Fluctuation-Driven Selection at Criticality in a Frustrated Magnetic System: the Case of Multiple-k Partial Order on the Pyrochlore Lattice

Abstract

We study the problem of partially ordered phases with periodically arranged disordered (paramagnetic) sites on the pyrochlore lattice, a network of corner-sharing tetrahedra. The periodicity of these phases is characterized by one or more wave vectors k=(1/2 1/2 1/2). Starting from a general microscopic Hamiltonian including anisotropic nearest-neighbor exchange, long-range dipolar interactions and second- and third-nearest neighbor exchange, we identify using standard mean-field theory (s-MFT) an extended range of interaction parameters that support partially ordered phases. We demonstrate that thermal fluctuations ignored in s-MFT are responsible for the selection of one particular partially ordered phase, e.g. the "4-k" phase over the "1-k" phase. We suggest that the transition into the 4-k phase is continuous with its critical properties controlled by the cubic fixed point of a Ginzburg-Landau theory with a 4-component vector order-parameter. By combining an extension of the Thouless-Anderson-Palmer method originally used to study fluctuations in spin glasses with parallel-tempering Monte-Carlo simulations, we establish the phase diagram for different types of partially ordered phases. Our results elucidate the long-standing puzzle concerning the origin of the 4-k partially ordered phase observed in the Gd2Ti2O7 dipolar pyrochlore antiferromagnet below its paramagnetic phase transition temperature.

13 pages, 4 figures

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• Unconventional magnetic phase separation in $\gamma$-CoV${}_2$O${}_6$
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• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• The free energy of anisotropic quantum spin systems: Functional integral representation
• Fragile magnetic order in metallic quasicrystals
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice