Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

Dynamics of the random field Ising model

Dynamics of the kinetic Ising model in the presence of static random fields is investigated using a self-consistent method. It is shown that if the interface fluctuations of the low temperature phase are small the system at low temperatures stays in a state without long range order. For this state the spin correlation function 〈S_q(t)S_?q(O)> averaged over all configurations of random fields decays exponentially in time with a single wavevector dependent relaxation time which is finite at the transition temperature T₀ and remains very long below T₀. In the mean field approximation the correlation time at the magnetic Bragg peak and at T₀ scales with the magnitude of the random field as τ∞h^?z_h with z_h = 1 for d = 2 and $\text{z}{}_{\mathrm{h}}\text{=}\text{4}\text{3}$ for d = 3, respectively.     

Critical behavior of a degenerate ferromagnet in a uniaxial random field: Exact results in a space of arbitrary dimension

The critical behavior of the transverse (with respect to the field) magnetization component in classical degenerate magnets with only nearest-neighbors interaction in a uniaxial random magnetic field at zero temperature is found exactly. For a Gaussian distribution of the random field the asymptotic transverse magnetization in strong fields does not depend on the dimension of the space and is of the form m _⊥ ∝ 1nh ₀/h ₀ ² , where h ₀ is the width of the distribution. For a bimodal distribution, where only the field direction is random and the amplitude is fixed, the transverse magnetization behaves as m _⊥∝exp(−const/(H _c −H) ^D/2), where H is the amplitude of the random field, D is the dimension of the space, and H _c is the critical field. Zh. éksp. Teor. Fiz. 115, 2143–2159 (June 1999)     

横向随机晶场Ising模型的相图和磁化行为研究

在有效场理论和切断近似框架内，选择自旋S=1的二维方格子，研究横向随机晶场Ising模型的相图和磁化行为，重点是横向随机晶场浓度和晶场比率对相图和磁化的影响.给出了i>T-D_x空间的相图和m-T空间的磁化图.在晶场稀疏情况下，负晶场方向存在临界温度的峰值，正方向可出现重入现象.晶场比率取+0.5和-0.5时，磁有序相范围缩小，特别是晶场比率取-0.5时，随晶场浓度的降低，临界温度峰值从横向晶场负方向渡越到正方向.固定某一负晶场值，不同晶场比率的磁化行为有明显差异.同时与纵向稀疏晶场Ising模型结果进行有意义的比较. 关键词： 横向随机晶场Ising模型 相图 磁化行为     

The magnetization of PrFeAsO0.60F0.12 superconductor

The magnetization of the PrFeAsO_0.60F_0.12 polycrystalline sample has been measured as functions of temperature and magnetic field (H). The observed total magnetization is the sum of a superconducting irreversible magnetization and a paramagnetic magnetization. Analysis of dc susceptibility χ(T) in the normal state shows that the paramagnetic component of magnetization comes from the Pr³⁺ magnetic moments. The intragrain critical current density (J_L) derived from the magnetization data is large. The J_L(H) curve displays a second peak which shifts towards the high-field region with decreasing temperature. In the low-field region, a plateau up to a field H^* followed by a power law H^?5/8 behavior of J_L(H) is the characteristic of the strong pinning. A vortex phase diagram for the present superconductor has been obtained from the magnetization and resistivity data.     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Analytic Verification of the Droplet Picture in the Two-Dimensional Ising Model

It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<T _c has an essential branch cut singularity at the origin H=0. The phenomenological droplet theory predicts that near the cut drawn along the negative real axis H<0, the imaginary part of the free energy per lattice site has the form ImF[exp(±i)|H|]=±B|H|exp(–A/|H|) for small |H|. We verify this prediction in analytical perturbative transfer matrix calculations for the square lattice Ising model for all temperatures 0<T<T _c and arbitrary anisotropy ratio J ₁/J ₂. We obtain an expression for the constant A which coincides exactly with the prediction of the droplet theory. For the amplitude B we obtain B=M/18, where M is the equilibrium spontaneous magnetization. In addition we find discrete-lattice corrections to the above mentioned phenomenological formula for ImF, which oscillate in H ^–1.     

Scattering of acoustic phonons by rare earth substitutional atoms in yttrium aluminum garnets

The diffusive maxima of phonon signals, and in particular their arrival timest _m are examined for a number of solid solutions of rare earth atoms in yttrium aluminum garnets. The phonon pulses are generated by metallic films of the characteristic lengthl _h heated by current pulses to the temperatureT _h slightly higher than the ambient temperatureT. The injected phonons travel in wafers of the thicknessL _z. They are scattered by substitutional atoms of rare earth occupying the yttrium dodecahedral sites, rare earth and yttrium atoms occupying the aluminum octahedral sites and by another lattice imperfections generated in the process of sample growing. The qualitative analysis based on our exact formula for the diffusion coefficientD allows us to extract the contribution of rare earth atoms substituting the Y atoms toD. Considering the dependence oft _m/L _z ² on the temperature and the ratiol _h/L_z we conclude thatD∼T _h ⁻⁴ and that the energy of phonons forming the diffusive maxima ranges from 3.2k _BT_H to 4.2k _BT_H, which is in reasonable agreement with the existing estimates.     

Anomalous temperature dependence of the 1.7T magnetic hyperfine field of fluorine in nickel

By means of time-differential perturbed angular distribution (TDPAD) techniques, the magnetic hyperfine field ofF atoms implanted in a ferromagnetic Ni lattice has been measured at temperatures from 80 K to 650 K obtaining, for example, a fieldH ₁(295 K)=+1.72(3)T at room temperature. The temperature dependence of the reduced fieldH ₁(T)/H ₁(0) has been found to deviate up to 38% from that of the reduced magnetization of the Ni host. Comparing this result for the halogenF with other nontransitional impurities in nickel, it seems that such deviations become more pronounced with increasing number of excessp-electrons of the impurity. With a simple two-zone model distinguishing between the hyperfine fields originating in the local and in the more distant undisturbed surrounding of theF impurity, the observed temperature dependence can be explained. In this approach the disturbed magnetization of the inner zone is described by localized Ni moments in the molecular field approximation.A satellite magnetic field of + 9.4T was observed at 80 K only.Supported by the Bundesministerium für Forschung und Technologie     

Molecular field theory analysis of R2Fe17C (R=PR,Nd, Gd,Tb, Dy,Ho, Er)

The temperature dependence of magnetization is analysed for R₂Fe₁₇C via the two-sublattice molecular field theory. The molecular field coefficients n_FF, n_RF and n_RR are obtained, by which T_C was calculated. Using the least-squares method, the fitted-form of H_R(T) varying with temperature for each compound is presented. The results are analysed. In addition, the parameters F=M_Fe²(0)n_FF/T_C was calculated for each R₂Fe₁₇C. By F, some phenomena different from the normal view were explained.     

The random field Ising model with an asymmetric trimodal probability distribution

The Ising model in the presence of a random field is investigated within the mean field approximation based on Landau expansion. The random field is drawn from the trimodal probability distribution P(h_i)=pδ(h_i−h₀)+qδ(h_i+h₀)+rδ(h_i), where the probabilities p,q,r take on values within the interval [0,1] consistent with the constraint p+q+r=1 (asymmetric distribution), h_i is the random field variable and h₀ the respective strength. This probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites. The current random field Ising system displays second order phase transitions, which, for some values of p,q and h₀, are followed by first order phase transitions, thus confirming the existence of a tricritical point and in some cases two tricritical points. Also, reentrance can be seen for appropriate ranges of the aforementioned variables. Using the variational principle, we determine the equilibrium equation for magnetization, solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.     

On the lower critical field and phase diagram of a thin cylindrical type-II superconductor

The lower critical field H _c1 ^cyl (T) of a superconducting cylinder with radius r ₀∼ξ(T)≪λ(T) is found on the basis of the Ginzburg-Landau theory with various boundary conditions. These results together with the well-known results for the upper critical field are used to construct phase diagrams in terms of the field versus the reduced radius r ₀∼ξ(T) variables. The jump in the average magnetization at H _c1 ^cyl (T) is calculated as a function of the reduced radius. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 537–542 (25 April 1999)     

The magnetic properties of one-dimensional spin-1 ferromagnetic Heisenberg model in a magnetic field within Callen approximation

The effect of magnetic field h on the magnetic properties of the one-dimensional spin-1 ferromagnetic Heisenberg model is studied by the double-time Green’s function method. The magnetization and susceptibility are obtained within the Callen approximation. The zero-field susceptibility is as a decreasing function of the temperature T. The magnetization m increases in the whole field region, but the susceptibility maximum χ(T_m) decreases. The position T_m of the susceptibility maximum is both solved analytically and fits well to be a power law T_m∼h^γ at low fields and to be linear increasing at high fields. The height χ(T_m) decreases as a power law χ(T_m)∼h^−β with h increasing. The exponents (γ,β) obtained in our results agree with the other theoretical results. Our results are roughly in agreement with the results obtained in the experiment of Ni(OH)(NO₃)H₂O.     

Low-temperature structural phase transition in a monoclinic KDy(WO4)2 crystal

The low-temperature thermal and magnetic-resonance properties of a monoclinic KDy(WO₄)₂ single crystal are investigated. It is established that a structural phase transition takes place at T _c=6.38 K. The field dependence of the critical temperature is determined for a magnetic field oriented along the crystallographic a and c axes. The initial part of the H-T phase diagram is plotted for H∥a. The prominent features of the structural phase transition are typical of a second-order Jahn-Teller transition, which is not accompanied by any change in the symmetry of the crystal lattice in the low-temperature phase. The behavior of C(T) in a magnetic field shows that the transition goes to an antiferrodistortion phase. An anomalous increase in the relaxation time (by almost an order of magnitude) following a thermal pulse is observed at T>T _c(H), owing to the structural instability of the lattice. A theoretical model is proposed for the structural phase transition in a magnetic field, and the magnetic-field dependence of T _c is investigated for various directions of the field. Fiz. Tverd. Tela (St. Petersburg) 40, 750–758 (April 1998)     

Spin-peierls systems in magnetic field: Phase transition from dimerized to soliton lattice state

The phase diagram for the spin-Peierls system in high magnetic field is studied. The line of transition from dimerized (D) to soliton lattice (SL) phase is found, and it is shown that the SL phase is stable in fields h;h_c. Magnetization vs h is calculated as well as the sound velocity u_s of the domain walls oscillations. The possible experimental verification of the proposed theory is discussed also.     

Random field effects in the three dimensional Ising magnet: Fe x Zn1−x F2

We have carried out a comprehensive neutron scattering study of random field effects in the diluted three dimensional Ising antiferromagnet Fe _x Zn_1–x F₂ withx=0.35 and 0.5. Emphasis is on the global trands from the small to the large random field regimes. It is found, as in previous experiments, that when the system is cooled in a field it evolves from the high temperature paramagnetic state to a low temperature domain wall state. The low temperature peaks are well-described by Lorentzian squared profiles although for thex=0.5 sample extinction made the measurements difficult. In both samples, the results show that in the field-cooled state the correlation length varies asH ^–v withv=2.2±0.1. In thex=0.35 sample this power law holds over a length scale varying from 2 to 1500 lattice constants. At low fields pretransitional behavior similar to that observed previously in Fe_0.6Zn_0.4F₂ is found. AtT _N (H=0) it is found that the correlation length also scales algebraically withH but withv=0.86±0.04. Pronounced history-dependent effects are observed below the phase boundary determined by the peak in the critical scattering. For example, on cooling in zero-field, raising the field and then warming, long range order survives up to the phase boundary; at this point it appears to convert abruptly into the finite correlation length field cooled state although elucidation of the explicit nature of this transition is complicated by rounding due to a concentration gradient. These results are discussed in the context of recent theories incorporating metastability effects as well as recent experiments.     

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).     

Distribution of Avalanche Sizes in the Hysteretic Response of the Random-Field Ising Model on a Bethe Lattice at Zero Temperature

We consider the zero-temperature single-spin-flip dynamics of the random-field Ising model on a Bethe lattice in the presence of an external field h. We derive the exact self-consistent equations to determine the distribution Prob(s) of avalanche sizes s as the external field increases from – to . We solve these equations explicitly for a rectangular distribution of the random fields for a linear chain and the Bethe lattice of coordination number z=3, and show that in these cases, Prob(s) decreases exponentially with s for large s for all h on the hysteresis loop. We find that for z4 and for small disorder, the magnetization shows a first-order discontinuity for several continuous and unimodal distributions of the random fields. The avalanche distribution Prob(s) varies as s ^–3/2 for large s near the discontinuity.     

The random-field Ising model with asymmetric bimodal probability distribution

The Ising model, in the presence of a random field, is investigated within the mean-field approximation based on Landau expansion. The random field is drawn from the bimodal probability distribution P(h)=pδ(h−h₀)+(1−p)δ(h+h₀), where the probability p assumes any value within the interval [0,1], asymmetric distribution. The prevailing transitions are of second-order but, for some values of p and h₀, first-order phase transitions take place for smaller temperatures and higher h₀, thus confirming the existence of a tricritical point. Also, the possible reentrant phenomena in the phase diagram (T−h₀ plane) occur for appropriate values of p and h₀. Using the variational principle, we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h₀.