Magnetic models from ab initio simulations. A methodological revision.

C. A LAMAS; J. M. MATERA; ERRICO L.; GIL REBAZA ARLES

Conferencia; statphys 27; 2019

The theoretical prediction of the phases present in magnetic materials is a major problem in condensed matter physics. Due to the quantum nature of magnetism, an exact description would in principle require solving the Schrödinger equation for a system of many electrons, which is computationally intractable. While first principles calculations provide a very powerful tool to approximate properties such as base energies and electron densities, they are intrinsically incapable of predicting the complex superpositions of spin states on the magnetic atoms found in frustrated magnetic systems. On the other hand, the use of effective models of localized spins, for which it is possible to treat these superpositions of states, requires as input a set of coupling constants that grows with the complexity of the system that is to be represented. The usual strategy for determining these constants is to compare the energies predicted by the calculation of first principles with that of the effective model, on a set of spin configurations, to define a system of linear constraints (overdetermined) on the coupling constants. Due to the huge number of possible spin configurations, in general, it is only possible to determine a small number of these restrictions.In this talk, I will discuss some ideas on how to efficiently choose the set of spin configurations to guarantee the stability of the system of equations, and a method for - once these restrictions are known - determine the confidence interval around the estimated values of the coupling constants. Finally, I will present a piece of software that allows for automatizing these tasks.