Imaging anomalous nematic order and strain in optimally doped BaFe$_2$(As,P)$_2$
Eric Thewalt, Ian M. Hayes, James P. Hinton, Arielle Little, Shreyas Patankar, Liang Wu, Toni Helm, Camelia V. Stan, Nobumichi Tamura, James G. Analytis, Joseph Orenstein
We present the strain and temperature dependence of an anomalous nematic phase in optimally doped BaFe$_2$(As,P)$_2$. Polarized ultrafast optical measurements reveal broken 4-fold rotational symmetry in a temperature range above $T_c$ in which bulk probes do not detect a phase transition. Using ultrafast microscopy, we find that the magnitude and sign of this nematicity vary on a ${50{-}100}~μ$m length scale, and the temperature at which it onsets ranges from 40 K near a domain boundary to 60 K deep within a domain. Scanning Laue microdiffraction maps of local strain at room temperature indicate that the nematic order appears most strongly in regions of weak, isotropic strain. These results indicate that nematic order arises in a genuine phase transition rather than by enhancement of local anisotropy by a strong nematic susceptibility. We interpret our results in the context of a proposed surface nematic phase.
The nematic susceptibility of hole-doped Ba1-xKxFe2As2 and electron-doped Ba(Fe1-xCox)2As2 iron-based superconductors is obtained from measurements of the elastic shear modulus using a three-point bending setup in a capacitance dilatometer. Nematic fluctuations, although weakened by doping, extend over the whole superconducting dome in both systems, suggesting their close tie to superconductivity. Evidence for quantum critical behavior of the nematic susceptibility is, surprisingly, only found for Ba(Fe1-xCox)2As2, the system with the lower maximal Tc value.
We study the antiferromagnetic (AFM) and structural phase transitions in single crystal $BaFe_2(As_{1-x}P_x)_2$ $(x=0, 0.3)$ at temperatures $T_N$ and $T_S$, respectively, by high resolution ac microcalorimetry and SQUID magnetometry. The specific heat measurements of both as grown and annealed $BaFe_2As_2$ displays a sharp peak at the AFM/Structural transitions. A kink in the entropy of annealed $BaFe_2As_2$ gives evidence for splitting of the two transitions by approximately 0.5K. No additional features could be identified in the specific heat of both $BaFe_2As_2$ and $BaFe_2(As_{0.7}P_{0.3}…
We use transport and neutron scattering to study electronic, structural, and magnetic properties of the electron-doped BaFe$_{2-x}$Ni$_x$As$_2$ iron pnictides in the external stress free detwinned state. Using a specially designed in-situ mechanical detwinning device, we demonstrate that the in-plane resistivity anisotropy observed in the uniaxial strained tetragonal state of BaFe$_{2-x}$Ni$_x$As$_2$ below a temperature $T^\ast$, previously identified as a signature of the electronic nematic phase, is also present in the stress free tetragonal phase below $T^{\ast\ast}$ ($<T^\ast$). By carryin…
We report comprehensive temperature and doping-dependences of the Raman scattering spectra for $\mathrm{BaFe_{2}}(\mathrm{As}_{1-x}\mathrm{P}_{x}\mathrm{)_{2}}$ ($x =$ 0, 0.07, 0.24, 0.32, and 0.38), focusing on the nematic fluctuation and the superconducting responses. With increasing $x$, the bare nematic transition temperature estimated from the Raman spectra reaches $T =$ 0 K at the optimal doping, which indicates a quantum critical point (QCP) at this composition. In the superconducting compositions, in addition to the pair breaking peaks observed in the $A_{\mathrm{1g}}$ and $B_{\mathrm{…
The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,$π$) should decrease with decreasing temperature below the structural transition temperature $T_s$. Here we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe$_{1.935}$Ni$_{0.065}$As$_2$ under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length …
The calculated specific heat of optimally K-doped BaFe$_2$As$_2$ in density functional theory is about five times smaller than that found in the experiment. We report that by adjusting the potential on the iron atom to be slightly more repulsive for electrons improves the calculated heat capacity as well as the structural, magnetic, and electronic properties of Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$. Applying the same correction to the antiferromagnetic state, we find that the electron-phonon coupling is strongly enhanced.
Understanding the microscopic origins of electronic phases in high-transition temperature (high-Tc) superconductors is important for elucidating the mechanism of superconductivity. In the paramagnetic tetragonal phase of BaFe2-xTxAs2 (where T is Co or Ni) iron pnictides, an in-plane resistivity anisotropy has been observed. Here we use inelastic neutron scattering to show that low-energy spin excitations in these materials change from four-fold symmetric to two-fold symmetric at temperatures corresponding to the onset of the in-plane resistivity anisotropy. Because resistivity and spin excitat…
The tetragonal-to-orthorhombic phase transition at $T_s$, which precedes the antiferromagnetic phase transition at $T_N$ in many iron-based superconductors, is considered as one of the manifestations of electronic \textit{nematic} order. By constructing temperature-pressure phase diagrams of pure and Co-doped BaFe$_2$As$_2$, we study the relation of $T_s$ and $T_N$ under pressure $p$. Our data disclose two qualitatively different regimes in which $ΔT\,=\,T_s-T_N$ either increases or decreases with $p$. We provide experimental evidence that the transition between the two regimes may be associat…
Nematicity plays an important role in the physics of iron-based superconductors (IBS). Its microscopic origin and in particular its importance for the mechanism of high-temperature superconductivity itself are highly debated. A crucial knowledge in this regard is the degree to which the nematic order influences the electronic structure of these materials. Earlier angle-resolved photoemission spectroscopy (ARPES) studies found that the effect is dramatic in three families of IBS including 11, 111 and 122 compounds: energy splitting reaches 70 meV and Fermi surface becomes noticeably distorted. …
We have systematically studied the nematic fluctuations in the electron-doped iron-based superconductor BaFe$_{2-x}$Ni$_x$As$_2$ by measuring the in-plane resistance change under uniaxial pressure. While the nematic quantum critical point can be identified through the measurements along the (110) direction as studied previously, quantum and thermal critical fluctuations cannot be distinguished due to similar Curie-Weiss-like behaviors. Here we find that a sizable pressure-dependent resistivity along the (100) direction is present in all doping levels, which is against the simple picture of an …
We perform, as a function of uniaxial stress, an optical-reflectivity investigation of the representative 'parent' ferropnictide BaFe$_2$As$_2$ in a broad spectral range, across the tetragonal-to-orthorhombic phase transition and the onset of the long-range antiferromagnetic order (AFM). The infrared response reveals that the $dc$ transport anisotropy in the orthorhombic AFM state is determined by the interplay between the Drude spectral weight and the scattering rate, but that the dominant effect is clearly associated with the metallic spectral weight. In the paramagnetic tetragonal phase, th…
The superconducting fluctuations well inside the normal state of Fe-based superconductors were experimentally studied through the in-plane paraconductivity in several high-quality optimally-doped BaFe$_{2-x}$Ni$_x$As$_2$ crystals. These measurements were performed in magnetic fields with amplitudes up to 14 T, and different orientations relative to the crystals c axis (0, 53 and 90 degrees). The results allowed a stringent check of the applicability of a recently proposed Ginzburg-Landau approach for the fluctuation electrical conductivity of 3D anisotropic materials in presence of finite appl…
Low temperature specific heat has been measured in optimally doped and highly overdoped non-superconducting BaFe$_{2-x}$TM$_x$As$_{2}$ ($TM$ = Co and Ni) single crystals. By using the data of the overdoped samples, we successfully removed the phonon contribution of the optimally doped ones, and derived the electronic specific heat coefficient $γ_e$. Remarkably, we found a continuing temperature dependent $γ_e(T)$ which follows the quadratic relation $γ_e=γ_0+αT^2$ in the low temperature limit. Together with the very small residual term $γ_0$, linear magnetic field dependence of $γ_e$, it is co…
We performed combined infrared reflection and ellipsometry measurements of the in-plane optical reponse of single crystals of the pnictide high temperature superconductor BaFe$_{1.87}$Co$_{0.13}$As$_{2}$ with $T_{c}$ = 24.5 K. We observed characteristic superconductivity-induced changes which provide evidence for at least three different energy gaps. We show that a BCS-model of isotropic gaps with 2$Δ/k_{B}T_{c}$ of 3.1, 4.7, and 9.2 reproduces the experimental data rather well. We also determine the low-temperature value of the in-plane magnetic penetration depth of 270 nm.
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…
Through detailed electronic structure simulations we show that the electronic orbital ordering (between d$_{yz}$ and d$_{xz}$ bands) takes place due to local breaking of in-plane symmetry that generates two non-equivalent $a$, $b$ directions in 122 family of Fe-based superconductors. Orbital ordering is strongly anisotropic and the temperature dependence of the corner zone orbital order maps to that of the orthorhombicity parameter. Orbital anisotropy results in two distinct spin density wave nesting wave vectors and causes inter-orbital charge and spin fluctuations. Temperature dependence of …
We use inelastic neutron scattering to study the effect of an in-plane magnetic field on the magnetic resonance in optimally doped superconductors FeSe$_{0.4}$Te$_{0.6}$ ($T_c=14$ K) and BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ ($T_c=20$ K). While the magnetic field up to 14.5 Tesla does not change the energy of the resonance, it particially suppresses $T_c$ and the corresponding superconductivity-induced intensity gain of the mode. However, we find no direct evidence for the field-induced spin-1 Zeeman splitting of the resonance. Therefore, it is still unclear if the resonance is the long-sought single…
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…
Superconductivity in BaFe2(As1-xPx)2 iron pnictides emerges when its in-plane two-dimensional (2D) orthorhombic lattice distortion associated with nematic phase at Ts and three-dimensional (3D) collinear antiferromagnetic (AF) order at TN (Ts = TN) are gradually suppressed with increasing x, reaching optimal superconductivity around x = 0.30 with Tc $\approx$ 30 K. Here we show that a moderate uniaxial pressure along the c-axis in BaFe2(As0.70P0.30)2 spontaneously induces a 3D collinear AF order with TN = Ts > 30 K, while only slightly suppresses Tc. Although a ~ 400 MPa pressure compresses th…
We review our recent experimental results on the electronic nematic phase in electron- and hole-doped BaFe$_2$As$_2$ and FeSe. The nematic susceptibility is extracted from shear-modulus data (obtained using a three-point-bending method in a capacitance dilatometer) using Landau theory and is compared to the nematic susceptibility obtained from elastoresistivity and Raman data. FeSe is particularly interesting in this context, because of a large nematic, i.e., a structurally distorted but paramagnetic, region in its phase diagram. Scaling of the nematic susceptibility with the spin lattice rela…
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 $d_{yz}$ …
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…
Magnetic measurements on optimally doped single crystals of BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ ($x\approx0.35$) with magnetic fields applied along different crystallographic axes were performed under pressure, enabling the pressure evolution of coherence lengths and the anisotropy factor to be followed. Despite a decrease in the superconducting critical temperature, our studies reveal that the superconducting properties become more anisotropic under pressure. With appropriate scaling, we directly compare these properties with the values obtained for BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ as a function o…
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.
We use inelastic neutron scattering to study temperature and energy dependence of spin excitations in optimally P-doped BaFe2(As0.7P0.3)2 superconductor (Tc = 30 K) throughout the Brillouin zone. In the undoped state, spin waves and paramagnetic spin excitations of BaFe2As2 stem from antiferromagnetic (AF) ordering wave vector QAF= (1/-1,0) and peaks near zone boundary at (1/-1,1/-1) around 180 meV. Replacing 30% As by smaller P to induce superconductivity, low-energy spin excitations of BaFe2(As0.7P0.3)2form a resonance in the superconducting state and high-energy spin excitations now peaks a…
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…
We have systematically studied the nematic susceptibility in non-superconducting Ba(Fe$_{1-x}$TM$_{x}$)$_2$As$_2$ (TM = Cr, Mn, V and Cu) by measuring the uniaxial pressure dependence of the resistivity along the Fe-As-Fe direction. The nematic susceptibilities in all samples show the Curie-Weiss-like behavior at high temperatures, where the nematic Curie constant $A_n$ can be derived, similar to the Curie constant in a paramagnetism. While all these dopants do not introduce superconductivity in BaFe$_2$As$_2$, their effects on nematic fluctuations are different. In Mn, Cr and V doped samples,…
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$…
Magnetic interactions are generally believed to play a key role in mediating electron pairing for superconductivity in iron arsenides; yet their character is only partially understood. Experimentally, the antiferromagnetic (AF) transition is always preceded by or coincident with a tetragonal to orthorhombic structural distortion. Although it has been suggested that this lattice distortion is driven by an electronic nematic phase, where a spontaneously generated electronic liquid crystal state breaks the C4 rotational symmetry of the paramagnetic state, experimental evidence for electronic anis…
We use transport and inelastic neutron scattering measurements to investigate single crystals of iron pnictide BaFe$_{2-x}$Ni$_{x}$As$_{2}$ ($x=0,0.03$), which exhibit a tetragonal-to-orthorhombic structural transition at $T_s$ and stripe antiferromagnetic order at $T_N$ ($T_s\geq T_N$). Using a tunable uniaxial pressure device, we detwin the crystals and study their transport and spin excitation properties at antiferromagnetic wave vector $S_1(1,0)$ and its 90$^\circ$ rotated wave vector $S_2(0,1)$ under different pressure conditions. We find that uniaxial pressure necessary to detwin and mai…
The in-plane resistivity and uniform magnetic susceptibility anisotropies of $BaFe_{2}As_{2}$ are obtained with a new method, in which a large symmetry-breaking uniaxial strain is applied using a substrate with a very anisotropic thermal expansion. The resistivity anisotropy and its corresponding elastoresistivity exhibit very similar diverging behavior as those obtained from piezo-stack experiments. This suggests that the resistivity anisotropy is more a direct measure of magnetism than of nematicity, since the nematic transition is no longer well-defined under a large strain. In strong contr…
The superconducting, transport, and structural properties of optimally electron-doped BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$ are investigated by combining the electrical resistance and synchrotron X-ray diffraction measurements at high pressures. The superconducting transition temperature of this system is found to decrease in a similar way of the axial ratio of $c/a$ with increasing pressure but vanishing at a critical pressure of 7.5 GPa where $c/a$ has a dip and an isostructural transformation from a tetragonal to a collapsed tetragonal phase takes place. The resistance is found to obey a linear te…
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 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 …
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…
The concept of an electronically-driven breaking of the rotational symmetry of a crystal, without involving magnetic order, has found experimental support in several systems, from semiconductor heterostructures and ruthenates, to cuprate and iron-pnictide superconductors. In the pnictide BaFe$_{2}$As$_{2}$, such an "electronic nematic state" appears above the magnetic transition dome, over a temperature range that can be controlled by external strain. Here, by measuring the in-plane resistivity anisotropy, we probe the electronic anisotropy of this material over the entire nematic/magnetic dom…
We report on measurements of isothermal irreversible magnetization loops (M(H)) of Ni-doped BaFe2-xNixAs2 single crystals with x=0.1 and x=0.14 in magnetic fields up to 14T. For both samples in field H//c-axis and H//ab-plane, critical current density calculated from M(H) curves exceeds 106 A/cm2 at low temperatures suggesting strong intrinsic pinning in our crystals. In a broad temperature range 2-17K in both field orientations nearly optimally doped single crystal displays second magnetization peak (fish-tail effect). For H//c-axis, curves of the normalized pinning force, as a function of re…
We used transport and inelastic neutron scattering to study the optimally phosphorus-doped BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$ superconductor ($T_c = 30$ K). In the normal state, we find that the previously reported linear temperature dependence of the resistivity below room temperature extends to $\sim$ 500 K. Our analysis of the temperature and energy ($E=\hbarω$) dependence of spin dynamical susceptibility at the antiferromagnetic (AF) ordering wave vector $χ^{\prime\prime}({\bf Q}_{\rm AF},ω)$ reveal an $ω/ T$ scaling within $1.1<E/k_BT<110$. These results suggest that the linear temperature…
Superconductivity (SC) in the Ba-122 family of iron-based compounds can be controlled by aliovalent or isovalent substitutions, applied external pressure, and strain, the combined effects of which are sometimes studied within the same sample. Most often, the result is limited to a shift of the SC dome to different doping values. In a few cases, the maximum SC transition at optimal doping can also be enhanced. In this work, we study the combination of charge doping together with isovalent P substitution and strain by performing ionic gating experiments on BaFe$_2$(As$_{0.8}$P$_{0.2}$)$_2$ ultra…
Temperature dependent high pressure electrical resistivity studies has been carried out on Ba(Fe_{1-x}Ru_{x})_{2}As_{2} single crystals with x = 0.12, 0.26 and 0.35, which correspond to under doped, optimally doped and over doped composition regimes respectively. The evolution of structural/magnetic (T_{S-M}) and superconducting transition (T_(c)) temperatures, with pressure for various compositions have been obtained. The normal state resistivity has been analyzed in terms of a model that incorporates both spin fluctuations and the opening of the gap in the spin density wave (SDW)phase. It is…
Quantum materials such as antiferromagnets or superconductors are complex in that chemical, electronic, and spin phenomena at atomic scales can manifest in their collective properties. Although there are some clues for designing such materials, they remain mainly unpredictable. In this work, we find that enhancement of transition temperatures in BaFe2As2-based crystals are caused by removing local-lattice strain and electronic-structure disorder by thermal annealing. While annealing improves Neel-ordering temperature in BaFe2As2 crystal (TN=132 K to 136 K) by removing in-plane electronic defec…
We use neutron resonance spin echo and Larmor diffraction to study the effect of uniaxial pressure on the tetragonal-to-orthorhombic structural ($T_s$) and antiferromagnetic (AF) phase transitions in iron pnictides BaFe$_{2-x}$Ni$_{x}$As$_{2}$ ($x=0,0.03,0.12$), SrFe$_{1.97}$Ni$_{0.03}$As$_2$, and BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$. In antiferromagnetically ordered BaFe$_{2-x}$Ni$_{x}$As$_{2}$ and SrFe$_{1.97}$Ni$_{0.03}$As$_2$ with $T_N$ and $T_s$ ($T_N\leq T_s$), a uniaxial pressure necessary to detwin the sample also increases $T_N$, smears out the structural transition, and induces an ortho…
The nature of the nematic state in FeSe remains one of the major unsolved mysteries in Fe- based superconductors. Both spin and orbital physics have been invoked to explain the origin of this phase. Here we present experimental evidence for frustrated, short-range magnetic order, as suggested by several recent theoretical works, in the nematic state of FeSe. We use a combination of magnetostriction, susceptibility and resistivity measurements to probe the in-plane anisotropies of the nematic state and its associated fluctuations. Despite the absence of long-range magnetic order in FeSe, we obs…
The nematic susceptibility of Ba$_{1-x}$Na$_{x}$Fe$_{2}$As$_{2}$ single crystals is studied by measuring the Young's modulus using a three-point-bending setup in a capacitance dilatometer over a wide doping range. Particular emphasis is placed on the behavior within the double-Q antiferromagnetic $C_{4}$ re-entrant phase. Here, we surprisingly still observe a sizable nematic susceptibility in spite of the well-developed magnetic order, consistent with recent theoretical calculations. Outside the $C_{4}$ re-entrant region, the behavior is very similar to that of K-doped BaFe$_{2}$As$_{2}$. A si…
Electronic nematicity plays important role in iron-based superconductors. These materials have layered structure and theoretical description of their magnetic and nematic transitions has been well established in two-dimensional approximation, i.e., when the layers can be treated independently. However, the interaction between iron layers mediated by electron tunneling may cause non-trivial three-dimensional behavior. Starting from the simplest model for orbital nematic in a single layer, we investigate the influence of interlayer tunneling on bulk nematic order and possible preemptive state wh…
Electronic nematic behavior has been identified and studied in iron-based superconductors for some time, particularly in the well-known BaFe$_2$As$_2$ system, where it is well-known to compete with superconductivity. On the other hand, it has been shown recently that FeSe displays a negligible effect of nematicity on superconductivity near the superconducting transition, and actual cooperation between the two orders when the system is doped with S. Recently it has also been proposed that LiFeAs undergoes a nematic transition in the superconducting state itself. Generally, we expect superconduc…
A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations, originally phonons. Other collective modes that can play the same role, especially spin-fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements on five optimally doped Fe-based superconductors to reveal that a diverging \emph{nematic…
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…
Magnetic excitations in Ba(Fe0.94Co0.06)2As2 are studied by polarized inelastic neutron scattering (INS) above and below the superconducting transition. In the superconducting state we find clear evidence for two resonance-like excitations. At a higher energy of about 8 meV there is an isotropic resonance mode with weak dispersion along the c-direction. In addition we find a lower excitation at 4 meV that appears only in the c-polarized channel and whose intensity strongly varies with the L-component of the scattering vector. These resonance excitations behave remarkably similar to the gap mod…
We report on the nonequilibrium quasiparticle dynamics in BaFe$_2$As$_2$ on both the hole doped (Ba$_{1-x}$K$_x$Fe$_2$As$_2$) and electron doped (BaFe$_{2-y}$Co$_y$As$_2$) sides of the phase diagram using ultrafast pump-probe spectroscopy. Below $T_c$, measurements conducted at low photoinjected quasiparticle densities in the optimally and overdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ samples reveal two distinct relaxation processes: a fast component whose decay rate increases linearly with excitation density and a slow component with an excitation density independent decay rate. We argue that these t…
Nematicity is ubiquitous in electronic phases of high-$T_c$ superconductors, particularly in the Fe-based systems. While several experiments have probed nematic fluctuations, they have been restricted to uniform or momentum averaged fluctuations. Here, we investigate the behavior of finite-momentum nematic fluctuations by utilizing the anomalous softening of acoustic phonon modes in optimally doped Ba(Fe$_{0.94}$Co$_{0.06}$)$_2$As$_2$. We determine the nematic correlation length and find that it sharply changes its $T$-dependence at $T_c$, revealing a strong connection between nematicity and s…
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 …
The momentum dependence of the nematic order parameter is an important ingredient in the microscopic description of iron-based high-temperature superconductors. While recent reports on FeSe indicate that the nematic order parameter changes sign between electron and hole bands, detailed knowledge is still missing for other compounds. Combining angle-resolved photoemission spectroscopy (ARPES) with uniaxial strain tuning, we measure the nematic band splitting in both FeSe and BaFe$_2$As$_2$ without interference from either twinning or magnetic order. We find that the nematic order parameter exhi…
