The hallmark of nematic order in iron-based superconductors is a resistivity anisotropy but it is unclear to which extent quasiparticle dispersions, lifetimes and coherence contribute. While the lifted degeneracy of the Fe $d_{xz}$ and $d_{yz}$ dispersions has been studied extensively, only little is known about the two other factors. Here, we combine in situ strain tuning with ARPES and study the nematic response of the spectral weight in BaFe$_2$As$_2$. The symmetry analysis of the ARPES spectra demonstrates that the $d_{xz}$ band gains quasiparticle spectral weight compared to the $d_{yz}$ band for negative antisymmetric strain $Δε_{yy}$ suggesting the same response inside the nematic phase. Our results are compatible with a different coherence of the $d_{xz}$ and $d_{yz}$ orbital within a Hund's metal picture. We also discuss the influence of orbital mixing.
We investigate coherent phonon oscillations of BaFe$_2$As$_2$ using optical pump-probe spectroscopy. Time-resolved optical reflectivity shows periodic modulations due to $A_{1g}$ coherent phonon of $c$-axis arsenic vibrations. Optical probe beams polarized along the orthorhombic $a$- and $b$-axes reveal that the initial phase of coherent oscillations shows a systematic deviation as a function of temperature, although these oscillations arise from the same $c$-axis arsenic vibrations. The oscillation-phase remains anisotropic even in the tetragonal structure, reflecting a nematic response of Ba…
We report a Raman scattering study of nematic degrees of freedom in the iron-based superconductor parent compound BaFe$_2$As$_2$ under tunable uniaxial strain. We demonstrate that the polarization resolved arsenic (As) phonon intensity can be used to monitor the nematic order parameter as a function of both temperature and strain. At low temperature in the nematic ordered phase we use it to track the continuous and reversible orientation of nematic domains under variable strain. At higher temperature, the evolution of the As phonon intensity under strain reflects an enhanced nematic susceptibi…
Raman scattering can detect spontaneous point-group symmetry breaking without resorting to single-domain samples. Here we use this technique to study $\mathrm{BaFe_2As_2}$, the parent compound of the "122" Fe-based superconductors. We show that an applied compression along the Fe-Fe direction, which is commonly used to produce untwinned orthorhombic samples, changes the structural phase transition at temperature $T_{\mathrm{s}}$ into a crossover that spans a considerable temperature range above $T_{\mathrm{s}}$. Even in crystals that are not subject to any applied force, a distribution of subs…
In several Fe-based superconductors, slight $C_4$ symmetry breaking occurs at $T^*$, which is tens of Kelvin higher than the structural transition temperature $T_S$. In this "hidden" nematic state at $T_S<T<T^*$, the orthorhombicity is tiny [$ϕ=(a-b)/(a+b) \ll 0.1$%], but clear evidences of bulk phase transition have been accumulated. To explain this long-standing mystery, we propose the emergence of antiferro-bond (AFB) order with the antiferro wavevector ${\bf q}=(0,π)$ at $T=T^*$, by which the characteristic phenomena below $T^*$ are satisfactorily explained. This AFB order originates from …
An instrumentation problem with the signal acquisition at high frequencies was discovered and we no longer believe that the experimental data presented in the manuscript, showing a frequency enhancement of the elastoresistivity, are correct. After correcting the problem, the elastoresistivity data is frequency independent in the range investigated. Therefore, the authors have withdrawn this submission. We would like to thank Alex Hristov, Johanna Palmstrom, Josh Straquadine and Ian Fisher (Stanford) for the kind discussions and assistance we received which helped us identify these problems.
A rich variety of nematic/smectic orders in Fe-based superconductors is an important unsolved problem in strongly correlated electron systems. A unified understanding of these orders has been investigated for the last decade. In this article, we explain the $B_{1g}$ symmetry nematic transition in FeSe$_{1-x}$Te$_x$, the $B_{2g}$ symmetry nematicity in AFe$_2$As$_2$ (A=Cs, Rb), and the smectic state in BaFe$_2$As$_2$ based on the same framework. We investigate the quantum interference mechanism between spin fluctuations by developing the density wave equation. The observed rich variety of nemat…
Laser angle-resolved photoemission spectroscopy (ARPES) is employed to investigate the temperature (T) dependence of the electronic structure in BaFe2As2 across the magneto-structural transition at TN ~ 140 K. A drastic transformation in Fermi surface (FS) shape across TN is observed, as expected by first-principles band calculations. Polarization-dependent ARPES and band calculations consistently indicate that the observed FSs at kz ~ pi in the low-T antiferromagnetic (AF) state are dominated by the Fe3dzx orbital, leading to the two-fold electronic structure. These results indicate that magn…
To elucidate the origin of nematic order in Fe-based superconductors, we report a Raman scattering study of lattice dynamics, which quantify the extent of $C_4$-symmetry breaking, in BaFe$_2$As$_2$ and FeSe. FeSe possesses a nematic ordering temperature $T_\mathrm{s}$ and orbital-related band-energy split below $T_\mathrm{s}$ that are similar to those in BaFe$_2$As$_2$, but unlike BaFe$_2$As$_2$ it has no long-range magnetic order. We find that the $E_g$ phonon-energy split in FeSe sets in only well below $T_\mathrm{s}$, and its saturated value is substantially smaller than that in BaFe$_2$As$…
We revisit the electronic structure of BaFe$_2$As$_2$, the archetypal parent compound of the Fe-based superconductors, using angle-resolved photoemission spectroscopy (ARPES). Our high-resolution measurements of samples detwinned by the application of a mechanical strain reveal a highly anisotropic 3D Fermi surface in the low temperature magnetic phase. By comparison of the observed dispersions with ab-initio calculations, we argue that overall it is magnetism, rather than orbital ordering, which is the dominant effect, reconstructing the electronic structure across the Fe 3d bandwidth. Finall…
We present evidence for nuclear spin-lattice relaxation driven by glassy nematic fluctuations in isovalent P-doped BaFe$_2$As$_2$ single crystals. Both the $^{75}$As and $^{31}$P sites exhibit stretched-exponential relaxation similar to the electron-doped systems. By comparing the hyperfine fields and the relaxation rates at these sites we find that the As relaxation cannot be explained solely in terms of magnetic spin fluctuations. We demonstrate that nematic fluctuations couple to the As nuclear quadrupolar moment and can explain the excess relaxation. These results suggest that glassy nemat…
Low energy electron diffraction (LEED) experiments, LEED simulations and finite slab density functional calculations are combined to study the cleavage surface of Co doped BaFe_{2-x}Co_{x}As_{2} (x = 0.1, 0.17). We demonstrate that the energy dependence of the LEED data can only be understood from a terminating 1/2 Ba layer accompanied by distortions of the underlying As-Fe_2-As block. As a result, surface related Fe 3d states are present in the electronic structure, which we identify in angle resolved photoemission experiments. The close proximity of the surface-related states to the bulk ban…
The electric field gradient (EFG) tensor at the $^{75}$As site couples to the orbital occupations of the As p-orbitals and is a sensitive probe of local nematicity in BaFe$_2$As$_2$. We use nuclear magnetic resonance to measure the nuclear quadrupolar splittings and find that the EFG asymmetry responds linearly to the presence of a strain field in the paramagnetic phase. We extract the nematic susceptibility from the slope of this linear response as a function of temperature and find that it diverges near the structural transition in agreement with other measures of the bulk nematic susceptibi…
We show that the strain-induced resistivity anisotropy in the tetragonal state of the representative underdoped Fe-arsenides BaFe$_2$As$_2$, Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$ is independent of disorder over a wide range of defect and impurity concentrations. This result demonstrates that the anisotropy in the in-plane resistivity in the paramagnetic orthorhombic state of this material is not due to elastic scattering from anisotropic defects, and is most easily understood in terms of an intrinsic anisotropy in the electronic structure.
Understanding the nature of the electronic nematic phase in iron pnictide superconductors is important for elucidating its impact on high-temperature superconductivity. Here we use transport and inelastic neutron scattering to study spin excitations and in-plane resistivity anisotropy in uniaxial pressure detwinned BaFe$_2$As$_2$ and SrFe$_2$As$_2$, the parent compounds of iron pnictide superconductors. While BaFe$_2$As$_2$ exhibits weakly first order tetragonal-to-orthorhombic structural and antiferromagnetic (AF) phase transitions below $T_s > T_N\approx 138$ K, SrFe$_2$As$_2$ has strongly c…
The iron-based high temperature superconductors exhibit a rich phase diagram reflecting a complex interplay between spin, lattice, and orbital degrees of freedom [1-4]. The nematic state observed in many of these compounds epitomizes this complexity, by entangling a real-space anisotropy in the spin fluctuation spectrum with ferro-orbital order and an orthorhombic lattice distortion [5-7]. A more subtle and much less explored facet of the interplay between these degrees of freedom arises from the sizable spin-orbit coupling present in these systems, which translates anisotropies in real space …
Nematic phase transitions in high-temperature superconductors have a strong impact on the electronic properties of these systems. BaFe$_2$As$_2$,\@ with an established nematic transition around 137 K induced by magnetic fluctuations, and BaNi$_2$As$_2$,\@ a non-magnetic analog of BaFe$_2$As$_2$ with a structural transition in the same temperature range,\@ share a common tetragonal aristotype crystal structure with space-group type $I4/mmm$.\@ In contrast to BaFe$_2$As$_2$ where collinear stripe magnetic order is found for the orthorhombic low-$T$ phase, a unidirectional charge density wave tog…
We report a comprehensive ARPES study of NaFeAs, a prototypical parent compound of the Fe-based superconductors. By mechanically detwinning the samples, we show that in the nematic phase (below the structural transition at $T_s$ = 54 K but above the antiferromagnetic transition at $T_N$ = 43 K) spectral weight is detected on only the elliptical electron pocket along the longer $a_{orth}$ axis. This dramatic anisotropy is likely to arise as a result of coupling to a fluctuating antiferromagnetic order in the nematic phase. In the long-range ordered antiferromagnetic state below $T_N$, this sing…
The main driven force of the electronic nematic phase in iron-based superconductors is still under debate. Here, we report a comprehensive study on the nematic fluctuations in a non-superconducting iron pnictide system BaFe$_{1.9-x}$Ni$_{0.1}$Cr$_{x}$As$_{2}$ by electronic transport, angle-resolved photoemission spectroscopy (ARPES) and inelastic neutron scattering (INS) measurements. Previous neutron diffraction and transport measurements suggested that the collinear antiferromagnetism persists to $x=0.8$, with similar Néel temperature $T_N$ and structural transition temperature $T_s$ around …
High-resolution single crystal neutron diffraction measurements are presented probing the magnetostructural response to uniaxial pressure in the iron pnictide parent system BaFe2As2. Scattering data reveal a strain-activated, anisotropic broadening of nuclear Bragg reflections, which increases upon cooling below the resolvable onset of global orthorhombicity. This anisotropy in lattice coherence continues to diverge until a lower temperature scale---the first-order onset of antiferromagnetism---is reached. Our data suggest that antiferromagnetism and strong magnetoelastic coupling drive the st…
In a magnetically driven electronic nematic state, an externally applied uniaxial strain rounds the nematic transition and increases the magnetic transition temperature. We study both effects in a simple classical model of the iron-pnictides expressed in terms of local SO(N) spins (with N = 3) which we solve to leading order in 1=N. The magnetic transition temperature is shown to increase linearly in response to an external strain while a sharp crossover, which is a remnant of the nematic transition, can only be identified for extremely small strain. We show that these results can reasonably a…
We present a comprehensive study of the evolution of the nematic electronic structure of FeSe using high resolution angle-resolved photoemission spectroscopy (ARPES), quantum oscillations in the normal state and elastoresistance measurements. Our high resolution ARPES allows us to track the Fermi surface deformation from four-fold to two-fold symmetry across the structural transition at ~87 K which is stabilized as a result of the dramatic splitting of bands associated with dxz and dyz character. The low temperature Fermi surface is that a compensated metal consisting of one hole and two elect…
Anisotropic strain is an external field capable of selectively addressing the role of nematic fluctuations in promoting superconductivity. We demonstrate this using polarization-resolved elasto-Raman scattering to probe the evolution of nematic fluctuations under strain in the normal and superconducting states of the paradigmatic iron-based superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. In the non-superconducting parent compound BaFe$_2$As$_2$ we observe a strain-induced suppression of the nematic susceptibility which follows the expected behavior of an Ising order parameter under a symmetry b…
We study the band structure of twinned and detwinned BaFe$_2$As$_2$ using angle-resolved photoemission spectroscopy (ARPES). The combination of measurements in the ordered and normal state along four high-symmetry momentum directions $Γ$/Z--X/Y enables us to identify the complex reconstructed band structure in the ordered state in great detail. We clearly observe the nematic splitting of the $d_{xz}$ and $d_{yz}$ orbitals as well as folding due to magnetic order with a wave vector of $(π,π,π)$. We are able to assign all observed bands. In particular we suggest an assignment of the electron ban…
A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe$_2$As$_2$, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature $T_s$. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature $T_N$ ($<T_s$) and create in-plane resistivity anisotropy above $T_s$. Here we use neutron polarization analysis to …
Using cluster-perturbation theory, we calculate the spectral density A(k,w) for a nematic phase of models describing pnictide superconductors, where very short-range magnetic correlations choose the ordering vector (pi,0) over the equivalent (0,pi) and thus break the fourfold rotation symmetry of the underlying lattice without inducing long-range magnetic order. In excellent agreement with angle resolved photo-emission spectroscopy (ARPES), we find that the yz bands at X move to higher energies. When onsite Coulomb repulsion brings the system close to a spin--density-wave (SDW) and renormalize…
We performed angle resolved photoelectron spectroscopy (ARPES) studies on mechanically detwinned BaFe2As2. We observe clear band dispersions and the shapes and characters of the Fermi surfaces are identified. Shapes of the two hole pockets around the Γ-point are found to be consistent with the Fermi surface topology predicted in the orbital ordered states. Dirac-cone like band dispersions near the Γ-point are clearly identified as theoretically predicted. At the X-point, split bands remain intact in spite of detwinning, barring twinning origin of the bands. The observed band dispersions are co…
We performed an angle-resolved photoemission spectroscopy study of BaMn$_2$As$_2$ and BaMn$_2$Sb$_2$, which are isostructural to the parent compound BaFe$_2$As$_2$ of the 122 family of ferropnictide superconductors. We show the existence of a strongly $k_z$-dependent band gap with a minimum at the Brillouin zone center, in agreement with their semiconducting properties. Despite the half-filling of the electronic 3$d$ shell, we show that the band structure in these materials is almost not renormalized from the Kohn-Sham bands of density functional theory. Our photon energy dependent study provi…
We consider the electronic spectrum near $M=(π,π)$ in the nematic phase of FeSe ($T<T_{\rm nem}$) and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the $M$ point. These have been identified as having $xz$ and $yz$ orbital character well below $T_{\rm nem}$, but remain split at $T>T_{\rm nem}$, in apparent contradiction to the fact that in the tetragonal phase the $xz$ and $yz$ orbitals are degenerate. Here we present two scenarios which can describe the data. In both scenarios, hybridization terms…
Using a variational Monte Carlo method, we investigate the nematic state in iron-base superconductors based on a three-band Hubbard model. Our results demonstrate that the nematic state, formed by introducing an anisotropic hopping order into the projected wave function, can arise in the underdoped regime when a realistic off-site Coulomb interaction $V$ is considered. {\color {red} We demonstrate that the off-site Coulomb interaction $V$, which is neglected so far in the analysis of iron-base superconductors, make a dominant contribution to the stabilization of nematic state. We calculate the…
We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson $ϕ$, which undergoes a continuous transition towards nematic order with $d-$wave form-factor. We consider two cases: (a) when $ϕ$ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter near an Ising-nematic transition. In both cases, the order-parameter is not a conserved quantity and the $d-$wave fermionic polarization $Π(q, Ω)$ remains finite even at $q=0$. The polari…
Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations, or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies 3-5 meV, indicating a gapped four-fold (C4)…
