Phase diagrams and magnetic properties of diluted Ising and Heisenberg magnets with competing interactions

Ising and Heisenberg magnets with nearest-neighbor ferromagnetic exchangeJ ₁ and next-nearest antiferromagnetic exchangeJ ₂ and randomly distributed frozen-in nonmagnetic impurities of arbitrary concentration 1–x are studied by several methods: systematic series expansions inx, 1–x and inverse temperature (1/T) as well as Monte Carlo simulation. Depending onRJ ₂/J ₁,T andx the model is in paramagnetic, ferromagnetic, antiferromagnetic or spin glass phases. The microscopic magnetic structures of all these phases are investigated and found to be more complicated than usually (e.g., the ferromagnetic state contains spins and clusters either aligned antiparallel or not aligned at all, when frustration effects make bonds ineffective). We suggest that the concentrationx _c of magnetic ions below which no (anti-)ferromagnetic long range order occurs depends onR continuously, andx _c 1 at the multicritical point (R _m ,T=0) where the order changes from ferromagnetic to antiferromagnetic. Our results for phase diagram, susceptibility etc. are compared to recent data on the Eu _x Sr_1–x S system and very good agreement is found.     

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.     

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 .     

Critical behavior of Griffiths ferromagnets

From a heuristic calculation of the leading order essential singularity in the distribution of Yang-Lee zeroes, we obtain new scaling relations near the ferromagnetic-Griffiths transition, including the prediction of a discontinuity on the analogue of the critical isotherm. We show that experimental data for the magnetization and heat capacity of La(0.7)Ca(0.3)MnO(3) are consistent with these predictions, thus supporting its identification as a Griffiths ferromagnet.     

Exact results for the diluted Ising model with competing interactions

We consider the random-bond Ising model with the exchange integrals J > 0, ?J and 0 with the respective probabilities p, q and r, where p + q + r = 1. We give the exact value of the averaged internal energy and an exact upper bound to the averaged specific heat at temperature T determined by $\text{k}{}_{\mathrm{B}}\text{T =}\text{2J}\text{In[}\text{p}\text{(1 ? p ? r)}\text{]}\text{,}$ where k_B is the Boltsmann constant. We show that all the averaged correlation functions of even spins are non-negative at this temperature.     

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.     

The spin-1/2 antiferromagnetic Heisenberg chain with competing interactions

We investigate the thermodynamical and magnetic properties of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with competing interactions near the transition between the "dimer phase" and the "frustrated phase".     

Critical behaviour of the magnetic susceptibility of two nearly bidimensional Heisenberg ferromagnets

The parallel magnetic susceptibilities of ferromagnetic K₂ Cu F₄ and (CH₃ NH₃)₂ Cu Cl₄ have been measured near the critical temperature. In both ferromagnets, the thermal dependence cannot be described by the simple power law ?^-γ with $\text{? =}\text{T}\text{T}{}_{\mathrm{<mtext>C</mtext>}}\text{? 1}$ over a large range of temperatures. Due to crossover with dimensionality, the γ value increases from 1 for K₂ Cu F₄ and 1.23 for (CH₃ NH₃)₂ Cu Cl₄ in the immediate vicinity of T_c, to a maximum value of about 2.     

Critical properties of the anisotropic Ising model with competing interactions

The critical properties of the anisotropic Ising model with competing interactions have been investigated by Monte Carlo methods. The region of localization of the Lifshitz point on the phase diagram has been computed. Relations of the finite-size scaling theory are used to calculate the critical exponents of the heat capacity, susceptibility, and magnetization at various values of the competing interaction parameter J ₁. A crossover to a critical behavior characteristic of a multicritical point with increasing parameter J ₁ is shown to be present in the system.     

Critical temperature studies of the anisotropic bilayer and multilayer Heisenberg ferromagnets in Pair Approximation

The Pair Approximation method is applied to studies of the bilayer and multilayer magnetic systems with simple cubic structure. The method allows to take into account quantum effects related to non-Ising couplings. The paper adopts the anisotropic Heisenberg model for spin S=1/2 and considers phase transition temperatures as a function of the strength of exchange integrals in line with the role of intra- and interplanar anisotropic interactions in the onset of low-dimensional magnetism. The compensation effect for the Curie temperature is found for asymmetric interactions within the neighbouring planes of the bilayer system. The paper predicts the saturation of the Curie temperature for strong interplanar interactions. However, such an effect for the multilayer system occurs only when the interplanar interactions are purely of isotropic character.     

Excitations in randomly diluted two-dimensional ferromagnets

The dynamics of a randomly diluted Heisenberg ferromagnet on a two-dimensional square lattice is calculated using a CPA procedure introduced by Theumann and Tahir-Kheli. The density of states and frequency-wave-vector-dependent response functions at various symmetry points of the Brillouin zone are presented for several magnetic concentrations. Our results for the density of states are compared with those obtained from computer-experiment calculations of Huber and are found to be in good agreement with them. The spin-wave stiffness coefficient is calculated, and comparison is made with results on two-dimensional resistor networks given by Watson et al.     

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.