First-principles Study On Multiferroic RMn₂O₅

Multiferroic materials, in which magnetic and electric forms of ordering coexist in a single phase, have long been of interest both for their interesting fundamental physic-s and for potential applications to tunable multi-functional devices. RMn2O5(R=rare earth)materials are of particular interests with complex phase diagram and novel physic-s. They exhibit remarkable physical phenomena such as colossal magnetodielectric and magneto-polarization-flop effects. However, the driving mechanism behind the phase diagram and novel physical effect is not clear. In this thesis, we study the phys-ical mechanism of this kind of materials using first-principle calculations and effective Hamiltonian simulation.The main content and conclusion of this thesis includes:The first chapter will briefly introduce the history and background of multiferroics.The introduction of first principles calculation and other related methods will be given in chapter2.In chapter3I will give a brief review on recent progress of research on multi-ferroics, both experimentally and theoretically. I will then focus on the first-principles theoretical work on multiferroics.In chapter4I study the phase diagram of RMn2O5. First Ⅰ construct an effec-tive Hamiltonian with the parameters fitted with first-principles calculations. Then I perform Monte Carlo simulations to study the Hamiltonian. I obtain the correct phase sequence which is in good agreement with experiments. I then analyze the model and the phase competition to interpret the phase diagram. The details of model construction and parameters fitting will also be given in this chapter.In chapter5, I revise the model proposed in chapter4, with anisotropy ener-gy added. I then investigate the dynamic properties through solving the model with Molecular-Spin dynamics simulations. I reproduce the experimental spectra of electro-magnon through simulation which leads to the conclusion that the dynamic magneto-electric mechanism in RMn2O5is also exchange-striction. I find that the electromagnon frequencies in RMn2O5are very sensitive to the ICM wave vector. I further predict that the electromagnon frequencies in TmMn2O5should be much higher. To investigate the relation between electromagnon and magnetodielectric effect, I further investigate the electromagnon behavior under magnetic field. The simulation results show that the electromagnon frequencies shift significantly under magnetic field. However, due to the spectral weight conservation, the dielectric constant almost keep constant. As a result, in our model I do not find direct correlation between electromagnon and magne-todielectric effect.In the appendix, I first give a detailed description of replica-exchange Monte Carlo method. Then I expand the replica-exchange Monte Carlo method to study three-tangle which is algorithmically an optimization problem in quantum information. I first test the method with examples which have analytical results. The results obtained with my calculations accurately match with analytical results and theoretically I can freely improve the accuracy through adjustment of the calculation parameters. After the test, I perform calculations on some cases without analytical results and give my prediction. This is the first time that a numerical method is proposed to calculate three-tangle.