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Abstract
We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr4O8 and LiGaCr4O8, a spiral spin liquid with two-dimensional degeneracy for CuInCr4Se8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr4S8, LiGaCr4S8, and CuInCr4S8. The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.
Highlights
Over the past 30 years, materials with magnetic moments on the vertices of networks of corner-shared triangular or tetrahedral units have played center stage in the experimental search for exotic magnetic states driven by competing, i.e. frustrated, interactions.[1]
The U values are very reasonable[26] for Cr3+ and are all located in a narrow interval 1:43 eV U 1:91 eV, indicating that the great diversity among the chromium breathing pyrochlores, varying from antiferromagnetic to ferromagnetic Heisenberg models, can all be described with roughly the same exchange correlation functional. We find that both oxides, LiInCr4O8 and LiGaCr4O8, are dominated by antiferromagnetic J and J0 couplings (Fig. 2a, b), with longer range couplings being very small
While we have previously pointed out the sensitivity of the spin structure factor order is realized in CuInCr4Se8
Summary
Over the past 30 years, materials with magnetic moments on the vertices of networks of corner-shared triangular or tetrahedral units have played center stage in the experimental search for exotic magnetic states driven by competing, i.e. frustrated, interactions.[1]. In contrast with the above rare-earth systems characterized by strongly anisotropic interactions at the Oð1Þ K scale, there is a paucity of magnetic compounds involving transition metal ions on a pyrochlore network and coupled via a primarily isotropic Heisenberg exchange of a high (Oð102Þ K) energy scale. The availability of such compounds in single-crystal form would empower researchers to explore and possibly discover novel collective behaviors existing over a wider and more experimentally accessible temperature window. The disorder-free so-called breathing chromium spinels, which define a fairly broad range of materials (e.g. LiInCr4O8, LiGaCr4O8, LiInCr4S8, LiGaCr4S8, CuInCr4S8, and CuInCr4Se8),[6,7,8,9,10,11,12,13,14,15,16] constitute a significant opportunity for carrying out the above research program in and below the Oð102Þ K temperature scale
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