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

Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work was performed a study based on density functional theory of the electronic and magnetic properties of the hexagonal multiferroic manganite HoMnO3. Were performed calculations with and without the inclusion of the spin-orbit interaction, using the full potential linearized augmented plane wave method. The exchange and correlation electronic effects were approximated via generalized gradient approximation (GGA) and the method "+ U" (or GGA + U). It is known that the magnetism in HoMnO3 is due to Mn 3d4- and Ho 4f10-states. In addition, exist a consensus that the magnetic order at Mn sub-lattice is non-collinear due to the triangular arranged of Mn magnetic moments () at a-b plane. In the case of Ho magnetic moments, the arrangement is collinear with parallel to c-axis. However, because of the complexity of crystalline symmetry and of the varieties of magnetic ions in the material, the literature has not yet reached a consensus on the magnetic ordering of them (antiferromagnetic-AFM, ferromagnetic-FM or a combination of the two), as well as the values. In this work, the main objectives were: (1) to determine the ground-state magnetic structure for Ho sub-lattice (2) to obtain the values of their respective , and (3) to describe the electronic structure of the compound. Considering the nine different magnetic structures simulated, four of them are shown with more details. These are the result of the combination of two possible configurations of spins collinear for the Mn (A type AFM, A-AFM, and G type, G-AFM) and two for the Ho (FM and AFM). It was observed that, among these, the lowest energy configuration is that for Mn is fixed according to the G – AFM type and the Ho in the A – AFM type. This result agrees with the prediction of experiments in respect of the order on the Ho sub-lattice, but the values of the magnetic moments did not agree. Was found that there is a close relationship between the simulated magnetic order and its electronic structure. In particular, the band gap for the magnetic orders less energetically favorable tends to leave the compound with metallic character which is not experimentally expected. The HoMnO3 is a semiconductor whose optical gap is about 1.7 eV. Using an U = 3.0 eV on 3d and 4f states of the Ho, we obtained an energy band gap of 1.29 eV. To analyze the electronic structure in more detail, was computed the total and partial states of compound, where it was possible to notice that the 4f states of Ho are localized predominantly at the top and bottom of conduction band which are hybridized with O’s 2p states. / Nesse trabalho foi realizado um estudo baseado na teoria do funcional da densidade das propriedades eletrônicas e magnéticas da manganita hexagonal multiferroica HoMnO3. Foram realizados cálculos com e sem a inclusão da interação spin-órbita utilizando o método full potential linearized augmented plane wave. Os efeitos de troca e correlação eletrônica foram aproximados via a generalized gradient approximation (GGA) e o método “+U” (ou GGA+U). É sabido que o magnetismo no HoMnO3 é devido aos estados 3d4 do Mn e 4f10 do Ho. Além disso, há consenso que a ordem magnética na sub-rede do Mn é não colinear devido aos momentos magnéticos () arranjados triangularmente no plano a-b do cristal. No caso dos dos átomos de Ho, o arranjo é colinear e com paralelos ao eixo c-cristalino. Porém, devido à complexidade da simetria cristalina e das variedades de íons magnéticos no material, a literatura ainda não chegou a um consenso quanto ao ordenamento magnético do estado fundamental deles (antiferromagnético – AFM, ferromagnético – FM ou uma combinação dos dois), bem como nas magnitudes dos . Neste trabalho, os principais objetivos foram: (1) avaliar a ordem magnética na sub-rede do Ho que corresponde ao estado fundamental magnético, (2) obter os valores dos respectivos atômicos e (3) descrever a estrutura eletrônica do composto. Das nove estruturas magnéticas diferentes que foram simuladas, quatro delas são apresentados com maiores detalhes. Essas são resultado da combinação de duas possíveis configurações de spins colineares para o Mn (AFM do tipo A, A-AFM, e do tipo G, G-AFM) e duas para o Ho (FM e A-AFM). Observou-se que, dentre essas, a configuração de menor energia é aquela onde o Mn está arranjado segundo o tipo G – AFM e o Ho no tipo A – AFM. Esse resultado concorda com a previsão de um dos experimentos no que diz respeito à ordem na sub-rede do Ho. Porém, os valores dos calculados para os átomos de Ho não concordaram. Verificou-se que existe uma estreita relação entre a ordem magnética simulada e a estrutura eletrônica. Em especial, o band gap para as ordens magnéticas menos favoráveis energeticamente tende a deixar o composto com caráter metálico o que não é esperado experimentalmente. O HoMnO3 em estudo é um semicondutor cuja energia de gap óptico é aproximadamente de 1,7 eV. Empregando um U = 3,0 eV nos estados 3d do Mn e 4f do Ho, obtém-se uma energia de band gap de 1,29 eV. Para avaliar a estrutura eletrônica mais detalhadamente, realizaram-se cálculos de densidade de estados total e parciais, onde foi possível notar que os estados 4f do Ho hibridizados com os 2p dos O’s predominam no top da banda de valência e fundo da banda de condução do material. / São Cristóvão, SE

Fundação de Apoio a Pesquisa e à Inovação Tecnológica do Estado de Sergipe - FAPITEC/SE / The RMnO3 (R=Y,Lu) compounds, members of the family of hexagonal manganites, are materials which exhibit strong magneto-electric coupling characteristic for multiferroic compounds. Despite the numerous studies with objective to reveal the origin of this phenomenon, the mechanism that is causing it is still not fully understood. The question that attracts special attention of scientific community is about the cause of ferroelectric distortion that occurs at certain temperatures in these materials. Although this issue is discussed in many papers, there is still no consensus what mechanism is responsible for it: (1) hybridization between the Mn dz2 orbital and O pz orbital (Mn d0 –ness model), (2) hybridization between the R dz2 orbital and O pz orbital (R d0 –ness model), (3) geometric effects or (4) charge transfer from Mn-O bonds to R-O bonds. Understanding of the mechanism that leads to ferroelectric polarization is necessary to speed application of these materials in ferroelectric memories or spintronics devices. Objective of the present work was to evaluate the first two possible mechanisms that might cause the ferroelectric distortion in RMnO3. Adopted strategy was to investigate what happens with the Mn-O and R-O chemical bonds after the structural phase transition from paraelectric to ferroelectric phase that occurs at high temperature, at which both phases are characterized by paramagnetic order of the Mn magnetic moments. For that purpose, the first-principles calculations based on density functional theory were carried on, with usage of the most modern exchange-correlation potentials. The chemical bonds were evaluated (1) qualitatively, by analysis of density of electronic states (DOS) and maps of electronic density along the bonds, and (2) quantitatively, in terms of topological analysis of Bader. The results revealed that no significant change occurred with Mn-O bonds, while the R-O bonds were affected by phase transition in the sense that R dz2 and O pz orbital exhibited enhanced hybridization in the ferroelectric phase. Therefore, the present study substantiates the R d0 –ness mechanism as the probable cause of ferroelectric distortions in RMnO3 compounds. / The RMnO3 (R=Y,Lu) compounds, members of the family of hexagonal manganites, are materials which exhibit strong magneto-electric coupling characteristic for multiferroic compounds. Despite the numerous studies with objective to reveal the origin of this phenomenon, the mechanism that is causing it is still not fully understood. The question that attracts special attention of scientific community is about the cause of ferroelectric distortion that occurs at certain temperatures in these materials. Although this issue is discussed in many papers, there is still no consensus what mechanism is responsible for it: (1) hybridization between the Mn dz2 orbital and O pz orbital (Mn d0 –ness model), (2) hybridization between the R dz2 orbital and O pz orbital (R d0 –ness model), (3) geometric effects or (4) charge transfer from Mn-O bonds to R-O bonds. Understanding of the mechanism that leads to ferroelectric polarization is necessary to speed application of these materials in ferroelectric memories or spintronics devices. Objective of the present work was to evaluate the first two possible mechanisms that might cause the ferroelectric distortion in RMnO3. Adopted strategy was to investigate what happens with the Mn-O and R-O chemical bonds after the structural phase transition from paraelectric to ferroelectric phase that occurs at high temperature, at which both phases are characterized by paramagnetic order of the Mn magnetic moments. For that purpose, the first-principles calculations based on density functional theory were carried on, with usage of the most modern exchange-correlation potentials. The chemical bonds were evaluated (1) qualitatively, by analysis of density of electronic states (DOS) and maps of electronic density along the bonds, and (2) quantitatively, in terms of topological analysis of Bader. The results revealed that no significant change occurred with Mn-O bonds, while the R-O bonds were affected by phase transition in the sense that R dz2 and O pz orbital exhibited enhanced hybridization in the ferroelectric phase. Therefore, the present study substantiates the R d0 –ness mechanism as the probable cause of ferroelectric distortions in RMnO3 compounds.

In this work we present a theoretical and computational study of the mechanism of ferroelectricity in multiferroic hexagonal manganite LuMnO3. Some structural and electronic properties are described in both paraelectric (PE) and ferroelectric (FE) phases. As theoretical and computation tool was employed the Full Potential Linear Augmented Plane Wave method, based on Density Functional Theory and embodied in WIEN2k computer code. The crystal structure of both PE and FE phases was optimized using two different types of exchange and correlation potentials. The local density approximation (LDA) and generalized gradient approximation (GGA). The lattice parameters from GGA calculation were obtained in better agreement with experimental than LDA result. Also, were analyzed two different GGA parameterizations: the so-called Perdew - Burke - Ernzerhof (PBE) and Wu - Cohen (WC). Comparing them, the result from GGA-PBE calculation is in better agreement with the experimental. After the structural optimization, the atomic positions were fully relaxed. In this step, was utilized the GGA with the PBE parameterization. The electronic properties were calculated from these optimized and relaxed structures and using the Tran and Blaha modified Becke-Johson potential. From these calculations were obtained an indirect band gap of 0,3 eV and a direct band gap of 1,6 eV in the PE and FE phases, respectively. The valence electronic density maps were obtained along the c axis of the phases PE and FE. It was observed when leave of the PE to the FE phase, the ionic character of Lu-O bonds was changed. By careful analysis of the calculated partial density of states, we showed that the loss of ionicity of the chemical bond is associated with the rehybridization of the 5dz2 - Lu with 2pz - O orbitals. This description corroborates with the model in which the mechanism of ferroelectricity of the hexagonal manganites is related with the rehybridization of the dz2 - Y or - Lu orbitals with 2pz - O s orbitals that are along the crystalline c axis. / No presente trabalho foi realizado um estudo teórico e computacional sobre o mecanismo da ferroeletricidade na manganita hexagonal multiferróica LuMnO3. Foram obtidas algumas das propriedades estruturais e eletrônicas desse composto nas fases paraelétrica (PE) e ferroelétrica (FE). Como ferramenta teórica e computacional foi utilizado o método de cálculo de estrutura eletrônica denominado de Full Potential Linearized Augmented Plane Wave que é baseado na Teoria do Funcional da Densidade e implementado no código computacional WIEN2k. Foi realizada a otimização dos parâmetros de rede usando duas diferentes aproximações para o potencial de troca e correlação. A aproximação da densidade local (LDA) e a do gradiente generalizado (GGA). Os parâmetros de rede obtidos com o cálculo GGA foram mais próximos do experimental do que aqueles obtidos usando a aproximação LDA. Para o cálculo usando a aproximação GGA foram testadas duas formas de parametrização: Perdew - Burke - Ernzerhof (PBE) e Wu - Cohen (WC). Nesse caso, o resultado obtido com a parametrização PBE é a que melhor se compara com o resultado experimental. Após a otimização dos parâmetros de rede, foram relaxadas as posições atômicas. Nessa etapa do cálculo, foi utilizada a aproximação GGA-PBE. Para o cálculo da estrutura eletrônica, foi usado o potencial modificado de troca de Becke-Johnson (mBJ). Com ele foi possível obter um band gap indireto de 0,3 eV na fase PE e um band gap direto de 1,6 eV na fase FE. Foram obtidos mapas de densidade eletrônica valência ao longo do eixo c cristalino das fases PE e FE. Observou-se, saindo da fase PE para a FE, que o caráter iônico da ligação Lu - O foi alterado. A análise da densidade de estados parciais mostrou que a perda da ionicidade da ligação química está associada à rehibridização dos orbitais 5dz2 do Lu com os orbitais 2pz do O. Esta descrição corrobora com o modelo em que o mecanismo da ferroeletricidade das manganitas hexagonais está associado à rehibridização dos orbitais dz2 do átomo R (Lu ou Y) com os orbitais 2pz dos átomos de oxigênio que estão ao longo do eixo cristalino c.