各向异性量子材料中的共振扭转磁学
Resonant torsion magnetometry in anisotropic quantum materials
摘要：
量子材料的不寻常行为通常源于其有效的低维物理，这反映了自旋和电荷自由度的潜在各向异性。转矩磁力测定法是一种高灵敏度的技术，用于直接量化量子材料中的各向异性，例如层状高T $_c$超导体、各向异性量子自旋液体和拓扑绝缘体的表面态。在这里，我们引入了磁致系数$k=\partial^2 F/\partial θ^2$，自由能F相对于样品与外加磁场之间的角度$θ$的二阶导数，并报告了一种简单有效的实验检测方法。将亚$μ$ g微晶放置在市售原子力显微镜悬臂梁的尖端，我们表明，$k$可以定量推断，从磁场下的共振频率的偏移。虽然与磁转矩$τ=\partial F/\partial θ$相关，但$k$扮演转矩敏感性的角色，因此提供了对各向异性材料的独特见解，类似于磁化和磁化率之间的差异。热力学系数$k$在二级相变时是不连续的，并与比热和磁化率服从Eklfest关系。我们将这种简单而定量的方法应用于Weyl半金属NbP和自旋液体候选者RuCl $_3$的示例性情况，但它在量子材料研究中具有广泛的适用性。
英文摘要：
Unusual behavior of quantum materials commonly arises from their effective low-dimensional physics, which reflects the underlying anisotropy in the spin and charge degrees of freedom. Torque magnetometry is a highly sensitive technique to directly quantify the anisotropy in quantum materials, such as the layered high-T$_c$ superconductors, anisotropic quantum spin-liquids, and the surface states of topological insulators. Here we introduce the magnetotropic coefficient $k=\partial^2 F/\partial θ^2$, the second derivative of the free energy F with respect to the angle $θ$ between the sample and the applied magnetic field, and report a simple and effective method to experimentally detect it. A sub-$μ$g crystallite is placed at the tip of a commercially available atomic force microscopy cantilever, and we show that $k$ can be quantitatively inferred from a shift in the resonant frequency under magnetic field. While related to the magnetic torque $τ=\partial F/\partial θ$, $k$ takes the role of torque susceptibility, and thus provides distinct insights into anisotropic materials akin to the difference between magnetization and magnetic susceptibility. The thermodynamic coefficient $k$ is discontinuous at second-order phase transitions and subject to Ehrenfest relations with the specific heat and magnetic susceptibility. We apply this simple yet quantitative method on the exemplary cases of the Weyl-semimetal NbP and the spin-liquid candidate RuCl$_3$, yet it is broadly applicable in quantum materials research.
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