# Brief summary of current research programs

**i. Local symmetry principles (LSP), local and global electric moments driven by spin canting in multiferroics.**

Professor T. A. Kaplan and I have been working on how to apply local symmetry principles - LSP (following the original ideas of T. Moriya who used LSP to predict the direction of anistropic exchange energy parameter D, appearing in the so called Dzyolizinsky-Moriya coupling energy) to predict the direction of local electric polarization P(r) in a system with canted spins. We have used this theory to understand the observed electric polarization in several multiferroics with spiral spin ordering. We also have connected our LSP theory to the usual global symmetry based Landau theory approach. For more details, please see "Canted-spin-caused electric dipoles: a local symmetry theory", TAK & SDM, Phys. Rev. B 83, 174432, (2011).

**ii. Critical examination of the applicability rigid band approximation in the study of transport properties of thermoelectric materials.**

I have been interested in the thermoelectric properties of complex materials as a part of DARPA, ONR-MURI, and DOE-EFRC projects. In order to get large thermopowers (S) one tries to (1) engineer the electronic states near the band gap by creating defect states and (2) optimize the carrier concentration by doping with impurities. One of the commonly used approximation in calculating S as a function of dopant concentration is the so called rigid band approximation (RBA) where one assumes that doping does not change the host electronic structure. Mal-Soon Lee and I have critically examined the validity of RBA and find that for the commonly used dopant concentrations, RBA fails badly in many cases. For more details, please see "Validity of the rigid band approximation in the study of the thermopower of narrow band gap semiconductors", Lee and Mahanti, Phys. Rev B 85, 165149, (2012).

**iii. Effect of intrasite Coulomb interaction and non-local exchange interaction on the properties of pseudo-gap systems containing transition metals, Fe2VAl.**

We have looked at the low energy electronic structure and transport properties of systems with d-electrons which show a pseudo-gap structure in their band structure obtained within local density approximation (LDA) near Fermi energy. It is known that LDA fails badly for the localized d-electrons for which strong intrasite Coulomb repulsions (large Hubbard parameter U) have to be handled better. We have been exploring the effect of U (beyond LDA) using the LDA+U approach. We find major changes in the pseudo gap structure with U. Implications on low energy thermodynamic (heat capacity and Pauli spin susceptibility) transport properties are under investigation. We are also going beyond LDA+U theory using dynamic mean field theory to understand the importance of excitonic effects. For more details, please see "Effect of onsite Coulomb repulsion on thermoelectric properties of full-Heusler compounds with pseudogaps", Do, Lee, and Mahanti, Phys. Rev. B 84, 125104 (2011).

**iv. Ground state degeneracy, topological equivalence, and freezing transition in frustrated Yukawa Lattice Gas (YLG) systems.**

This is a follow-up of one of our earlier studies (with my previous students Khang Hoang and Keyur Desai) of ordering and phase transition in a Coulomb Lattice Gas (CLG) system on an FCC lattice (frustrated Ising model with long range interaction). In the YKG system one tunes the range of the interaction to see how frustration effects depend on the range of interaction. This model was originally proposed to explain some of the observed nanostructures in a new thermoelectric system LAST-m which was discovered here at MSU. But the problem became extremely interesting from a statistical mechanics point of view when River discovered that for a particular concentration, the ground state has 2-fold degeneracy (layered and tubular structures: Sheets and Tubes) independent of the range of interaction in YLG model. We are trying to understand the origin of this degeneracy in terms of topology of the lattice and also studying the melting/freezing transition of these two completely different ground state structures.