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Register a new userFrustrated magnetism and resonating valence bond physics in two-dimensional kagome-like magnets
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Ioannis Rousochatzakis
Publication date
2013
fields
Physics
and research's language is
English
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We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks.
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We overview physical effects of exchange frustration and quantum spin fluctuations in (quasi-) two dimensional (2D) quantum magnets ($S=1/2$) with square, rectangular and triangular structure. Our discussion is based on the $J_1$-$J_2$ type frustrated exchange model and its generalizations. These models are closely related and allow to tune between different phases, magnetically ordered as well as more exotic nonmagnetic quantum phases by changing only one or two control parameters. We survey ground state properties like magnetization, saturation fields, ordered moment and structure factor in the full phase diagram as obtained from numerical exact diagonalization computations and analytical linear spin wave theory. We also review finite temperature properties like susceptibility, specific heat and magnetocaloric effect using the finite temperature Lanczos method. This method is powerful to determine the exchange parameters and g-factors from experimental results. We focus mostly on the observable physical frustration effects in magnetic phases where plenty of quasi-2D material examples exist to identify the influence of quantum fluctuations on magnetism.
The trimer resonating valence bond (tRVB) state consisting of an equal-weight superposition of trimer coverings on a square lattice is proposed. A model Hamiltonian of the Rokhsar-Kivelson type for which the tRVB becomes the exact ground state is written. The state is shown to have $9^g$ topological degeneracy on genus g surface and support $Z_3$ vortex excitations. Correlation functions show exponential behavior with a very short correlation length consistent with the gapped spectrum. The classical problem of the degeneracy of trimer configurations is investigated by the transfer matrix method.
We apply a variational wave function capable of describing qualitatively and quantitatively the so called resonating valence bond in realistic materials, by improving standard ab initio calculations by means of quantum Monte Carlo methods. In this framework we clearly identify the Kekule and Dewar contributions to the chemical bond of the benzene molecule, and we establish the corresponding resonating valence bond energy of these well known structures ($simeq 0.01$eV/atom). We apply this method to unveil the nature of the chemical bond in undoped graphene and show that this picture remains only within a small resonance length of few atomic units.
The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order parameter should split the optical phonons degeneracy near the zone center. Addition of weak next to nearest neighbor coupling is discussed.
A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong onsite Hunds interactions develop intra-atomic tRVBs between the t$_{2g}$ orbitals. On doping, the presence of two iron atoms per unit cell allows these inter-orbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of onsite pair correlations, detectable as an alternating $pi$ phase shift in a scanning tunnelling Josephson microscope.
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