Landau Expansion for the Kugel-Khomskii t2gt_{2g} Hamiltonian

The Kugel-Khomskii (KK) Hamiltonian for the titanates describes spin and orbital superexchange interactions between $d^1$ ions in an ideal perovskite structure in which the three $t_{2g}$ orbitals are degenerate in energy and electron hopping is constrained by cubic site symmetry. In this paper we implement a variational approach to mean-field theory in which each site, $i$, has its own $n \times n$ single-site density matrix \rhov(i), where $n$, the number of allowed single-particle states, is 6 (3 orbital times 2 spin states). The variational free energy from this 35 parameter density matrix is shown to exhibit the unusual symmetries noted previously which lead to a wavevector-dependent susceptibility for spins in $\alpha$ orbitals which is dispersionless in the $q_\alpha$-direction. Thus, for the cubic KK model itself, mean-field theory does not provide wavevector `selection', in agreement with rigorous symmetry arguments. We consider the effect of including various perturbations. When spin-orbit interactions are introduced, the susceptibility has dispersion in all directions in ${\bf q}$-space, but the resulting antiferromagnetic mean-field state is degenerate with respect to global rotation of the staggered spin, implying that the spin-wave spectrum is gapless. This possibly surprising conclusion is also consistent with rigorous symmetry arguments. When next-nearest-neighbor hopping is included, staggered moments of all orbitals appear, but the sum of these moments is zero, yielding an exotic state with long-range order without long-range spin order. The effect of a Hund's rule coupling of sufficient strength is to produce a state with orbital order.Comment: 20 pages, 5 figures, submitted to Phys. Rev. B (2003

DOSE AND FLUX MEASUREMENTS ON GODIVA RADIATION EFFECTS EXPERIMENTS

Flux and dose measurements of fast neutrons, thermal neutrons and gamma rays under perturbing conditions using Godiva as a source are described and discussed. The limitations of single monitoring devices are noted. It is pointed out that in order to improve the accuracy of flux and dose measurements in radiation effects studies, specific detectors must be used at the position of the experimental object. (auth

Order induced by dipolar interactions in a geometrically frustrated antiferromagnet

We study the classical Heisenberg model for spins on a pyrochlore lattice interacting via long range dipole-dipole forces and nearest neighbor exchange. Antiferromagnetic exchange alone is known not to induce ordering in this system. We analyze low temperature order resulting from the combined interactions, both by using a mean-field approach and by examining the energy cost of fluctuations about an ordered state. We discuss behavior as a function of the ratio of the dipolar and exchange interaction strengths and find two types of ordered phase. We relate our results to the recent experimental work and reproduce and extend the theoretical calculations on the pyrochlore compound, Gd$_2$Ti$_2$O$_7$, by Raju \textit{et al.}, Phys. Rev. B {\bf 59}, 14489 (1999).Comment: 5 pages, 5 figures, AMSLaTe

The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System

It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical kagome Heisenberg antiferromagnet (AFM). For weak disorder, it is found that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of ``spin origami'') which has conformations similar to those of tethered membranes.Comment: REVTEX, 11 pages + 3 pictures upon reques

Strong Gravitational Lensing in a Charged Squashed Kaluza- Klein Black hole

In this paper we investigate the strong gravitational lensing in a charged squashed Kaluza-Klein black hole. We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole and then we study the strong gravitational lensing theory and estimate the numerical values for parameters and observables of it. We explore the effects of the scale of extra dimension $\rho_0$ and the charge of black hole $\rho_q$ on these parameters and observables.Comment: 17 pages, 10 figure

Energy conditions, traversable wormholes and dust shells

Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the ``volume integral quantifier'', which provides a measure of the ``total amount'' of energy condition violating matter. Secondly, we present a specific metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity of an observer journeying through the wormhole, are also found by imposing the traversability conditions.Comment: 11 pages, 3 figures, Revtex

Bond order from disorder in the planar pyrochlore magnet

We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.Comment: Minor clarifications + reference to an informal introduction cond-mat/030809

Susceptibility and dilution effects of the kagome bi-layer geometrically frustrated network. A Ga-NMR study of SrCr_(9p)Ga_(12-9p)O_(19)

We present an extensive gallium NMR study of the geometrically frustrated kagome bi-layer compound SrCr_(9p)Ga_(12-9p)O_(19) (Cr^3+, S=3/2) over a broad Cr-concentration range (.72<p<.95). This allows us to probe locally the kagome bi-layer susceptibility and separate the intrinsic properties due to the geometric frustration from those related to the site dilution. Our major findings are: 1) The intrinsic kagome bi-layer susceptibility exhibits a maximum in temperature at 40-50 K and is robust to a dilution as high as ~20%. The maximum reveals the development of short range antiferromagnetic correlations; 2) At low-T, a highly dynamical state induces a strong wipe-out of the NMR intensity, regardless of dilution; 3) The low-T upturn observed in the macroscopic susceptibility is associated to paramagnetic defects which stem from the dilution of the kagome bi-layer. The low-T analysis of the NMR lineshape suggests that the defect can be associated with a staggered spin-response to the vacancies on the kagome bi-layer. This, altogether with the maximum in the kagome bi-layer susceptibility, is very similar to what is observed in most low-dimensional antiferromagnetic correlated systems; 4) The spin glass-like freezing observed at T_g=2-4 K is not driven by the dilution-induced defects.Comment: 19 pages, 19 figures, revised version resubmitted to PRB Minor modifications: Fig.11 and discussion in Sec.V on the NMR shif

Zero temperature phases of the frustrated J1-J2 antiferromagnetic spin-1/2 Heisenberg model on a simple cubic lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J1 and J2) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Neel phase for small J2 (AF), and a collinear antiferromagnetic phase at large J2 (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, pc = 0.28. Our results for the value of pc are in excellent agreement with results from Monte-Carlo simulations and variational spin wave theory. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.Comment: 19 pages, 4 figures, Fig. 1b modified, Appendix B text modifie