Spin Deviations Research Articles

The Heisenberg Model after an Interaction Quench

In accordance with the recent experimental progress of the controllable spin-spin interactions, the Heisenberg model after an interaction quench is discussed. The Hamiltonian of the system out of equilibrium is introduced and treated by the flow equation method. As a result, the spectrum and zero-point spin deviation are obtained with the help of time-evolved operators. Additionally, other methods are applied to verify the results in mathematics. It is found that the observables show an oscillating behavior. The feasible experimental scheme of the concerned scenario is also mentioned.

Constraining the spin and the deformation parameters from the black hole shadow

Within 5–10 years, very-long baseline interferometry (VLBI) facilitieswill be able to directly image the accretion flow around SgrA*, thesuper-massive black hole candidate at the center of the Galaxy, and observethe black hole ``shadow''. In 4-dimensional general relativity, the no-hair theoremasserts that uncharged black holes are described by the Kerr solution and arecompletely specified by their mass M and by their spin parameter a. In thispaper, we explore the possibility of distinguishing Kerr and Bardeen black holesfrom their shadow. In Hioki & Maeda (2009), under the assumption that thebackground geometry is described by the Kerr solution, the authors proposedan algorithm to estimate the value of a/M by measuring the distortion parameterδ, an observable quantity that characterizes the shape of the shadow.Here, we try to extend their approach. Since the Hioki-Maeda distortionparameter is degenerate with respect to the spin and possible deviations fromthe Kerr solution, one has to measure another quantity to test the Kerr blackhole hypothesis. We study a few possibilities. We find that it is extremely difficultto distinguish Kerr and Bardeen black holes from the sole observation of theshadow, and out of reach for the near future. The combination of the measurementof the shadow with possible accurate radio observations of a pulsar in a compactorbit around SgrA* could be a more promising strategy to verify the Kerr blackhole paradigm.

Measuring the Kerr spin parameter of a non-Kerr compact object with the continuum-fitting and the iron line methods

Under the assumption that astrophysical black hole candidates are the Kerr black holes of general relativity, the continuum-fitting method and the analysis of the Kα iron line are today the only available techniques capable of providing a relatively reliable estimate of the spin parameter of these objects. If we relax the Kerr black hole hypothesis and we try to test the nature of black hole candidates, we find that there is a strong correlation between the measurement of the spin and possible deviations from the Kerr solution. The properties of the radiation emitted in a Kerr spacetime with spin parameter a* are indeed very similar, and practically indistinguishable, from the ones of the radiation emitted around a non-Kerr object with different spin. In this paper, I address the question whether measuring the Kerr spin with both the continuum-fitting method and the Kα iron line analysis of the same object can be used to claim the Kerr nature of the black hole candidate in the case of consistent results. In this work, I consider two non-Kerr metrics and it seems that the answer does depend on the specific background. The two techniques may either provide a very similar result (the case of the Bardeen metric) or show a discrepancy (Johannsen-Psaltis background).

Theory of Nano-Carbon Based Materials: Cyclotron Resonance, Kohn's Theorem and Hubbard Model

A monolayer of carbon is called graphene. It exhibits unusual properties in the Hall effect and in the cyclotron resonance. It is found that it exhibits fractional charge in the Hall effect. The interactions amongst electrons almost become constant at low temperatures. Hence, the Kohn's theorem, which shows that the interactions do not play much role in determining the cyclotron resonance, becomes operative at low temperatures. The experiments on graphene do not depend on the wave vector dependence of the frequency. Hence whether the dispersion depends on k2 or on k does not matter. The Hubbard model has been very successful in explaining the ground state of several electron systems. We consider a triangle with three vortices. Each vortex can be occupied by two electrons. By using the spin in a particular way, we can obtain new features in the Hubbard model. There is a doubling in the Peierls-Luttinger phase factor and eigen values acquire higher multiplicities than are known for the usual treatment of spin. The flux is distributed on the area of the triangle. The graphene consists of hexagons of carbon atoms but the Hall effect shows that there are defects on which electrons form clusters so that there is spin wave type behaviour. A cluster of electrons shows spin-waves leading to "spin deviation" of several per cent.

Magnetism of LiMn2O4 manganite in structurally ordered and disordered states

The specific features of the crystal structure and the magnetic state of stoichiometric lithium manganite in the structurally ordered Li[Mn2]O4 and disordered Li1 − δMnδ[Mn2 − δLiδ]O4 (δ = 1/6) states have been investigated using neutron diffraction, X-ray diffraction, and magnetic methods. The structurally disordered state of the manganite was achieved under irradiation by fast neutrons (E eff ≥ 1 MeV) with a fluence of 2 × 1020 cm−2 at a temperature of 340 K. It has been demonstrated that, in the initial sample, the charge ordering of manganese ions of different valences arises at room temperature, which is accompanied by orthorhombic distortions of the cubic spinel structure, and the long-range antiferromagnetic order with the wave vector k = 2π/c(0, 0, 0.44) is observed at low temperatures. It has been established that the structural disordering leads to radical changes in the structural and magnetic states of the LiMn2O4 manganite. The charge ordering is destroyed, and the structure retains the cubic symmetry even at a temperature of 5 K. The antiferromagnetic type of ordering transforms into ferrimagnetic ordering with local spin deviations in the octahedral sublattice due to the appearance of intersublattice exchange interactions.

Anomalous spin Hall effects in Dresselhaus (110) quantum wells

Anomalous spin Hall effects that belong to the intrinsic type in Dresselhaus (110) quantum wells are discussed. For the out-of-plane spin component, antisymmetric current-induced spin polarization induces opposite spin Hall accumulation, even though there is no spin-orbit force due to Dresselhaus (110) coupling. A surprising feature of this spin Hall induction is that the spin accumulation sign does not change upon bias reversal. Contribution to the spin Hall accumulation from the spin Hall induction and the spin deviation due to intrinsic spin-orbit force as well as extrinsic spin scattering can be straightforwardly distinguished simply by reversing the bias. For the in-plane component, inclusion of a weak Rashba coupling leads to a new type of ${S}_{y}$ intrinsic spin Hall effect solely due to spin-orbit-force-driven spin separation.

Spin configurations in hard/soft coupled bilayer systems: Transitions from rigid magnet to exchange-spring

We investigate equilibrium properties of an exchange-spring magnetic system constituted of a soft layer (e.g., Fe) of a given thickness on top of a hard magnetic layer (e.g., FePt). The magnetization profile $M(z)$ as a function of the atomic position ranging from the bottom of the hard layer to the top of the soft layer is obtained in two cases with regard to the hard layer: (i) in the case of a rigid interface (the FePt layer is a single layer), the profile is obtained analytically as the exact solution of a sine-Gordon equation with Cauchy's boundary conditions. Additional numerical simulations also confirm this result. Asymptotic expressions of $M(z)$ show a linear behavior near the bottom and the top of the soft layer. In addition, a critical value of the number of atomic planes in the soft layer, that is necessary for the onset of spin deviations, is obtained in terms of the anisotropy and exchange coupling between the adjacent plane in the soft layer. (ii) In the case of a relaxed interface (the FePt layer is a multilayer), the magnetization profile is obtained numerically for various Fe and FePt films thicknesses and applied field.

Particle-hole symmetry in algebraic Bethe Ansatz for the XXX model

It is well known that the space of all quantum states of the XXX model for a magnetic ring of N nodes, each with the spin 1/2, decomposes into sectors with r spin deviations, r = 0,1, 2,..., N [1, 2, 3, 4]. The sectors r and N – r are related mutually by the particle-hole transformation which exchanges the signs + and – on each node. We discuss here effects of this transformation on the formalism of algebraic Bethe Ansatz, in particular on the form of the monodromy matrix, the main tool of this formalism. We derive explicitly appropriate transformation rules for CN- orbits of magnetic configurations and the corresponding Fourier transformations within the bases of wavelets. In particular, we point out some important phase relations between orbits on both sides of the equator.

Low-temperature stability limit of the coherent spin precession in 3He-B

It has been shown that the instability of uniform spin precession in the bulk of the 3He-B superfluid phase is due to the joint action of the anisotropy of the velocities of spin waves and dipole interaction. In the leading approximation in the ratio of the Leggett frequency to the Larmor frequency, the growth increments of the amplitudes of spin waves for all of the possible decay channels have been found. The maximum increment has been determined for all of the angles of spin deviation from the equilibrium orientation. The minimum temperature to which precession is stable has been estimated.

Schwinger Geometry, Bethe Ansatz, and a Magnonic Qudit

Schwinger approach of unitary geometry for a finite-dimensional Hilbert space is interpreted in terms of a magnonic qudit — a hypothetic elementary unit of memory of a quantum computer. The space is interpreted within the Heisenberg model for a magnetic ring, its calculational basis as the classical configuration space for a single spin deviation, treated as a Bethe pseudoparticle, and the dual basis corresponds to quasimomenta, so that the classical phase space spans the quantum algebra of observables. Effects of the Schur-Weyl duality and Bethe ansatz exact eigenstates of the Heisenberg Hamiltonian for the XXX model on properties of the magnonic qudit are presented.

Bethe Ansatz and Geometry of the Classical Configuration Space

We demonstrate that the seminal one-dimensional model of the Heisenberg magnet, consisting of N spins 1/2 with the nearest-neighbour isotropic interaction, solved exactly by Bethe ansatz, admits an interpretation of a system of r = N/2 − M pseudoparticles (spin deviations) which are indistinguishable, have hard cores and move on the chain by local hoppings. Such an approach allows us to construct a manifold with some boundaries, which is genericly r-dimensional, and whose F -dimensional regions, 0 < F < r, point out all l-strings. The latter classify, in terms of rigged string configurations of Kerov, Kirillov and Reshetikhin, all exact Bethe eigenfunctions. In this way, we interpret these eigenfunctions in terms of the classical configuration space, in particular on the structure of islands of adjacent spin deviations, in a way independent of the size N .

Magnetism of the intermetallic compound Ce2Fe17 in the crystalline and amorphous states

Magnetic and neutron-diffraction methods have been used to study the magnetic state of polycrys- talline and amorphous samples of the intermetallic compound Ce 2 Fe 17 . The amorphous state was obtained by irradiating the intermetallic compound by fast neutrons. It has been shown that the competition of ferromag- netic and antiferromagnetic interactions between the nearest-neighbor iron atoms, which is responsible for the formation of the magnetic state, manifests itself differently in the crystalline and amorphous states. In the crys- talline sample, an increase in temperature leads to a transition of a collinear ferromagnet into an antiferromag- net. In the amorphous intermetallic compound, the competition leads to local spin deviations, which cause the appearance of some low-temperature features in its magnetic properties. Based on experimental data, H - T mag- netic phase diagrams of the crystalline and amorphous Ce 2 Fe 17 have been constructed. It has been shown that the magnetic field destroys both the antiferromagnetic state in the crystalline Ce 2 Fe 17 and the low-temperature mixed (combining properties of ferromagnets and spin glasses) magnetic state in the amorphous Ce 2 Fe 17 .

Spin modes and layer magnetization for surface and impurity layer embedded in a ferromagnet

A theoretical study is made for the role of an impurity layer embedded within a semi-infinite ferromagnet in determining the spectra of (0 0 1) surface spin waves and the layer magnetization for the surface and impurity layer. The calculations are described using simultaneously a closed form of the spin-wave Green's function and the matching procedure in the random-phase approximation. Analytic expressions for the Green's functions are also derived in a low-temperature spin-wave approximation. The theoretical approach determines the bulk and evanescent spin fluctuation fields in the two-dimensional plane normal to the surface. The results are used to calculate the energies of localized modes associated with the impurity layer as well as with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the impurity layer and surface modes. The results derived from the dynamic correlation functions between a pair of spin operators at any two sites are employed to evaluate the spin deviation in the ferromagnet due to the localized modes associated with the surface and with the impurity layer obtained by means of the matching procedure. The correlation functions and the layer magnetization are then illustrated as function of the impurity layer distance from the surface for a given temperature.

Multiple Critical Behavior of Probabilistic Limit Theorems in the Neighborhood of a Tricritical Point

We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffiths model. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters $n$, $\beta$, and $K$, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence of 18 scaling limits and 18 MDPs for the total spin. These limit results are obtained as $(\beta,K)$ converges along appropriate sequences to points belonging to various subsets of the phase diagram, which include a curve of second-order points and a tricritical point. The forms of the limiting densities in the scaling limits and of the rate functions in the MDPs reflect the influence of one or more sets that lie in neighborhoods of the critical points and the tricritical point. Of all the scaling limits, the structure of those near the tricritical point is by far the most complex, exhibiting new types of critical behavior when observed in a limit-theorem phase diagram in the space of the two parameters that parametrize the scaling limits.

Finite energy solitons in highly anisotropic two dimensional ferromagnets

e study the solitons, stabilized by spin precession in a classical two--dimensional lattice model of Heisenberg ferromagnets with non-small easy--axis anisotropy. The properties of such solitons are treated both analytically using the continuous model including higher then second powers of magnetization gradients, and numerically for a discrete set of the spins on a square lattice. The dependence of the soliton energy $E$ on the number of spin deviations (bound magnons) $N$ is calculated. We have shown that the topological solitons are stable if the number $N$ exceeds some critical value $N_{\rm{cr}}$. For $N < N_{\rm{cr}}$ and the intermediate values of anisotropy constant $K_{\mathrm{eff}} <0.35J$ ($J$ is an exchange constant), the soliton properties are similar to those for continuous model; for example, soliton energy is increasing and the precession frequency $ \omega (N)$ is decreasing monotonously with $N$ growth. For high enough anisotropy $K_{\mathrm{eff}} > 0.6 J$ we found some fundamentally new soliton features absent for continuous models incorporating even the higher powers of magnetization gradients. For high anisotropy, the dependence of soliton energy E(N) on the number of bound magnons become non-monotonic, with the minima at some "magic" numbers of bound magnons. Soliton frequency $\omega (N)$ have quite irregular behavior with step-like jumps and negative values of $\omega $ for some regions of $N$. Near these regions, stable static soliton states, stabilized by the lattice effects, exist.

Rigged strings, Bethe Ansatz, and the geometry of the classical configuration space of the Heisenberg magnetic ring

Composition of two combinatoric algorithms, Robinson–Schensted (RS) and Kerov–Kirillov–Reshetikhin (KKR), defines the bijection which maps the set of all magnetic configurations of the Heisenberg ring of N nodes with the spin 1 2 onto that of all exact Bethe Ansatz (BA) eigenstates of the nearest neighbour isotropic Hamiltonian. We point out here that this bijection allows one to predict all quantum numbers of an exact BA eigenstate (encoded as rigged string configurations of KKR) from each magnetic configuration. Moreover, this bijection provides completeness of solutions on each orbit of the symmetric group of N nodes, acting on the set of all magnetic configurations. Each such an orbit can be interpreted as the classical configuration space of the system of r Bethe pseudoparticles—spin deviations which are hard-core objects, moving on the magnetic ring by jumps to non-occupied nearest neighbours. Such an interpretation provides a transparent and combinatorially unique description of all exact BA eigenstates in terms of magnetic configurations—the initial basis for quantum calculations. Within this picture, an l-string introduced by Bethe corresponds to an extended object, consisting of 2 l consecutive nodes: first l spin deviations, and then l nodes with the spin projection + 1 2 , all bounded together and put somewhere inside the magnetic chain. Each BA solution is a rigged string configuration, i.e. a distribution of a number q, 0 ⩽ q ⩽ r , of such objects inside the chain. Allowed distributions are subjected to certain combinatoric restrictions (rules of navigation), expressed in terms of l-holes and riggings, and presented graphically as paths, associated with schemes of consecutive coupling of N spins 1 2 along the RS algorithm. We discuss here thoroughly some implications of existence of such a bijection. In particular, we demonstrate the way in which structure of orbits of the translation group C N on the classical configuration space for r Bethe pseudoparticles imposes the corresponding arrangement of rigged string configurations. Essentially, within a single cycle along a C N -orbit, each l-string moves from the left to the right with increase of its rigging by one unit until reaching the last node N of the ring, then shortens its length to zero, and next arises at the first (leftmost) node and elongates up to its previous length l. Such considerations allow us also to discuss the geography of rigged string configurations on the classical configuration space. In particular, we put emphasis on the fact that—within this combinatoric picture—the l-strings originate from corresponding sizes of islands of consecutive Bethe pseudoparticles in the classical configuration space. Thus, the set of all magnetic configurations with r spin deviations acquires the interpretation of an r-dimensional manifold with F-dimensional boundaries, the integer F, 1 ⩽ F ⩽ r , being the number of islands of consecutive Bethe pseudoparticles. Each magnetic configuration belonging to the generic part F = r yields only a 1-string under considered here bijection, whereas l-strings with l > 1 arise from islands located in appropriate boundaries.

Geometry and rigged strings in Bethe Ansatz

The main purpose of this report is a thorough analysis of completeness of solutions of the one-dimensional Heisenberg Hamiltonian through the hypothesis of strings. A somehow astonishing conclusion emerges from studying of the structure of the classical configuration space of this system. Namely, all allowed information concerning quantum states, which are exact solutions of the Bethe equations, encoded in quantum numbers, are predictable via a bijection between the set of the magnetic configurations and the string configurations. This startling and beautiful observation constitutes the proof of the completeness of the eigenstates of the Heisenberg Hamiltonian, deduced in a purely combinatorial way. We interpret the set of all magnetic configurations with a fixed number r of spin deviations as the classical configuration space of a hypothetic system of r Bethe pseudoparticles, which move, in a stroboscopic manner, on the magnetic ring. The geometry of this configuration space, induced by the action of Heisenberg Hamiltonian and the translation symmetry group of the ring, implies the structure of a locally r-dimensional hypercubic lattice with well defined F-dimensional boundaries, 1 ⩽ F ⩽ r. We demonstrate that rigged string configurations originate from these boundaries, depending upon the island structure of spin deviations. We show that a relatively simple combinatoric definition of rigged strings reproduces completely exact results of Bethe Ansatz. It is expressed in terms of a combined bijection: Robinson-Schensted with Kerov- Kirillov-Reshetikhin (RSKKR) which produces a geography of exact Bethe Ansatz solutions on the classical configuration space.

Continuity of Bethe solutions with respect to chain length N and winding numbers {λl}

Bethe solutions for r reversed spins are characterized by a set of winding numbers {λ1⩽λ2⩽⋯⩽λr}. Such classification is, however, not unique since the same sequences can describe different solutions and different sequences yield essentially equivalent states. These ambiguities should find their resolution in a complete configuration. We demonstrate here that in general a solution with a fixed sequence of winding numbers evolves in a quasicontinuous way as the function of N, the number of spins. This property could be disturbed in some cases at special transition point Ntr. We explain analytically the origin of this discontinuity. Consideration was addressed for three and four spin deviations.

The basis of wavelets for a finite Heisenberg magnet

Abstract We propose here a method for an immediate diagonalisation of the XXX Heisenberg magnetic ring for the spin 1 2 with a finite number N of nodes. The key ingredient is the basis of wavelets, i.e. Fourier transforms on orbits of the translation group on the set of all magnetic configurations with a definite number r of spin deviations from ferromagnetic saturation. The method demonstrates the Yang–Baxter structure of the relevant classical configuration space, reduces by N the size of the secular equation, and explains the dynamics of the Heisenberg ring in terms of geometry of orbits. We show in particular, that a κ-tuply rarefied orbit, with κ a divisor of N, stimulates neighbour regular (N-element) orbits to twist in a way to become a κ-tuply cover of the adjacent rarefied orbit.

On the significance of quantum effects and interactions for the apparent universality of Bloch laws for Ms( T)

The apparent universality of Bloch's T 3/2-law for the temperature dependence of the spontaneous magnetisation, and of generalisations thereof, is considered. It is argued that in the derivation one should not only consider the exchange interaction between the spins, but also the other interactions between them, leading to elliptical spin precession and deviations from the parabolic dispersion of magnons. Also interaction effects are important to explain the apparent universality of generalised Bloch law exponents ε B, defined by M s( T)= M s(0)−const. T ε B , valid in a wide temperature range T 1< T< T 2, and for dimensionalities d=1, 2 , and 3. The above-mentioned temperature range, the ‘Bloch range’, lies above the quantum range, where magnetic long-range order (e.g. in d=2 dimensions) is non-trivially enforced by the additional interactions, but below the thermal critical region, where universal ‘anomalous scaling dimensions’ apply. In contrast, for the Bloch temperature region, the universality is only apparent, i.e. a crossover-phenomenon, and simple scaling considerations with ‘normal dimensions’ apply. However, due to interactions, the Bloch exponent ε B depends not only on the dimensionality d of the system, but also on the spin quantum number s ( mod(1/2)) of the system, i.e. for given d the Bloch exponent ε B is different for half-integer s and for integer s.