Single-polaron properties of the one-dimensional breathing-mode Hamiltonian

Abstract

We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave-functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron's Green's function. We contrast these results with results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings the breathing-mode polaron dispersion has non-monotonic dependence on the polaron momentum k. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation.

Magnetothermal study of a Dy-stuffed spin ice:Dy2(DyxTi2−x)Ueland1, Lau2, Freitas3 et al. 2008Phys. Rev. B16140View full textAdd to dashboardCite

“…Recent neutron diffraction and electron microscopy experiments have, however, shown that the local structure is more subtle, with features that were irresolvable in the earlier X-ray diffraction data [28]. In fact, these new data on fully stuffed Ho SSI, Ho 2.67 Ti 1.33 O 6.67 , show that a separation of the Ho and Ti sites occurs due to the mismatch in the cation sizes, resulting in complex structural domains.…”

“…A possible explanation is that the dissimilarity in the entropy data arises from the differences in the structural domains of local pyrochlore order. Contrary to data for Ho SSI, X-ray diffraction data for Dy SSI do show peaks 9 corresponding to pyrochlore order for all values of x [27], and recent electron microscopy measurements, similar to those performed on Ho SSI [28], show that the pyrochlore domains in Dy SSI are an order of magnitude larger than those in the Ho SSI [36]. We hypothesize that the observed zero point entropy in Ho SSI may be associated with spins in the boundary regions between such domains, and the larger domains found in Dy SSI result in the observation of less zero point entropy due to the relatively smaller fraction of spins in such boundary regions.…”

“…In these "pyrochlore order" 4 domains, one of the sublattices of corner-sharing tetrahedra is purely Ho while the other sublattice is a mixture of Ho/Ti. These domains, with sizes on the order of 50 Å or less in the Ho SSI [28], are defined by regions of such order, with boundaries at which the sublattices switch their chemical content between pure Ho and the Ho/Ti mixture.…”

“…In this series of materials, fits made to low field susceptibility data using the Curie-Weiss law showed that the effective spin-spin interaction becomes more antiferromagnetic (AFM) with increasing stuffing, x, while, surprisingly, the residual entropy per spin remains at the spin ice (x = 0) value for all x. X-ray experiments performed to determine the crystal structure of Ho SSI found that diffraction peaks corresponding to pyrochlore order decreased in intensity with increasing x for x > 0.3, and completely disappeared at x = 0.67, suggesting that Ti mixed on to the pyrochlore A sites [25,27]. These data led to the conclusion that the crystal transformed into a disordered fluorite lattice, meaning that Ho 3+ and Ti 4+ were randomly distributed on both the A and B pyrochlore sites, presumably resulting in a disordered and frustrated mixed Ho/Ti lattice of side sharing tetrahedra [25,27].Recent neutron diffraction and electron microscopy experiments have, however, shown that the local structure is more subtle, with features that were irresolvable in the earlier X-ray diffraction data [28]. In fact, these new data on fully stuffed Ho SSI, Ho 2.67 Ti 1.33 O 6.67 , show that a separation of the Ho and Ti sites occurs due to the mismatch in the cation sizes, resulting in complex structural domains.…”

“…In these "pyrochlore order" 4 domains, one of the sublattices of corner-sharing tetrahedra is purely Ho while the other sublattice is a mixture of Ho/Ti. These domains, with sizes on the order of 50 Å or less in the Ho SSI [28], are defined by regions of such order, with boundaries at which the sublattices switch their chemical content between pure Ho and the Ho/Ti mixture.Because of the small domain sizes, the average structure of the lattice appears to be of the disordered fluorite type in the X-ray measurements, yet, in fact, the material locally retains a pyrochlore order (i.e. small domains exist with purely Ho on the A sites and Ho/Ti mixtures on the B sites, or vice versa).…”