First-Order Transition in XY Fully Frustrated Simple Cubic Lattice

We study the nature of the phase transition in the fully frustrated simple cubic lattice with the XY spin model. This system is the Villain's model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than twenty years

Monte Carlo Study of the Spin Transport in Magnetic Materials

The resistivity in magnetic materials has been theoretically shown to depend on the spin-spin correlation function which in turn depends on the magnetic-field, the density of conduction electron, the magnetic ordering stability, etc. However, these theories involved a lot of approximations, so their validity remained to be confirmed. The purpose of this work is to show by extensive Monte Carlo (MC) simulation the resistivity of the spin current from low-$T$ ordered phase to high-$T$ paramagnetic phase in a ferromagnetic film. We take into account the interaction between the itinerant spins and the localized lattice spins as well as the interaction between itinerant spins themselves. We show that the resistivity undergoes an anomalous behavior at the magnetic phase transition in agreement with previous theories in spite of their numerous approximations. The origin of the resistivity peak near the phase transition in ferromagnets is interpreted here as stemming from the existence of magnetic domains in the critical region. This interpretation is shown to be in consistence with previous theoretical pictures. Resistivity in a simple cubic antiferromagnet is also shown. The absence of a peak in this case is explained

Theory and Simulation of Spin Transport in Antiferromagnetic Semiconductors: Application to MnTe

We study in this paper the parallel spin current in an antiferromagnetic semiconductor thin film where we take into account the interaction between itinerant spins and lattice spins. The spin model is an anisotropic Heisenberg model. We use here the Boltzmann's equation with numerical data on cluster distribution obtained by Monte Carlo simulations and cluster-construction algorithms. We study the cases of degenerate and non-degenerate semiconductors. The spin resistivity in both cases is shown to depend on the temperature with a broad maximum at the transition temperature of the lattice spin system. The shape of the maximum depends on the spin anisotropy and on the magnetic field. It shows however no sharp peak in contrast to ferromagnetic materials. Our method is applied to MnTe. Comparison to experimental data is given

Phase Transition in Heisenberg Fully Frustrated Simple Cubic Lattice

The phase transition in frustrated spin systems is a fascinated subject in statistical physics. We show the result obtained by the Wang-Landau flat histogram Monte Carlo simulation on the phase transition in the fully frustrated simple cubic lattice with the Heisenberg spin model. The degeneracy of the ground state of this system is infinite with two continuous parameters. We find a clear first-order transition in contradiction with previous studies which have shown a second-order transition with unusual critical properties. The robustness of our calculations allows us to conclude this issue putting an end to the 20-year long uncertainty.Comment: submitted for publicatio

Frustrated spin systems: history of the emergence of a modern physics

In 1977, Gérard Toulouse has proposed a new concept termed as “frustration" in spin systems. Using this definition, several frustrated models have been created and studied, among them we can mention the Villain’s model, the fully frustrated simple cubic lattice, the antiferromagnetic triangular lattice. The former models are systems with mixed ferromagnetic and antiferromagnetic bonds, while in the latter containing only an antiferromagnetic interaction, the frustration is caused by the lattice geometry. These frustrated spin systems have novel properties that we will review in this paper. One of the striking aspects is the fact that well-established methods such as the renormalization group fail to deal with the nature of the phase transition in frustrated systems. Investigations of properties of frustrated spin systems have been intensive since the 80’s. I myself got involved in several investigations of frustrated spin systems soon after my PhD. I have learned a lot from numerous discussions with Gérard Toulouse. Until today, I am still working on frustrated systems such as skyrmions. In this review, I trace back a number of my works over the years on frustrated spin systems going from exactly solved 2D Ising frustrated models, to XY and Heisenberg 2D and 3D frustrated lattices. At the end I present my latest results on skyrmions resulting from the frustration caused by the competition between the exchange interaction and the Dzyaloshinskii–Moriya interaction under an applied magnetic field. A quantum spin-wave theory using the Green’s function method is shown and discussed

Crossover from First to Second-Order Transition in Frustrated Ising Antiferromagnetic Films

In the bulk state, the Ising FCC antiferromagnet is fully frustrated and is known to have a very strong first-order transition. In this paper, we study the nature of this phase transition in the case of a thin film, as a function of the film thickness. Using Monte Carlo (MC) simulations, we show that the transition remains first order down to a thickness of four FCC cells. It becomes clearly second order at a thickness of two FCC cells, i.e. four atomic layers. It is also interesting to note that the presence of the surface reduces the ground state (GS) degeneracy found in the bulk. For the two-cell thickness, the surface magnetization is larger than the interior one. It undergoes a second-order phase transition at a temperature $T_C$ while interior spins become disordered at a lower temperature $T_D$. This loss of order is characterized by a peak of the interior spins susceptibility and a peak of the specific heat which do not depend on the lattice size suggesting that either it is not a real transition or it is a Kosterlitz-Thouless nature. The surface transition, on the other hand, is shown to be of second order with critical exponents deviated from those of pure 2D Ising universality class. We also show results obtained from the Green's function method. Discussion is given.Comment: 20 pages, 14 figure

Finsler Geometry Modeling and Monte Carlo Study on Geometrically Confined Skyrmions in Nanodots

Using the Finsler geometry modeling (FG) technique without spontaneous magnetic anisotropy, we numerically study the stability and morphology of geometrically confined skyrmions experimentally observed in nanodots. We find a confinement effect that stabilizes skyrmions for a low external magnetic field without mechanical stresses by decreasing the diameter of the cylindrical lattice and strain effects that cause the sky and vortex to emerge under the zero magnetic field. Moreover, the obtained MC data on the morphological changes are also consistent with the reported experimental data.Comment: 4 pages, 9 figure