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arXiv:1612.08312 · Physics Letters A

Large-scale calculation of ferromagnetic spin systems on the pyrochlore lattice

Konstantin S Soldatov, Konstantin Valentinovich Nefedev, Yukihiro Komura, Yutaka Okabe

Published Dec 24, 2016• 8 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2016.12.039

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We consider the quantum spin-sss XXZXXZXXZ 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=64N=64N=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.
A simple phenomenological real-space renormalization group method for quantum Heisenberg spins with nearest and next nearest neighbour interactions on a pyrochlore lattice is presented. Assuming a scaling law for the order parameter of two clusters of different sizes, a set of coupled equations that gives the fixed points of the renormalization group transformation and, thus, the critical temperatures and ordered phases of the system is found. The particular case of spins 1/2 is studied in detail. Furthermore, to simplify the mathematical details, from all the possible phases arising from the renormalization group transformation, only those phases in which the magnetic lattice is commensurate with a subdivision of the crystal lattice into four interlocked face-centred cubic sublattices are considered. These correspond to a quantum spin liquid, ferromagnetic order, or non-collinear order in which the total magnetic moment of a tetrahedral unit is zero. The corresponding phase diagram is constructed and the differences with respect to the classical model are analysed. It is found that this method reproduces fairly well the phase diagram of the pyrochlore lattice under the aforementioned constraints.