate values of the quadrupolar coupling frequency ωQ/2π, residual quadrupolar coupling ωQ/2π, and corresponding spherical order parameter S0*, which showed a linear dependence on the extent of uniform hydrogel stretching and compression. The analytical expressions were completely concordant with the numerical approach. The insights gained here can be extended to more complicated (biological) systems such as 23Na+ bound to proteins or located inside and outside living cells in high-field NMR experiments and, by extension, to the anisotropic environments found in vivo with 23Na magnetic resonance imaging.

Influence of the ac magnetic field on the elastic and electric characteristics of a quantum paramagnet

It is shown that electric, piezoelectric, and elastic characteristics of the orthorhombic quantum paramagnet depend on the applied ac magnetic field, collinear to the dc one. The dependence is due to the renormalization of the quadrupole spin susceptibility. In the dynamical regime, the quadrupole susceptibility oscillates with the frequency of the ac field, and with the Rabi-like frequency. In the steady-state regime, the quadrupole susceptibility oscillates with the frequency of the ac field only about the renormalized with respect to the initial one value. That renormalization can change the values of the electric, piezoelectric, and elastic characteristics of the system.

Manifestation of spin nematic ordering in the spin-1 chain system

Spin-1 chain material is considered. Recently, it was predicted that the spin nematic ordered phase can be realized due to the spin-elastic coupling. In this study we show that the appearance of the spin nematic ordering and phase transitions to such ordered states can be studied using magneto-acoustic experiments. One can observe such phases and phase transitions considering relative changes of the velocity of sound (related to the changes of the elastic modulus of the crystal) as a function of temperature and the external magnetic field. It is shown that those relative changes are proportional to the spin quadrupole susceptibility of the system. The results are obtained using the exact Bethe ansatz solution and Quantum Monte Carlo simulations for several typical values of the biquadratic spin-spin exchange interaction and for various values of the spin-elastic coupling and elastic modules.

Universal intrinsic higher-rank spin tensor Hall effect

The spin Hall effect with nonzero transverse spin current but vanishing charge current has important applications in spintronics. Owing to the half-spin nature of electrons, the spin transport has hitherto been restricted to the rank-1 spin vector, whereas higher-rank spin tensors exist and play important roles in larger-spin ($\ensuremath{\ge}1$) systems. For instance, there are five linearly independent rank-2 spin quadrupole tensors, characterizing the spin nematics, in a spin-1 system. While these internal spin-tensor degrees of freedom substantially enrich the quantum phases and dynamics of large-spin ultracold gases, the quantum transport of spin tensors remains largely unexplored yet. Here we investigate the higher-rank spin tensor current and introduce the concept of the spin tensor Hall effect (STHE) in a large-spin system. We find that a net transverse spin tensor current can be driven by an external field in the longitudinal direction, while no lower-rank spin or charge current exists. Significantly, we identify a universal rank-2 spin tensor Hall conductivity $q/8\ensuremath{\pi}$ (with the carrier charge $q$) in a spin-1 model with intrinsic spin-orbit coupling, which is independent of the detailed model parameters. The STHE requires the violation of time-reversal symmetry (TRS) but can be protected by a unique pseudo-TRS associated with the rank-2 spin tensor. An experimental scheme is proposed to realize and detect the STHE with pseudospin-1 ultracold fermionic atoms and through the spin tensor accumulation. A general route towards the generalization of the STHE for larger spins is provided, using the SU(2) subalgebra and generalized Gell-Mann matrix representation of the $\mathrm{SU}(N$) group. Our work reveals an intrinsic spin tensor transport phenomenon and introduce a new member to the Hall effect families, which may pave the way to spin-tensor-tronics.

Quantifying quadrupole effects in the NMR spectra of spin-1/2 nuclei in rotating solids.

Quantifying the NMR spectra of spin I = 1/2 nuclei coupled to quadrupolar spins (nuclei with spin quantum number, S > 1/2) has remained an arduous task in solid-state magic angle spinning (MAS) NMR experiments. In particular, extraction of chemical shift anisotropy (CSA) tensors from line-shapes of spin I = 1/2 nuclei coupled to quadrupolar spin (S = 1) in MAS experiments has remained challenging owing to the simultaneous presence of both heteronuclear dipolar interactions and quadrupolar interactions. Unlike experiments that involve only spin-1/2 nuclei, both faster spinning frequencies and stronger decoupling field strengths on the quadrupolar spins are essential to average/minimize the contributions from heteronuclear dipolar interactions. To this end, a quantitative theory based on the concept of "effective fields" is proposed to deduce optimal conditions in experiments that involve simultaneous recoupling and decoupling of heteronuclear dipolar interactions. Through analytic expressions, the spectral frequencies and intensities observed in experiments are quantified and rigorously verified. Since extraction of molecular constraints in NMR experiments involves iterative fitting of experimental data, we believe that the analytic expressions derived would speed up and be beneficial in quantifying such experiments.

Fragmented Spin Ice and Multi-k Ordering in Rare-Earth Antiperovskites.

We study near-neighbor and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilizes a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbor perturbations cause the two components to order independently, resulting in unusual multi-k orders. We propose experimental realizations of our model in rare-earth antiperovskites.

A nuclear quadrupolar spin quantum heat engine

We give an implementable scheme which uses intrinsic quadrupolar nuclear spin interactions to harvest efficient energy from a quantum Otto cycle. We employ realistic parameter regimes for the 23Na nucleus in sodium nitrate. The processes of the cycle are accomplished by orienting the sample with respect to the static magnetic field. The effects of stroke duration on the work output and efficiency are revealed in detail. Finite-time adiabatic transformations leading to quantum friction are found to substantially reduce cycle outputs which are stimulated from the non-secular parts of the quadrupolar interaction. An estimation for the power output at maximum efficiency is also given. We show that with the precise control and manipulation of the intrinsic nuclear spin interactions, for example in an advanced nuclear magnetic resonance setup, makes our scheme implement as a powerful quantum Otto cycle.

Magnetic field dependent thermodynamic properties of square and quadrupolar artificial spin ice

Applied magnetic fields are an important tuning parameter for artificial spin ice (ASI) systems, as they can drive phase transitions between different magnetic ground states, or tune through regimes with high populations of emergent magnetic excitations (e.g., monopole-like quasiparticles). Here, using simulations supported by experiments, we investigate the thermodynamic properties and magnetic phases of square and quadrupolar ASI as a function of applied in-plane magnetic fields. Monte Carlo simulations are used to generate field-dependent maps of the magnetization, the magnetic specific heat, the thermodynamic magnetization fluctuations, and the magnetic order parameters, all under equilibrium conditions. These maps reveal the diversity of magnetic orderings and the phase transitions that occur in different regions of the phase diagrams of these ASIs, and are experimentally supported by magneto-optical measurements of the equilibrium "magnetization noise" in thermally-active ASIs.

Slip/Stick Viscosity Models of Nanoconfined Liquids: Solvent-Dependent Rotation in Metal-Organic Frameworks.

Artificial molecular machines are expected to operate in environments where viscous forces impact molecules significantly. With that, it is well-known that solvent behaviors dramatically change upon confinement into limited spaces as compared to bulk solvents. In this study, we demonstrate the utility of an amphidynamic metal-organic framework with pillars consisting of 2H-labeled dialkynyltriptycene and dialkynylphenylene barrierless rotators that operate as NMR sensors for solvent viscosity. Using line-shape analysis of quadrupolar spin echo spectra we showed that solvents such as dimethylformamide, diethylformamide, 2-octanone, bromobenzene, o-dichlorobenzene, and benzonitrile slow down their Brownian rotational motion (103-106 s-1) to values consistent with confined viscosity values (ca. 100-103 pa s) that are up to 10000 greater than those in the bulk. Magic angle spinning assisted 1H T2 measurements of included solvents revealed relaxation times of approximately 100-1000 ms over the explored temperature ranges, and MAS-assisted 1H T1 measurements of included solvents suggested a much lower activation energy for rotational dynamics as compared to those measured by the rotating pillars using 2H measurements. Finally, translational diffusion measurements of DMF using pulsed-field gradient methods revealed intermediate dynamics for the translational motion of the solvent molecules in MOFs.

Accelerating the acquisition of high-resolution quadrupolar MQ/ST-HETCOR 2D spectra under fast MAS via 1H detection and through-space population transfers

Recently, we established an experimental setup protocol to perform the population transfer from half-integer quadrupolar spin to 1H nuclei under fast MAS in the context of MQ-HETCOR experiments. In this article, we further develop the high-resolution 2D HETCOR methods by ST-based approaches, making use of the sensitivity advantage of STMAS over its MQMAS counterpart. In a similar manner to the previous work, which utilized CP and RINEPT for the population transfer, we also demonstrate the experimental setup protocol for PRESTO. Using {23Na}-1H and {27Al}-1H spin systems of powder samples, we compare a series of MQ/ST-HETCOR 2D spectra to discuss the pros and cons of the distinct MQ/ST-based approaches for spin 3/2 and 5/2 nuclei, respectively. We also incorporate two experimental tricks to reduce the experimental time of such long 2D experiments, the Optimized Rotor-Synchronization (ORS) and the Non-Uniform Sampling (NUS), in the context of high-resolution spectra of half-integer quadrupolar spin nuclei.

Intergalactic filaments spin

ABSTRACT Matter in the Universe is arranged in a cosmic web, with a filament of matter typically connecting each neighbouring galaxy pair, separated by tens of millions of light-years. A quadrupolar pattern of the spin field around filaments is known to influence the spins of galaxies and haloes near them, but it remains unknown whether filaments themselves spin. Here, we measure dark matter velocities around filaments in cosmological simulations, finding that matter generally rotates around them, much faster than around a randomly located axis. It also exhibits some coherence along the filament. The net rotational component is comparable to, and often dominant over, the known quadrupolar flow. The evidence of net rotations revises previous emphasis on a quadrupolar spin field around filaments. The full picture of rotation in the cosmic web is more complicated and multiscale than a network of spinning filamentary rods, but we argue that filament rotation is substantial enough to be an essential part of the picture. It is likely that the longest coherently rotating objects in the Universe are filaments. Also, we speculate that this rotation could provide a mechanism to generate or amplify intergalactic magnetic fields in filaments.

A comparison of through-space population transfers from half-integer spin quadrupolar nuclei to 1H using MQ-HETCOR and MQ-SPAM-HETCOR under fast MAS

In this article, we compare the various schemes of magnetization transfer from half-integer quadrupolar spins to 1H nuclei and we establish an efficient protocol to perform these transfers under MQMAS high-resolution with the MQ-HETCOR and MQ-SPAM-HETCOR experiments under fast MAS. The MQMAS efficiencies are analyzed with SIMPSON simulations, and the CPMAS and RINEPT magnetization transfers are compared at 62.5 kHz MAS using {23Na}-1H and {27Al}-1H MQ-HETCOR and MQ-SPAM-HETCOR experiments performed on NaH2PO4, Na2HPO4, Na citrate dihydrate and ipa-AlPO-14 powder samples. We discuss the pros and cons of these approaches, aiming to record 2D spectra of the best possible quality under fast MAS. We also incorporate some experimental approaches to reduce the total experiment time of such long 2D experiments.

Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and spin-2 XY chains with rhombic single-ion anisotropy

We investigate quantum phase transitions and quantum coherence in infinite biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy. All considered coherence measures such as the ${l}_{1}$ norm of coherence, the relative entropy of coherence, and the quantum Jensen-Shannon divergence, and the quantum mutual information show consistently that singular behaviors occur for the spin-1 system, which enables to identify quantum phase transitions. For the spin-2 system, the relative entropy of coherence and the quantum mutual information properly detect no singular behavior in the whole system parameter range, while the ${l}_{1}$ norm of coherence and the quantum Jensen-Shannon divergence show a conflicting singular behavior of their first-order derivatives. Examining local magnetic moments and spin quadrupole moments lead to the explicit identification of novel orderings of spin quadrupole moments with zero magnetic moments in the whole parameter space. We find the three uniaxial spin nematic quadrupole phases for the spin-1 system and the two biaxial spin nematic phases for the spin-2 system. For the spin-2 system, the two orthogonal biaxial spin nematic states are connected adiabatically without an explicit phase transition, which can be called quantum crossover. The quantum crossover region is estimated by using the quantum fidelity. Whereas for the spin-1 system, the two discontinuous quantum phase transitions occur between three distinct uniaxial spin nematic phases. We discuss the quantum coherence measures and the quantum mutual information in connection with the quantum phase transitions including the quantum crossover.

Quadrupole spin polarization as signature of second-order topological superconductors

We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.