我们报道了YbRu $_2$ Ge $_2$单晶的拉曼散射结果，以探索声子和晶体场（CF）激发。这种重费米子金属被认为在T $_0$ =10 K以下进入铁四极（FQ）相。四重CF势将Yb $^{3+}$ $^2F_{7/2}$基态多重峰分裂为两个$Γ_6$和两个$Γ_7$ Kramers双重峰。我们建立了如下的CF能级结构：一个$Γ_6$基态，两个$Γ_7$态分别位于2 cm $^{-1}$和95 cm $^{-1}$，另一个$Γ_6$态位于239 cm $^{-1}$ . CF基态和第一激发态之间的$\sim$ 2 cm $^{-1}$分离与先前提出的准四重CF基态一致。最低能量的CF过渡的强度显着增加冷却，表明耦合的CF激发以上T $_0$的四极波动。通过对称性分析，我们认为FQ阶具有B $_{1g}$对称性.此外，温度依赖性研究的四个拉曼活性声子模式表明，A $_{1g}$和一个E $_{g}$模式的强度显着增加冷却，这是由近共振耦合这两个声子模式和CF跃迁。
英文摘要：
We report Raman-scattering results of YbRu$_2$Ge$_2$ single crystals to explore the phononic and crystal-field (CF) excitations. This heavy-fermion metal is suggested to enter a ferroquadrupolar (FQ) phase below T$_0$=10 K. The tetragonal CF potential splits the Yb$^{3+}$ $^2F_{7/2}$ ground multiplet into two $Γ_6$ and two $Γ_7$ Kramers doublets. We establish the following CF level scheme of the ground multiplet: a $Γ_6$ ground state, with the two $Γ_7$ states at 2 cm$^{-1}$, 95 cm$^{-1}$ and the other $Γ_6$ state at 239 cm$^{-1}$. The $\sim$2 cm$^{-1}$ separation between the CF ground and first excited states is in agreement with the previously proposed quasi-quartet CF ground state. The intensity of the lowest-energy CF transition remarkably increases on cooling, indicating a coupling of this CF excitation to the quadrupolar fluctuations above T$_0$. From symmetry analysis, we suggest that the FQ order has B$_{1g}$ symmetry. Moreover, temperature-dependent study of four Raman-active phonon modes shows that the intensities of the A$_{1g}$ and one E$_{g}$ modes increase significantly on cooling, which is explained by a near-resonant coupling between these two phonon modes and CF transitions.
Quantum spin liquid and electric quadrupolar states of single crystal Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$
通过比热测量研究了阻挫烧绿石氧化物Tb $_{2+x}$ Ti $_{2-x}$ O $_{7+y}$的基态，该基态灵敏地依赖于小的偏离化学计量参数$x$.用标准浮区法生长的Tb $_{2+x}$ Ti $_{2-x}$ O $_{7+y}$单晶具有浓度（$x$）梯度。这种偏离化学计量参数是通过精确测量从晶体梨晶切割的小样品的晶格常数来确定的。比热表明，在$x$ - $T$相图中，电四极态的相界具有圆顶结构，在约$x = 0.01$处具有最高的$T_{\text{c}} \simeq 0.5$ K。该相图表明Tb $_{2+x}$ Ti $_{2-x}$ O $_{7+y}$的U（1）量子自旋液体态存在于$x<x_{\text{c}} \simeq -0.0025 $范围内，其通过一阶相变线$x=x_{\text{c}}$与四极态分离。
Hidden non-Fermi liquid behavior due to crystal field quartet
利用数值重整化群方法，研究了具有磁性和非磁性（四极）交换耦合的晶体场四重态基态的近藤模型.我们专注于依赖于单重激发态耦合到四重态，这大大减少了非磁耦合和驱动器的非费米液体行为中观察到的计算四极磁化率的局部效应。从非费米液体状态到费米液体状态的交叉的特征在于小的能量尺度对非磁耦合非常敏感。另一方面，在磁化率中观察到的近藤温度不太敏感。这两种交换耦合的不同晶场依赖性可能与Ce $_x$ La $_{1-x}$ B $_6$中四极和磁有序温度的不同$x$依赖性有关。
The cubic compound PrTi$_2$Al$_{20}$ is a quadrupolar Kondo lattice system that exhibits quadrupolar ordering due to the non-Kramers $Γ_3$ ground doublet and has strong hybridization between $4f$ and conduction electrons. Our study using high-purity single crystal reveals that PrTi$_2$Al$_{20}$ exhibits type-II superconductivity at $T_{\rm c} = 200$ mK in the nonmagnetic ferroquadrupolar state. The superconducting critical temperature and field phase diagram suggests moderately enhanced effective mass of $m^*/m_0 \sim 16$.
宏观研究中早些时候报道的PrTi $_2$ Al $_{20}$中非磁性相变的起源已使用弹性和非弹性中子散射技术在微观上得到证实。光谱表明，晶体电场基态是一个非磁性的$Γ_3$双峰，而激发态是两个三重态（$Γ_4$和$Γ_5$）和一个单重态（$Γ_1$）。外磁场下的衍射实验表明，非磁跃迁确实是铁四极有序的，这是基态二重态简并度协同去除的结果。因此，可以得出结论，PrTi $_2$ Al $_{20}$是另一个罕见的例子Pr化合物表现出非磁性四极顺序。
Vibronic collapse of ordered quadrupolar ice in the pyrochore magnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$
University of Geneva（日内瓦大学）；Université Grenoble Alpes, CNRS, Institut Néel（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，内耳研究所）；Synchrotron SOLEIL（索雷尔同步辐射中心）；ICMMO, Université Paris-Saclay, CNRS（有机与无机分子和材料化学研究所，巴黎萨克雷大学，法国国家科学研究中心）；Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）
Quadrupolar Singlet Ground State of Praseodymium in a Modulated Pyrochlore
用中子散射和EXAFS研究了Pr $_{2-x}$ Bi $_x$ Ru $_2$ O $_7$的结构和磁性. Pr的基态近似为二重态，第一激发态为单重态。该整体晶场能级方案类似于本文也报道的金属Pr $_2$ Ir $_2$ O $_7$。虽然B位（Ru）是完全有序的，但A位（Pr/Bi）的情况并非如此。Pr-O2键长的分布表明Pr环境即使对于$x=0$也是不均匀的。表面上由于Bi $^{3+}$上的6s孤对，Bi环境高度无序。相应地，我们发现非Kramers双重基态简并，否则预计Pr的烧绿石结构被解除，从而产生一个四极单基态与空间变化的能隙。对于$x=0$，低于T $_N$，Ru亚晶格反铁磁有序，传播矢量\textbf{k} =（0，0，0），对于Y $_2$ Ru $_2$ O $_7$。没有秩序与Pr子晶格观察到下降到100 mK。Pr $_{2-x}$ Bi $_x$ Ru $_2$ O $_7$的低能磁响应具有与Pr准二重态基态的不均匀分裂相关的宽谱磁激发。对于$x=0$（$x=0.97$），光谱与温度相关（无关）。看来与Bi合金化相关的无序增强了不均匀Pr晶场能级分裂，使得位间相互作用对于$x=0.97$变得无关。A位的结构复杂性可以反映在B位钌在Néel相中的滞后均匀磁化中。
Spontaneous lattice distortion and crystal field effects in HoB4
Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Hochfeld-Magnetlabor Dresden (HLD-EMFL) and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿强磁场实验室（HLD-EMFL）与维尔茨堡-德累斯顿卓越集群ct.qmat，亥姆霍兹德累斯顿-罗斯多夫中心）；Department of Condensed Matter Physics, Charles University（查理大学凝聚态物理系）；Department of Quantum Matter, AdSE, Hiroshima University（广岛大学量子物质研究中心（AdSE））；Department of Physics, University of Warwick（华威大学物理系）；National Physical Laboratory（英国国家物理实验室）；Institut fur Festkörper- und Materialphysik, TU Dresden（德累斯顿工业大学固体与材料物理研究所）
Theory of Distinct Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs: the Specific Role of Alkalis
AC 60的聚合物相形成不同的晶体结构，其特征在于（C60-）n链的相互取向。我们表明，链之间的直接电四极相互作用总是有利于正交结构Pmnn交替链取向。然而，特定的四极极化率的碱金属离子导致一个间接的链间耦合，有利于单斜结构I2/m具有相等的链取向。直接和间接相互作用之间的竞争解释了KC 60与RbC 60、CsC 60之间的结构差异。
Quantum magnets with spin $J=2$, which arise in spin-orbit coupled Mott insulators, can potentially display multipolar orders. We carry out an exact diagonalization study of a simple octahedral crystal field Hamiltonian for two electrons, incorporating spin-orbit coupling (SOC) and interactions, finding that either explicitly including the $e_g$ orbitals, or going beyond the rotationally invariant Coulomb interaction within the $t_{2g}$ sector, causes a degeneracy breaking of the $J\!=\!2$ level degeneracy. This can lead to a low-lying non-Kramers doublet carrying quadrupolar and octupolar mom…
We use complementary optical spectroscopy methods to directly measure the lowest crystal-field energies of the rare-earth quantum magnet LiY$_{1-x}$Ho$_{x}$F$_{4}$, including their hyperfine splittings, with more than 10 times higher resolution than previous work. We are able to observe energy level splittings due to the $^6\mathrm{Li}$ and $^7\mathrm{Li}$ isotopes, as well as non-equidistantly spaced hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal field parameters and extract the dipolar and quadrupolar hyperfine constants ${A_…
Excitonic insulator is a coherent electronic phase that results from the formation of a macroscopic population of bound particle-hole pairs - excitons. With only a few candidate materials known, the collective excitonic behavior is challenging to observe, being obscured by crystalline lattice effects. Here we use polarization-resolved Raman spectroscopy to reveal the quadrupolar excitonic mode in the candidate zero-gap semiconductor Ta$_2$NiSe$_5$ disentangling it from the lattice phonons. The excitonic mode pronouncedly softens close to the phase transition, showing its electronic character, …
Tunable inter-bilayer magnetic correlations and candidate multipolar physics in the van der Waals oxyhalides DyOCl, DyOBr, and DyOI
School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院）；Department of Physics and Astronomy, Louisiana State University（路易斯安那州立大学物理与天文系）；School of Chemistry and Biochemistry, Georgia Institute of Technology（佐治亚理工学院化学与生物化学学院）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）；NIST Center for Neutron Research（美国国家标准与技术研究院中子研究中心）
