Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

Size and anisotropy effects on magnetic properties of antiferromagnetic nanoparticles

Based on the Heisenberg model taking into account single-ion anisotropy and using a Green's function technique we have studied the influence of size and anisotropy effects on magnetization M, Neel temperature T_N, coercive field H_c and spin excitation energy of antiferromagnetic nanoparticles. The properties are compared with those of ferromagnetic nanoparticles. We have shown that the enhanced magnetization M and coercive field H_c of antiferromagnetic nanoparticles is a surface effect, which is due to uncompensated surface spins. Moreover, the shape of the coercive field curve can be significantly influenced by surface magnetic anisotropy.     

Computer simulation of magnetization relaxation in amorphous magnetics with random anisotropy

On the basis of Heisenberg model, the magnetic properties of amorphous terbium were studied by the Monte Carlo method. The temperature dependences of spontaneous magnetization and magnetic susceptibility were plotted as functions of the fraction of the constant of anisotropy to the exchange constant D/J ₀. The behavior of magnetization in an external magnetic field was studied, and the dependence of a coercive field and residual magnetization on the value D/J ₀ was found. The relaxation of magnetization was investigated after the external magnetic field was switched off.     

Magnetic anisotropy and ordering in equiatomic FeCo alloy equilibrium state vs. temperature

A spherical single crystal, initially disordered by quenching, is ordered at different temperatures in the range 400–730°C. The measured magnetic anisotropy energy shows a cubic symmetry characteristic of the degree of order. In the case of a heat treatment carried out under an applied magnetic field, there is an additional uniaxial anisotropy energy which characterises the presence of directional order.     

Imprints of a primordial magnetic field upon the cosmic microwave background anisotropy and polarization

We review the imprints that a primordial magnetic field may have left upon the cosmic microwave background (CMB) anisotropy and polarization through Faraday rotation around the time of decoupling. Differential Faraday rotation reduces the degree of linear polarization acquired through anisotropic Thomson scattering. Depolarization reduces the damping due to photon diffusion, which results in an increase of the anisotropy on small angular scales. The effect is significant at frequencies around and below 10 GHz {ie2513-1} whereB ₀ is the present strength of the primordial magnetic field.     

Magnetic field anisotropy based MR tractography

Non-invasive measurements of structural orientation provide unique information regarding the connectivity and functionality of fiber materials. In the present study, we use a capillary model to demonstrate that the direction of fiber structure can be obtained from susceptibility-induced magnetic field anisotropy. The interference pattern between internal and external magnetic field gradients carries the signature of the underlying anisotropic structure and can be measured by MRI-based water diffusion measurements. Through both numerical simulation and experiments, we found that this technique can determine the capillary orientation within 3°. Therefore, susceptibility-induced magnetic field anisotropy may be useful for an alternative tractography method when diffusion anisotropy is small at higher magnetic field strength without the need to rotate the subject inside the scanner.     

具有条纹磁畴结构的NiFe薄膜的制备与磁各向异性研究

具有条纹磁畴结构的磁性薄膜表现出面内转动磁各向异性,对于解决高频电子器件的方向性问题起着至关重要的作用.本文采用射频磁控溅射的方法,研究了NiFe薄膜的厚度、溅射功率密度、溅射气压等制备工艺参数对条纹磁畴结构、面内静态磁各向异性、面内转动磁各向异性、垂直磁各向异性的影响规律.研究发现,在功率密度15.6 W/cm~2与溅射气压2 mTorr(1 Torr=1.33322×102Pa)下生长的NiFe薄膜,表现出条纹磁畴的临界厚度在250 nm到300 nm之间.厚度为300 nm的薄膜比250 nm薄膜的垂直磁各向异性场增大近一倍,从而磁矩偏离膜面形成条纹磁畴结构,并表现出面内转动磁各向异性.高溅射功率密度可以降低薄膜出现条纹磁畴的临界厚度.在相同功率密度15.6 W/cm~2下生长300 nm的NiFe薄膜,随着溅射气压由2 mTorr增大到9 mTorr,NiFe薄膜的垂直磁各向异性场逐渐由1247.8 Oe(1 Oe=79.5775 A/m)增大到3248.0 Oe,面内转动磁各向异性场由72.5 Oe增大到141.9 Oe,条纹磁畴周期从0.53μm单调减小到0.24μm.NiFe薄膜的断面结构表明柱状晶的形成是表现出条纹磁畴结构的本质原因,高功率密度下低溅射气压有利于柱状晶结构的形成,表现出规整的条纹磁畴结构,高溅射气压会导致柱状晶纤细化,面内转动磁各向异性与面外垂直磁各向异性增强,条纹磁畴结构变得混乱.     

Crystallographic anisotropy and distortions in helicoidal magnetic structure

The appearance and development of aperiodic distortions in a helicoidal, layered magnetic structure with increasing crystallographic magnetic anisotropy in the magnetization rotation plane have been theoretically studied. A simple phase diagram for this system is proposed. It is established that, at a weak anisotropy, the spiral splits into regions of various lengths with an approximately uniform rotation of the magnetization in each region and a deviation from uniformity at the boundaries; the stronger the anisotropy, the shorter the regions and the greater the deviations. In the limit of high anisotropy, the minimum energy of the system corresponds (depending on the ratio of interlayer exchange integrals J ₁ and J ₂) to either a spiral with constant angular pitch (a multiple of the angle between easy axes) or a double antiferromagnetic structure with a four-layer period. In the case of sixth-order anisotropy with |J ₁| = −J ₂, the energies of phases with different periods (four and six layers for J ₁ > 0; four and three layers for J ₁ < 0) coincide and the excess boundary energy vanishes. In the case of a fourth- and second-order anisotropy, the analogous anomalies appear at |J ₁| = −2J ₂. As a result, the magnetic structure at these points becomes unstable and the phase diagram exhibits the corresponding singularities.     

New experiments on origin of anisotropy in Permalloy films

A series of new experiments has been performed to determine the origin of the uniaxial anisotropy in Permalloy films. By means of a double magnetic shield enclosing the vacuum system, it was possible to deposit films in extremely small ambient fields (10^–6 to 10^–3 oersted). It was found that for deposition field strengths higher than about 10^–1 oersted, the anisotropy constant and the squareness of the hysteresis loop are essentially invariant with respect to the value of the deposition field. However, forH _d <10^–1 oersted, both the anisotropy and squareness of the loop decreases dramatically. From these experimental results, it appears that both the anisotropic Fe-pair orientation and anisotropic imperfection-alignment are deposition-field induced.     

Magnetization and magnetocrystalline anisotropy in YCo4B compound

Easy and hard magnetization curves of YCo₄B compound have been measured in the temperature range from 1.5 to 300 K. It was found that the uniaxial magnetic anisotropy field decreases with decreasing temperature, and the magnetic anisotropy changes from the easy c-axis to the easy cone at approximately 150 K. The easy and hard magnetization curves did not cross up to 6 T. High field susceptibility of the compound for magnetic field parallel to the alignment direction seems different from that for a field perpendicular to the alignment direction. A jump was observed along the easy magnetization curve at 1.5 and 77 K. The critical field of the jump is about 1.5 T at 1.5 K and 1.2 T at 77 K. The jump was shown to be reversible at 1.5 K by down hill measurement.     

Magnetic anisotropy and domain patterns in electrodeposited cobalt nanowires

The magnetic anisotropy and domain structure of electrodeposited cylindrical Co nanowires with length of 10 or 20 μm and diameters ranging from 30 to 450 nm are studied by means of magnetization and magnetic torque measurements, as well as magnetic force microscopy. Experimental results reveal that crystal anisotropy either concurs with shape anisotropy in maintaining the Co magnetization aligned along the wire or favours an orientation of the magnetization perpendicular to the wire, hence competing with shape anisotropy, depending on whether the diameter of the wires is smaller or larger than a critical diameter of 50 nm. This change of crystal anisotropy, originating in changes in the crystallographic structure of Co, is naturally found to strongly modify the zero (or small) field magnetic domain structure in the nanowires. Except for nanowires with parallel-to-wire crystal anisotropy (very small diameters) where single-domain behaviour may occur, the formation of magnetic domains is required to explain the experimental observations. The geometrical restriction imposed on the magnetization by the small lateral size of the wires proves to play an important role in the domain structures formed. Received 14 September 2000     

11-year and 22-year variations in the anisotropy of galactic cosmic rays

An 11-year modulation of the electric drift anisotropy directed across the force lines of the interplanetary magnetic field and a 22-year modulation of the magnetic drift anisotropy along the interplanetary magnetic field have been found on the basis of the data of the Yakutsk underground complex of muon telescopes. Some specific features of the anisotropy during the pole reversal of the total solar magnetic field are discussed.     

Electron spin resonance and magnetocrystalline anisotropy in YCo3

We present the electron spin resonance measurements in powdered samples of the intermetallic compound YCo₃ in Q, K and X microwave bands. The grains of the powdered samples were magnetically aligned in a static magnetic field. The resonant spectra consist of the lines connected with localized and unlocalized magnetic moments. We were able to describe only the part of the spectrum associated with localized moments and to estimate the anisotropy field at the room temperature. Next we present the magnetization data by the pulse magnetometer. The anisotropy field which was determined from these data is much larger than that from ferromagnetic resonance. We suggested a possible reason for such discrepancy.     

Field-induced spin-reorientation transitions in magnetic superlattices with uniaxial anisotropy and biquadratic exchange

Phase transitions induced by an external field are investigated in magnetic multilayer systems with uniaxial anisotropy and biquadratic exchange. A magnetic field directed perpendicular to the plane of the layers changes the effective anisotropy and exchange constants, determining the orientation of the magnetization in the plane of the layers, and can give rise to spin-reorientation transitions. All possible types of such transitions are investigated for the case of uniaxial anisotropy, which differs substantially from the case of cubic anisotropy by the different renormalization of the effective anisotropy constants. Fiz. Tverd. Tela (St. Petersburg) 41, 461–463 (March 1999)     

The measurements of anisotropy of ultrasound propagation and magnetic susceptibility in viscous ferrofluid

Results of experimental study of anisotropy of ultrasound propagation and anisotropy of magnetic susceptibility in a ferrofluid of considerable viscosity are reported. The dependence of the propagation velocity and absorption coefficient of ultrasonic wave on the angle between the direction of measurement and that of the magnetic field provides important information on the ferrofluid structure in a magnetic field. The results show that the ultrasonic absorption coefficient of a wave propagating in a viscous ferrofluid in a DC magnetic field depends mainly on the rotational degree of freedom. Measurements of the anisotropy of the magnetic susceptibility of a ferrofluid bring the information on the magnetic moment of the magnetic particles and their mean radius.     

Unidirectional anisotropy in ferromagnetic-ferrimagnetic film structures

A mechanism of unidirectional anisotropy formation in an exchange-coupled ferromagnetic-ferrimagnetic film structure with orthogonal effective magnetizations in the layers is investigated. The reason for unidirectional anisotropy is the magnetic heterogeneity of the ferrimagnetic layer in the compensation range. Magnetization reversal in the magnetically soft layer of an (REE–transition metal)/NiFe film structure is discussed based on a model of uniform rotation of magnetization. It is found that unidirectional anisotropy sharply decreases the magnetic noise level in the magnetically soft layer. The field of application of these materials is outlined.     

Current distribution and giant magnetoimpedance in composite wires with helical magnetic anisotropy

The giant magnetoimpedance effect in composite wires consisting of a non-magnetic inner core and soft magnetic shell is studied theoretically. It is assumed that the magnetic shell has a helical anisotropy. The current and field distributions in the composite wire are found by means of a simultaneous solution of Maxwell equations and the Landau–Lifshitz equation. The expressions for the diagonal and off-diagonal impedance are obtained for low and high frequencies. The dependences of the impedance on the anisotropy axis angle and the shell thickness are analyzed. Maximum field sensitivity is shown to correspond to the case of the circular anisotropy in the magnetic shell. It is demonstrated that the optimum shell thickness to obtain maximum impedance ratio is equal to the effective skin depth in the magnetic material.     

铁磁/反铁磁双层薄膜中应力各向异性研究

采用铁磁共振方法,研究了铁磁/反铁磁双层薄膜中交换各向异性和应力各向异性对其物理性质的影响.结果表明,单向各向异性来源于界面交换作用,应力各向异性对材料的磁化难易程度有较大影响.当外磁场方向与应力场方向平行时,应力场的存在将促进该方向的磁化.反之,应力场将会阻碍该方向的磁化.     

Magnetic anisotropy of YFe11Ti and its hydride

A study of the magnetic anisotropy of single-crystal YFe₁₁Ti and of its hydride is reported. The measurements were performed on a vibrating-sample and a torsion magnetometer on field-oriented single-crystal and powder samples. The temperature dependence of the magnetic anisotropy constants K ₁ and K ₂ was determined by a mathematical treatment of experimental torque curves and by applying the Sucksmith-Thompson technique to magnetization data. It is shown that the temperature dependence of the magnetic anisotropy constants of YFe₁₁Ti and of its hydride does not follow the prediction of the single-ion exchange model. It is found that hydrogenenation results in a growth of the magnetic anisotropy constant, which can be explained by an electron-density redistribution near the lattice positions occupied by iron atoms. Fiz. Tverd. Tela (St. Petersburg) 40, 285–289 (February 1998)