NiGa$_2$S$_4$ is a triangular lattice S=1 system with strong two-dimensionality of the lattice, actively discussed as a candidate to host spin-nematic order brought about by strong quadrupole coupling. Using Raman scattering spectroscopy we identify a phonon of E$_g$ symmetry which can modulate magnetic exchange $J_1$ and produce quadrupole coupling. Additionally, our Raman scattering results demonstrate a loss of local inversion symmetry on cooling, which we associate with sulfur vacancies. This will lead to disordered Dzyaloshinskii-Moriya interactions, which can prevent long range magnetic order. Using magnetic Raman scattering response we identify 160~K as a temperature of an upturn of magnetic correlations. The temperature below 160~K, but above 50~K where antiferromagnetic magnetic start to increase, is a candidate for spin-nematic regime.
Coherent Behavior and Nonmagnetic Impurity Effects of the Spin Disordered State in NiGa$_2$S$_4$
通过对Ni $_{1-x}$ Zn $_x$ Ga $_2$ S $_4$（0.0 \le x \le 0.3）的磁性和热测量，研究了三角形反铁磁体NiGa $_2$ S $_4$中自旋无序态的非磁杂质效应.仅1%的取代就足以强烈抑制在自旋无序态中观察到的相干性。然而，这种抑制并不完全，依赖于T^2的比热及其随外斯温度的标度行为的鲁棒特征表明存在相干的南武-戈德斯通模。既没有传统的磁序，也没有自旋冻结，这表明基态存在一种新的对称性破缺。
Spin dependent impurity effects in the 2D frustrated magnetism of NiGa$_2$S$_4$
研究了杂质对三角形反铁磁体Ni $_{1-x}M_x$ Ga $_2$ S $_4$（$M=$ Mn、Fe、Co和Zn）的影响。二维冻结自旋无序态的NiGa $_2$ S $_4$对Zn $^{2+}$（$S=0$）和Heisenberg Fe $^{2+}$（$S=2$）自旋的取代是稳定的，并表现出$T^2$依赖的磁比热，由外斯温度标度。相反，用具有Ising样各向异性的Co $^{2+}$（$S=3/2$）自旋和Heisenberg Mn $^{2+}$（$S=5/2$）自旋取代诱导常规自旋玻璃相。从这些比较中，它表明，海森堡自旋的整数大小是重要的，以稳定在冻结自旋无序态中观察到的二维相干行为。
We theoretically study low-temperature properties of the antiferromagnetic Heisenberg model with half-integer spin $S$ on the Kagome lattice with large trimerization. We have derived a low-energy effective model for general $S$ in terms of spin and nematicity operators in triangular units, and studied their low-temperature correlations for S=3/2 by classical Monte Carlo simulations. The previous study for the S=1/2 case [M. Ferrero et al., Phys. Rev. B 68, 214431 (2003)] reported a spin liquid state at low temperatures driven by a glassy behavior of isolated dimers and trimers of nematicities.…
We investigate the effect of spin-lattice coupling (SLC) on the magnetic properties of the classical kagome-lattice Heisenberg antiferromagnet (KHAF) using improved Monte Carlo updates. The lattice modes are represented by Einstein site phonons, which introduce effective further-neighbor spin interactions in addition to the nearest-neighbor biquadratic interactions. In the weak SLC, the macroscopically degenerate coplanar ground state remains at zero field, while a $\sqrt{3} \times \sqrt{3}$ ordered phase accompanied by a 1/3-magnetization plateau appears in external magnetic fields. In the st…
Tunable chiral and nematic states in the triple-Q antiferromagnet Co$_{1/3}$TaS$_2$
National High Magnetic Field Laboratory, Los Alamos National Lab（国家高磁场实验室，洛斯阿拉莫斯国家实验室）；Materials Science and Technology Division, Oak Ridge National Laboratory（橡树岭国家实验室材料科学与技术部）；Department of Physics and Astronomy, Seoul National University（首尔大学物理与天文学系）；Department of Physics and Astronomy, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校物理与天文学系）；Shull Wollan Center—A Joint Institute for Neutron Sciences, Oak Ridge National Laboratory（橡树岭国家实验室舒尔-沃兰中子科学联合研究所）；Institute of Applied Physics, Seoul National University（首尔大学应用物理研究所）
Interrelationships between nematicity, antiferromagnetic spin fluctuations and superconductivity: Role of hotspots in FeSe$_{1-x}$S$_{x}$ revealed by high pressure $^{77}$Se NMR study
Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, most prominently in the tetragonal Fe-based superconductors where the parent state is four-fold symmetric. In this case the nematic director takes on only two directions, and the order parameter in such "Ising-nematic" systems is a simple scalar. Here, using a novel spatially-resolved optical polarimetry technique, we show that a qualitatively…
The sulfur substituted FeSe system, FeSe$_{1-x}$S$_{x}$, provides a versatile platform for studying the relationship between nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on FeSe$_{0.91}$S$_{0.09}$, we established the pressure($p$)-temperature($T$) phase diagram in which the nematic state is suppressed with pressure showing a nematic quantum phase transition (QPT) around $p$ = 0.5 GPa, two SC regions, separated by the QPT, appear and antiferromagnetic (AFM) phase emerges above $\sim$3.3 GPa. From the…
Spin Fluctuations from Hertz to Terahertz on a Triangular Lattice
利用超高分辨非弹性中子散射、μ子自旋弛豫、交流和非线性磁化率测量研究了三角晶格反铁磁体NiGa $_2$ S $_4$的13个十年（$10^{-13}-1$ ~sec）的时间磁关联.与短程的{ \it空间}关联不同，{ \it时间}关联的温度依赖性显示出明显的异常。自旋涨落率在向$T^{\ast}=8.5$ ~K冷却时急剧下降，但微秒时间尺度上的涨落则在4 K $<T\le T^{\ast}$的异常动力学区域中持续存在。由于这个时间尺度超过了单网站动态的6个数量级，这些波动承担的证据紧急程度的自由度内的短程相关的无公度态的NiGa $_2$ S $_4$。
We report the properties of a triangular lattice iron-chalcogenide antiferromagnet FeAl$_{2}$Se$_{4}$. The spin susceptibility reveals a significant antiferromagnetic interaction with a Curie-Weiss temperature Θ$_{CW}$ ~ -200K and a spin-2 local moment. Despite a large spin and a large |Θ$_{CW}$|, the low-temperature behaviors are incompatible with conventional classical magnets. No long-range order is detected down to 0.4K. Similar to the well-known spin-1 magnet NiGa$_{2}$S$_{4}$, the specific heat of FeAl$_{2}$Se$_{4}$ exhibits an unusual double-peak structure and a T$^{2}$ power law at low…
Strong interplay of spin and charge/orbital degrees of freedom is the fundamental characteristic of the iron-based superconductors (FeSCs), which leads to the emergence of a nematic state as a rule in the vicinity of the antiferromagnetic state. Despite intense debate for many years, however, whether nematicity is driven by spin or orbital fluctuations remains unsettled. Here, by use of transport, magnetization, and $^{75}$As nuclear magnetic resonance (NMR) measurements, we show a striking transformation of the relationship between nematicity and spin fluctuations (SFs) in Na$_{1-x}$Li$_x$FeA…
High magnetic fields induce a pronounced in-plane electronic anisotropy in the tetragonal antiferromagnetic metal CeRhIn$_{5}$ at $H^{*} \gtrsim 30$ T for fields $\simeq 20^{\mathrm{o}}$ off the $c$-axis. Here we investigate the response of the underlying crystal lattice in magnetic fields to $45$ T via high-resolution dilatometry. Within the antiferromagnetic phase of CeRhIn$_{5}$, a finite magnetic field component in the tetragonal $ab$-plane explicitly breaks the tetragonal ($C_{4}$) symmetry of the lattice well below $H^{*}$ revealing a finite nematic susceptibility at low fields. A modest…
Spin-Orbit Interactions and the Nematicity Observed in the Fe-Based Superconductors
用高分辨角分辨光电子能谱学研究了FeTe $_{0.5}$ Se $_{0.5}$在布里渊区中心附近的电子能带结构。观察到$α_{1}$和$α_{2}$带的一致分离，其中$α_{1}$带几乎不依赖于$k_{z}$。第一性原理计算表明，Fe原子间的反铁磁耦合和杂化诱导的自旋轨道效应提高了Fe $d_{xz}$和$d_{yz}$轨道在区域中心的简并度，导致轨道有序化.这些实验和计算结果为铁基超导体中观察到的向列性提供了自然的微观基础。
Electric Transport of a Single Crystal Iron Chalcogenide FeSe Superconductor: Evidence of Symmetry Breakdown Nematicity and Additional Ultrafast Dirac cone-Like Carriers
在FeAs超导体中普遍观察到SDW反铁磁（SDW-AF）低温相变，AF自旋涨落对超导配对机制起着重要作用.然而，在FeSe超导体中没有观察到类似的磁相变，这引起了相当多的讨论。我们报告的内在电子状态的铁硒阐明运输测量下磁场使用高品质的单晶。一个迁移率谱分析，从头算方法，不作假设的多载流子系统中的输运参数，提供了非常重要和明确的证据，另一个隐藏的顺序，最有可能的对称性破缺从四碳C4对称性的C2对称向列性与选择性d-轨道分裂，存在于超导FeSe的情况下以外的AF磁序自旋涨落。FeSe中的本征低温相处于几乎补偿的半金属态，但另外伴随有狄拉克锥状超快电子$\sim$ 10 $^4$ cm $^2$（VS）$^{-1}$作为少数载流子。
Electronic nematicity is an important order in most iron-based superconductors, and FeSe represents a unique example, in which nematicity disentangles from spin ordering. It is commonly perceived that this property arises from strong electronic correlation, which can not be properly captured by density functional theory (DFT). Here, we show that by properly considering the paramagnetic condition and carefully searching the energy landscape with symmetry-preconditioned wavefunctions, two nematic solutions stand out at either the DFT+$U$ or hybrid functional level, both of which are lower in ene…
We report a $^{75}$As nuclear magnetic resonance study in LaFeAsO single crystals, which undergoes nematic and antiferromagnetic transitions at $T_\text{nem}\sim 156$ K and $T_N \sim 138$ K, respectively. Below $T_\text{nem}$, the $^{75}$As spectrum splits sharply into two for an external magnetic field parallel to the orthorhombic $a$ or $b$ axis in the FeAs planes. Our analysis of the data demonstrates that the NMR line splitting arises from an electronically driven rotational symmetry breaking. The $^{75}$As spin-lattice relaxation rate as a function of temperature shows that spin fluctuati…
Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-$d$ and O-$p$ orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the $p$-orbitals inevitably generate a biquadratic coupling between the spins of the $d$-orbitals. The key point revealed by our classical Monte Carlo simu…
Two ordering states, antiferromagnetism and nematicity, have been observed in most iron-based superconductors (SCs). In contrast to those SCs, the newly discovered SC CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ exhibits an antiferromagnetic (AFM) state, called hedgehog spin-vortex crystal structure, without nematic order, providing the opportunity for the investigation into the relationship between spin fluctuations and SC without any effects of nematic fluctuations. Our $^{75}$As nuclear magnetic resonance studies on CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (0$\le x\le$ 0.049) revealed that CaKFe$_4$As$_4$ is loc…
Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
我们研究了二维量子三角海森堡反铁磁体在零温量子相变附近的低温性质。利用由$SO(3)\times SO(2)/SO(2)$矩阵Ginzburg-Landau-Wilson模型描述的有效场论和非微扰重整化群方法，我们阐明了量子涨落和热涨落如何影响系统在参数区域的长波行为，在该区域系统表现出涨落驱动的一级跃迁到长程有序态.结果表明，在有限温度下，从量子$ϕ^6$理论到重正化二维经典非线性西格玛模型区域出现了交叉，在这个交叉区域中，具有线性色散的无质量涨落模和自旋波支配着低能物理.我们的结果与最近对二维三角形海森堡自旋系统NiGa $_2$ S $_4$的实验观察符合得很好.
CeRhIn$_5$ provides a textbook example of quantum criticality in a heavy fermion system: Pressure suppresses local-moment antiferromagnetic (AFM) order and induces superconductivity in a dome around the associated quantum critical point (QCP) near $p_{c} \approx 23\,$kbar. Strong magnetic fields also suppress the AFM order at a field-induced QCP at $B_{\rm c}\approx 50\,$T. In its vicinity, a nematic phase at $B^*\approx 28\,$T characterized by a large in-plane resistivity anisotropy emerges. Here, we directly investigate the interrelation between these phenomena via magnetoresistivity measure…
Elastoresistivity Signatures of Nematic Fluctuations in Layered Antiferromagnet CoTa3S6
Division of Physics, Mathematics and Astronomy, California Institute of Technology（加州理工学院物理、数学与天文学部）；Institute of Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Department of Physics and Astronomy, University of Utah（犹他大学物理与天文学系）
Recent studies in heavily hole-doped iron-based superconductor RbFe$_2$As$_2$ have suggested the emergence of novel electronic nematicity directed along the Fe-As direction, 45$^\circ$ rotated from the usual nematicity ubiquitously found in BaFe$_2$As$_2$ and related materials. This motivates us to study the physical properties of Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$, details of which remain largely unexplored. Here we report on the normal-state charge transport in Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ superconductors by using high-quality single crystals in the range of Rb concentration $0.14\le x…
Understanding the interplay between nematicity, magnetism and superconductivity is pivotal for elucidating the physics of iron-based superconductors. Here we use neutron scattering to probe magnetic and nematic orders throughout the phase diagram of NaFe$_{1-x}$Ni$_x$As, finding that while both static antiferromagnetic and nematic orders compete with superconductivity, the onset temperatures for these two orders remain well-separated approaching the putative quantum critical points. We uncover local orthorhombic distortions that persist well above the tetragonal-to-orthorhombic structural tran…
The ground state of the spin$-1/2$ kagome antiferromagnet remains uncertain despite decades of active research. Here we step aside from this debated question to address the ground-state nature of a related, and potentially just as rich, system made of corner-sharing triangles: the square-kagome lattice (SKL). Our work is motivated by the recent synthesis of a distorted SKL compound mentioned in [Morita & Tohyama, J. Phys. Soc. Japan 87, 043704 (2018)]. We have studied its spin$-1/2$ $J_{1}$-$J_{2}$ phase diagram with an unrestricted Schwinger boson mean-field theory (SBMFT). We show that, in a…
We perform a two-loop renormalization group (RG) analysis of a 2D effective multiband model, which is relevant for describing the low-energy properties of some iron-chalcogenide superconducting materials. Crucial ingredients in this analysis are the calculation of higher-order contributions in the RG scheme that go beyond the widely-used parquet approximation and the consequent inclusion of nontrivial self-energy effects of the model that yield an anisotropic renormalization of the quasiparticle weight in the system. The motivation of our work is the experimental discovery by Sprau et al. (201…
