String order and degenerate entanglement spectrum of S = 1 / 2 and S = 1 Heisenberg bond-alternating chains

Generalized string orders and entanglement spectrum of S = 1/2 and S = 1 Heisenberg bond-alternating chains have been investigated by the infinite time-evolving block decimation (iTEBD) method. Generalized string order parameters with appropriate θ are capable of distinguishing all the topological phases. Central charges c ? 1 and critical exponents β ?1/12 indicate all the topological QPTs belong to the Gaussian universality class. Interestingly, odd- and even-fold degeneracies of the entanglement spectrum are observed. Even-fold (doubly) degenerate entanglement spectra and the typical two-fold degenerate lowest-lying level are found to exist in both the spin-1/2 dimer and the S = 1 Haldane phases. However, odd-fold degenerate entanglement spectra with three-fold degenerate lowest-lying level are observed in both the S = 1 dimer and the S = 2 Haldane phase. The degeneracy of the lowest-lying entanglement spectrum level, which can be understood by entanglement spectra in the dimer limit (J ₁ = 0), is adopted to estimate the lowest boundary of the bipartite entanglement. The entanglement spectrum and the generalized string orders are valuable for uncovering the underlying features of these symmetry-protect topological (SPT) states. Similar entanglement spectrum shows that the S = 1 (S = 2) Haldane phase is essentially the same as the S = 1/2 (S = 1) dimer phase.     

Magnetic-field-induced quantum criticality in a spin-<Emphasis Type="Italic">S</Emphasis> planar ferromagnet with single-ion anisotropy

The effects of single-ion anisotropy on quantum criticality in a d-dimensional spin-S planar ferromagnet is explored by means of the two-time Green’s function method. We work at the Tyablikov decoupling level for exchange interactions and the Anderson-Callen decoupling level for single-ion anisotropy. In our analysis a longitudinal external magnetic field is used as the non-thermal control parameter and the phase diagram and the quantum critical properties are established for suitable values of the single-ion anisotropy parameter D. We find that the single-ion anisotropy has sensible effects on the structure of the phase diagram close to the quantum critical point. However, for values of the uniaxial crystal-field parameter below a positive threshold, the conventional magnetic-field-induced quantum critical scenario remains unchanged.     

A multisublattice magnetic phase induced by external field in a singlet magnet

The theory of magnetization in a longitudinal magnetic field is developed for an easy-plane multisublattice antiferromagnet with a singlet ground state and a strong single-ion anisotropy exceeding the magnitude of exchange interaction. The magnetic-field-induced phase transition from the singlet (magnetically dis-ordered) state to a multisublattice antiferromagnetic state represents a displacive magnetic phase transition. At T=0, this transition proceeds continuously and belongs to second-order phase transitions, while at T ≠0, the behavior changes to jumplike and the process becomes the first-order phase transition.     

Quantum analogue of the spin-flop transition for a spin pair

Quantum (step) magnetization curves have been analyzed for a spin pair with antiferromagnetic interaction in the presence of a magnetic field that is parallel to the easy magnetization axis. Both semiclassical and numerical analyses have been performed for a wide range of the anisotropy parameter and spins up to S ? 100. In the dependence of the anisotropy character (single-ion or exchange), a spin jump larger than unity can appear in the magnetization curve or jumps can be concentrated in a narrow range of the field. In addition, regions of the problem parameters have been revealed where behavior is semiclassical for low spins on the order of S = 5 and where behavior is substantially quantum even for S → ∞.     

Theoretical prediction of a surface-induced spin-reorientation phase transition in BaFe<Subscript>12</Subscript>O<Subscript>19</Subscript> nanocrystals

The equation of the magnetization of a hexagonal crystal is derived for the first time for an arbitrary orientation of the external magnetic field relative to the crystallographic c axis. In order to clarify the magnetization mechanism for a real ensemble of small particles in the framework of the given problem, surface anisotropy (which is significant for nanosize objects) was taken into account along with crystalline magnetic anisotropy and anisotropy in the particle shape. Model computer experiments prove that the magnetization curves for nanocrystals oriented in a polar angle range of 65–90° exhibit an anomaly in the form of a jump, indicating a first-order spin-reorientation phase transition. This explains a larger steepness of the experimental curve reconstructed taking into account the interaction between particles as compared to the theoretical dependence obtained by Stoner and Wohlfarth [IEEE Trans. Magn. MAG 27 (4), 3469 (1991)]. An analysis of variation of the characteristic anisotropy surface and its cross section with increasing ratio |K₂|/K₁ of the crystalline magnetic anisotropy constants upon a transition from a macroscopic to a nanoscopic crystal shows that surface anisotropy leads to a change in the magnetic structure. As a result, an additional easy magnetization direction emerges in the basal plane apart from the easiest magnetization direction (along the c axis). The direction of hard magnetization emerges from the basal plane, the angle of its orientation relative to the c axis being a function of the ratio | K₂|/K₁.     

Temperature-induced magnetic phase transitions in crystals with competing single-ion and interionic magnetic anisotropies

Temperature-induced phase transitions in a uniaxial ferromagnetic system of spins S = 1 with competing one-particle and two-particle anisotropies are studied. It is shown that, in the case where easy-plane single-ion anisotropy dominates over easy-axis two-particle anisotropy, the transition from the paramagnetic state to a ferromagnetic state with magnetization perpendicular to the anisotropy axis is a second-order displacive magnetic phase transition. In the opposite case, where two-particle anisotropy dominates over single-particle anisotropy, the transition to a ferromagnetic state with magnetization perpendicular to the anisotropy axis is also continuous but of the order-disorder type. In a system with competing second-order one-and two-particle anisotropies, the orientational first-order phase transition can occur to a state with the magnetization directed along or perpendicular to the anisotropy axis.     

Quantum Oscillations of Magnetization in Antiferromagnetic Semimetals on a Triangular Lattice

The specific features of magnetization in antiferromagnetic semimetals with a low charge carrier density on a triangular lattice in a high magnetic field are studied. It is demonstrated that the well-known plateau in the magnetic field dependence of the magnetization manifesting itself in the subsystem of localized S = 1/2 spins is actually not strictly horizontal but has a slight positive slope. It is found that an abrupt change in the frequency of quantum oscillations of the magnetization in the itinerant subsystem should be observed at the magnetic field values corresponding to the edges of this plateau owing to the strong s–d(f) exchange coupling.     

Quantum to classical transition in the ground state of a spin-S quantum antiferromagnet

We study a frustrated spin-S staggered-dimer Heisenberg model on square lattice by using the bond-operator representation for quantum spins, and investigate the emergence of classical magnetic order from the quantum mechanical (staggered-dimer singlet) ground state for increasing S. Using triplon analysis, we find the critical couplings for this quantum phase transition to scale as 1 /S(S + 1). We extend the triplon analysis to include the effect of quintet dimer-states, which proves to be essential for establishing the classical order (Néel or collinear in the present study) for large S, both in the purely Heisenberg case and also in the model with single-ion anisotropy.     

Anomalous influence of spin fluctuations on the heat capacity and entropy in a strongly correlated helical ferromagnet MnSi

The influence of spin fluctuations on the thermodynamic properties of a helical ferromagnet MnSi has been investigated in the framework of the Hubbard model with the electronic spectrum determined from the first-principles LDA + U + SO calculation, which is extended taking into account the Hund coupling and the Dzyaloshinskii–Moriya antisymmetric exchange. It has been shown that the ground state of the magnetic material is characterized by large zero-point fluctuations, which disappear at the temperature T* (<T _c is the temperature of the magnetic phase transition). In this case, the entropy abruptly increases, and a lambdashaped anomaly appears in the temperature dependence of the heat capacity at constant volume (C _V (T)). In the temperature range T* < T < T _c , thermal fluctuations lead to the disappearance of the inhomogeneous magnetization. The competition between the increase in the entropy due to paramagnon excitations and its decrease as a result of the reduction in the amplitude of local magnetic moments, under the conditions of strong Hund exchange, is responsible for in the appearance of a “shoulder” in the dependence C _V (T)).     

Magnetic properties of Fe<Subscript>3</Subscript>C ferromagnetic nanoparticles encapsulated in carbon nanotubes

The low-temperature dependences of magnetic characteristics (namely, the coercive force H _c , the remanent magnetization M _r , local magnetic anisotropy fields H _a, and the saturation magnetization M _s ) determined from the irreversible and reversible parts of the magnetization curves for Fe₃C ferromagnetic nanoparticles encapsulated in carbon nanotubes are investigated experimentally. The behavior of the temperature dependences of the coercive force H _c (T) and the remanent magnetization M _r (T) indicates a single-domain structure of the particles under study and makes it possible to estimate their blocking temperature T _B = 420–450 K. It is found that the saturation magnetization M _s and the local magnetic anisotropy field H _a vary with temperature as ～T ^5/2.     

Monte Carlo simulation of magnetic phase transitions in amorphous alloys of the Re-Tb system

The magnetic properties of amorphous alloys of the Re-Tb system and pure amorphous terbium have been investigated by the Monte Carlo method within the Heisenberg model. The temperature dependences of the spontaneous magnetization and magnetic susceptibility have been constructed for different ratios of the anisotropy constant to the exchange constant, D/J. The minimum value of D/J at which the spin-glass transition occurs is determined. The magnetic phase diagram of amorphous Re-Tb alloys, obtained by the simulation, is in qualitative agreement with the experimental data.     

Magnetic Resonance Properties of a Nanogranular Ni<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>C<Subscript>100 − <Emphasis Type="Italic">m</Emphasis></Subscript> Film Structure

Magnetic resonance properties characteristic of nanogranular film structure Ni_mC_{100 ? m} with different concentrations m of its magnetic phase are studied. Samples are subjected to annealing at temperatures of 200 and 300°C. With tangential magnetization in the planes of films with m ranging from 70 to 89.8 at %, anisotropy is observed for the resonance field and the width of the absorption line. This anisotropy is explained by the uneven shapes of magnetic granules along different directions in the films.     

Optimization of multiferroic properties in the absence of single-ion magnetic anisotropy

The dependence of the average magnetization per site of perovskite B sublattice has been calculated on the assumption of weak single-ion magnetic anisotropy for a quasy-binary solution of Fe³⁺ and nonmagnetic ions. The technique of application of the obtained results to optimize the magnetoelectric characteristics of solid solutions is qualitatively described.     

High-frequency susceptibility and ferromagnetic resonance in multidomain thin films of the yttrium-iron garnet type

The field dependence of the high-frequency susceptibility and the ferromagnetic resonance were experimentally studied in a thin (d≈0.1 µm) (111)-oriented single-crystal film of substituted yttrium-iron garnet with the factor q?1. It was shown that the anomaly in the high-frequency susceptibility observed in a magnetic field H parallel to the normal to the film surface in the magnetization saturation region (H≈H_s) has a dual nature; more specifically, this anomaly is associated with an abrupt collapse of the stripe domain structure and a ferromagnetic resonance in the experimental configuration H ∥ [111] and h ⊥ H. In this case, the film transition from the inhomogeneous multidomain state to the homogeneous (single-domain) state at the point H≈H_s has no indications of a second-order phase transition. The experimental frequency-field dependence of ferromagnetic resonance (FMR) in the sample under study, having a characteristic minimum at the point ω₀=5 MHz and H_FMR=H_s, agrees qualitatively and quantitatively with calculations. The influence of the cubic magnetic anisotropy and the film thickness on the FMR spectrum and the orientation of the spontaneous magnetization in domains with respect to the film plane in the zero field H was theoretically studied.     

Entanglement in Mixed-Spin (1/2, 3/2) Heisenberg XXZ Model with Dzyaloshinskii-Moriya Interaction

In this paper, the entanglement in a mixed-spin (1/2, 3/2) Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction in an inhomogeneous external magnetic field is studied. We not only calculate the ground-state entanglement but also investigate the behaviors of quantum phase transition following the changes of DM interaction and nonuniform magnetic field. More importantly, we note that the DM interaction improves the critical magnetic field B _c , the critical temperature T _c and broadens the region of entanglement.     

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpiński gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with 0 ≤ J_b/J_a< 1, and an interesting crossover behavior between different phases at J_b/J_a = 1 is unveiled, whose dynamics can be described by the J_b/J_a-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpiński gasket are obtained in both the 1 / 3 plateau disordered phase and the 5/9 plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpiński gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.     

Monogamy Relations in Terms of Tsallis-Q Entropy in any Dimensional System

Monogamy of entanglement is a fundamental property of multipartite entangled states. In this article, due to the convexity of Trρ^q with respect to q when q ≥ 1, we give a monogamy-like relation in terms of Tsallis-q entanglement entropy of assistance (TqEEA) for pure states over an n- partite any dimensional system and monogamy-like relations in terms of Tsallis-q entanglement entropy (TqEE) for mixed states for any dimensional system, we also give a lower bound for the TqEE of a four-partite pure state. At last, we show that the generalized W-class states satisfy the polygamy relation in terms of TqEE when q = 2.     

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ? 0.68 and α_c2 ? 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α<α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.     

Magnetization behavior and metamagnetic transitions in electron-doped manganites induced by a strong magnetic field

The behavior of magnetization M of the R_xA_1?xMnO₃ manganites (R=La, Pr, Nd, Sm, etc., A=Ca, Sr, Ba) in the electron doping region (x<0.4) is studied as a function of external magnetic field H. The M(H) relations for homogeneous magnetic structures are obtained by performing band calculations in the double-exchange model. Three different types of magnetization behavior corresponding to three electron concentration ranges (x<0.14, 0.14<x<0.27, x>0.27) are revealed. The M(H) relations are interpreted in terms of the phase diagram for the homogeneous ground state of the manganites calculated for H=0, and the results agree qualitatively with experimental data on the magnetization of Sm_xCa_1?xMnO₃.     

Magnetic Properties of Composite Materials Based on a Solid Solution of Type (CuInSe<Subscript>2</Subscript>)<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>(MeSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> (Me = Mn,Fe) and Polyethylene

Basic magnetic characteristics (coercive force H_c, residual magnetization M_r, magnetization M, and saturation magnetization M_s) of solid solutions of type (CuInSe₂)_1–x(MeSe)_x (Me = Mn, Fe) have been investigated in a wide temperature interval (100–300 K). The existence of a magnetic phase transition has been established for all studied solid solutions at low temperatures, and the Néel temperatures have been determined from the temperature dependences of the magnetization. It is shown that the temperature dependences of coercive force H_c and of magnetization M can be described using the thermal relaxation (fluctuation) theory.