Magnetism and covalency in the two-dimensional three-band Peierls-Hubbard model

A Lattice Litany for Transition Metal Oxides

In this tribute to K Alex Müller, I describe how his early insights have influenced future decades of research on perovskite ferroelectrics and more broadly transition metal oxides (TMOs) and related quantum materials. I use his influence on my own research journey to discuss impacts in three areas: structural phase transitions, precursor structure, and quantum paraelectricity. I emphasize materials functionality in ground, metastable, and excited states arising from competitions among lattice, charge, and spin degrees of freedom, which results in highly tunable landscapes and complex networks of multiscale configurations controlling macroscopic functions. I discuss competitions between short- and long-range forces as particularly important in TMOs (and related materials classes) because of their localized and directional metal orbitals and the polarizable oxygen ions. I emphasize crucial consequences of elasticity and metal–oxygen charge transfer.

Competition between double exchange and purely magnetic Heisenberg models in mixed valence systems: Application to half-doped manganites

A truncated Hubbard model is developed for the description of the electronic structure of odd-electron TM-L-TM units (TM=transition metal and L=ligand). The model variationally treats both the double exchange and purely magnetic Heisenberg configurations. This Hubbard model can either be mapped on a purely magnetic Heisenber model in which the bridging oxygen is also magnetic or on a double exchange model owing to the hybridization of the magnetic and ligand or bitals. The purely magnetic Heisenberg model is analytically solved in the general case of two metals (having n magnetic orbitals) bridged by a magnetic oxygen. The comparison of the analytical expressions of the Heisenberg energies to those of the double exchange model reveals that the two model spectra are identical except for one state which does not belong to the model space of the double exchange Hamiltonian. Consequently, the fitting of the model spectra to accurate ab initio spectra does not discriminate between the physically different models. These concepts are illustrated for the Mn-O-Mn unit (or Zener polaron) found in the half-doped manganite Pr(0.6)Ca(0.4)MnO3. It is shown that in the present case the projections of the ab initio ground state wave function onto both model spaces are almost identical provided that one uses properly localized orbitals, proving that the magnetic description of the Zener polaron and the double exchange viewpoint of the electronic structure are equally valid.

Formation of electron strings in narrow band polar semiconductors

We show that linear electron strings may arise in polar semiconductors. A single string consists of M spinless fermions trapped by an extended polarization well of a cigar shape. Inside the string the particles are free although they interact with each other via Coulomb forces. The strings arise as a result of an electronic phase separation associated with an instability of small adiabatic polarons. We have found the length of the string which depends on dielectric constants of semiconductors. The appearance of these electron strings may have an impact on the effect of stripe formation observed in a variety of high- T(c) experiments.