Phase transitions in random anisotropy magnets

We report a study of magnetic properties and phase transitions in random anisotropy glasses rich in the rare-earth elements Gd, Tb and Nd. For the Gd glass, which has a small magnetic anisotropy, we find an extremely large, possibly infinite, susceptibility below 120 K and no intrinsic spontaneous magnetization. Below 55 K an hysteretic state develops. The Tb and Nd glasses, both of which have large anisotropy, exhibit transitions to a speromagneic state and they do not show an infinite susceptibility phase. The results are discussed in terms of recent theoretical predictions concerning phase transitions in the presence of random magnetic anisotropy.     

Critical behaviour of random compressible magnets

The critical properties of a compressible random magnet are studied using renormalization group methods. Then-component orderparameter is coupled to quenched disorder and to the elastic fluctuations of the anisotropic solid. It is shown, that the critical behaviour of a compressible random magnet is in general the same as that of a random magnet on a rigid lattice. However, if the specific heat exponent of the ideal magnet is positive and the disorder is sufficiently weak, a macroscopic instability may prevent the system in reaching the critical point. The resulting first-order transition may be preceded by pseudocritical behaviour characteristic to pure compressible magnets. The effect of random magnetic fields on the critical properties of compressible magnets is also discussed.     

On the susceptibility exponent of random anisotropy magnets

The temperature dependence of the non-linear susceptibility ≈₂(T) of random anisotropy magnets in the Ising limit (speromagnets) is calculated for temperatures above the freezing temperature T_f within the framework of the correlated molecular field theory. For the effective susceptibility exponent λ_s(T) = (T?T_f)≈₂d^-1_≈2/dT a non-monotonic temperature dependence is found as for the case of spin glasses. This must be taken into account in order to obtain reliable values for the critical susceptibility exponent from experimental data.     

Magnetic properties of solids with small random anisotropy

Equilibrium state and magnetic excitations are studied within a phenomenological model for disordered magnetic systems with ferromagnetic exchange and weak random anisotropies. These systems exhibit the new type of magnetic behaviour characterized by finite ferromagnetic correlation length at zero temperature. Effects of coherent anisotropy and external magnetic field are considered.     

Critical dynamics of magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole-dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin-wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon spin resonance, electron spin resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three-dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin-wave spectrum in two-dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.     

Magnetic properties of amorphous heisenberg ferromagnet with random anisotropy

Magnetization, susceptibility, and the critical temperature for a spin-one amorphous Heisenberg ferromagnet with random local anisotropy are calculated in the molecular field approximation for the exchange interactions. The effects of random fluctuations of the magnitude of the local anisotropy about its crystalline value are studied for various probability distributions. It is found that for a given randomness, measured in terms of the root mean square fluctuation of the magnitude of the local anisotropy, the magnetization and the critical temperature depend more on the range, denned as the magnitude of the maximum value of the fluctuation from its mean value, than the shape of the probability distribution function. The effect of randomness decreases as the crystalline value of the anisotropy increases. Calculation of the susceptibility shows that above the critical temperature, randomness has no effect.     

Homogenization of random anisotropy properties in polycrystalline magnetic materials

This paper is devoted to the determination of the equivalent anisotropy properties of polycrystalline magnetic materials, modelled by an assembly of monocrystalline grains with a stochastic spatial distribution of easy axes. The mathematical theory of $\Gamma \text{-}\mathrm{convergence}$ is applied to homogenize the anisotropic term in the Gibbs free energy. The procedure is validated focusing on the micromagnetic computation of reversal processes in polycrystalline magnetic thin films.     

Phase transitions in diluted magnets: Critical behavior,percolation, and random fields

Transition metal halides provide realizations of Ising,XY, and Heisenberg antiferromagnets in one, two, and three dimensions. The interactions, which are of short range, are generally well understood. By dilution with nonmagnetic species such as Zn⁺⁺ or Mg⁺⁺ one is able to prepare site-random alloys which correspond to random systems of particular interest in statistical mechanics. By mixing two magnetic ions such as Fe⁺⁺ and Co⁺⁺ one can produce magnetic crystals with competing interactions-either in the form of competing anisotropies or competing ferromagnetic and antiferromagnetic interactions. In this paper the results of a series of neutron scattering experiments on these systems carried out at Brookhaven over the past several years are briefly reviewed. First the critical behavior in Rb₂Mn_0.5Ni_0.5F₄ and Fe_cZn_1–cF₂ which correspond to two-dimensional and three-dimensional random Ising systems, respectively, are discussed. Percolation phenomena have been studied in Rb₂Mn_cMg_l–cF₄, Rb₂Co_cMg_l–cF₄, KMn_cZ_l-cF₃, and Mn_cZn_l–cF₂ which correspond to two-and three-dimensional Heisenberg and Ising models, respectively. In these casesc is chosen to be in the neighborhood of the nearest-neighbor percolation concentration. Application of a uniform field to the above systems generates a random staggered magnetic field; this has facilitated a systematic study of the random field problem. As we shall discuss in detail, a variety of novel, unexpected phenomena have been observed.     

Critical properties of randomly triangulated planar random surfaces

A discrete version of the Polyakov string is studied by analytical and numerical methods. The role of the intrinsic metric is played by random triangulation. The results only qualitatively agree with the Liouville perturbation theory. In particular, the critical exponents for the solvable cases D = 0 and D = ?2 are shown to be larger than those calculated perturbatively. Our numerical simulations for D = 3 indicate a large but finite Hausdorff dimension dH = 10.0 ±0.2.     

Renormalization group study of random quantum magnets

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ～ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erd?s-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.     

Critical exponents of magnets with lengthy defects

The critical behaviour of magnets with non-zero-dimensional defects is investigated by the renormalization group method. Expansions of the critical exponents in the small parameters ? and ?_d are obtained, where ?_d is the defect dimensionality. The corresponding renormalization group equations are shown to possess a focus-type fixed point.     

Novel domain growth law in random magnets

We investigate the kinetics of domain growth in Ising magnets where a fraction 1 - p of the magnetic atoms or ions (spins) are randomly substituted by non-magnetic impurities. We argue that close to the percolation threshold p_c, the statistical self-similarity of the underlying structure gives rise to a novel crossover in the growth law. We propose a method to detect any evidence of this new prediction from the kinetics of domain growth in the dilute Ising model (DIM) during intermediate time scales by carrying out Monte Carlo simulations not at p = p_c but at slightly higher spin concentrations. We analyze the results of our extensive Monte Carlo simulation of the strongly diluted two-dimensional Ising model and find the growth to be consistent with the proposed scenario. We also compare our observations with those in the recent experiments on the kinetics of ordering in Rb₂Co_pMg_1−pF₄.     

Critical microphase properties of crosslinked polymer blends with quenched random impurities

We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties.     

Pair model of anisotropy and magnetostriction in soft amorphous magnets

A pair model for amorphous alloys has been developed, considering both the spherical symmetry (isotropic alloys) and the cylindrical one (alloys exhibiting pair ordering or microstructural anisotropy). The elastic energy has been first derived. Then starting from the Heisenberg exchange, the pseudodipolar (PSD), the cluster electric field (CEF) and the simple dipolar couplings, the magnetoelastic coupling and magnetic anisotropy energies have been written in the limiting case of a very small random anisotropy.