AI 中文总结
该研究将电场梯度（EFG）系统纳入朗道理论，建立适配对称性的序参量框架，通过实验和计算验证，还对BaFe₂As₂的向列相变提出可证伪预测。
AI 中文摘要
四极超精细光谱技术，包括核四极共振（NQR）、核磁共振（NMR）、时间微分扰动角关联（TDPAC）和穆斯堡尔光谱，长期以来一直将核位点处的电场梯度（EFG）作为结构和电子相变的序参量的经验替代物，但EFG从未被系统地纳入朗道理论。本文提供了该框架：EFG是定义在晶体学位点处的无迹对称二阶张量，通过位点对称群分解并在Wyckoff轨道上诱导，可确定其在母空间群中的不可约表示内容。当存在布里渊区中心跃迁的表示时，对称性要求对应的EFG组合在跃迁之上消失，在跃迁之下随序参量线性增长，继承其临界指数、符号和畴结构；对称性正交通道为二次项，可恢复经典经验关系，这产生了对初级、次级和禁阻EFG响应的可证伪分类。该框架通过五十年的四极实验得到验证，重现了临界指数、一级不连续性和零结果，还通过满足预测奇偶性和零定理的第一性原理计算得到验证。对α-石英的全电子计算证实了轨道选择规则：仅对应软模不可约表示变换的EFG组合随畸变振幅线性变化，而正交组合则被抑制两个数量级。针对BaFe₂As₂中向列相变处的⁷⁵As位点，本文提出了一项研究，给出了五项可证伪预测，包括此前未提及的零结果。
英文摘要
Quadrupolar hyperfine spectroscopies, including Nuclear Quadrupole Resonance (NQR), Nuclear Magnetic Resonance (NMR), Time-Differential Perturbed Angular Correlations (TDPAC), and Mössbauer spectroscopy, have long used the electric field gradient (EFG) at a nuclear site as an empirical proxy for order parameters in structural and electronic phase transitions, yet the EFG has never been systematically incorporated into Landau theory. Here we provide that framework. The EFG is an exactly traceless, symmetric rank-2 tensor defined at a crystallographic site. Decomposing it under the site-symmetry group and inducing over the Wyckoff orbit determines its irreducible representation content in the parent space group. Whenever the representation of a zone-center transition is present, symmetry requires the corresponding EFG combination to vanish above the transition and grow linearly with the order parameter below it, inheriting its critical exponent, sign, and domain structure. Symmetry-orthogonal channels are quadratic, recovering the classic empirical relations. This yields a falsifiable classification of primary, secondary, and forbidden EFG responses. The framework is validated against five decades of quadrupolar experiments, reproducing critical exponents, first-order discontinuities, and a null result, and by first-principles calculations satisfying the predicted parity and zero theorems. All-electron calculations for $α$-quartz confirm the orbit-selection rule: only the EFG combination transforming as the soft-mode irreducible representation varies linearly with distortion amplitude, while the orthogonal combination remains suppressed by two orders of magnitude. A proposed study of the $^{75}$As site across the nematic transition in BaFe$_2$As$_2$ provides five falsifiable predictions, including a previously unstated null result.
Comments23 pages (15 main article and 8 pages supplementary materials), 9 figures. In the process of submission to Newton Journal
