Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets

Abstract

Pyrochlore magnets have proven to provide an excellent arena for the realization of a variety of many-body phenomena such as classical and quantum order-by-disorder, as well as spin liquid phases described by emergent gauge field theories. These phenomena arise from the competition between different symmetry-breaking magnetic orders. In this work, we consider a subspace of the most general bilinear nearest-neighbor Hamiltonian on the pyrochlore lattice, parameterized by the local interaction parameter $J_{z\pm }$, where three symmetry-breaking phases converge. We demonstrate that for small values of $|J_{z\pm }|$, a conventional $\mathbf{q}=0$ ordered phase is selected by a thermal order-by-disorder mechanism. For $|J_{z\pm }|$ above a certain finite threshold, a novel spin-nematic phase is stabilized at low temperatures. Instead of the usual Bragg peaks, the spin-nematic phase features lines of high intensity in the spin structure factor. At intermediate temperatures above the low-temperature orders, a rank-2 U(1) classical spin liquid is realized for all $J_{z\pm }\ne 0$. We fully characterize all phases using classical Monte-Carlo simulations and a self-consistent Gaussian approximation.

17 pages, 17 figures; v2: published

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Cited by in corpus (4)

• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Quantum effects on pyrochlore higher-rank U(1) spin liquids: Pinch-line singularities, spin nematics, and connections to oxide materials
• Quantum Coulomb Liquids of Different Rank in the Breathing Pyrochlore Antiferromagnet
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice