We expose the theoretical mechanisms underlying disorder-induced nematicity in systems exhibiting strong fluctuations or ordering in the nematic channel. Our analysis consists of a symmetry-based Ginzburg-Landau approach and associated microscopic calculations. We show that a single featureless point-like impurity induces nematicity locally, already above the critical nematic transition temperature. The persistence of fourfold rotational symmetry constrains the resulting disorder-induced nematicity to be inhomogeneous and spatially average to zero. Going beyond the single impurity case, we discuss the effects of finite disorder concentrations on the appearance of nematicity. We identify the conditions that allow disorder to enhance the nematic transition temperature, and we provide a concrete example. The presented theoretical results can explain a large series of recent experimental discoveries of disorder-induced nematic order in iron-based superconductors.
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 have performed high-resolution angle-resolved photoemission spectroscopy on FeSe superconductor (Tc ~ 8 K), which exhibits a tetragonal-to-orthorhombic structural transition at Ts ~ 90 K. At low temperature we found splitting of the energy bands as large as 50 meV at the M point in the Brillouin zone, likely caused by the formation of electronically driven nematic states. This band splitting persists up to T ~ 110 K, slightly above Ts, suggesting that the structural transition is triggered by the electronic nematicity. We have also revealed that at low temperature the band splitting gives r…
We review the recent developments in electronic Raman scattering measurements of charge nematic fluctuations in iron-based superconductors. A simple theoretical framework of a $d$-wave Pomeranchuk transition is proposed in order to capture the salient features of the spectra. We discuss the available Raman data in the normal state of 122 iron-based systems, particularly Co doped BaFe$_2$As$_2$, and we show that the low energy quasi-elastic peak, the extracted nematic susceptibility and the scattering rates are consistent with an electronic driven structural phase transition. In the superconduc…
Fermi surface fluctuations and lattice instabilities in the 2D metallic kagome superconductor CsV$_3$Sb$_5$ are elucidated via polarization-resolved Raman spectroscopy. The presence of a weak electronic continuum in high-quality samples marks the cross-over into the charge-density-wave (CDW) ordered phase, while impurity-rich samples promote strong defect-induced electronic scattering processes that affect the coherence of the CDW phase. CDW-induced phonon anomalies appear below $T_{\mathrm{CDW}}$, with emergent $C2$ symmetry for one of the CDW amplitude modes, alluding to nematicity. In conju…
In correlated electrons system, quantum melting of electronic crystalline phase often gives rise to many novel electronic phases. In cuprates superconductors, melting the Mott insulating phase with carrier doping leads to a quantum version of liquid crystal phase, the electronic nematicity, which breaks the rotational symmetry and exhibits a tight twist with high-temperature superconductivity. Recently, the electronic nematicity has also been observed in Fe-based superconductors. However, whether it shares a similar scenario with its cuprates counterpart is still elusive. Here, by measuring nu…
Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-$T_c$ superconductors. Here, we report $^{17}$O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa$_2$Cu$_4$O$_8$ to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below $T_{\rm nem} \sim$ 185 K, which is close to the pseudogap temperature $T^{\ast}$. Our result provides a microscopic evidence for int…
We study the in-plane anisotropy of the thermoelectric power and electrical resistivity on detwinned single crystals of isovalent substituted EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_2$. Compared to the resistivity anisotropy the thermopower anisotropy is more pronounced and clearly visible already at temperatures much above the structural and magnetic phase transitions. Most remarkably, the thermopower anisotropy changes sign below the structural transition. This is associated with the interplay of two contributions due to anisotropic scattering and orbital polarization, which dominate at high- and low…
In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave (CDW) order. Whether rotational symmetry breaking (nematicity) occurs intrinsically and generically or as a consequence of other orders is under debate. Here we employ resonant x-ray scattering in stripe-ordered (La,M)_2CuO_4 to probe the relationship between electronic nematicity of the Cu 3d orbitals, structure of the (La,M)_2O_2 layers, and CDW order. We find distinct temperature dependences for the structure of the (La,M)_2O_2 layers and the electronic nematicity of the CuO_2 …
In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced1. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within CuO2 unit cell. We analyze spectroscopic-imaging scanning tunn…
An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model (RFIM). Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network, and use what is known about the RFIM to predict new ways to test for electron nematicity using nois…
The origin of the electronic nematicity and its remarkable material-dependence are famous longstanding unsolved issues in Fe-based superconductors. To attack these issues, we focus on the in-plane anisotropy of the resistivity: In the nematic state in FeSe, the relation $ρ_x>ρ_y$ holds, where $ρ_{x(y)}$ is the resistivity along the longer (shorter) Fe-Fe axis. In contrast, the opposite anisotropy $ρ_x<ρ_y$ is realized in other undoped Fe-based superconductors. Such nontrivial material dependence is naturally explained in terms of the strongly orbital-dependent inelastic quasiparticle scatterin…
Mechanical strain is a powerful technique for tuning electronic structure and interactions in quantum materials. In a system with tetragonal symmetry, a tunable uniaxial in-plane strain can be used to probe nematic correlations in the same way that a tunable magnetic field is used to probe magnetic correlations. Here, we present a new spectroscopic scanned probe technique that provides atomic-resolution insight into the effect of anisotropic strain on the electronic structure. We use this technique to study nematic fluctuations and nematic order across the phase diagram of a prototypical iron-…
In a material prone to a nematic instability, anisotropic strain in principle provides a preferred symmetry-breaking direction for the electronic nematic state to follow. This is consistent with experimental observations, where electronic nematicity and structural anisotropy typically appear hand-in-hand. In this work, we discover that electronic nematicity can be locally decoupled from the underlying structural anisotropy in strain-engineered iron-selenide (FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe with a nanoscale network of modulations that give rise to sp…
The electronic nematic responses in Fe-based superconductors have been observed ubiquitously in various experimental probes. One novel nematic character is the d-wave {\it bond} orbital-relevant nematic charge order which was firstly proposed by symmetry analysis and then conformed by angle-resolved photoemission spectroscopy. In this paper, we present a mechanism that the driving force of the orbital-relevant nematic charge order is the reduction of the large Hubbard energy in the particle-hole charge channel by virtual hopping processes. This is one scenario from strong-coupling consideratio…
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
One of central issues in iron-based superconductors is the role of structural change to the superconducting transition temperature (T_c). It was found in FeSe that the lattice strain leads to a drastic increase in T_c, accompanied by suppression of nematic order. By angle-resolved photoemission spectroscopy on tensile- or compressive-strained and strain-free FeSe, we experimentally show that the in-plane strain causes a marked change in the energy overlap (DeltaE_{h-e}) between the hole and electron pockets in the normal state. The change in DeltaE_{h-e} modifies the Fermi-surface volume, lead…
During the last decade, translational and rotational symmetry-breaking phases -- density wave order and electronic nematicity -- have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant x-ray scattering in a cuprate high-temperature superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ (Nd-LSCO) to navigate the cuprate phase diagram, probing the rel…
Electronic nematicity have attracted a great deal of interest in the unconventional superconductivity research. We present an experimental method to investigate reflectivity anisotropy by the electronic nematicity and its non-equilibrium dynamics. Our experimental results on Ba(Fe$_{0.955}$Co$_{0.045}$)$_{2}$As$_{2}$ single crystal clearly feature the broken four-fold symmetry along directions parallel to Fe-Fe bonding. Numerical simulations using WVASE from Woollam Co. demonstrate that our method is highly reliable under various experimental conditions. Finally, we perform time-resolved refle…
Study of Fe based compounds have drawn much attention due to the discovery of superconductivity as well as many other exotic electronic properties. Here, we review some of our works in these materials carried out employing density functional theory and angle resolved photoemission spectroscopy. The results presented here indicate that the dimensionality of the underlying electronic structure plays important role in deriving their interesting electronic properties. The nematicity found in most of these materials appears to be related to the magnetic long range order. We argue that the exoticity…
The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is one of the most intriguing property of the iron based superconductors (Fe SC), and has relevance for the cuprates as well. Establishing the critical electronic modes behind nematicity remains however a challenge, because their associated susceptibilities are not easily accessible by conventional probes. Here using FeSe as a model system, and symmetry resolved electronic Raman scattering as a probe, we unravel the presence of critical charge nematic fluctuations near the structural …
The mechanism behind the nematicity of FeSe is not known. Through elastoresitivity measurements it has been shown to be an electronic instability. However, so far measurements have extended only to small strains, where the response is linear. Here, we apply large elastic strains to FeSe, and perform two types of measurements. (1) Using applied strain to control twinning, the nematic resistive anisotropy at temperatures below the nematic transition temperature Ts is determined. (2) Resistive anisotropy is measured as nematicity is induced through applied strain at fixed temperature above Ts. In…
The electronic nematic order characterized by broken rotational symmetry has been suggested to play an important role in the phase diagram of the high temperature cuprates. We study the interplay between the electronic nematic order and a spin density wave order in the presence of a magnetic field. We show that a cooperation of the nematicity and the magnetic field induces a finite coupling between the spin density wave and spin-triplet staggered flux orders. As a consequence of such a coupling, the magnon gap decreases as the magnetic field increases, and it eventually condenses beyond a crit…
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…
Electronic nematics, an electron orientational order which breaks the underlying rotational symmetry, have been observed in iron pnictide superconductors several years after their discovery. However, the universality of the doping dependence of this phase and its relation to other symmetry-breaking orders (such as superconductivity) in distinct families of iron pnictides, remain outstanding questions. Here we use torque magnetometry as a probe to study the rotational symmetry breaking in EuFe$_2$(As$_{1-x}$P$_x$)$_2$ without introducing external pressure. The nematic phase is found to prolifer…
Nematicity in LaFeAsO single crystals studied by elastoresistance, high-resolution thermal expansion and shear-modulus measurements
Leibniz-Institut für Festkörper u. Werkstoffforschung (IFW) Dresden（德累斯顿莱布尼茨固体与材料研究所）；Bergische Universität Wuppertal（伍珀塔尔大学）；Kirchhoff Institute for Physics, Heidelberg University（海德堡大学基尔霍夫物理研究所）
Charge order in cuprate superconductors is a possible source of anomalous electronic properties in the underdoped regime. Intra-unit cell charge ordering tendencies point to electronic nematic order involving oxygen orbitals. In this context we investigate charge instabilities in the Emery model and calculate the charge susceptibility within diagrammatic perturbation theory. In this approach, the onset of charge order is signalled by a divergence of the susceptibility. Our calculations reveal three different kinds of order: a commensurate ($q=0$) nematic order, and two incommensurate nematic p…
The cuprate superconductors are characterized by numerous ordering tendencies, with the nematic order being the most distinct form of order. Here the intertwinement of the electronic nematicity with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconductivity. It is shown that the optimized Tc takes a dome-like shape with the weak and strong strength regions on each side of the optimal strength of the electronic nematicity, where the optimized Tc reaches its maximum. This dome-like shape nematic-order strength dependence of Tc indicates that the …
Electronic nematic phases have been proposed to occur in various correlated electron systems and were recently claimed to have been detected in scanning tunneling microscopy (STM) conductance maps of the pseudogap states of the cuprate high-temperature superconductor Bi2Sr2CaCu2O8+x (Bi-2212). We investigate the influence of anisotropic STM tip structures on such measurements and establish, with a model calculation, the presence of a tunneling interference effect within an STM junction that induces energy-dependent symmetry-breaking features in the conductance maps. We experimentally confirm t…
The pseudogap regime of the cuprate high-temperature superconductors is characterized by a variety of competing orders, the nature of which are still widely debated. Recent experiments have provided evidence for electron nematic order, in which the electron fluid breaks rotational symmetry while preserving translational invariance. Raman spectroscopy, with its ability to symmetry resolve low energy excitations, is a unique tool that can be used to assess nematic fluctuations and nematic ordering tendencies. Here, we compare results from determinant quantum Monte Carlo simulations of the Hubbar…
The pseudogap (PG) state and its related intra-unit-cell symmetry breaking remain the focus in the research of cuprate superconductors. Although the nematicity has been studied in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, especially underdoped samples, its behavior in other cuprates and different doping regions is still unclear. Here we apply a scanning tunneling microscope to explore an overdoped (Bi, Pb)$_2$Sr$_2$CuO$_{6+δ}$ with a large Fermi surface (FS). The establishment of a nematic order and its real-space distribution is visualized as the energy scale approaches the PG.
The large anisotropy in the electronic properties across a structural transition in several correlated systems has been identified as the key manifestation of electronic nematic order, breaking rotational symmetry. In this context, FeSe is attracting tremendous interest, since electronic nematicity develops over a wide range of temperatures, allowing accurate experimental investigation. Here we combine angle-resolved photoemission spectroscopy and theoretical calculations based on a realistic multi-orbital model to unveil the microscopic mechanism responsible for the evolution of the electroni…
A hallmark of the phase diagrams of quantum materials is the existence of multiple electronic ordered states, which, in many cases, are not independent competing phases, but instead display a complex intertwinement. In this review, we focus on a particular realization of intertwined orders: a primary phase characterized by a multi-component order parameter and a fluctuation-driven vestigial phase characterized by a composite order parameter. This concept has been widely employed to elucidate nematicity in iron-based and cuprate superconductors. Here we present a group-theoretical framework tha…
Surface probes such as scanning tunneling microscopy (STM) have detected complex patterns at the nanoscale, indicative of electronic inhomogeneity, in a variety of high temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high temperature superconducting state. Symmetry breaking (i.e. from C4 to C2) in the form of electronic nematicity has recently been implicated as a unifying theme of the pseudogap phase,[1] however the fundamental physics governing the nanoscale pattern formation has not yet been identified. Here we use u…
The physical properties of high-$T_c$ superconductors are affected by spatial inhomogeneities introduced by impurities. In addition, superconductivity and electronic nematicity seem intertwined in these materials. To address these questions, we apply inhomogeneous cluster dynamical mean field theory to the study of superconductivity in the Hubbard model, in the presence of a repeated impurity, at zero temperature. We find that the superconducting phase is shifted slightly away from half-filling due to the presence of the impurity. This can be explained by a competition with the Mott insulating…
To understand the rich electronic phase diagram in FeSe under pressure that vividly demonstrates the strong interplay between the nematicity, magnetism and superconductivity, we analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). We predict the pressure-induced emergence of xy-orbital hole-pocket based on the first-principles analysis. Due to this pressure-induced Lifshitz transition, the spin fluctuations on the xy orbital are enhanced, whereas those on xz,yz orbitals are gradually reduced. For this reason, nonmagnetic orbital order…
The NMR spectrum of FeSe shows a dramatic broadening on cooling towards the bulk nematic phase at $T_s=90$ K, due to the formation of a quasi-static, short-range-ordered nematic domain structure. However, a quantitative understanding of the NMR broadening and its relationship to the nematic susceptibility is still lacking. Here, we show that the temperature and pressure dependence of the broadening is in quantitative agreement with the mean-field Edwards-Anderson parameter of an Ising-nematic model in the presence of random-field disorder introduced by non-magnetic impurities. Furthermore, the…
We systematically studied in-plane optical conductivity of FeSe$_{1-x}$Te$_{x}$ thin films fabricated on CaF$_{2}$ substrates for $x$ = 0, 0.1, 0.2, and 0.4. This system shows a large enhancement of superconducting transition temperature $T_{\mathrm{c}}$ at $x \sim$ 0.2 and a gentle decrease in $T_{\mathrm{c}}$ with further increasing $x$. The low-energy optical conductivity spectrum is described by the sum of narrow and broad Drude components, associated with coherent and incoherent charge dynamics, respectively. With increasing Te content, the spectral weight of the narrow Drude component de…
The origin of spontaneous electronic nematic ordering provides important information for understanding iron-based superconductors. Here, we analyze a scenario where the $d_{xy}$ orbital strongly contributes to nematic ordering in FeSe. We show that the addition of $d_{xy}$ nematicity to a pure $d_{xz}/d_{yz}$ order provides a natural explanation for the unusual Fermi surface and correctly reproduces the strongly anisotropic momentum dependence of the superconducting gap. We predict a Lifshitz transition of an electron pocket mediated by temperature and sulphur doping, whose signatures we discu…
The driving forces behind electronic nematicity in the iron pnictides remain hotly debated. We use atomic-resolution variable-temperature scanning tunneling spectroscopy to provide the first direct visual evidence that local electronic nematicity and unidirectional antiferroic (stripe) fluctuations persist to temperatures almost twice the nominal structural ordering temperature in the parent pnictide NaFeAs. Low-temperature spectroscopic imaging of nematically-ordered NaFeAs shows anisotropic electronic features that are not observed for isostructural, non-nematic LiFeAs. The local electronic …
Electronic nematicity is rarely observed as an isolated instability of a correlated electron system. Instead, in iron pnictides and in certain cuprates and heavy-fermion materials, nematicity is intertwined with an underlying spin-stripe or charge-stripe state. As a result, random strain, ubiquitous in any real crystal, creates both random-field disorder for the nematic degrees of freedom and random-bond disorder for the spin or charge ones. Here, we put forward an Ashkin-Teller model with random Baxter fields to capture the dual role of random strain in nematic systems for which nematicity is…
Nematicity is ubiquitous in electronic phases of high transition temperature superconductors, particularly in iron-based superconductors (IBSCs). Order parameter that characterizes the nematic phase has been investigated in momentum space, but its real-space arrangement remains largely unclear. We use linear dichroism (LD) in low-temperature laser-photoemission electron microscope to map out the nematic order parameter of nonmagentic FeSe and antiferromagnetic BaFe2(As0.87P0.13)2. In contrast to the structural domains that have atomic-scale domain walls, the LD patterns in both materials show …
In the electronic nematic state, an electronic system has a lower symmetry than the crystal structure of the same system. Electronic nematic states have been observed in various unconventional superconductors such as cuprate- and iron-based, heavy-fermion, and topological superconductors. The relation between nematicity and superconductivity is a major unsolved problem in condensed matter physics. By angle-resolved specific heat measurements, we report bulk quasi-particle evidence of nematicity in the topological superconductor Sr$_x$Bi$_2$Se$_3$. The specific heat exhibited a clear 2-fold sym…
Electronic nematicity, the breaking of the crystal lattice rotational symmetry by the electronic fluid, is a fascinating quantum state of matter. Recently, BaNi$_2$As$_2$ has emerged as a promising candidate for a novel type of nematicity triggered by charge fluctuations. In this work, we scrutinize the electronic nematicity of BaNi$_2$(As$_{1-x}$P$_x$)$_2$ with $0 \leq x \leq 0.10$ using electronic transport measurements under strain. We report a large $B_{1g}$ elastoresistance coefficient that is maximized at a temperature slightly higher than the first-order triclinic transition, and that c…
The angular-dependent magnetoresistance (AMR) of the ab plane is measured on the single crystals of FeSe1-xSx (x = 0, 0.07, 0.13 and 1) and FeSe1-yTey (y = 0.06, 0.61 and 1) at various temperatures under fields up to 9 T. A pronounced twofold-anisotropic carrier-scattering effect is identified by AMR, and attributed to a magnetic-field-induced spin nematicity that emerges from the tetragonal normal-state regime below a characteristic temperature Tsn. This magnetically polarized spin nematicity is found to be ubiquitous in the isoelectronic FeSe1-xSx and FeSe1-yTey systems, no matter whether th…
Using electronic Raman spectroscopy, we report direct measurements of charge nematic fluctuations in the tetragonal phase of strain-free Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$ single crystals. The strong enhancement of the Raman response at low temperatures unveils an underlying charge nematic state that extends to superconducting compositions and which has hitherto remained unnoticed. Comparison between the extracted charge nematic susceptibility and the elastic modulus allows us to disentangle the charge contribution to the nematic instability, and to show that charge nematic fluctuations are we…
The electronic structure of the enigmatic iron-based superconductor FeSe has puzzled researchers since spectroscopic probes failed to observe the expected electron pocket at the $Y$ point in the 1-Fe Brillouin zone. It has been speculated that this pocket, essential for an understanding of the superconducting state, is either absent or incoherent. Here, we perform a theoretical study of the preferred nematic order originating from nearest-neighbor Coulomb interactions in an electronic model relevant for FeSe. We find that at low temperatures the dominating nematic components are of inter-orbit…
Formation of electronic nematicity is a common thread of unconventional superconductors. In iron-based materials, the long-range nematic order is revealed by the orthorhombic lattice distortion, which importance is a highly controversial topic due the small magnitude of the distortion. Here, we study the local crystal structure of FeSe and its interaction with electronic degrees of freedom using ultrafast electron diffraction, x-ray pair distribution function analysis, and transmission electron microscopy and find a significant lattice response to local nematicity. The study demonstrates how l…
Single crystals of LaFeAsO were successfully grown out of KI flux. Temperature dependent electrical resistivity was measured with current flow along the basal plane, ρ_perpend(T), as well as with current flow along the crystallographic c-axis, ρ_parallel(T), the latter one utilizing electron beam lithography and argon ion beam milling. The anisotropy ratio was found to lie between ρ_parallel/ρ_perpend = 20 - 200. The measurement of ρ_perpend(T) was performed with current flow along the tetragonal [1 0 0] direction and along the [1 1 0] direction and revealed a clear in-plane anisotropy already…
Although the existence of nematic order in iron-based superconductors is now a well-established experimental fact, its origin remains controversial. Nematic order breaks the discrete lattice rotational symmetry by making the $x$ and $y$ directions in the Fe plane non-equivalent. This can happen because of (i) a tetragonal to orthorhombic structural transition, (ii) a spontaneous breaking of an orbital symmetry, or (iii) a spontaneous development of an Ising-type spin-nematic order - a magnetic state that breaks rotational symmetry but preserves time-reversal symmetry. The Landau theory of phas…
