发表机构
CRISP – Centre de Recerca Independent de sa Pobla; Universitat de les Illes Balears（萨波布拉独立研究中心; 巴利阿里群岛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究14种布拉维晶格的偶极有序性，通过统一框架计算得出其结构原理、特殊晶格的基态特征，优化后布拉维空间坍缩为四个吸引子，重现相关基准结果。
AI 中文摘要
每一种晶体都是由基元修饰的布拉维晶格，因此，14种布拉维晶格的偶极有序性是三维偶极磁性任何系统理论的自然起点。本文在统一框架下确定该有序性：通过埃瓦尔德求和计算相互作用张量，在整个布里渊区上最小化最低卢廷格-蒂萨（Luttinger–Tisza）带以获得经典基态，对所有有序为共线的晶格计算线性自旋波谱及其零点修正。得到三个非单个晶格特有而是整个体系的结果：其一，三维偶极张量的精确无迹性，以及所有立方对称晶格在波矢k=0处张量严格为零这两个结构原理，解释了有序类型、一阶立方各向异性的缺失以及零点矩缩减的系统性；其二，恰好有一种晶格不符合卢廷格-蒂萨构造：面心正交晶格的最优本征向量非圆形，单k态是长度非恒定的自旋密度波，表格化能量为严格下界，直接超胞最小化得到真实基态；其三，对每个家族的自由度量参数优化后，整个布拉维空间仅坍缩为四个吸引子，体心四方晶格为全局最优，菱面体α=62.42°处的单个内部最优低于面心立方，重现了三项已发表的独立基准结果。
英文摘要
Every crystal is a Bravais lattice decorated by a basis, so the dipolar ordering of the fourteen Bravais lattices is the natural starting point for any systematic theory of dipolar magnetism in three dimensions. We determine it here in a single common framework: the interaction tensor is Ewald-summed, the classical ground state is obtained by minimising the lowest Luttinger--Tisza band over the entire Brillouin zone, and the linear spin-wave spectrum with its zero-point corrections is computed for every lattice whose order is collinear. Three results emerge that are not properties of individual lattices but of the landscape. First, two structural principles --- the exact tracelessness of the dipolar tensor in three dimensions, and its identical vanishing at $\mathbf k=0$ for every cubic-symmetric lattice --- explain the ordering type, the absence of first-order cubic anisotropy, and the systematics of the zero-point moment reduction. Second, exactly one lattice defeats the Luttinger--Tisza construction: for face-centred orthorhombic the optimal eigenvector is not circular, the single-$\mathbf k$ state is a spin-density wave of non-constant length, and the tabulated energy is a strict lower bound; direct supercell minimisation gives the true ground state. Third, optimising each family over its free metric parameters collapses the whole of Bravais space onto only \emph{four} attractors, with body-centred tetragonal the global optimum and a single interior optimum at rhombohedral $α=62.42^\circ$ lying below face-centred cubic. Three independent published benchmarks are reproduced.
