Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, was theoretically studied the structural, electronic and magnetic properties of multiferroic hexagonal manganite LuMnO3. For this compound, was simulated the crystal structure with P63cm and P63 crystallographic space group (CSG). Was employed the formalism of Density Functional Theory and the Full Potential Linearized Augmented Plane Wave (FP-LAPW) method implemented in Elk code. The exchange and correlation electronic effects were simulated by mean of LSDA. To better describe these effects, was employed the +U method (LSDA+U). Test with different +U method was performed. First, for both P63cm and P63 CSG, three collinear magnetic structures (ferromagnetic (FM), antiferromagnetic of type A (A-AFM) and of type G (G-AFM) were simulated. According to our results, the P63cm CSG with G-AFM state was found the most energetic favorable. This result was independent of either LSDA or LSDA+U method applied. In the second stage of the calculations, 2,3,4 and 3+4 non-collinear magnetic structures were performed. For these simulations, was employed only the LSDA scheme. Again, the P63cm CSG was found as the ground state for LuMnO3. Between the non-collinear magnetic structure simulated, the 3+4 was the lowest energy. For this magnetic structure, the band gap energy was underestimated (0.7 eV) in relation to experimental value (1.1 eV). However, the calculated spin magnetic (3.1uB) moment agree with experimental value (3.3 uB). / Neste trabalho, foram estudadas teoricamente as propriedades estruturais, eletrônicas e magnéticas da manganita hexagonal multiferróica LuMnO3. Para esse composto, foram simuladas as estruturas cristalinas com grupos espaciais cristalográficos (GEC) P63cm e P63. Foi empregado o formalismo da Teoria do Funcional da Densidade utilizado o método de cálculo de estrutura eletrônica denominada de Full Potential Linearized Augmented Plane Wave (FP-LAPW) implementado no código Elk. Os efeitos de troca e correlação eletrônica foram simulados através da LSDA. Para melhorar a descrição desses efeitos, foi empregado o método +U (LSDA+U). Avaliação do método +U mais apropriado foi realizado. Primeiro, para os GEC P63cm e P63, foram simuladas três configurações magnéticas colineares: ferromagnética (FM), antiferromagnética do tipo A (A-AFM) e do tipo G (G-AFM). De acordo com os resultados, o grupo espacial P63cm com a configuração magnética G-AFM é a energeticamente favorável. Este resultado foi independente da aplicação dos métodos LSDA ou LSDA+U. Na segunda etapa dos cálculos, para os dois GEC, foram simuladas as configurações de spin não colineares do tipo 2,3,4 e 3+4. Nessas simulações foi empregado apenas o método LSDA. Novamente, obteve-se que o GEC P63cm é o estado fundamental para o composto. Entre as configurações magnéticas simuladas, a de menor energia foi a 3+4. A energia de band gap encontrada para essa configuração de spin é subestimada (0,7 eV) em relação ao valor experimental (1,1 eV). Porém, o momento magnético calculado (3,1uB) concordou bem com o valor experimental (3,3uB). / São Cristóvão, SE

This thesis presents the synthesis and investigations of physical and chemical properties of multiferroic materials experimentally as well as theoretically. Multiferroics are materials in which at least two of the three ferroic orders, ferroelectricity, ferromagnetism and ferroelasticity occur in the same phase. Multiferroics, have the potential to be used as a four state as well as cross switchable memory devices. The thesis is organized into seven Chapters. Chapter 1 gives a brief overview of the different facets of multiferroics, explaining the origin of Multiferroicity and magnetoelectric coupling, their possible technological applications and the challenges involved. Chapter 2-4 concerns the experimental aspects and chapter 5-7 concerns the theoretical aspects. Chapter 2 deals with experimental investigations on nanoscale charge-ordered rare earth manganites. It shows with decreasing particle size the ferromagnetic interaction increases and the charge-ordering vanishes down to the lowest sizes. Chapter 3 describes magneto-dielectric, magnetic and ferroelectric properties of hexagonal LuMnO3. It also describes the Raman spectroscopy of this compound through the magnetic and ferroelectric transition temperatures. Chapter 4 deals with the anisotropic multiferroic properties in single crystals of hexagonal ErMnO3. In chapter 5 a brief introduction of density functional theory (DFT) is given. Chapter 6 deals with the magneto-structural changes, spin-phonon couplings and crystal field splittings for the different magnetic orderings LuMnO3. Chapter 7 elucidates the role of Lu d0-ness for the ferroelectricity observed of this compound.