Observation of three-state nematicity in the triangular lattice antiferromagnet Fe$_{1/3}$ NbS$_2$
Arielle Little, Changmin Lee, Caolan John, Spencer Doyle, Eran Maniv, Nityan L. Nair, Wenqin Chen, Dylan Rees, Jörn W. F. Venderbos, Rafael Fernandes, James G. … 展开作者
Arielle Little, Changmin Lee, Caolan John, Spencer Doyle, Eran Maniv, Nityan L. Nair, Wenqin Chen, Dylan Rees, Jörn W. F. Venderbos, Rafael Fernandes, James G. Analytis, Joseph Orenstein
备注：
The main text is 16 pages, including 5 figures and references. Supplementary information is appended at the end of the article
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 distinct nematic state arises in the triangular lattice antiferromagnet Fe$_{1/3}$NbS$_2$. The crucial difference is that the nematic order on the triangular lattice is a Z$_3$, or three-state Potts-nematic order parameter. As a consequence, the anisotropy axes of response functions such as the resistivity tensor can be continuously re-oriented by external perturbations. This discovery provides insight into realizing devices that exploit analogies with nematic liquid crystals.
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…
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 …
The Dzyaloshinskii-Moriya (DM) interaction is present in the transition metal dichalcogenides (TMDC) magnets of form $M_{1/3}T$S$_{2}$ ($M$ $=$ 3d transition metal, $T$ $\in$ {Nb, Ta}), given that the intercalants $M$ form $\sqrt{3}\times\sqrt{3}$ superlattices within the structure of the parent materials $T$S$_2$ and break the centrosymmetry. Competition between the DM and ferromagnetic exchange interactions in these systems has been shown to stabilize a topological defect known as a chiral soliton in select intercalated TMDCs, initiating interest both in terms of fundamental physics and the …
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$3.3 GPa. From the…
A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature ($T_{\rm c}$). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving nonmagnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe overlap with each other, the effects of two orders on superconductivity remain perplexing. Here we construct the three-dimensional electronic phase diagram, temperature ($T$) against pressure ($P$) and isovalent S-su…
Recent finding of an {\it unusual} in-plane resistivity anisotropy in the underdoped 122-family at high temperature ($T$) suggests an orbital nematic (ON) order, posing a challenge to extant theories. The {\it sign} of the anisotropy contradicts expectations from weakly correlated as well as pure spin-only nematic views. Here, we show how such an ON order with accompanying structural distortion arises from {\it residual}, intersite and inter-orbital two-body interactions in an incoherent "bad metal" close to Mottness. Enhancement of orbital-selective incoherence is shown to be necessary for un…
Tunable chiral and nematic states in the triple-Q antiferromagnet Co$_{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）
We present $^{77}$Se-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\rm s}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperat…
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…
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…
The nematic order (nematicity) is considered one of the essential ingredients to understand the mechanism of Fe-based superconductivity. In most Fe-based superconductors (pnictides), nematic order is reasonably close to the antiferromagnetic order. In FeSe, in contrast, a nematic order emerges below the structure phase transition at T_s = 90 K with no magnetic order. The case of FeSe is of paramount importance to a universal picture of Fe-based superconductors. The polarized ultrafast spectroscopy provides a tool to probe simultaneously the electronic structure and the magnetic interactions th…
We perform high-field magnetization measurements on the triangular lattice antiferromagnet Fe$_{1/3}$NbS$_2$. We observe a plateau in the magnetization centered at approximately half the saturation magnetization over a wide range of temperature and magnetic field. From density functional theory calculations, we determine a likely set of magnetic exchange constants. Incorporating these constants into a minimal Hamiltonian model of our material, we find that the plateau and of the $Z_3$ symmetry breaking ground state both arise from interplane and intraplane antiferromagnetic interactions acting…
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…
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…
To understand the role of electronic nematic order in the interplay between s- and d-wave particle-particle or particle-hole condensate states, relations between various s- and d-wave order parameters are studied. We find that the nematic operator transforms two independent six-dimensional vectors. The d-wave superconducting, d-density wave, and antiferromagnetic orders are organized into one vector, and the s-wave superconducting, charge density wave, and spin-triplet d-density wave orders into the other vector. Each vector acts as a superspin and transforms under the action of SO(6) where ch…
In common with other iron-based high temperature superconductors, FeSe exhibits a transition to a ``nematic'' phase below 90Kelvin in which the crystal rotation symmetry is spontaneously broken. However, the absence of strong low-frequency magnetic fluctuations near or above the transition has been interpreted as implying the primacy of orbital ordering. In contrast, we establish that quantum fluctuations of spin-1 local moments with strongly frustrated exchange interactions can lead to a nematic quantum paramagnetic phase consistent with the observations in FeSe. We show that this phase is a …
Magnetic order and excitations in the magnetically intercalated van der Waals material Cr$_{\frac{1}{4}}$NbSe$_2$
The Institute for Solid State Physics, University of Tokyo（东京大学固体离子体研究所）；Department of Applied Physics, University of Tokyo（东京大学应用物理系）；Institute of Materials Structure Science, High Energy Accelerator Research Organization（高能加速器研究机构物质结构科学研究所）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）；College of Engineering, Shibaura Institute of Technology（芝浦工业大学工程学院）；Research Center for Advanced Science and Technology, University of Tokyo（东京大学先端科学技术研究中心）
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…
An SDW antiferromagnetic (SDW-AF) low temperature phase transition is generally observe and the AF spin fluctuations are considered to play an important role for the superconductivity paring mechanism in FeAs superconductors. However, a similar magnetic phase transition is not observed in FeSe superconductors, which has caused considerable discussion. We report on the intrinsic electronic states of FeSe as elucidated by transport measurements under magnetic fields using a high quality single crystal. A mobility spectrum analysis, an ab initio method that does not make assumptions on the transp…
We analyze density-wave and Pomeranchuk orders in twisted bilayer graphene. This compliments our earlier analysis of the pairing instabilities. We assume that near half-filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole …
The importance of antiferromagnetic fluctuations are widely acknowledged in most unconventional superconductors. In addition, cuprates and iron pnictides often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. However, these nematic correlations are intertwined with antiferromagnetic or charge orders, preventing us to identify the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systemati…
Elucidating the microscopic origin of nematic order in iron-based superconducting materials is important because the interactions that drive nematic order may also mediate the Cooper pairing. Nematic order breaks fourfold rotational symmetry in the iron plane, which is believed to be driven by either orbital or spin degrees of freedom. However, as the nematic phase often develops at a temperature just above or coincides with a stripe magnetic phase transition, experimentally determining the dominant driving force of nematic order is difficult. Here, we use neutron scattering to study structura…
The effects of Sr doping on the structural properties of Na$_{2}$BaCo(PO$_{4}$)$_{2}$, a spin-1/2 triangular-lattice antiferromagnet as a quantum spin liquid candidate, are investigated by complementary x-ray and neutron powder diffraction measurements. It is found that in Na$_{2}$Ba$_{1-x}$Sr$_{x}$Co(PO$_{4}$)$_{2}$ (NBSCPO), the trigonal phase (space group $\mathit{P}$$\bar{3}$$\mathit{m}$1) with a perfect triangular lattice of Co$^{2+}$ ions is structurally stable when the doping level of Sr is below 30% ($\mathit{x}$ $\le$ 0.3), while a pure monoclinic phase (space group $\mathit{P}$2$_{1}…
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）
Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) on FeSe and iron pnictide families of iron-based superconductors, we have studied the orbital nematic order and its interplay with antiferromagnetism within the two-orbital Hubbard model. We used random phase approximation (RPA) to calculate the dependence of the orbital and magnetic susceptibilities on the strength of interactions and electron density (doping). To account for strong electron correlations not captured by RPA, we further employed non-perturbative variational cluster approximation (VCA) capable of capturin…
Electronic nematics are exotic states of matter where electronic interactions break a rotational symmetry of the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals. Intriguingly such phases appear in the copper- and iron-based superconductors, and their role in establishing high-temperature superconductivity remains an open question. Nematicity may take an active part, cooperating or competing with superconductivity, or may appear accidentally in such systems. Here we present experimental evidence for a phase of nematic character …
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 $0.14\le x…
We provide evidence that spin ferroquadrupolar (FQ) order is the likely ground state in the nonmagnetic nematic phase of stoichiometric FeSe. By studying the variational mean-field phase diagram of a bilinear-biquadratic Heisenberg model up to the 2nd nearest neighbor, we find the FQ phase in close proximity to the columnar antiferromagnet commonly realized in iron-based superconductors; the stability of FQ phase is further verified by the density matrix renormalization group. The dynamical spin structure factor in the FQ state is calculated with flavor-wave theory, which yields a qualitativel…
Intrinsic translational symmetry-breaking charge stripes in underdoped iron pnictides
Tsinghua University（清华大学）；Southern University of Science and Technology（南方科技大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
The ground state of the spin$-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…
The in-plane resistivity anisotropy has been studied with the Montgomery method on two detwinned parent compounds of the iron-based superconductors, NaFeAs and FeTe. For NaFeAs, the resistivity in the antiferromagnetic (AFM) direction is smaller than that in the ferromagnetic (FM) direction, similar to that observed in BaFe2As2 before. While for FeTe, the resistivity in the AFM direction is larger than that in the FM direction. We show that these two opposite resistivity anisotropy behaviors could be attributed to the strong Hund's rule coupling effects: while the iron pnictides are in the iti…
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…
