Planar Spin Research Articles

Einstein-Podolsky-Rosen steering, depth of steering, and planar spin squeezing in two-mode Bose-Einstein condensates

We show how one can prepare and detect entanglement and Einstein-Podolsky-Rosen (EPR) steering between two distinguishable groups (modes) of atoms in a Bose-Einstein condensate (BEC) atom interferometer. Our paper extends previous work that developed criteria for two-mode entanglement and EPR steering based on the reduced variances of two spins defined in a plane. Observation of planar spin squeezing will imply entanglement, and sufficient planar spin squeezing implies EPR steering, between the two groups of atoms. By using a two-mode dynamical model to describe BEC interferometry experiments, we show that the two-mode entanglement and EPR steering criteria are predicted to be satisfied for realistic parameters. The reported observation of spin squeezing in these parameter regimes suggests it is very likely that the criteria can be used to infer an EPR steering between mesoscopic groups of atoms, provided the total atom number can be determined to sub-Poissonian uncertainty. The criteria also apply to a photonic Mach-Zehnder interferometer. Finally, we give a method based on the amount of planar spin squeezing to determine a lower bound on the number of particles that are genuinely comprise the two-mode EPR steerable state - the so-called two-mode EPR steering depth.

Entanglement and extreme planar spin squeezing

We introduce an entanglement-depth criterion optimized for planar quantum squeezed (PQS) states. It is connected with the sensitivity of such states for estimating an arbitrary, not necessarily small phase. We compare numerically our criterion with the well-known extreme spin squeezing condition of S{\o}rensen and M{\o}lmer [Phys. Rev. Lett. 86, 4431 (2001)] and show that our condition detects a higher depth of entanglement when both planar spin variances are squeezed below the standard quantum limit. We employ our theory to monitor the entanglement dynamics in a PQS state produced via quantum non-demolition (QND) measurements using data from a recent experiment [Phys. Rev. Lett. 118, 233603 (2017)].

Modulation of Nickel Pyridinedicarboxamidate Complexes to Explore the Properties of High-valent Oxidants.

High-valent Ni oxidants have been implicated in hydrocarbon oxidation catalysis, however, little is understood about the properties of these oxidants. Herein, a family of NiII complexes supported by a pyridinedicarboxamidate ligand and different ancillary ligands was synthesized. The series spans coordination numbers 4, 5, and 6, and contains neutral, mono- and di-anionic donor types. X-ray crystallography and magnetic measurements showed that the 4-coordinate complexes were square planar and low spin (S=0) and the 5- and 6-coordinate were intermediate spin (S=1). The NiII complexes could be oxidized by one electron to form a series of metastable NiIII species. EPR analysis confirmed their description as S=1/2 NiIII compounds with signal shape and hyperfine coupling dependent on the coordination environment. The oxidation of phenols by the NiIII species was probed, providing evidence for a correlation between oxidizing power and electron-donating properties of the supporting ligands. Critically, we found that the pyridinedicarboxamidate ligand may be a non-innocent proton acceptor in the oxidation reactions.

Polar-core spin vortex of quasi-2D ferromagnetic spin-1 condensate in a flat-bottomed optical trap with a weak magnetic field

Motivated by the recent experiments realized in a flat-bottomed optical trap (Navon et al., 2015; Chomaz et al., 2015), we study the ground state of polar-core spin vortex of quasi-2D ferromagnetic spin-1 condensate in a finite-size homogeneous trap with a weak magnetic field. The exact spatial distribution of local spin is obtained with a variational method. Unlike the fully-magnetized planar spin texture with a zero-spin core, which was schematically demonstrated in previous studies for the ideal polar-core spin vortex in a homogeneous trap with infinitely large boundary, some plateaus and two-cores structure emerge in the distribution curves of spin magnitude in the polar-core spin vortex we obtained for the larger effective spin-dependent interaction. More importantly, the spin values of the plateaus are not 1 as expected in the fully-magnetized spin texture, except for the sufficiently large spin-dependent interaction and the weak-magnetic-field limit. We attribute the decrease of spin value to the effect of finite size of the system. The spin values of the plateaus can be controlled by the quadratic Zeeman energy q of the weak magnetic field, which decreases with the increase of q.

Proposed neutron-interferometry test of Berry's phase for a circulating planar spin

The energy eigenstates of a spin$-\frac{1}{2}$ particle in a magnetic field confined to a plane, define a planar spin. If the particle moves adiabatically around a loop in this plane, it picks up a topological Berry phase that can only be an integer multiple of $\pi$. We propose a neutron interferometry test of the Berry phase for a circulating planar spin induced by a magnetic field caused by a very long current-carrying straight wire perpendicular to the plane. This Berry phase causes destructive interference in the direction of the incoming beam of thermal neutrons moving through a triple-Laue interferometer.

Polar-Core Spin Vortex of Quasi-2D Spin-2 Condensate in a Flat-Bottomed Optical Trap**Supported by the National Natural Science Foundation of China under Grant No. 11274095, the Key Scientific Research Project of Henan Province of China under Grant No. 16A140011, and the High Performance Computing Center of Henan Normal University

Motivated by the recent experiments realized in a flat-bottomed optical trap [Science 347 (2015) 167; Nat. Commun. 6 (2015) 6162], we study the ground state of polar-core spin vortex of quasi-2D spin-2 condensate in a homogeneous trap plus a weak magnetic field. The exact spatial distribution of local spin is obtained and the vortex core are observed to decrease with the growth of the effective spin-spin interaction. For the larger effective spin-spin interaction, the spatial distribution of spin magnitude in spin-2 condensate we obtained agrees well with that of spin-1 condensate in a homogeneous trap, where a polar-core spin vortex was schematically demonstrated as a fully-magnetized planar spin texture with a zero-spin core. The effective spin-spin interaction is proportional to both the bare spin-spin interaction and the radius of the homogeneous trap, simultaneously. Thus the polar-core spin vortex we obtained can be easily controlled by the radius of the trap.

Spin-Wave Analysis for Kagome-Triangular Spin System and Coupled Spin Tubes: Low-Energy Excitation for the Cuboc Order

The coupled spin tube system, which is equivalent to a stacked Kagome-triangular spin system, exhibits the cuboc order -- a non-coplanar spin order with a twelve-sublattice structure accompanying spontaneous breaking of the translational symmetry -- in the Kagome-triangular plane. On the basis of the spin-wave theory, we analyze spin-wave excitations of the planar Kagome-triangular spin system, where the geometric phase characteristic to the cuboc spin structure emerges. We further investigate spin-wave excitations and dynamical spin structure factors for the coupled spin tubes, assuming the staggered cuboc order.

Discovery of Enhanced Magnetoelectric Coupling through Electric Field Control of Two-Magnon Scattering within Distorted Nanostructures.

Electric field control of dynamic spin interactions is promising to break through the limitation of the magnetostatic interaction based magnetoelectric (ME) effect. In this work, electric field control of the two-magnon scattering (TMS) effect excited by in-plane lattice rotation has been demonstrated in a La0.7Sr0.3MnO3 (LSMO)/Pb(Mn2/3Nb1/3)-PbTiO3 (PMN-PT) (011) multiferroic heterostructure. Compared with the conventional strain-mediated ME effect, a giant enhancement of ME effect up to 950% at the TMS critical angle is precisely determined by angular resolution of the ferromagnetic resonance (FMR) measurement. Particularly, a large electric field modulation of magnetic anisotropy (464 Oe) and FMR line width (401 Oe) is achieved at 173 K. The electric-field-controllable TMS effect and its correlated ME effect have been explained by electric field modulation of the planar spin interactions triggered by spin-lattice coupling. The enhancement of the ME effect at various temperatures and spin dynamics control are promising paradigms for next-generation voltage-tunable spintronic devices.

Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction

The quantum coherence of one dimensional planar spin models with the Dzyaloshinsky-Moriya interaction is investigated. The anisotropic XY model, the isotropic XX model and the transverse field model are studied in the large N-limit using the two qubit reduced density matrices and the two point correlation functions. From our investigations we find that the coherence as measured using the Jensen-Shannon divergence can be used to detect the quantum phase transitions and the quantum critical points. The derivative of coherence shows non-analytic behavior at the critical points leading to the conclusions that these transitions are of second order. Further we show that the presence of the Dzyaloshinsky-Moriya coupling suppresses the phase transition due to the residual ferromagnetism which is caused by spin canting.

In memoriam: Sir Peter Mansfield (1933–2017)

In memoriam: Sir Peter Mansfield (1933–2017)

Orbital driven impurity spin effect on the magnetic order of quasi-3D cupric oxide

Density functional calculations are performed to study the magnetic order of the severely distorted square planar cupric oxide (CuO) and local spin disorder in it in the presence of the transition metal impurities M (=Cr, Mn, Fe, Co and Ni). The distortion in the crystal structure, arisen to reduce the band energy by minimizing the covalent interaction, creates two crisscrossing zigzag spin-1/2 chains. From the spin dimer analysis we find that while the spin chain along has strong Heisenberg type antiferromagnetic coupling (J ~ 127 meV), along it exhibits weak, but robust, ferromagnetic coupling (J ~ 9 meV) mediated by reminiscent p-d covalent interactions. The impurity effect on the magnetic ordering is independent of M and purely orbital driven. If the given spin-state of M is such that the orbital is spin-polarized, then the original long-range ordering is maintained. However, if orbital is unoccupied, the absence of corresponding covalent interaction breaks the weak ferromagnetic coupling and a spin-flip takes place at the impurity site leading to breakdown of the long range magnetic ordering.

ESR study of the frustrated S=12 chain magnet LiCuVO4 in spiral and spin-modulated phases

We report on the electron spin resonance (ESR) study of ${\mathrm{LiCuVO}}_{4}$ in spiral and spin-modulated phases ($0l{\ensuremath{\mu}}_{0}Hl10$ T). The measurements have been made on high quality samples that allowed getting rid of absorption lines arising from defects. In the field range of spiral phase ($0l{\ensuremath{\mu}}_{0}Hl7.5$ T) all observed branches of the spectrum can be ascribed to uniform oscillations of planar spin structure. The ESR spectrum observed in spin-modulated phase (${\ensuremath{\mu}}_{0}Hg7.5$ T) has two branches. One of them can be explained by uniform oscillations of spin structure, whereas the second branch, surprisingly demonstrates only a weak dependence on field orientation, which indicates the exchange nature of this mode. Allegedly this mode can be associated with soliton excitations.

Particle on a torus knot: Constrained dynamics and semi-classical quantization in a magnetic field

Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in Dirac’s Hamiltonian framework, both in toroidal and Cartesian coordinate systems. This algebra has been used to study the dynamics, in particular small fluctuations in motion around a specific torus. The spatial symmetries of the system have also been studied.In the second part of the paper we have considered the quantum theory of a charge moving in a torus knot in the presence of a uniform magnetic field along the axis of the torus in a semiclassical quantization framework. We exploit the Einstein–Brillouin–Keller (EBK) scheme of quantization that is appropriate for multidimensional systems. Embedding of the knot on a specific torus is inherently two dimensional that gives rise to two quantization conditions. This shows that although the system, after imposing the knot condition reduces to a one dimensional system, even then it has manifested non-planar features which shows up again in the study of fractional angular momentum. Finally we compare the results obtained from EBK (multi-dimensional) and Bohr–Sommerfeld (single dimensional) schemes. The energy levels and fractional spin depend on the torus knot parameters that specifies its non-planar features. Interestingly, we show that there can be non-planar corrections to the planar anyon-like fractional spin.

Spontaneous Currents in a Bosonic Ring

Nonequilibrium dynamics of noninteracting bosons in a one-dimensional ring-shaped lattice is studied by means of the Kinetic Monte Carlo method. The system is approximated by the classical XY model (the kinetic term is neglected) and then the simulations are performed for the planar classical spins. We study the dynamics that follows a finite-time quench to zero temperature. If the quench is slow enough the system can equilibrate and finally reaches the ground state with uniform spin alignment. However, we show that if the quench is faster than the relaxation rate, the system can get locked in a current-carrying metastable state characterized by a nonzero winding number. We analyze how the zero-temperature state depends on the quench rate.

Spin-Swapping Transport and Torques in Ultrathin Magnetic Bilayers.

Planar spin transport in disordered ultrathin magnetic bilayers comprising a ferromagnet and a normal metal (typically used for spin pumping, spin Seebeck and spin-orbit torque experiments) is investigated theoretically. Using a tight-binding model that puts the extrinsic spin Hall effect and spin swapping on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on the ratio between the layer thickness d and the mean free path λ. While the spin Hall effect dominates in the diffusive limit (d≫λ), spin swapping dominates in the Knudsen regime (d≲λ). A remarkable consequence is that spin swapping induces a substantial fieldlike torque in the Knudsen regime.

Charge and spin density in the helical Luttinger liquid

The weakly interacting helical Luttinger liquid, due to spin momentum locking, is characterized by extremely peculiar local observables: we show that the density-density correlation functions do not exhibit signatures of Friedel and Wigner oscillations, and that spin-spin correlation functions, which are strongly anisotropic, witness the formation of a planar spin wave. Moreover, we demonstrate that the most relevant scattering potentials involving a localized impurity are not able to modify the electron density, while only magnetic impurities can pin the planar spin density wave.

Realization of adiabatic Aharonov-Bohm scattering with neutrons

The adiabatic Aharonov-Bohm (AB) effect is a manifestation of the Berry phase acquired when some slow variables take a planar spin around a loop. While the effect has been observed in molecular spectroscopy, direct measurement of the topological phase shift in a scattering experiment has been elusive in the past. Here, we demonstrate an adiabatic AB effect by explicit simulation of the dynamics of unpolarized very slow neutrons that scatter on a long straight current-carrying wire.

Protection against a spin gap in two-dimensional insulating antiferromagnets with a Chern-Simons term

We propose a mechanism for the protection against spin gapped states in doped antiferromagnets. It requires the presence of a Chern-Simons term that can be generated by a coupling between spin and an insulator. We first demonstrate that in the presence of this term the vortex loop excitations of the spin sector behave as anyons with fractional statistics. To generate such a term, the fermions should have a massive Dirac spectrum coupled to the emergent spin field of the spin sector. The Dirac spectrum can be realized by a planar spin configuration arising as the lowest-energy configuration of a square lattice antiferromagnet Hamiltonian involving a Dzyaloshinskii-Moriya interaction. The mass is provided by a combination of dimerization and staggered chemical potential. We finally show that for realistic parameters, anyonic vortex loop condensation will likely never occur and thus the spin gapped state is prevented. We also propose real magnetic materials for an experimental verification of our theory.

Diffusion Weighted Magnetic Resonance Imaging for the Characterization of Solitary Pulmonary Lesions.

We evaluated the differential diagnosis of solitary pulmonary lesions on magnetic resonance imaging. To investigate the value of diffusion weighted imaging on the differential diagnosis of solitary pulmonary lesions. Randomized prospective study. This prospective study included 48 solitary pulmonary nodules and masses (18 benign, 30 malignant). Single shot echo planar spin echo diffusion weighted imaging (DWI) was performed with two b factors (0 and 1000 s/mm(2)). Apparent diffusion coefficients (ADCs) were calculated. On diffusion weighted (DW) trace images, the signal intensities (SI) of the lesions were visually compared to the SI of the thoracic spinal cord using a 5-point scale: 1: hypointense, 2: moderately hypointense, 3: isointense, 4: moderately hyperintense, 5: significantly hyperintense. For the quantitative evaluation, the lesion to thoracic spinal signal intensity ratios and the ADCs of the lesions were compared between groups. On visual evaluation, taking the density of the spinal cord as a reference, most benign lesions were found to be hypointense, while most of the malignant lesions were evaluated as hyperintense on DWI with a b factor of 1000 s/mm(2). In contrast, on T2 weighted images, it was seen that the distinction of malignant lesions from benign lesions was not statistically significant. The ADCs of the malignant lesions were significantly lower than those of benign lesions (mean ADC was 2.02×10(-3) mm(2)/s for malignant lesions, and 1.195×10(-3)±0.3 mm(2)/s for benign lesions). Setting the cut-off value at 1.5×10(-3), ADC had a sensitivity of 86.7% and a specificity of 88.9% for the differentiation of benign lesions from malignant lesions. DWI may aid in the differential diagnosis of solitary pulmonary lesions. (ClinicalTrials.gov Identifier: NCT02482181).

Spectrum of noncollinear metastable configurations of a finite-size discrete planar spin chain with a collinear ferromagnetic ground state

A theoretical method is used to find, in an accurate and systematic way, all the possible equilibrium magnetic states of a finite-size one-dimensional chain of classical planar spins, interacting via ferromagnetic nearest-neighbor symmetric exchange and subjected to a uniaxial anisotropy which favors the orientation of the spins along an easy axis within the plane perpendicular to the chain. For a chain with $N$ spins, the energy is a function of $N$ absolute orientation angles $({\ensuremath{\theta}}_{i}$, $i=1,...,N)$ and, owing to the absence of energy competition, the ground state is collinear ferromagnetic and doubly degenerate (either ${\ensuremath{\theta}}_{i}=0$ $\ensuremath{\forall}i$, or ${\ensuremath{\theta}}_{i}=\ensuremath{\pi}$ $\ensuremath{\forall}i$). The ground state corresponds to a global minimum of the energy in the $N$-dimensional space, while metastable states correspond to local minima. As a function of $N$, we have numerically determined the minimal value ${\ensuremath{\gamma}}_{\mathrm{min}}$ to be assumed by the ratio $\ensuremath{\gamma}$ between the anisotropy and the exchange constant for the first noncollinear metastable state to appear. For $N\ensuremath{\le}13$, all the noncollinear equilibrium spin configurations of the system were calculated with great accuracy at two different values, $\ensuremath{\gamma}=0.18$ and 0.21. A stability analysis was subsequently performed, showing that metastable noncollinear states can appear in the model even in the absence of energy competition. The various kinds of metastable states can be classified, in order of increasing energy, on the basis of the increasing number of $\ensuremath{\pi}$ walls (including both domains and antidomains) which can be inserted into the discrete finite chain with open ends when $N$ and/or $\ensuremath{\gamma}$ are increased. The effects of open boundary conditions and finite size on the Peierls-Nabarro barrier (i.e., the difference between the energy of an unstable onsite-centered domain wall and the energy of a stable intersite-centered domain wall) were also investigated.