Non-collinear Magnetic Order in the Double Perovskites: Double Exchange on a Geometrically Frustrated Lattice

Double perovskites of the form A_2BB'O_6 usually involve a transition metal ion, B, with a large magnetic moment, and a non magnetic ion B'. While many double perovskites are ferromagnetic, studies on the underlying model reveal the possibility of antiferromagnetic phases as well driven by electron delocalisation. In this paper we present a comprehensive study of the magnetic ground state and T_c scales of the minimal double perovskite model in three dimensions using a combination of spin-fermion Monte Carlo and variational calculations. In contrast to two dimensions, where the effective magnetic lattice is bipartite, three dimensions involves a geometrically frustrated face centered cubic (FCC) lattice. This promotes non-collinear spiral states and `flux' like phases in addition to collinear anti-ferromagnetic order. We map out the possible magnetic phases for varying electron density, `level separation' epsilon_B - epsilon_B', and the crucial B'-B' (next neighbour) hopping t'.Comment: 15 pages pdflatex + 19 figs, revision: removed redundant comment

Ground state of an S=1/2S=1/2 distorted diamond chain - model of Cu3Cl6(H2O)2⋅2H8C4SO2\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2

We study the ground state of the model Hamiltonian of the trimerized $S=1/2$ quantum Heisenberg chain $\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2$ in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant $J_1$ and the inter-trimer coupling constants $J_2$ and $J_3$. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the $\tilde J_2 - \tilde J_3$ plane ($\tilde J_2 \equiv J_2/J_1$, $\tilde J_3 \equiv J_3/J_1$), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the two-fold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in $\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2$. We also obtain the phase diagram on the $\tilde J_2 - \tilde J_3$ plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.Comment: LaTeX2e, 15 pages, 21 eps figures, typos corrected, slightly detailed explanation adde

Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the exponent associated to the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0,1] has an unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x) is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev. Let

Spin Gap of Two-Dimensional Antiferromagnet Representing CaV4_4O9_9

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV$_4$O$_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e \simeq$ 610 K and $J_c \simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $\Delta \sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.Comment: 12 pages of LaTex, 4 figures availavule upon reques

Ground states with cluster structures in a frustrated Heisenberg chain

We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interactions which frustrate each other. The system undergoes phase changes when the ratio $\lambda$ between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of $\lambda$ in the S=1/2 case. For S=1/2 we show that there are three ground state phases and determine their boundaries.Comment: 4 pages, uses revtex.sty, 2 figures available on request from [email protected], to be published in J. Phys.: Cond. Mat

Exact dimer ground states for a continuous family of quantum spin chains

Using the matrix product formalism, we define a multi-parameter family of spin models on one dimensional chains, with nearest and next-nearest neighbor anti-ferromagnetic interaction for which exact analytical expressions can be found for its doubly degenerate ground states. The family of Hamiltonians which we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a particular point in this parameter space. Like the Majumdar-Ghosh model, the doubly degenerate ground states of our models have a very simple structure, they are the product of entangled states on adjacent sites. In each of these states there is a non-zero staggered magnetization, which vanishes when we take their translation-invariant combination as the new ground states. At the Majumdar-Ghosh point, these entangled states become the spin-singlets pertaining to this model. We will also calculate in closed form the two point correlation functions, both for finite size of the chain and in the thermodynamic limit.Comment: 11 page

Finite Size Effect in Persistence

We have investigated the random walk problem in a finite system and studied the crossover induced in the the persistence probability scales by the system size.Analytical and numerical work show that the scaling function is an exponentially decaying function.The particle here is trapped with in a box of size $L$ . We have also considered the problem when the particle in trapped in a potential. Direct calculation and numerical result show that the scaling function here also an exponentially decaying function. We also present numerical works on harmonically trapped randomly accelerated particle and randomly accelerated particle with viscous drag.Comment: revtex4, 4 pages, 4 figure