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Register a new userThe Pair Approximation method for the ferromagnetic Heisenberg model with spin $S=1$ and arbitrary range of interactions. Application for the magnetic semiconductor CrIAs
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The Pair Approximation method has been formulated for the isotropic ferromagnetic Heisenberg model with spin $S=1$. The exchange interactions of arbitrary range have been taken into account. The single-ion anisotropy has been considered as well as the external magnetic field. Within the method, the Gibbs free-energy has been derived, from which all thermodynamic properties can be self-consistently obtained. In order to illustrate the developed formalism, the numerical calculations have been performed for CrIAs planar magnetic semiconductor, a hypothetical material whose existence has been recently predicted by the Density Functional Theory-based calculations. For this model material, all the relevant thermodynamic magnetic properties have been studied. The numerical results have been presented in the figures and discussed.
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A parallel implementation of coupled spin-lattice dynamics in the LAMMPS molecular dynamics package is presented. The equations of motion for both spin only and coupled spin-lattice dynamics are first reviewed, including a detailed account of how magneto-mechanical potentials can be used to perform a proper coupling between spin and lattice degrees of freedom. A symplectic numerical integration algorithm is then presented which combines the Suzuki-Trotter decomposition for non-commuting variables and conserves the geometric properties of the equations of motion. The numerical accuracy of the serial implementation was assessed by verifying that it conserves the total energy and the norm of the total magnetization up to second order in the timestep size. Finally, a very general parallel algorithm is proposed that allows large spin-lattice systems to be efficiently simulated on large numbers of processors without degrading its mathematical accuracy. Its correctness as well as scaling efficiency were tested for realistic coupled spin-lattice systems, confirming that the new parallel algorithm is both accurate and efficient.
In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.
Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase I, a phase characterized by a change from out-of-plane to in-plane in the magnetization II, and a high-temperature paramagnetic phase III. It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phases II and III is of the BKT type.
The existence of Neel order in the S=1/2 Heisenberg model on the square lattice at T=0 is shown using inequalities set up by Kennedy, Lieb and Shastry in combination with high precision Quantum Monte Carlo data.
Magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions is investigated within mean-field theory. It is shown that a competition between paramagnetism, diamagnetism and ferromagnetism exists in this system. It is shown that diamagnetism, being concerned with spontaneous magnetization, cannot exceed ferromagnetism in very weak magnetic field. The critical value of reduced ferromagnetic coupling of paramagnetic phase to ferromagnetic phase transition $bar I_{c}$ increases with increasing temperature. The Lande-factor $g$ is introduced to describe the strength of paramagnetic effect which comes from the spin degree of freedom. The magnetization density $bar M$ increases monotonically with $g$ for fixed reduced ferromagnetic coupling $bar I$ as $bar I>bar I_{c}$. In a weak magnetic field, ferromagnetism makes immense contribution to the magnetization density. While at a high magnetic field, the diamagnetism inclines to saturate. Evidence for condensation can be seen in the magnetization density at weak magnetic field.
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