First - Principles Study On The Effect Of Strain On Perovskite Single - Phase Multi - Iron Materials

With the development of science and technology, the size of silicon based electronic device will reach the limitation. In order to breakthrough the limitation, one promising solution is multifunctional device. Magnetoelectric multiferroics that simultaneously show ferroelectricity (FE) and magnetic order are gaining more and more importance in science and engineering. This originates not only from the desire to understand the mechanisms of magneto-electric coupling, but also from the design of multifunctional device applications. However, ferromagnetism and ferroelectricity rarely coexist in nature in a single homogeneous phase. One possible reason is the so-called d0rule, which states that empty d shell favors a ferroelectric distortion, but contradicts a magnetic ordering associated with partially filled d shell. This means that the ferroelectricity and magnetism are mutually excluded in a single phase.In order to breakthrough the limitation of the d0rule, we try our best to find multiferroics in crystals with the perovskite structure. We calculate the г point phonon frequencies of BaTcO3at different isotropic strain. The polar vibrational mode is strongly sensitive to the strain and softens to imaginary frequency at the4%tensile strain. The partial density of states (PDOS) of BaTcO3shows that the tensile strain inverts the lowest unoccupied state from t2g to eg orbital. This inversion is very important for the conversion of BaTcO3from paraelectric to ferroelectric structure. There is an interesting phenomenon occurs in PbMnO3. There is an unstable polar mode in the г-point phonon of cubic PbMnO3. The6s2"ione-pair" electrons of Pb are responsible for the ferroelectric distortion and the3d electrons of Mn result into the antiferromagnetism. After applying isotropic tensile strain, the Born effective charge (BEC) of Mn is substantially raised, but that of Pb decreases. The component of Mn of unstable phonon mode increases and exceeds that of Pb. Therefore, tensile strain turns PbMnO3into B-site driven FE and breaks the d0rule.We choose perovskite BaTcO3as our first research object. The ground state of BaTcO3is antiferromagnetic cubic structure. The PDOS contribution from Ba is negligibly small. In technetium oxides, the exchange splitting is smaller than the crystal field splitting. Therefore, the energy of unoccupied eg state is determined by crystal field splitting, while the unoccupied t2g state is determined by exchange splitting. The delocalization of4d orbital results into smaller exchange splitting compared with crystal field splitting. Thereafter, the unoccupied t2g states are below the unoccupied eg state. Therefore, the top of valence state of BaTcO3is mainly composed of the t2g state.Strain has been playing an important role to modify the ferroelectric perovskite oxide. The г point phonon frequencies of BaTcO3are calculated at different isotropic strain. The lowest frequency corresponds to the Tc atom moving opposite to the oxygen octahedron. This vibrational mode is strongly sensitive to the strain and softens to imaginary frequency at the4%tensile strain. This indicates that ferroelectricity and magnetism can be driven by the same cation in BaTcO3. Additionally, the Born effective charge of Tc increases with the increasing of tensile strain. The phonon dispersion throughout the Brillouin zone at4.5%tensile strain is calculated, which is very similar with the phonon dispersion of BaTiO3. We fully relax the structure at the volume of (1.045α0)3and get a tetragonal BaTcO3with the polarization of30.7μC/cm2. Furthermore, we apply coherent epitaxial strain to BaTcO3. When the epitaxial tensile strain reaches5.5%, the ferroelectric vibration mode becomes unstable. In this condition, BaTcO3is driven into ferroelectric state with the polarization of13.9μC/cm2. Therefore, tensile strain turns BaTcO3from an antiferromagnetic paraelectric structure into an antiferromagnetic ferroelectric structure (multiferroics).The PDOS of BaTcO3shows that the tensile strain inverts the lowest unoccupied state from t2g to eg orbital. At the same time, tensile strain reduces the repulsive forces between Tc and O and reduces the energy difference between the occupied2p orbital of O and the unoccupied3d orbital of Tc. All these factors contribute to the occurrence of ferroelectric BaTcO3. Therefore, our finding prescribes a way to break the d0rule.We employ the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional to deal with perovskites PbMnO3. The HSE hybrid functional is applied to various kinds of systems and provides a considerable improved description on crystal structure, electronic band dispersion, magnetic property, and phonon frequency with respect to the PBE and PBE+U. We firstly study the antiferromagnetic cubic PbMnO3. We find an unstable polar mode in the phonon calculation of cubic PbMnO3. This vibration mode consists of significant component of displacement of Pb, which is similar with that in PbTiO3. This indicates that the stereochemically active6s "lone-pair" electrons of Pb are the main driving force for ferroelectric distortion. Going further, we relax the structure of PbMnO3according to the eigenvector of the soft mode. As expected, a tetragonal ferroelectric structure is obtained. Therefore, both antiferromagnetic and ferroelectric ordering coexisted in PbMnO3.After applying isotropic tensile strain, we find the BEC of Mn is substantially raised. On the contrary, the tensile strain lowers the BEC of Pb. In the unstable phonon mode, the components of Pb decreases with the increase of tensile strain, but the component of Mn increases and exceeds that of Pb. When the tensile strain reached+6%, the component of Mn makes predominant contribution to the eigenvector and is Over forty times larger than that of Pb. The evolutions of both eigenvectors of the unstable phonon and BECs with strain indicate that the tensile strain turns PbMnO3from A-site driven (no strain) FE to B-site driven (under tensile strain) FE. Therefore, the ferroelectric and magnetic order of strained PbMnO3comes from the same cation Mn, which breaks the d0rule.Therefore, we can obtain more magnetoelectric multiferroics by applying strain through two routes. The first one is converting paraelectric magnetic material into multiferroics (BaTcO3). The second is changing the ferroelectric driving cation of multiferroics (PbMnO3).