The phase transition in the anisotropic Heisenberg model with long range dipolar interactions

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.Comment: Accepted for publication in the Journal of Magnetism and Magnetic Materials. arXiv admin note: substantial text overlap with arXiv:1109.184

Monomial transformations of the projective space

We prove that, over any field, the dimension of the indeterminacy locus of a rational transformation $f$ of $P^n$ which is defined by monomials of the same degree $d$ with no common factors is at least $(n-2)/2$, provided that the degree of $f$ as a map is not divisible by $d$. This implies upper bounds on the multidegree of $f$

Spin Orbit Coupling and Spin Waves in Ultrathin Ferromagnets: The Spin Wave Rashba Effect

We present theoretical studies of the influence of spin orbit coupling on the spin wave excitations of the Fe monolayer and bilayer on the W(110) surface. The Dzyaloshinskii-Moriya interaction is active in such films, by virtue of the absence of reflection symmetry in the plane of the film. When the magnetization is in plane, this leads to a linear term in the spin wave dispersion relation for propagation across the magnetization. The dispersion relation thus assumes a form similar to that of an energy band of an electron trapped on a semiconductor surfaces with Rashba coupling active. We also show SPEELS response functions that illustrate the role of spin orbit coupling in such measurements. In addition to the modifications of the dispersion relations for spin waves, the presence of spin orbit coupling in the W substrate leads to a substantial increase in the linewidth of the spin wave modes. The formalism we have developed applies to a wide range of systems, and the particular system explored in the numerical calculations provides us with an illustration of phenomena which will be present in other ultrathin ferromagnet/substrate combinations