Session S15: Focus Session: Magnetism and More on Cornersharing Tetrahedra

Spin nematics in pyrochlore antiferromagnet with ferromagnetic next-nearest-neighbor interaction

The classical Heisenberg antiferromagnet on the pyrochlore lattice remains disordered down to zero temperature. A weak ferromagnetic interaction between second neighbors $J_2$ leads to a discontinuous ordering at a temperature $T_c\sim |J_2|$. Below the transition, a spin order with an extended unit cell containing as many as 1024 spins was found in Monte-Carlo simulations for $J_2 = -0.1 J_1$ [1]. Here we present the characterization of ordered states at a smaller $J_2 = -0.01 J_1$. This time the magnet shows a layered structure in the ordered phase: tetrahedra of the same layer develop a collinear N\'eel order with an in-plane wavevector ${\bf q}= 2\pi(1,1)$. At the mean-field level, each different layer has its own preferred spin direction. Thermal fluctuations, however, favor a collinear alignment of spins in different layers. There still remains a $Z_2$ symmetry for each layer: the N\'eel vector of a plane can be parallel or antiparallel to the common preferred direction, rendering the magnet a \textit{spin nematic,} possibly with an additional bond order. [1] D. Tsuneishi, M. Ioki, and H. Kawamura, J. Phys. Condens. Matter, to be published; cond-mat/0609655.   

Diffuse Magnetic Scattering in GeCo$_{2}$O$_{4}$

The spinel GeCo$_{2}$O$_{4}$, in which the spin-3/2 Co$^{2+}$ ions are located on the vertices of a lattice of corner-sharing tetrahedra, exhibits interesting magnetic and structural properties. GeCo$_{2}$O$_{4 }$has a N\'{e}el transition (T$_{N}$ = 20.6 K) that coincides closely with a cubic to tetragonal structural phase transition, below which $c$/$a \quad >$ 1. In the past we have reported magnetic susceptibility, heat capacity, synchrotron x-ray powder diffraction, neutron powder diffraction and inelastic neutron scattering measurements for this material. In this talk we will describe the results of diffuse magnetic scattering measurements made at temperatures above and below T$_{N}$ using the PRISMA spectrometer at ISIS. The sample was a single crystal grown by the floating zone technique at AIST. The presence of significant amounts of magnetic short-range order at temperatures well above T$_{N}$, and the effect of this short-range order upon the data obtained with other experimental techniques, will be described.   

Quantum Spin Ordering in Tb$_2$Ti$_2$O$_7$

Group theoretical methods are used to analyse quantum spin states in the geometrically frustrated pyrochlore Tb$_2$Ti$_2$O$_7$. The magnetic rare earth spins, with $J=6$, have a ground state doublet due to local crystal electric field. With 4 Tb ions per unit cell, there is therefore a 16-fold degeneracy of the ground state. Symmetry considerations predict a lifting of the degeneracy into a singlet, three doublets and three triplets. One of the triplet configurations is found to be responsible for the $[0,0,2]$ peak in diffuse neutron scattering.   

Static Spin Disorder and Field-Induced Low Dimensionality in the Spin Ice Phase of Ho$_2$Ti$_2$O$_7$

The pyrochlore magnet Ho$_2$Ti$_2$O$_7$ displays a disordered, geometrically frustrated state at low temperature known as ``Spin Ice.'' This short-range correlated magnetic state is so named because it maps onto the proton-disorder problem in water ice. Unique to spin ice, as opposed to water ice, is the tunable parameter of applied magnetic field, which allows a new dimension of its phase behavior to be studied [Fennell et.al, PRB 72, 224411(2005)]. We report time-of-flight neutron scattering experiments probing the magnetic field-induced behavior of Ho$_2$Ti$_2$O$_7$ with the field applied along a crystallographic [110] direction. These results show elastic short-range correlations in Ho$_2$Ti$_2$O$_7$ in zero field, and a decomposition of the pyrochlore lattice into two orthogonal sets of weakly interacting chains in the presence of a [110] magnetic field. One of these subsystems of the pyrochlore lattice undergoes a 3D to 1D crossover with applied field. We compare our results with expectations for a dipolar spin ice model, and with recent results for the antiferromagnetic sister compound Tb$_2$Ti$_2$O$_7$.   

Order-by-disorder in frustrated diamond lattice antiferromagnets

Normal spinels constituting antiferromagnets on a diamond lattice have recently been the subject of intensive experimental study. To understand the behavior of the many systems in this class exhibiting strong frustration, such as MnSc$_2$S$_4$, we have studied theoretically a model for frustrated diamond lattice antiferromagnets that exhibits complex behavior in accord with numerous observations. Remarkably, with sufficiently strong frustration a massive ground state degeneracy develops amongst coplanar spirals whose propagation wavevectors reside on a two-dimensional ``spiral surface'' in momentum space. We argue that an important ordering mechanism is entropic splitting of these degenerate states, an elusive phenomenon known as order-by-disorder. Extensive Monte Carlo simulations reveal the order-by-disorder phase, with a low ordering temperature.   

Spiral spin liquid correlations in diamond antiferromagnets

We have introduced a simple model for frustrated magnetism on a diamond lattice, appropriate for a number of recently studied normal spinel materials. The model possesses a massive degeneracy of coplanar spin spiral states, characterized by propagation wavevectors that reside on a two-dimensional surface in momentum space. The degeneracy of low energy states significantly suppresses the ordering temperature relative to the Curie-Weiss temperature $\Theta_{CW}$. In the intermediate temperature regime $T_c [Preview Abstract]

High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets

Spin $S = 1/2$ Klein models on the checkerboard and pyrochlore lattices contain in their ground--state manifold the subspace generated by the set of singlet dimer coverings, and thus possess an extensive ground--state degeneracy. Among the many exotic consequences is the presence of deconfined fractional excitations (spinons) which propagate through the entire system. While a realistic electronic model on the pyrochlore lattice is close to the Klein point, this point is in fact inherently unstable because any perturbation $\epsilon$ restores spinon confinement at $T = 0$. We demonstrate that deconfinement is recovered in the finite--temperature region $\epsilon \ll T \ll J$, where the deconfined phase can be characterized as a dilute Coulomb gas of thermally excited spinons. We investigate the zero--temperature phase diagram away from the Klein point by means of a variational approach based on the singlet dimer coverings of the pyrochlore lattices and taking into account their non--orthogonality.   

Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons

A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft $\omega\sim k^2$ dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this novel phase is described by a new set of Maxwell's equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott Insulator phase. In the 2 dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the 2 dimensional quantum critical point at which the vertex operators are tuned to zero.   

Topological order and topological entropy in classical systems

We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, namely that of a toric code, we show how to use pure state density matrices to construct corresponding thermally mixed ones that retain precisely half the original topological entropy, a result that we generalize to a whole class of quantum systems. In particular, we suggest that classical topological order is likely to arise from the presence of frustration in magnetic systems. Finally, we discuss some of the characteristic properties of classical systems exhibiting topological order, and we argue how the latter may be related to a display of glassy behavior.