Single-ion Anisotropy Constant Research Articles

Effects of temperature on the dynamic and static properties of a non-heisenberg anisotropic ferromagnet

In the mean-field approximation, the influence of both temperature and the value of the single-ion anisotropy constant of the “easy axis” type on the phase states and excitation spectra of a non-Heisenberg ferromagnet with S = 1 is studied. The temperature dependences of the vector and tensor order parameters in both the ferromagnetic and nematic phases have been determined. The dependence of excitation spectra on temperature and the value of the anisotropy constant is studied. It is shown that at a temperature different from zero, an additional (non-relaxation) branch of excitations arises in both the ferromagnetic and nematic phases. The temperature dependence of the phase diagram is studied.

Effect of an external magnetic field on the phase states and dynamic properties of the strongly anisotropic antiferromagnet

The effect of an external magnetic field on both the static and spectral properties of a highly anisotropic Ising antiferromagnet with magnetic ion spin S = 1 is studied. It is shown that at sufficiently low fields and large values of the single-ion anisotropy constant, a state with a zero value of the average magnetic moment (at the site), which is characterized by tensor order parameters (QU phase), is realized in the system. A further increase in the magnetic field turns the magnet (via a first-order transition) into the “quasi-ferrmagnetic” state. In this state is characterized by the fact that one of the sublattices is magnetized to saturation, whereas in the second the average magnetic moment (per site) is equal to zero. We called this phase the LS (low spin) phase. A further increase in the field leads to the realization of a ferromagnetic phase. All phase transitions are first-order transitions, as evidenced by the behavior of their spectra of elementary excitations.

Magnons in AgF2, AgCuF4, and AgNiF4

We report on the analytical derivation of the spin-wave dispersion and magnon density of states in the orthorhombic AgF2 within J1–J2–J3 model and within 2D limit. Numerical calculations allowed us to estimate the effect of the Dzyaloshinskii–Moriya interaction, and explore closely related systems AgCuF4 and AgNiF4 in different pressure-induced phases. Obtained results will pave a direct way to link abinitio calculations with experiments via determination of the exchange and single-ion anisotropy constants based on any method which is able to probe spin dynamics, such as Raman or infrared spectroscopy.

Ab-initio and Monte Carlo study of Fe-based two-dimensional magnets at borophene supported by Ag(111) surface

Two-dimensional (2D) magnetic crystals are ideal platforms for the employment of simple physical models in the exploration of magnetism in a 2D limit. Instead of examining 2D van der Waals materials, the focus of our study is on adatoms that carry intrinsic magnetic moments and are assembled into 2D arrays at a suitable surface. We applied density functional theory (DFT) to investigate Fe nanostructures formed on a borophene sheet deposited at Ag(111) surface and identified stable Fe-based 2D magnets formed either on top of the borophene or at the interface between the borophene and Ag(111) surface. The structures are composed of close-packed Fe wires, featuring ferromagnetism within the chain and the interchain antiferromagnetic coupling. Exchange- and single-ion anisotropy constants extracted from DFT calculations are used to describe these systems with the classical Ising and Heisenberg models. The corresponding Monte Carlo simulations revealed finite temperature magnetic ordering, with the estimates of critical temperatures of 105 and 30 K derived from the anisotropic Heisenberg model, for the Fe-based magnets grown above and under borophene, respectively.

Magnetoelectric properties of multiferroic CuCrO2 studied by means of ab initio calculations and Monte Carlo simulations

Motivated by the discovery of multiferroicity in the geometrically frustrated triangular antiferromagnet ${\mathrm{CuCrO}}_{2}$ below its N\'eel temperature ${T}_{N}$, we investigate its magnetic and ferroelectric properties using ab initio calculations and Monte Carlo simulations. Exchange interactions up to the third nearest neighbors in the $ab$ plane, interlayer interaction, and single ion anisotropy constants in ${\mathrm{CuCrO}}_{2}$ are estimated by a series of density functional theory calculations. In particular, our results evidence a hard axis along the [110] direction due to the lattice distortion that takes place along this direction below ${T}_{N}$. Our Monte Carlo simulations indicate that the system possesses a N\'eel temperature ${T}_{N}\ensuremath{\approx}27$ K very close to the ones reported experimentally (${T}_{N}=24--26$ K). Also we show that the ground state is a proper-screw magnetic configuration with an incommensurate propagation vector pointing along the [110] direction. Moreover, our work reports the emergence of spin helicity below ${T}_{N}$ which leads to ferroelectricity in the extended inverse Dzyaloshinskii-Moriya model. We confirm the electric control of spin helicity by simulating $P\text{\ensuremath{-}}E$ hysteresis loops at various temperatures.

Quadrupole hysteresis in uniaxial magnet with unity spin

Uniaxial spin-1 magnets with tensor interactions have been studied in the absence of external magnetic field. The model with the most general form of interactions for the uniaxial symmetry has been investigated. Conditions for the implementation of only two quadrupole phases are considered: the phase with a quadrupole ordering along the lattice symmetry axis and the phase with ordering in the plane normal to the lattice symmetry axis. It has been shown that components of the quadrupole order parameter as a function of the single-ion anisotropy constant at low temperatures has “hysteresis” character. An analytical expression for the remagnetization energy per lattice site has been obtained.

High-field multi-frequency ESR in the S=2 heisenberg antiferromagnetic chain compound MnCl3(bpy)

We report the results of high-field multi-frequency electron spin resonance (ESR) experiments on a powder sample of MnCl3 (bpy) (bpy=2, 2′-bipyridine). This compound is one of the rare examples of the spin (S) 2 quasi one-dimensional (1D) Heisenberg antiferromagnets (HAFs), and magnetic properties of tiny single crystal samples were reported previously (G. E. Granroth et al., Phys. Rev. Lett. 77, 1616 (1996).). In our previous paper on this compound (M. Hagiwara et al., J. Phys.: Conf. Ser. 400, 032014 (2012).), we reported, for the S=2 1D HAF, good agreement between experiment and calculation for the temperature dependence of magnetic susceptibility and the high-field magnetization process at 1.3 K. In this work, we have observed some high-frequency resonance modes with zero-field gaps of about 800 GHz that may correspond to antiferromagnetic resonance modes with orthorhombic anisotropy in a long-range-ordered phase that emerged at low temperatures above the critical field at which the energy gap (Haldane gap) closes. The single-ion anisotropy constant D evaluated from the analysis of these ESR modes is larger than that reported previously.

Possible Phase Diagrams of Systems with Competing Anisotropies

Possible types of the phase diagrams are investigated for mixtures composed of two kinds of spin systems with orthogonal anisotropies. It is shown on the basis of Landau's second order phase transition theory that possible phase diagrams are classified into four types, which are qualitatively different from one another. Calculations by the use of the free energy obtained in a single spin approximation show that all of these four types of the phase diagrams can be realized by suitably choosing the values of the anisotropic exchange couplings and the single ion anisotropy constants.

Phase transition “polydomain state-single-domain state” with exchange springs in the antiferromagnetic interlayer of the spin-valve structure

The phase transition “polydomain state-single-domain state” with exchange springs in the antiferromagnetic interlayer of the spin-valve ferromagnet-antiferromagnet-ferromagnet structure, which occurs as the ratio of the interlayer thickness to the width of atomic steps on the interfaces between the layers increases, has been investigated using mathematical simulation. The critical value of this ratio, at which the phase transition occurs, and the deflection of exchange springs that appear at the interfaces between the layers have been determined in a wide range of values of the single-ion anisotropy constant.

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume–Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume–Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h0/zJ) and (T/zJ, D/zJ), where T absolute temperature, h0, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).

10.1007/s11451-008-2013-0

A thermodynamic analysis of spin ordering in an Ising antiferromagnet with single-ion easy-plane anisotropy is carried out. The solutions of the equations of state are analyzed, and the phase diagram is constructed. It is shown that an increase in the single-ion anisotropy constant as a result of increasing competition between single-ion anisotropy and exchange interaction brings about a crossover from the continuous phase transition to the abrupt phase transition. This is initiated by a change in the ion state populations due to single-ion anisotropy and by the freezing of ionic states with a nonzero spin projection. An increase in the single-ion anisotropy also leads to a crossover of the phase transformation between the paramagnetic and antiferromagnetic states from the order-disorder to order-order type.

Ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with competing single-ion anisotropies

Employing various numerical methods, we determine the ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S=1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.

Phase transitions in 2D and 3D non-Heisenberg ferromagnets with temperature-dependent anisotropy

A model of a non-Heisenberg ferromagnet is considered in which the single-ion anisotropy constant is linearly dependent on temperature. The conditions are found under which phase transitions occur in 2D and 3D non-Heisenberg ferromagnets as the temperature is varied. It is shown that, in the case where the biquadratic interaction is dominant, quadrupole states can occur in the system, which are specified by the orientation of the quadrupole moment. As the temperature is varied, a phase transition between quadrupole states can occur in 2D magnets. Depending on the ratios between the material constants, this transition can be either a second-order phase transition with the continuously changing orientation of the principal axes of the quadrupole moment tensor or a first-order phase transition with hysteresis through a state with a nonhomogeneous distribution of the principal axes of the quadrupole moment tensor. In 3D magnets, the phase transition between quadrupole states is of the first order with hysteresis. Phase diagrams of the system are constructed.

Multicritical dynamical phase diagrams of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling in an oscillating field

We study, within a mean-field approach, the stationary states of the kinetic Blume–Emery–Griffiths model with repulsive biquadratic coupling under the presence of a time-varying (sinusoidal) magnetic field. We employ the Glauber-type stochastic dynamics to construct set of dynamic equations of motion. The behavior of the time dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as functions of the reduced temperature are investigated. The dynamic phase transition points are calculated and phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. The dynamical transition from one regime to the other can be of first- or second order depending on the region in the phase diagram. According to the values of the crystal field interaction or single-ion anisotropy constant and biquadratic exchange constant, we find 20 fundamental types of phase diagrams which exhibit many dynamic critical points, such as tricritical points, zero-temperature critical points, double critical end points, critical end point, triple point and multicritical point. Moreover, besides a disordered and ordered phases, seven coexistence phase regions exist in the system.

Specific features of spin ordering in an Ising antiferromagnet with single-ion easy-plane anisotropy

A thermodynamic analysis of spin ordering in an Ising antiferromagnet with single-ion easy-plane anisotropy is carried out. The solutions of the equations of state are analyzed, and the phase diagram is constructed. It is shown that an increase in the single-ion anisotropy constant as a result of increasing competition between single-ion anisotropy and exchange interaction brings about a crossover from the continuous phase transition to the abrupt phase transition. This is initiated by a change in the ion state populations due to single-ion anisotropy and by the freezing of ionic states with a nonzero spin projection. An increase in the single-ion anisotropy also leads to a crossover of the phase transformation between the paramagnetic and antiferromagnetic states from the order-disorder to order-order type.

One-Third Magnetization Plateau in an Anisotropic (S,S')=(1,2) Spin-Alternating Chain

Employing numerical methods, we study the ground-state magnetization curve of a ( S , S ')=(1,2) spin-alternating chain with uniaxial single-ion anisotropies, where S =1 and S '=2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the one-third plateau, which appears at one third of the saturation magnetization in the ground-state magnetization curve. We find that three kinds of one-third plateaux appear, one of which has a quantum nature, while the remaining two have a classical (Ising) nature. We determine the one-third plateau phase diagram on the D 2 versus D 1 plane, where D 1 ( D 2 ) is the ratio of the single-ion anisotropy constant for the S =1 ( S '=2) spin to the exchange interaction constant. This phase diagram consists of a phase boundary line between the quantum and classical one-third plateau states as well as three phase boundary lines between the one-third plateau and plateauless states. We emphasize that there is no phase trans...

Increase in the magnetostrictive susceptibility of Tb0.3Dy0.67Ho0.03Fe2−x Co x alloys upon substitution of cobalt for iron

This paper reports on the results of investigations into the concentration dependences of the magnetostrictive susceptibility, the magnetostriction, the magnetization, and the Curie temperature for Tb0.3Dy0.67Ho0.03Fe2−x Co x alloys upon substitution of cobalt for iron. It is revealed that the temperature of the spin-reorientation transition shifts toward room temperature with an increase in the cobalt content in the range 0 ≤ x ≤ 1.3. Substitution of cobalt for iron in the alloys leads to a decrease in the contribution of the 3d transition metal sublattice to the magnetic anisotropy owing to the opposite signs of the single-ion anisotropy constants for iron and cobalt. The decrease observed in the magnetocrystalline anisotropy compensated in both rare-earth and 3d transition metal sublattices is responsible for the high magnetostrictive susceptibility of the studied compounds at a high cobalt content (x = 1.3) in the room-temperature range.

Phase transitions in a ferromagnet with biquadratic exchange and hexagonal single-ion anisotropy

The phase states and the spectra of elementary excitations of a ferromagnet with a biquadratic exchange interaction and a spin-2 magnetic ion are investigated. The phase diagrams of the system are constructed for different relationships among the material constants. It is shown that the phase diagram is substantially altered at large values of the single-ion anisotropy constants and biquadratic exchange constant.

Influence of magnetoelastic coupling on the formation of a spatially inhomogeneous phase in two-dimensional ferromagnets

The influence of magnetoelastic coupling on the existence region of a spatially inhomogeneous state in a two-dimensional anisotropic ferromagnet is investigated. The phase transitions to the spatially inhomogeneous state under the influence of magnetic field and upon a change in the single-ion anisotropy constant are examined. It is shown that the magnetoelastic coupling enlarges the existence region of this phase substantially and also increases the domain width.

MIXED SPIN-1 AND SPIN-$\frac{3}{2}$ BLUME–CAPEL ISING FERRIMAGNETIC SYSTEM ON THE BETHE LATTICE

The mixed spin-1 and spin-[Formula: see text] Blume–Capel Ising ferrimagnetic system for the central spin with spin-1 is studied on the Bethe lattice using the exact recursion equations. The exact expressions for the magnetization, the quadrupolar moment, the Curie temperature and the free energy are found and the phase diagrams are constructed on the Bethe lattice with the coordination numbers q = 3, 4 and 6 for the various values of the single-ion anisotropy constants dA = DA/J for spin-1 and dB = DB/J for spin-[Formula: see text]. The existence of a tricritical point is investigated for different values of q and the single-ion anisotropy constants. The phase diagrams in the (kTc/J, dA) plane for the central spin are obtained for two different cases; (1) dA = dB and (2) dA is varied for selected values of dB. The results are compared with those of other approximate methods.