Session N23: Focus Session: MAG.THY III: Oxides and Phase Transitions

Antiferromagnetic Heisenberg Spin Layers coupled with Dipolar Interaction -- a Monte Carlo study of Rb$_{2}$MnF$_{4}$

Rb$_{2}$MnF$_{4}$ is a quasi-2D antiferromagnetic (AF) system, in which Mn$^{2+}$ ions carrying spin-5/2 occupy square lattices perpendicular to the c-axis of the tetragonal unit cell. These spins interact via mostly nearest neighbor isotropic AF exchanges, while the dipolar interaction contributes to the effective anisotropy that stabilizes the AF phase at low temperatures. In a magnetic field parallel to the c-axis, the AF phase is terminated along a spin-flop line, and a transverse (XY) phase appears. We perform large scale extensive Monte Carlo simulations to map out the phase diagram and investigate the critical behavior along the phase boundaries. A novel reweighting technique is used to efficiently handle the dipolar interaction. Our results suggest that both the AF phase and the XY phase experience continuous transitions across the spin-flop line, which is consistent with a bicritical point at zero temperature. We also found that the effect of the weak inter-planar coupling is not completely negligible for the spin-flop transition and the properties of the XY phase.   

RVB liquid phase of a quantum dimer model with competing kinetic terms

Starting from a spin-orbital model adapted to the case of LiNiO$_2$, we derived an effective quantum dimer model including 6-dimer loops. We argue that the relevant terms of this model are of kinetic type. Using numerical techniques like exact diagonalizations and Green's function Monte-Carlo we show that a competition between two kinetic terms can lead to a resonating valence bond state for a finite range of the parameters.   

Dynamical correlations of the Quantum Dimer Model on the triangular lattice

Using Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model (QDM)on the triangular lattice [1] on clusters with up to 588 sites. A detailed comparison of the static properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, and to to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, in agreement with an earlier suggestion [2]. We have also extended the Green's function Monte Carlo algorithm to calculate dynamical correlation functions. Preliminary results on the dimer-dimer correlations confirm the extension of the RVB phase and bring new insight on the nature of the transition to the $\sqrt{12} \times \sqrt{12}$ phase and on the type of long-range order realized in that phase.\\ {[1]} A. Ralko, M. Ferrero, F. Becca, D. Ivanov and F. Mila, Phys. Rev. B, {\bf 71}, 224109 (2005).\\ {[2]} R. Moessner and S.L. Sondhi, Phys. Rev. Lett, {\bf 86}, 1881 (2001).   

Towards material-specific simulations of high-temperature superconducting cuprates

Simulations of high-temperature superconducting (HTSC) cuprates have typically fallen into two categories: (1) studies of generic models such as the two-dimensional (2D) Hubbard model, that are believed to capture the essential physics necessary to describe the superconducting state, and, (2) first principles electronic structure calculations that are based on the local density approximation (LDA) to density functional theory (DFT) and lead to materials specific models. With advent of massibely parallel vector supercomputers, such as the Cray X1E at ORNL, and cluster algorithms such as the Dynamical Cluster Approximation (DCA), it is now possible to systematically solve the 2D Hubbard model with Quantum Monte Carol (QMC) simulations and to establish that the model indeed describes $d$-wave superconductivity [1]. Furthermore, studies of a multi-band model with input parameters generated from LDA calculations demonstrate that the existence of a superconducting transition is very sensitive to the underlying band structure [2]. Application of the LDA to transition metal oxides is, however, hampered by spurious self-interactions that particularly affects localized orbitals. Here we apply the self-interaction corrected local spin-density method (SIC-LSD) to describe the electronic structure of the cuprates. It was recently applied with success to generate input parameters for simple models of Mn doped III-V semiconductors [3] and is known to properly describe the antiferromagnetic insulating ground state of the parent compounds of the HTSC cuprates. We will discus the models for HTSC cuprates derived from the SIC-LSD study and how the differences to the well-known LDA results impact the QMC-DCA simulations of the magnetic and superconducting properties. \newline \newline [1] T. A. Maier, M. Jarrell, T. C. Schulthess, P. R. C. Kent, and J. B. White, Phys. Rev. Lett. 95, 237001 (2005). \newline [2] P. Kent, A. Macridin, M. Jarrell, T. Schulthess, O. Andersen, T. Dasgupta, and O. Jepsen, Bulletin of the American Physical Sosciety 50, 1057 (2005). \newline [3] T. C. Schulthess, W. Temmerman, Z. Szotek, W. H. Butler, and G. M. Stocks, Nature Materials 4, 838 (2005).   

Mechanism of Noncollinearity and Magnetoelectric Coupling in Incommensurate Multiferroics

Using extensive Monte-Carlo simulations of a modified orbitally degenerate double-exchange model applied to the multiferroic perovskites $R$MnO$_3$ ($R=$Gd, Tb, Dy), we show that the spiral magnetic phase results from the interplay between the double exchange coupling, superexchange, Jahn-Teller and Dzyaloshinskii-Moriya (DM) interactions. The DM interaction also induces a small ferroelectric moment and provides the mechanism of the strong coupling between the unusual magnetism and ferroelectricity. We also discuss the magnetoelectric effects in the applied magnetic fields.   

Numerical Study of Magnetism in the Periodic Anderson Model

The periodic Anderson model is believed as a candidate of the minimal lattice models for itinerant ferromagnetism. Several numerical methods, including exactly diagonalization, constrained-path Monte Carlo method and mean field method, are employed to investigate the magnetic properties of the model in one dimension and two dimensions. By changing the band-filling, chemical potential of the impurity band and the hybridyzation between conduction band and impurity band, we found that in some parameter regions, different magnetic ordering exist. Some of results confirm the previous works and some are new.   

Bond-diluted Heisenberg spin systems on coupled ladders

We study spin-1/2 Heisenberg spin systems with bond dilution on coupled ladders or striped phases. The diluted bond configurations can be static or dynamic. The dynamic case with motion of the bonds is described by pseudo-spins and modeled by anisotropic Heisenberg spin chains in an external field. The systems are studied using the stochastic series expansion quantum Monte Carlo method. We find the quantum critical point for real spins from the ordered phase to the disordered phase is sensitive to the bond configuration. A study of the ground state energy shows strong differences for different bond configurations, which may be related to phase separation. Under certain conditions, real spin systems with bond-dilution can be described by a coupling-weakened fully coupled spin systems. For the pseudo-spins, an effective field induced by the real spins is observed.   

Thin Ising films with both competing surface fields and a magnetic field gradient: A Monte Carlo study

Extensive Monte Carlo simulations are used to study the interesting effects resulting from a linearly varying magnetic field on a thin Ising film (equivalent to applying gravity to the corresponding lattice-gas model). Besides competing surface fields acting on two LxL free surfaces a distance D apart from each other, we also apply a magnetic field g that varies linearly between the surfaces and which competes with the surface fields. To determine the phase diagram, we look for bulk two-phase conexistence at different values of g and temperature T. In situations with only competing surface fields applied, the interface unbinding transition \footnote{K.Binder, D.P.Landau, A.M.Ferrenberg, Phys.Rev.E {\bf 51}, 2824(1995)} happens at temperature T$_{c}$(D). The addition of the g field produces a phase diagram in which, as g increases, the temperature bounding bulk two-phase coexistence first goes up from T$_{c}$(D), and then decreases. For small g, we find a second order transition, whereas for large g, the transition appears to be first order. We will compare our simulation results with theoretical predictions \footnote{J.Rogiers, J.O.Indekeu, Europhys.Lett. {\bf 24}, 21(1993)}. \\ \\ $^*$Research supported by NSF   

Electronic structure and excitation spectra of transition metal monoxides investigated via orbital-dependent functionals

We are investigating the electronic structure of strongly correlated 3d transition metal monoxides with two orbital dependent functionals, the self-interaction corrected local spin-density method (SIC-LSD) as well as the LDA+U method. Both functionals are known to reproduce the antiferromagnetic insulating ground state of, for example, CoO and NiO. We perform a detailed comparison of magnetic moments, exchange, and electronic structure calculated with the two methods. In addition, we study the interplay between the electronic structure and the electron-hole excitations in both the insulating and the metallic phases. Our results are compared with available experimental data.   

Ab initio calculations on the frustrated magnet ZnCr$_2$O$_4$

The complex oxide ZnCr$_2$O$_4$ is a good realization of the Heisenberg antiferromagnet on a pyrochlore lattice and is a strongly frustrated magnetic system. Recent experiments have shown that ZnCr$_2$O$_4$ undergoes a lattice distortion and a transition from paramagnetic to antiferromagnetic order at $T_c = 12.5 \ K$. Infrared spectroscopy has shown a large splitting of a phonon mode involving magnetic ions. We perform ab initio total energy calculations of the exchange coupling constant and phonon modes using the plane-wave pseudopotential formalism with the LSDA+U method, and we compare the results to experiment. This work was supported by National Science Foundation Grant No. DMR04-39768 and by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, U.S. Department of Energy under Contract No. DE-AC03-76SF00098. Computational resources have been provided by NPACI and NERSC.   

Anisotropic magnetic phases

We study how magnetic phases vary with uniaxial and fourfold anisotropy constants, C and D. We do this for classical magnetic dipoles on cubic lattices with dipolar and nearest neighbor exchange interactions. By mean field and by Monte Carlo calculations, results are obtained for bulk and n-layer film systems under no applied external field. We pay special attention to the spin reorientation (SR) transition. We find (1) a reentrant SR transition for a narrow range of C/D values, and (2) that the ratio of the ordering temperature to the SR temperature varies with C/D but depends rather weakly on the exchange constant.   

Alternative methods to characterize phase transitions in Ising systems

The Binder cumulant (BC) is defined in terms of average values of second and fourth momenta of an order parameter q. Simulations for Ising systems show that the curves for BCs they all cross at the same temperature regardless of the size of the system. We present here two alternative and different methods to obtain the critical temperature after finding the time evolution of any order parameter q(t), after equilibration. First, we consider the time autocorrelation functions for the absolute value of a site order parameter, $\vert $q$\vert $, for different system sizes, showing that they also cross at the same temperature where BCs cross. Second, we show that the ``weight'' in bites of the compressed file containing vector q(t) maximizes at a temperature close to the critical temperature; a scaling analysis takes us back to the temperature of previous crossing. The main advantage of the new methods is its easy physical interpretation.