Strongly frustrated random antiferromagnets

A high dimensionality calculation (Weiss like) has been carried out for antiferromagnetism (AFM) in structures with many sublattices. By allowing quenched disorder in the exchange interactions our results clearly exhibit the interplay between the effects of lattice frustration and disorder on the system's properties. For given number of sublattices present, there are several possible phases (ordering of the spins) and as many metastable states in the ergodic phases. It is found that the glassy behavior, and metastability, for multi-sublattices systems is substantially enhanced as compared with simple structures, exhibiting structure dependent de Almeida-Thouless lines. Strongly disordered systems have the long-range AFM ordering, ergodic metastable states and glassy phases intermingled in a non-trivial way. Also, even small fluctuations in the exchange parameters do induce sizeable glassy behavior in structures with many sublattices. Spin glass behavior in apparently non-disordered systems as certain pyrochlores may be accounted for within the present context. Received 9 April 1999 and Received in final form 8 June 1999     

Nested cluster algorithm for frustrated quantum antiferromagnets

Frustrated antiferromagnets are important materials whose quantum Monte Carlo simulation suffers from a severe sign problem. We construct a nested cluster algorithm which uses a powerful strategy to address this problem. For the spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square lattice the sign problem is eliminated for large systems. The method is applicable to general lattice geometries but limited to moderate temperatures.     

Anomalous excitation spectra of frustrated quantum antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Néel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs2CuCl4.     

Magnons versus free spinons in finite quantum frustrated antiferromagnets

We have investigated the validity of doping with a vacancy the J₁–J₃ frustrated Heisenberg model on a finite square lattice as a way to test the existence of fractional spin excitations. Using a generalized t–J₁–J₃ model we have computed the vacancy spectral functions in the self-consistent Born approximation. We have found that by including spiral fluctuations in the magnetic ground state, the spectral functions on finite systems agree very well with the unbiased exact ones. In contrast to the recent proposal that the quasiparticle weight reduction could be a signal of a spinon free excitation in finite systems, we have found strong evidence that such a reduction is due to the existence of spiral fluctuations.     

Spin freezing in geometrically frustrated antiferromagnets with weak disorder

We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbor exchange on the pyrochlore lattice, we examine low-temperature behavior. We show that spatial modulation of exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random strains in the presence of magnetoelastic coupling, may account for the spin freezing observed in many geometrically frustrated magnets.     

Quantum order by disorder in frustrated diamond lattice antiferromagnets

We present a quantum theory of frustrated diamond lattice antiferromagnets. Considering quantum fluctuations as the predominant mechanism relieving spin frustration, we find a rich phase diagram comprising of six phases with coplanar spiral ordering in addition to the Néel phase. By computing the specific heat of these ordered phases, we obtain a remarkable agreement between (k, k, 0) spiral ordering and the experimental specific heat data for the diamond lattice spinel compounds MnSc2S4, Co3O4, and CoRh2O4, i.e., specific heat data is a strong evidence for (k, k, 0) spiral ordering in all of these materials. This prediction can be tested in future neutron scattering experiments on Co3O4 and CoRh2O4, and is consistent with existing neutron scattering data on MnSc2S4. Based on this agreement, we infer a monotonically increasing relationship between frustration and the strength of quantum fluctuations.     

Field induced magnetic ordering transition in Kondo insulators

We study the 2D Kondo insulators in a uniform magnetic field using quantum Monte Carlo simulations of the particle-hole symmetric Kondo lattice model and a mean field analysis of the Periodic Anderson model. We find that the field induces a transition to an insulating, antiferromagnetically ordered phase with staggered moment in the plane perpendicular to the field. For fields in excess of the quasi-particle gap, corresponding to a metal in a simple band picture of the periodic Anderson model, we find that the metallic phase is unstable towards the spin density wave type ordering for any finite value of the interaction strength. This can be understood as a consequence of the perfect nesting of the particle and hole Fermi surfaces that emerge as the field closes the gap. We propose a phase diagram and investigate the quasi-particle and charge excitations in the magnetic field. We find good agreement between the mean-field and quantum Monte Carlo results.Received: 17 December 2003, Published online: 8 June 2004PACS: 71.27. + a Strongly correlated electron systems; heavy fermions - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.30. + h Metal-insulator transitions and other electronic transitions - 75.30.Mb Valence fluctuation, Kondo lattice, and heavy-fermion phenomena - 75.30.Fv Spin-density waves     

Fully frustrated Ising antiferromagnets at the fractal to Euclidean crossover

We present a study of the residual entropies of the frustrated Ising antiferromagnets in a zero field, situated on the Sierpiński gasket type of fractals. Our results render it possible to establish the fractal residual entropy crossover towards Wannier's exact value for the Euclidean triangular lattice.