Critical hysteresis for n-component magnets (original) (raw)

Complex critical magnetic behaviour in three dimensions

Journal of Magnetism and Magnetic Materials, 2007

Experimental results on the critical magnetic behaviour of magnets with a three-dimensional (3D) spin and isotropic 3D interactions are presented. It is observed that the critical behaviour can be rather complicated. This is because two magnetic order parameters can occur even in magnets with only one magnetic lattice site. The two order parameters must be attributed to an ordered longitudinal and transverse spin component meaning that the spin precession is elliptic rather than circular. Usually, one of the two order parameters is discontinuous at T c. Characteristic for this type of first-order phase transition is that the continuous part in the rise of the order parameter follows critical power law with exponent b and that the paramagnetic susceptibility diverges. The exponent g belongs not necessarily to the same universality class as b meaning that the scaling hypothesis can be violated. It appears necessary to distinguish between magnets with integer and half-integer spin. For magnets with integer spin, the critical exponent b is close to the Heisenberg value but for magnets with half-integer spin b is close to the Landau (mean field) value. The different critical behaviour seems to be associated with the opening of a magnetic excitation gap at T c for integer spin values while for half-integer spins the magnetic excitation spectrum is essentially continuous. The magnon gap of the magnets with integer spin is identified as a second-order parameter. The origin of the gap is a mystery. Discontinuous phase transitions and the appearance of a second-order parameter can be considered as signatures of higher order interactions such as four-spin interactions. Higher order interactions seem to be especially important in three dimensions.

Magnetic hysteresis in two model spin systems

Physical Review B, 1990

A systematic study of hysteresis in model continuum and lattice spin systems is undertaken by constructing a statistical-mechanical theory wherein spatial fluctuations of the order parameter are incorporated. The theory is used to study the shapes and areas of the hysteresis loops as functions of the amplitude (Ho) and frequency (a) of the magnetic field. The response of the spin systems to a pulsed magnetic field is also studied. The continuum model that we study is a three-dimensional (CP2)' model with 0 (M symmetry in the large4 limit. The dynamics of this model are specified by a Langevin equation. We find that the area A of the hysteresis loop scales as A-H:66f20,33 for low values of the amplitude and frequency of the magnetic field. The hysteretic response of a twodimensional, nearest-neighbor, ferromagnetic Ising model is studied by a Monte Carlo simulation on 1OX 10, 20x20, and 50X 50 lattices. The framework that we develop is compared with other theories of hysteresis. The relevance of these results to hysteresis in real magnets is discussed.

16 I 2 8-4-h 2 0-b ,4-8-12-16------ Magnetic hysteresis in two model spin systems

2004

A systematic study of hysteresis in model continuum and lattice spin systems is undertaken by constructing a statistical-mechanical theory wherein spatial fluctuations of the order parameter are incorporated. The theory is used to study the shapes and areas of the hysteresis loops as functions of the amplitude (Ho) and frequency (a) of the magnetic field. The response of the spin systems to a pulsed magnetic field is also studied. The continuum model that we study is a three-dimensional (CP2)’ model with 0 (M symmetry in the large4 limit. The dynamics of this model are specified by a Langevin equation. We find that the area A of the hysteresis loop scales as A H:66f20,33 for low values of the amplitude and frequency of the magnetic field. The hysteretic response of a twodimensional, nearest-neighbor, ferromagnetic Ising model is studied by a Monte Carlo simulation on 1OX 10, 20x20, and 50X 50 lattices. The framework that we develop is compared with other theories of hysteresis. The ...

Effective critical behaviour of diluted Heisenberg-like magnets

Journal of Magnetism and Magnetic Materials, 2003

In agreement with the Harris criterion, asymptotic critical exponents of threedimensional (3d) Heisenberg-like magnets are not influenced by weak quenched dilution of non-magnetic component. However, often in the experimental studies of corresponding systems concentration-and temperature-dependent exponents are found with values differing from those of the 3d Heisenberg model. In our study, we use the field-theoretical renormalization group approach to explain this observation and to calculate the effective critical exponents of weakly diluted quenched Heisenberg-like magnet. Being non-universal, these exponents change with distance to the critical point T c as observed experimentally. In the asymptotic limit (at T c) they equal to the critical exponents of the pure 3d Heisenberg magnet as predicted by the Harris criterion.

Model C critical dynamics of disordered magnets

Journal of Physics A: Mathematical and General, 2006

The critical dynamics of model C in the presence of disorder is considered. It is known that in the asymptotics a conserved secondary density decouples from the nonconserved order parameter for disordered systems. However couplings between order parameter and secondary density cause considerable effects on non-asymptotic critical properties. Here, a general procedure for a renormalization group treatment is proposed. Already the one-loop approximation gives a qualitatively correct picture of the diluted model C dynamical criticality. A more quantitative description is achieved using two-loop approximation. In order to get reliable results resummation technique has to be applied.

The field-space perspective on hysteresis in uniaxial ferromagnets

1998

A procedure for the analysis of hysteresis in the H space of a uniaxial ferromagnet with higher-order anisotropy is put forward. The formulation is valid to any order n in the anisotropy expansion. The critical boundaries separating stable from metastable states are cast in a formally decoupled parametric way as H x ϭH x (M x ), H z ϭH z (M z ). The analytic expressions provide the basis for the construction of generalized astroids to any order. For nϾ1, new features are found and interpreted in their relation to rotational hysteresis and possible spin-reorientation transitions in uniaxial materials. The shape and symmetry of the critical boundaries depend crucially on up to nϪ1 independent ratios of the anisotropy constants against a suitable normalizing quantity; the normalizer can be any from among the set of constants or any linear combination thereof. Self-crossing of an astroid indicates the existence of additional extrema and, hence, of complicated hystereses.

Magnetic Systems at Criticality: Different Signatures of Scaling

Acta Physica Polonica A, 2013

Dierent aspects of critical behaviour of magnetic materials are presented and discussed. The scaling ideas are shown to arise in the context of purely magnetic properties as well as in that of thermal properties as demonstrated by magnetocaloric eect or combined scaling of excess entropy and order parameter. Two non-standard approaches to scaling phenomena are described. The presented concepts are exemplied by experimental data gathered on four representatives of molecular magnets.

Simple scheme to calculate magnetization loops in critical-state models

Applied Superconductivity, 1995

A new and highly simplifying procedure for the calculation of magnetization loops for type-II superconductors in the critical-state is presented. It is shown that the various parts of high-field hysteresis loops can be expressed in terms of the formula for the virgin magnetization branch. The relations are valid for critical current densities with a general magnetic field dependence J,(B). The results are derived for an infinitely long rectangular bar or circular cylinder placed in a field applied parallel to the long z-axis. Isotropic properties in the v-plane are assumed, and the lower critical field and surface effects are neglected. To illustrate the model-independent relations the special case of the generalized power-law model J,(B) = J,/[ 1 + (B/&J"] is treated.