Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length $S$ is a highly frustrated model with an macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic order) spin wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating {\it effective Hamiltonian}, acting within the subspace of Ising spin configurations representing the {\it collinear} ground states. It consists of products of Ising spins around loops, i.e has the form of a $Z_2$ lattice gauge theory. The remaining ground state entropy is still infinite but not extensive, being $O(L)$ for system size $O(L^3)$. All these ground states have unit cells bigger than those considered previously.Comment: 4pp, one figur

Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field

Quantum Heisenberg antiferromagnets on pyrochlore and checkerboard lattices in a strong external magnetic field are mapped onto hard-core lattice gases with an extended exclusion region. The effective models are studied by the exchange Monte Carlo simulations and by the transfer matrix method. The transition point and the critical exponents are obtained numerically for a square-lattice gas of particles with the second-neighbor exclusion, which describes a checkerboard antiferromagnet. The exact structure of the magnon crystal state is determined for a pyrochlore antiferromagnet.Comment: 11 pages, accepted versio

Quantum order by disorder and accidental soft mode Er2Ti2O7

Motivated by recent neutron scattering experiments, we derive and study an effective "pseudo-dipolar" spin-1/2 model for the XY pyrochlore antiferromagnet Er2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it does lead to a one-parameter `accidental' classical degeneracy. This degeneracy is lifted by quantum fluctuations in favor of the non-coplanar spin structure observed experimentally -- a rare experimental instance of quantum order by disorder. A non-Goldstone low-energy mode is present in the excitation spectrum in accordance with inelastic neutron scattering data. Our theory also resolves the puzzle of the experimentally observed continuous ordering transition, absent from previous models.Comment: 5 pages, 4 figures, final versio

BaCu3O4: High Temperature Magnetic Order in One-Dimensional S=1/2 Diamond-Chains

The magnetic properties of the alkaline earth oxocuprate BaCu3O4 are investigated. We show that the characteristic Cu3O4 layers of this material can be described with diamond chains of antiferromagnetically coupled Cu 1/2 spins with only a weak coupling between two adjacent chains. These Cu3O4 layers seem to represent a so far unique system of weakly coupled one-dimensional magnetic objects where the local AF ordering of the Cu2+ ions leads to an actual net magnetic moment of an isolated diamond chain. We demonstrate a magnetic transition at a high N\'eel temperature T_{N}=336 K

Semiclassical degeneracies and ordering for highly frustrated magnets in a field

We discuss ground state selection by quantum fluctuations in frustrated magnets in a strong magnetic field. We show that there exist dynamical symmetries -- one a generalisation of Henley's gauge-like symmetry for collinear spins, the other the quantum relict of non-collinear weathervane modes -- which ensure a partial survival of the classical degeneracies. We illustrate these for the case of the kagome magnet, where we find zero-point energy differences to be rather small everywhere except near the collinear `up-up-down` configurations, where there is rotational but not translational symmetry breaking. In the effective Hamiltonian, we demonstrate the presence of a term sensitive to a topological `flux'. We discuss the connection of such problems to gauge theories by casting the frustrated lattices as medial lattices of appropriately chosen simplex lattices, and in particular we show how the magnetic field can be used to tune the physical sector of the resulting gauge theories.Comment: 10 pages, 8 figure

Three dimensional generalization of the J1J_1-J2J_2 Heisenberg model on a square lattice and role of the interlayer coupling JcJ_c

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been actively discussed recently. However, recent neutron scattering data has shown that the pnictides have a relatively large spin wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$ model that is the three dimensional generalization of the $J_1$-$J_2$ Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling $J_c$ suppresses the quantum fluctuations and strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable upon increasing $J_1$. Either the magnetization or one of the spin wave velocities vanishes. For $S = 1/2$ renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of general theoretical interest, however, the results show that it is unlikely that the model is relevant to undoped pnictides.Comment: 11 pages, 10 figures. Updated version, several references adde

Neutron Scattering and magnetization studies of Ba2_2Cu2.95_{2.95}Co0.05_{0.05}O4_4Cl2_2: A decorated two-dimensional antiferromagnet

Ba$_2$Cu$_3$O$_4$Cl$_2$ has two inter-penetrating square Cu sublattices, one with square root 2 times the in-plane spacing of the other. Isotropic magnetic interactions between the two sublattices are completely frustrated. Quantum fluctuations resolve the intrinsic degeneracy in the ordering direction of the more weakly coupled sublattice in favor of collinear ordering. We present neutron scattering and magnetization studies of the magnetic structure when the Cu ions are substituted with Co. The Co spins create new magnetic interactions between the two sublattices. The ordering behavior of both Cu sublattices is retained largely unmodified. Between the phase transitions of the two sublattices spin-glass behavior is observed. Magnetization results show a strong enhancement to the ferromagnetic aspect of the magnetic structure. The combination of glassy behavior and large moments strongly suggest that the Co moments induce the formation of local canted states.Comment: 4 figure

Quantum stabilization of 1/3-magnetization plateau in Cs_2CuBr_4

We consider the phase diagram of a spatially anisotropic 2D triangular antiferromagnet in a magnetic field. Classically, the ground state is umbrella-like for all fields, but we show that the quantum phase diagram is much richer and contains a 1/3 magnetization plateau, two commensurate planar states, two incommensurate chiral umbrella phases, and, possibly, a planar state separating the two chiral phases. Our analysis sheds light on several recent experimental findings for the spin-1/2 system Cs_2CuBr_4.Comment: 4+ pages, 2 figure

Symplectic N and time reversal in frustrated magnetism

Identifying the time reversal symmetry of spins as a symplectic symmetry, we develop a large N approximation for quantum magnetism that embraces both antiferromagnetism and ferromagnetism. In SU(N), N>2, not all spins invert under time reversal, so we have introduced a new large N treatment which builds interactions exclusively out of the symplectic subgroup [SP(N)] of time reversing spins, a more stringent condition than the symplectic symmetry of previous SP(N) large N treatments. As a result, we obtain a mean field theory that incorporates the energy cost of frustrated bonds. When applied to the frustrated square lattice, the ferromagnetic bonds restore the frustration dependence of the critical spin in the Neel phase, and recover the correct frustration dependence of the finite temperature Ising transition.Comment: added reference

Tunable Quantum Fluctuation-Controlled Coherent Spin Dynamics

Temporal evolution of a macroscopic condensate of ultra cold atoms is usually driven by mean field potentials, either due to scattering between atoms or due to coupling to external fields; and coherent quantum dynamics have been observed in various cold-atom experiments. In this article, we report results of studies of a class of quantum spin dynamics which are purely driven by zero point quantum fluctuations of spin collective coordinates. Unlike the usual mean-field coherent dynamics, quantum fluctuation-controlled spin dynamics or QFCSD studied here are very sensitive to variation of quantum fluctuations and can be tuned by four to five order of magnitude using optical lattices. They have unique dependence on optical lattice potential depths and quadratic Zeeman fields. QFCSD can be potentially used to calibrate quantum fluctuations and investigate correlated fluctuations and various universal scaling properties near quantum critical points.Comment: 14 pages, 12 figures included; including detailed discussions on thermal effects, trapping potentials and spin exchange losses. (To appear in PRA