Classical Heisenberg ferromagnets with defects

A ferromagnet (dimensionality d) containing defects (of dimensionality d′) is treated by the phenomenological Landau theory. It is shown that for d′<d?1 no change of the critical exponent of the local magnetization near the defect occurs, in contrast to the case of the local magnetization near a surface (d′=d?1). The case of point defects (d′=0) in classical Heisenberg ferromagnets with nearest neighbor interactions is treated both by the mean field approximation and the Monte-Carlo method with effective field boundary conditions. We obtain rough agreement between these two approaches—two special cases are considered in detail: (a) interaction with, the defect being zero, (b) anti-ferromagnetic interactions across the defect (which is a crude model of superexchange). It is pointed out that it is a reasonable approximation to express the deviation of the local magnetization from the bulk value near the defect in terms of the spin pair correlation functions of the undisturbed system.     

Elementary excitations in easy-plane Heisenberg ferromagnets

We study the influence of the non-diagnonal terms in an easy-plane Heisenberg ferromagnet on the cross-section for inelastic neutron scattering from single spin-wave states. We show that these terms modify the wavevector dependence of the cross-section for unpolarized neutrons, and the created polarization. An appropriate experiment on CsNiF₃, for example, should be a good test of these predictions, and would eventually clarify some uncertainties about the appropriate Boson Hamiltonian for an easy-plane ferromagnet.     

Critical behavior of diluted Heisenberg ferromagnets with competing interactions

The pure and the site-diluted classical Heisenberg model on the face centered cubic (fcc) lattice with ferromagnetic exchange J_nn between nearest neighbors and antiferromagnetic exchange J_nn = −J_nn/2 between next nearest neighbors is studied by Monte Carlo simulation. Data are generated by the heat bath algorithm for lattice sizes L = 4, 8, 12, 16, 20 and 24, using histogram reweighting techniques and sampling up to several hundred configurations of the random site disorder. From a finite size scaling analysis both the critical temperature and the critical exponents are estimated. For the pure system, the data are in very good agreement with the critical exponent estimates 1/v ≈ 1.42, β/v ≈ 0.51 obtained from other methods (as a check of the accuracy of our approach, we also study the nearest neighbor model — where J_nn ≡ 0− and again obtain very good agreement with the known behavior). However, for the diluted systems evidence for a new universality class is found. While for concentration c = 0.875 of occupied sites strong crossover phenomena preclude us from giving exponent estimates, for c = 0.75 we find 1/v ≈ 1.2 and β/v ≈ 0.45. Possible reasons why the Harris criterion may not apply for this system are discussed. The application of this study to experiments on Eu_xSr_1−xS is briefly mentioned.     

Critical temperatures of the anisotropic Heisenberg ferromagnets

High temperature series expansions for the fluctuation in the long range order M_x is obtained through order T^?7 for a spin-$\text{1}\text{2}$ anisotropic Heisenberg Hamiltonian. The critical temperatures at which the spontaneous magnetization occurs on the xy-plane are determined.     

Green's-function theory for disordered anisotropic Heisenberg ferromagnets

The Green's function theory for disordered Heisenberg Ferromagnets developed by Montgomery et al. has been extended for anisotropic systems. The densities of spin-wave states for such systems exhibit split-bands. This behavior differs qualitatively from that of the isotropic case and offers a partial explanation for the neutron scattering experiment of Buyers et al. in which they observe two well defined branches of magnetic excitations in disordered substitutional anti-ferromagnetic alloys.     

Phase transitions in anisotropic classical Heisenberg ferromagnets

The method of Peierls is used to prove the existence of a spontaneous magnetization for a spin system with nearest-neighbor interactions and Hamiltonian a (classical) unit vector at thei'th site, with ||<0.0298 and 0.0198 for a square lattice and simple cubic lattice, respectively.Research supported by the National Science Foundation Grant No. GP 11454.     

Self-consistent theory of spin-phonon interactions in Heisenberg ferromagnets

A Green function technique is used to study the effects of spin-phonon interactions in a Heisenberg ferromagnet. The transverse and longitudinal damping of the spin-wave energy for two different spin-phonon interaction mechanisms are evaluated for the first time beyond the RPA. The results are valid below and aboveT _c .     

Phase transitions of classical Heisenberg ferromagnets with arbitrary parameter of anisotropy

The existence of a phase transition of the first kind is proved for anisotropic classical Heisenberg ferromagnet in two or more dimensions and with arbitrary parameter of anisotropy α, |α|<1; a similar fact is proved for much more general lattice spin systems.     

Classical one-dimensional Heisenberg magnet with biquadratic exchange interaction

The pair- and four-spin correlation functions and susceptibility have been calculated rigorously for a classical Heisenberg linear chain with biquadratic exchange interaction by extending Fisher's method.     

Simulation of spin reorientation in cubic ferromagnets with defects

Nucleation processes in spin-reorientation phase transitions in real magnets are studied theoretically. The magnetization distribution corresponding to zero-degree domain wall forms the basis of the model representation of nuclei of the new phase, which are pinned at detects. As a result of numerical implementation of the corresponding variational problem for a finite-thickness plate, stable states of such magnetic inhomogeneities are determined and it is shown that their structure and properties are mainly controlled by parameters of a defect and the Q factor of the sample. The dependences obtained in this way make it possible to describe the behavior of new-phase nuclei in the vicinity of the spin-reorientation phase transition, which is in qualitative agreement with experimental data.     

Longitudinal spin fluctuations in Heisenberg ferromagnets: the hydrodynamic regime

Summary The dynamics associated with the magnetization fluctuations in Heisenberg ferromagnets in an external field is investigated both by a purely microscopic approach and by a projection operator technique which emphasizes the role of quasi-conserved, collective dynamical variables. Particular attention is devoted to ?hydrodynamic? wave vectors and frequencies; in such a situation the projection operator technique proves very convenient, and in particular at low temperatures the inclusion of the momentum density in the set of relevant variables gives rise to a new excitation, referred to as ?second magnon? by previous authors. Its appearance in the longitudinal spectra is studied for arbitrary dimensionalityd: in particular, the theory is applied both to thed=1 classical case (where second magnons have been observed in simulation experiments) and to thed=3 quantum case, where the conditions for the observability of the effect in real systems are discussed.

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Riassunto Le proprietà dinamiche associate con le fluttuazioni di magnetizzazione in un ferromagnete di Heisenberg in un campo sono studiate sia con un approccio microscopico sia mediante una tecnica proiettiva che mette in risalto il ruolo delle variabili dinamiche collettive quasi conservate. Il secondo metodo risulta piú conveniente quando si considerino frequenze e vettori d'onda nel regime idrodinamico; in particolare, a bassa temperatura l'inclusione nel set delle variabili rilevanti della densità di momento dà luogo ad una nuova eccitazione, riferita precedentemente come un ?secondo magnone?. La sua comparsa nello spettro longitudinale è studiata per un sistema con dimensionalitàd qualsiasi. In particolare, la teoria è applicata al casod=1, spin classici (dove le nuove eccitazioni sono state osservate con esperimenti di simulazione) ed al caso quantistico cond=3, dove sono discusse le condizioni di effettiva osservabilità per sistemi reali.

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Резюме Исследуется динамика, связанная с флуктуациями намагниченности в ферромагнетиках Гайзенберга во внешнем поле. Исследование проводится в рамках чисто микроскопического подхода и с помощью техники проекционных операторов, которая подчеркивает роль квази-сохраняющихся, коллективных линамических переменных. Особое внимание уделяется ?гидродинамическим? волновым векторам и частотам. В зтой ситуации техника проекционных операторов оказывается очень удобной и, в частности, при низких темпетурах вклйчение плотности импульса в систему соответствующих переменных приводит к новому возбуждению, называемому ?вторым магноном?. Исследуется возникновение ?второго магнона? в продольных спектрах для произвольной размерностиd. В частности, предложенная теория применяется к классическому случаюd=1 (где ?вторые магноны? наблюдаются в эксперимериментах по моделрованию) и к квантовому случаюd=3, где обсуждаются условия наблюдаемости этого эффекта в реальных системах.

     

Simulation of magnetization reversal processes in finite ferromagnets with defects

The magnetization and magnetization reversal processes that occur through the mechanism of incoherent rotation of magnetic moments in cubic ferromagnets with limited sizes are investigated theoretically. It is established that the appropriate model representation of magnetic inhomogeneities arising in the region of defects is provided by 0° domain walls. The influence of the external magnetic field on the structure and the stability region of the 0° domain walls is determined. This makes it possible to reveal the characteristic features of the magnetization reversal of real crystals as a function of the material and defect parameters, in particular, in the vicinity of the spin-reorientation phase transition.     

Classical one-dimensional Heisenberg model with an interaction of finite range

It is shown that the thermodynamic quantities and spin correlation functions of the classical Heisenberg model on a linear chain are expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of a homogeneous linear integral equation, where the range of the interaction is assumed to be finite. The magnetization and susceptibility at nonzero external magnetic fields are given as a function of temperature, for the case of the nearest neighbour ferromagnetic and antiferromagnetic interaction. Efforts are paid to determine the properties near zero temperature.     

Classical spin dynamics of anisotropic Heisenberg dimmers

In the present work we study the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of an external magnetic field using the Landau-Lifshitz equation. The interaction between particles is through the exchange energy. We study both conservative and dissipative cases. In the first one, we characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and bifurcation diagrams. In particular, we explore the dependence of the largest Lyapunov exponent respect to the magnitude of applied magnetic field and exchange constant. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated topology of intricately intermingled chaotic and regular regions. In the dissipative case, we calculate the final saturation states as a function of the magnitude of the applied magnetic field, exchange constant as well as the anisotropy constants.