阻挫磁体的相图绘制：烧绿石晶格上的简并态、平带与倾斜循环
Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
AI总结：
本研究绘制了含键依赖各向异性两自旋相互作用的烧绿石稀土磁体的完整经典相图，揭示了简并相、孤立三重点、拓扑不变量等特征，为经典自旋液体的研究提供了关键相图信息。
摘要：
我们绘制了描述烧绿石稀土磁体的自旋哈密顿量的完整经典相图，该哈密顿量包含所有对称性允许的最近邻键依赖各向异性两自旋相互作用。我们对自旋组织为张量自由度的过程进行了简单推导，这些张量自由度描述四面体的多极矩，其分量对应四面体对称群$T_d$的不可约表示（irreps）。通过直接根据单个不可约表示的能量参数化哈密顿量，我们对所有可能的、可容纳稳定经典自旋液体的不可约表示简并情况进行了穷尽搜索。研究发现了四个一参数模型族，沿这些模型族存在三个简并相，所有四个模型族均在海森堡反铁磁体及其对偶处合并，我们给出了完整的三维相图图像，展示了所有相及其交点。单个不可约表示的两个副本的出现意味着存在一条额外的简并轨迹，该轨迹在特殊点处穿过相边界，产生两个额外的孤立三重点。我们证明，一参数哈密顿量族以一种拓扑不变量为特征，该不变量描述基态自旋构型围绕该简并轨迹绝热传输时的缠绕方式，类似“恶魔轨迹”。我们提供了相图中所有平带简并的综合目录，并讨论了可能允许或阻碍由张量规范场描述的多种经典自旋液体实现的机制，这些自旋液体表现出捏合线奇点及伴随的四重捏合点。最后，我们列出了所有基态上方三个不可约表示简并的情况，这可能在每个有序相的自旋波谱中产生有趣特征。
英文摘要：
We map the complete classical phase diagram of the spin Hamiltonian describing pyrochlore rare-earth magnets with all symmetry-allowed nearest-neighbor bond-dependent anisotropic two-spin interactions. We provide a simple derivation of the organization of spins into tensor degrees of freedom describing the multipole moments of a tetrahedron, whose components correspond to irreducible representations (irreps) of the tetrahedral symmetry group $T_d$. By parameterizing the Hamiltonian directly in terms of the energies of the individual irreps, we perform an exhaustive search of all possible irrep degeneracies which may host stable classical spin liquids. Doing so reveals four one-parameter families of models along which three phases are degenerate, all four of which merge at the Heisenberg antiferromagnet and its dual, and we give a complete three-dimensional picture of the phase diagram showing all of the phases and their intersections. The appearance of two copies of a single irrep implies an extra degenerate locus which pierces the phase boundaries at special points, yielding two additional isolated triple points. We demonstrate that one-parameter families of Hamiltonians are characterized by a topological invariant describing how the ground state spin configuration winds when adiabatically transported around this degenerate locus, analogous to a "diabolical locus". We provide a comprehensive catalog of all flat band degeneracies in the phase diagram and discuss the mechanisms that may allow for or impede the realization of a variety of classical spin liquids described by tensor gauge fields exhibiting pinch line singularities and concomitant four-fold pinch points. Lastly, we provide a list of all cases where three irreps are degenerate above the ground state, which may lead to interesting features in the spin wave spectrum within each ordered phase.
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