Session L9: Focus Session: Complex Bulk Oxides: Theoretical techniques for oxides

Thermodynamics of Ferrotoroidic Materials

The three primary ferroics, namely ferromagnets, ferroelectrics and ferroelastics exhibit corresponding large (or even giant) magnetocaloric, electrocaloric and elastocaloric effects when a phase transition is induced by the application of an appropriate external field ($E$, $H$ and stress). Recently the suite of primary ferroics has been extended to include ferrotoroidic materials in which there is an ordering of toroidic moments in the form of magnetic vortex-like structures, examples being LiCo(PO$_4$)$_3$ and Ba$_2$CoGe$_2$O$_7$. We formulate the thermodynamics of ferrotoroidic materials. Within a Landau free energy framework we calculate the toroidocaloric effect by quantifying isothermal entropy change (or adiabatic temperature change) in the presence of an applied toroidic field ($G=E\times H$) when usual magnetization and polarization may also be present simultaneously.   

Theory of K-edge Resonant Inelastic X-ray Scattering for Perovskite Manganites

We present calculations of K-edge resonant inelastic x-ray scattering (RIXS) spectrum for layered and three dimensional perovskite manganites with charge, orbital, and spin orderings. We extend the approach in Ref. [1] to the tight binding model for the manganites, calculate RIXS intensity in momentum and energy space, and compare with experiment data. The results show strong dependence of the RIXS intensity on momentum, which agrees well with experimental observation. We discuss its implications on the material properties and the RIXS process. \\[4pt] [1] K. H. Ahn, A. J. Fedro, and M. van Veenendaal, Phys. Rev. B 79, 045103 (2009).   

Nonreciprocal Directional Dichroism and Toroidalmagnons in Helical Magnets

We investigate a dynamical magnetoelectric effect owing to a magnetic resonance in helical spin structures through a coupling between magnetization and electric polarization via a spin current mechanism [1]. We show that the magnon has a dynamical magnetic moment dM and an electric moment dP which is perpendicular to dM, simultaneously, i.e., a dynamical toroidal moment T\^{}d = dM x dP under the external magnetic fields, and thus named it as a toroidalmagnon. The toroidalmagnon exists in most conical spin structures due to generality of the spin current mechanism. In absorption of electromagnetic wave, the toroidalmagnon excitation process generally induces nonreciprocal directional dichroism as a consequence of an interference of the magnetic and the electric responses. The nonvreciprocal directional dichroism should be experimentally observed in various cycloidal multiferroic materials,$ e.g. \quad R$MnO{\_}3. [1] H. Katsura, A.V. Balatsky, and N. Nagaosa: Phys. Rev. Lett.\textbf{ 98} 027203 (2007)   

First-principles Wannier function based methods for disordered materials and applications to studies of oxides and Fe-superconductors

This talk will discuss recently developed first-principles methods for materials with disordered impurities, and their applications to case studies of correlated oxides and Fe-based superconductors containing vacancies, substitutions and intercallants. Simplified via the use of Wannier functions, the first method [1] is to unfold the one-particle spectral function from the reduced Brillouin zone of a broken symmetry state back to the regular Brillouin zone of the normal state. This unfolding not only allows a clearer visualization of the physical effects of the broken translational symmetry, but also connects directly to the experimental spectral weight of angular resolved photo emission spectroscopy. The second method [2] is to reduce the computational expense of configuration-averaged spectral function of disordered materials by orders of magnitude, to allow inclusion of large length scale required for weakly localized states and short-range orders. This Wannier function based method is systematically improvable, beyond-mean-field, and not perturbation limited. Case studies to be discussed include dilute magnetic semiconductors [3], transition metal oxides[1,2], and Fe-based superconductors [4,5]. \\[4pt] [1] Wei Ku et al, PRL 104, 216401 (2010)\\[0pt] [2] T. Berlijn et al, PRL 106, 077005 (2011)\\[0pt] [3] T. S. Herng et al, PRL 105, 207201 (2010)\\[0pt] [4] C.-C. Lee et al, PRL 103, 267001 (2009)\\[0pt] [5] C.-H. Lin et al, arXiv:1107.1485   

Incommensurate spin excitations stabilized multiferroic phase in CuO

Cupric oxide is a unique magnetoferroelectrics with transition temperature way above the boiling point of liquid nitrogen. However, the mechanism of high T$_c$ multiferroicity in CuO is still puzzling. In this paper, we clarify the mechanism of high T$_c$ multiferroicity in CuO using combined first-principles calculations and an effective Hamiltonian model. We find that CuO contains two magnetic sublattices, with strong intra-sublattice interactions and weakly frustrated inter-sublattice interactions, which might be one of the main reasons that the compound has a high ordering temperature. The weak spin frustration leads to incommensurate spin excitations that dramatically enhances the entropy of the mutliferroic phase, and eventually stabilize the mutliferroic phase in CuO.   

Pressure-driven high-spin to low-spin and orbital-selective insulator to metal transition in cubic CoO

We studied the magnetic and spectral properties for cubic para-magetic phases of CoO under high pressures by using \emph{ab initio} many-body method which combining local density approximation with dynamical mean-field theory. Experimentally observed metal-insulator transition at high pressure is successfully reproduced in calculations. Our calculation predicts CoO as a Mott insulator at ambient pressure and metal at extreme high pressure. In the intermediate pressure regime, our results indicate that there is an orbital selective Mott phase with $t_{2g}$ orbitals being metallic and $e_{g}$ orbitals being insulating. In contrast with MnO and Fe$_{2}$O$_{3}$ ($d^5$ configuration) where metal-insulator transition is accompanied by a high-spin to low-spin transition, we found that the local moment of CoO ($d^7$ configuration) decreases gradually from 2.8 ($S = 3$ states) to 1.4 ($S = 1$ states) with increasing pressure, which is in agreement with experimental data.   

Mott physics in multi-band Hubbard model with strong spin-orbit interaction

Spin-orbit coupling and electron correlation both play very crucial roles in the Mott physics of $4d$ and $5d$ transition-metal oxides. By studying three band Hubbard model with full Hund's rule coupling and spin-orbit coupling, we show that spin-orbit coupling intends to strongly enhance the Mott transition. By means of generalized Gutzwiller variational method and dynamical mean field (DMFT) with continuous time quantum Monte Carlo (CTQMC) as impurity solver, we obtain the complete phase diagram for this problem, which can be divided into metal, Mott insulator and band insulator phases. At mean while, we have also studied the effect of the Coulomb interaction on the strength of the spin-orbital coupling in the metallic phase. Our conclusion is that the correlation effect on the spin-orbital coupling is far beyond the mean field treatment even in the intermediate coupling regime.   

Covalency, Excitons, Double Counting and the Metal-Insulator Transition in Transition Metal Oxides

We present single-site dynamical mean-field studies of realistic models of transition metal oxides, including the cuprate superconductors and rare earth nickelates (in bulk and superlattice form). We include orbital multiplet effects and hybridization to ligands. We explicitly calculate the d-d exciton spectra for cuprates, finding sharp exciton lines in both metallic and insulating phases, which should be visible in experiments. We also find that the additional $d_{3z^2-r^2}$ orbital does not contribute to an additional Fermi surface at any reasonable doping, in contradiction to previous slave-boson studies. The hybridization to ligands is shown to have crucial effects, for example suppressing the ferro-orbital order previously found in Hubbard model studies of nickelates. Hybridization to ligands is shown to be most naturally parametrized by the d-orbital occupancy. For cuprates and nickelates, insulating behavior is found to be present only for a very narrow range of d-occupancy, irrespective of the Coulomb repulsion. The d-occupancy predicted by standard band calculations is found to be very far from the values required to obtain an insulating phase, calling into question the interpretation of these materials as charge transfer insulators. \\[4pt] This work is done in collaboration with A.J. Millis, M.J. Han, C.A. Marianetti, L. de' Medici, and H.T. Dang, and is supported by NSF-DMR-1006282, the Army Office of Scientific Research, and the Condensed Matter Theory Center and CNAM at University of Maryland. \\[4pt] [1] X. Wang, H. T. Dang, and A. J. Millis, Phys. Rev. B 84, 014530 (2011).\\[0pt] [2] X. Wang, M. J. Han, L. de' Medici, C. A. Marianetti, and A. J. Millis, arXiv:1110.2782.\\[0pt] [3] M. J. Han, X. Wang, C. A. Marianetti, and A. J. Millis, Phys. Rev. Lett. 107, 206804 (2011).   

Ab initio study of the anti-ferromagnetic, non-collinear CuB$_2$O$_4$ crystal

The spiky features in the crystal absorption spectrum, and the distinct differences in the directional oxygen K-edge absorption spectroscopy of the non-collinear anti-ferromagnetic, incommensurate CuB$_2$O$_4$, had led us to this LDA+U study of the crystal, although in the commensurate phase, due to the instrumental limitation. The calculated band structure matches the spiky features in the absorption spectrum, while the orbital analyzed DOS data explain the differences in the directional oxygen K-edge absorption spectroscopy. The two groups of dispersion-less bands, immediately above the gap, come from different groups of plaquettes, of Cu(A) and Cu(B), and are responsible for the spiky features observed experimentally.   

Exact results on magnon-mediated pairing of spin-polarons

The motion of a charged particle in a magnetically ordered background determines the electronic behavior of weakly doped, magnetically ordered insulators and semiconductors. This problem can be solved exactly for a single charge carrier in a ferromagnetic background at zero-temperature. The solution is a spin-polaron, {\em i.e} a dressed quasiparticle consisting of a charge carrier and a bound magnon which is dynamically emitted and reabsorbed by the charge carrier. If the exchange interaction between the charged particle and the ferromagnetic background is antiferromagnetic, then the spin polaron describes the low-energy states. We generalized the exact solution to the case of two charge carriers. This allows us to characterize the conditions (what ranges of parameters and for what types of lattices) under which magnon-mediated pairing occurs, so that spin-bipolarons describe the low-energy states.   

Understanding the interplay between crystal structures and magnetic states of RCo$_{2}$ ( R = heavy rare earths)

The RCo$_{2}$ compounds with R = heavy lanthanides are well known model systems for both experimentalists and theorists because of the complex nature of the magnetism of these materials. Better understanding of the magnetism can be achieved from parameter-free first principles calculations as well as carefully executed experiments. From first principles calculations we show that the indirect 4$f $- 4$f$ exchange polarizes the 5$d$ spins and the spin up 5$d$ and spin down 3$d$ hybridization gives rise to ferrimagnetism, i.e. antiparallel 5$d$ and 3$d$ itinerant magnetic moments at low temperature. The itinerant electron metamagnetism is known to support first order phase transformations in some of the RCo$_{2}$ compounds. However the clear understanding of this mechanism is lacking and, therefore, we clarify this mechanism from first principles calculations and experimentally confirm the nature of phase transformation of TbCo$_{2}$. The interrelation between the crystal structure and the magnetic states has also been investigated considering TbCo$_{2}$ as an example.