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.
Physica A: Statistical Mechanics and its Applications, 2002
The purpose of this work is the investigation of critical dynamic properties of two strongly coupled paramagnetic sublattices exhibiting a paramagnetic-ferrimagnetic transition. To go beyond the mean-ÿeld approximation, and in order to get a correct critical dynamic behavior, use is made of the renormalization-group (RG) techniques applied to a ÿeld model describing such a transition. The model is of Landau-Ginzburg type, whose free energy is a functional of two kinds of order parameters (local magnetizations) ' and , which are scalar ÿelds associated with these sublattices. This free energy involves, beside quadratic and quartic terms in both ÿelds ' and , a lowest-order coupling, −C0' , where C0 is the coupling constant measuring the interaction between the two sublattices. Within the framework of mean-ÿeld theory, we ÿrst compute exactly the partial dynamic structure factors, when the temperature is changed from an initial value Ti to a ÿnal one T f very close to the critical temperature Tc. The main conclusion is that, physics is entirely controlled by three kinds of lengths, which are the wavelength q −1 , the static thermal correlation length and an extra length Lt measuring the size of ordered domains at time t. Second, from the Langevin equations (with a Gaussian white noise), we derive an e ective action allowing to compute the free propagators in terms of wave vector q and frequency !. Third, through a supersymmetric formulation of this e ective action and using the RG-techniques, we obtain all critical dynamic properties of the system. In particular, we derive a relationship between the relaxation time and the thermal correlation length , i.e., ∼ z , with the exponent z = (4 − Á)=(2 + 1), where and Á are the usual critical exponents of Ising-like magnetic systems. At two dimensions, we ÿnd the exact value z = 5 4. At three dimensions, and using the best values for exponents and Á, we ÿnd z = 1:7562 ± 0:0027.
Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
Journal of Statistical Mechanics: Theory and Experiment, 2007
Within the universality class of ferromagnetic vector models with O(n) symmetry and purely dissipative dynamics, we study the non-equilibrium critical relaxation from a magnetized initial state. Transverse correlation and response functions are exactly computed for Gaussian fluctuations and in the limit of infinite number n of components of the order parameter. We find that the fluctuation-dissipation ratios (FDRs) for longitudinal and transverse modes differ already at the Gaussian level. In these two exactly solvable cases we completely describe the crossover from the short-time to the long-time behavior, corresponding to a disordered and a magnetized initial condition, respectively. The effects of non-Gaussian fluctuations on longitudinal and transverse quantities are calculated in the first order in the ǫ-expansion (ǫ = 4 − d) and reliable three-dimensional estimates of the two FDRs are obtained.
Effective and asymptotic criticality of structurally disordered magnets
arXiv (Cornell University), 2022
Changes in magnetic critical behaviour of quenched structurally-disordered magnets are usually exemplified in experiments and in MC simulations by diluted systems consisting of magnetic and non-magnetic components. By our study we aim to show, that similar effects can be observed not only for diluted magnets with non-magnetic impurities, but may be implemented, e.g., by presence of two (and more) chemically different magnetic components as well. To this end, we consider a model of the structurally-disordered quenched magnet where all lattice sites are occupied by Ising-like spins of different length L. In such random spin length Ising model the length L of each spin is a random variable governed by the distribution function p(L). We show that this model belongs to the universality class of the site-diluted Ising model. This proves that both models are described by the same values of asymptotic critical exponents. However, their effective critical behaviour differs. As a case study we consider a quenched mixture of two different magnets, with values of elementary magnetic moments L 1 = 1 and L 2 = s, and of concentration c and 1 − c, correspondingly. We apply field-theoretical renormalization group approach to analyze the renormalization group flow for different initial conditions, triggered by s and c, and to calculate effective critical exponents further away from the fixed points of the renormalization group transformation. We show how the effective exponents are governed by difference in properties of the magnetic components.
Critical behavior of low dimensional magnetic systems
Journal of Magnetism and Magnetic Materials, 2017
In this study, critical behavior of low dimensional magnetic systems as cyano-bridged Tb(III)-Cr(III) bimetallic assembly was investigated with the mixed spin 3-spin 3/2 Ising model. The mixed spin Ising model is simulated with Cellular Automaton cooling and heating algorithms on one-dimensional lattices in periodic boundary conditions. The Ising model Hamiltonian includes only antiferromagnetic nearest-neighbor interaction (J > 0). The mixed spin system behaves like the isolated one-dimensional chain for zero magnetic field (h = H J = 0). In the presence of the magnetic field, the magnetization is calculated using zero-field cooling (ZF C) and field cooling (F C) processes. The one-dimensional Ising model results are compatible with the cyano-bridged Tb(III)-Cr(III) bimetallic quasi-one dimensional assembly ((Tb(H 2 O) 2 (DMF) 4 Cr(CN) 6 •H2O(DMF= dimethylformamide)) results.
Hysteresis in rotation magnetic field
Physica B: Condensed Matter, 2000
The di!erent properties of the vector Jiles}Atherton hysteresis operator is proved under forced H-and B-"eld supply. Feeding the magnetic material with alternating and circular polarised rotational excitation, the di!erent properties of the model under the input "eld intensity and the #ux density are investigated and the results are proved in "gures.
Critical behaviour of the compressible magnet with exchange anisotropy
Zeitschrift für Physik B Condensed Matter and Quanta, 1978
The n-component magnet with exchange anisotropy on a compressible lattice, with isotropic elastic properties, is studied. The renormalization group method is applied in d = 4-~ dimensions. The fixed points and the stability regions are explored to the order e 2, and the analysis is concentrated upon the case n < 4-2 e + O(e2). Investigation of the fixed points reveals various crossover phenomena which are not present in the corresponding rigid model. Renormalization of the anisotropy crossover exponent is demonstrated. It is shown that macroscopic instabilities, leading to the first order phase transition, may appear.
Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model
We study hysteretic phenomena in random ferromagnets. We argue that the angle dependent magnetostatic (dipolar) terms introduce frustration and long-range interactions in these systems. This makes it plausible that the Sherrington-Kirkpatrick (SK) model may be able to capture some of the relevant physics of these systems. We use scaling arguments, replica calculations, and large scale numerical simulations to characterize the hysteresis of the zero temperature SK model. By constructing the distribution functions of the avalanche sizes, magnetization jumps, and local fields, we conclude that the system exhibits self-organized criticality everywhere on the hysteresis loop.
Hysteretic properties of a magnetic particle with strong surface anisotropy
2002
We study the influence of surface anisotropy on the zero-temperature hysteretic properties of a small single-domain ferromagnetic particle, and investigate limiting cases where deviations from the Stoner-Wohlfarth model are observed due to non-uniform reversal of the particle's magnetization. We consider a spherical particle with simple cubic crystal structure, a uniaxial anisotropy for core spins and radial anisotropy on the surface. The hysteresis loop is obtained by solving the local (coupled) Landau-Lifshitz equations for classical spin vectors. We find that when the surface anisotropy constant Ks assumes large values, e.g. of the order of the exchange coupling J, large deviations are observed with respect to the Stoner-Wohlfarth model in the hysteresis loop and thereby the limitof-metastability curve, since in this case the magnetization reverses its direction in a non-uniform manner via a progressive switching of spin clusters. This characteristic value of Ks depends on the surface-to-volume ratio of exchange coupling and the angle between the applied field and core easy axis.
Hysteresis loop critical exponents in 6-ε dimensions
Physical Review Letters, 1993
The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the "infinite avalanche" first disappears, are described by mean-field theory. We expand the critical exponents about mean-field theory, in 6 − ǫ dimensions, to first order in ǫ.