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.

我们解决了长期存在的铬呼吸性烧绿石材料系列中各种现象的微观起源的问题。结合电子结构和归一化分组技术，我们解决了磁相互作用并分析了它们的相互空间磁化率。我们表明，这些材料的物理原理主要受远距离海森堡哈密顿相互作用的支配，这是迄今尚未发现的事实。我们的计算发现，在这些同构化合物中，硫族元素的选择触发了材料与经典自旋液体的接近，这些自旋液体具有不同尺寸的波矢的简并流形：LiInCr ₄ O ₈和LiGaCr ₄具有三维简并性的库仑相。Ø ₈，对于CuInCr ₄ Se ₈具有二维简并性的螺旋自旋液体，对于LiInCr ₄ S ₈，LiGaCr ₄ S ₈和CuInCr ₄ S ₈具有面心立方反铁磁体的一维线简并性。我们在铬尖晶石中发现的令人惊讶的原型烧绿石行为复杂阵列可能会激发通过掺杂或压力研究不同半经典自旋液体之间的跃迁路径。