Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields

Abstract

We consider the quantum spin-$s$ $XXZ$ Heisenberg antiferromagnet on the two- and three-dimensional pyrochlore lattices and examine a spin-Peierls mechanism of lowering the total energy by a lattice distortion in a high magnetic field. For the exact eigenstates consisting of several independent localized magnons in a ferromagnetic environment we show the existence of a spin-Peierls instability by rigorous analytical calculations. In addition we report on exact diagonalization data for finite two-dimensional pyrochlore lattices up to N=64 sites. We discuss a scenario of the field-tuned changes in the ground-state properties of the frustrated spin lattices due to the coupling between spin and lattice degrees of freedom.

10 pages (4 figures included)

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• Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
• Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
• Interacting spinless fermions in a diamond chain
• Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario
• The sawtooth chain: From Heisenberg spins to Hubbard electrons
• Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks
• Conductance through geometrically frustrated itinerant electronic systems
• The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond