Session R37: Focus Session: Fe-based Superconductors: Nematicity and Related Phenomena

Effects of competing Neel-type magnetic fluctuations and nematic order on the superconductivity of the iron arsenides

In many iron-based superconductors, the presence of two matching electron pockets displaced by $(\pi,\pi)$ gives rise to Neel-type magnetic fluctuations, in addition to the usual stripe-type magnetic fluctuations peaked at $(\pi,0)$ and $(0,\pi)$. Indeed, recent neutron scattering experiments observed both types of fluctuations in certain hole-doped iron pnictides, which intriguingly do not display superconductivity. In this talk, we employ an Eliashberg approach to address the impact of competing $(\pi,\pi)$ and $(\pi,0)$ fluctuations on the superconducting state of the iron arsenides. We show that, surprisingly, even weak short-ranged Neel fluctuations strongly suppress the $s^{\pm}$ state. The main contribution to this suppression comes from a repulsive $s^{\pm}$ interaction induced by the Neel fluctuations, and not from the inelastic scattering pair-breaking that they promote. Upon enhancing the strength of the Neel fluctuations, a d-wave state appears, preceded by either an intermediate $s+id$ state or a non-superconducting region, forming a two-dome structure. We compare our results to experimental findings, and discuss their implications to the optimal $T_c$ of the iron arsenides, arguing that it can be enhanced via a tetragonal-symmetry breaking induced by nematic order.   

Divergent nematic charge susceptibility in iron-pnictide

We report doping dependent low energy Electronic Raman Scattering measurements in the normal state of Ba(Fe$_{1-x}$Co$_{x}$As) $_{2}$ stress-free twinned single crystals. The Raman response shows a systematic increase at low energy upon approaching the magneto-structural transition. This quasi-elastic peak displays a distinct symmetry dependence which links it to the nematic charge response in the x$^{2}$-y$^{2}$ symmetry channel, indicating an incipient tetragonal symmetry breaking instability in the charge sector. The extracted static nematic charge response shows Curie - Weiss behavior above the magneto-structural transition with a characteristic temperature which decreases with doping. These results allow us to disentangle the respective roles of spin, charge and lattice degrees of freedom in the mechanism of tetragonal symmetry breaking in iron-pnictides superconductors.   

Divergent nematic susceptibility in an iron arsenide superconductor

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition can be complicated by coupling between distinct order parameters. We show how measurement of the divergent nematic susceptibility of the iron pnictide superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also indicate an electronic nematic quantum phase transition near the composition with optimal superconducting transition temperature.   

In-plane structural and electronic anisotropy in de-twinned CaFe$_2$As$_2$ compounds

In-plane structural and electronic anisotropy has been studied in a wide range of iron-based superconductors by detwinning via uniaxial stress or strain [1]. In particular, materials based on BaFe$_2$As$_2$ ("112") are among the most studied systems, where different dopants, annealing protocols and different flux growths were extensively explored. However CaFe$_2$As$_2$ remains a much less studied compound and it exhibits properties quite different from Ba-based 122's [2]. Here we report polarized-light microscopy and electric transport measurements of strain-detwinned CaFe$_2$As$_2$ compounds. Our results reveal unusual evolution of the structural, electronic and magnetic properties dependent on annealing, growth from Sn flux vs FeAs flux, and doping, as compared to BaFe$_2$As$_2$. Among the key observations are the differences in twin domain evolution, and a hysteresis in structural and electronic anisotropy upon warming and cooling. This work was supported by the Department of Energy Office of Science, Basic Energy Sciences under Contract No. DE-AC02-O7CH11358.\\[4pt] [1] M. A. Tanatar, E. C. Blomberg, et. al. Phys. Rev. B 81, 184508 (2010).\\[0pt] [2] S. Ran, et. al. Phys. Rev. B 85, 224528 (2012).   

Chasing the nematic phase in detwinned Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with optical investigations

A renewed interest in the study of symmetry-breaking competing states in complex interacting systems followed the discovery of a broken rotational symmetry, due to stripe or nematic order, in the pseudogap phase of the copper oxide superconductors. The most recent playground in which to address the competition between structural, magnetic and superconducting phases is provided by the iron-pnictide superconductors. In these systems, the non-superconducting parent compounds undergo an antiferromagnetic transition into a broken-symmetry ground state at T$_N$, which is always preceded by or coincident with a tetragonal-to-orthorhombic structural distortion at T$_s$. Here, we investigate the optical conductivity with light polarized along the in-plane orthorhombic a- and b-axis of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ for x=0, 2.5\% and 4.5\% (i.e., in the so-called underdoped regime) under $tunable$ uniaxial pressure across their structural and magnetic transitions. We estimate the dichroism, which extends to high frequencies and temperatures. All together, our results on such single domain specimens reveal a nematic susceptibility as well as the electronic nature of the structural transition.   

Coupled orthorhombic distortion, antiferromagnetism, and superconductivity in a single twin domain of Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{2}$As$_{2}$ (x$=$0.047)

The interplay between structure, magnetism, and superconductivity in single crystal Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{2}$As$_{2}$ (x$=$0.047) has been studied using high-resolution X-ray diffraction by monitoring charge Bragg peaks in each twin domain separately. The emergence of superconducting state is correlated with the suppression of theorthorhombic distortion around $T_{C}$, exhibiting the competition between orthorhombicity and superconductivity. Above $T_{S}$, the Bragg peak widths gradually broaden, possibly induced by orthorhombic (nematic) fluctuations in the paramagnetic tetragonal phase. Upon cooling, anomalies in the peak width are observed at $T_{S}$ and also $T_{N}$ indicative of strong magnetoelastic coupling. Using the capability to study individual twin domains, the peak widths in the \textit{ab}-plane are found to exhibit anisotropic behavior along and perpendicular to the stripe-type AFM wave vector. In contrast, the temperature dependencies of the out-of-plane peak width showan anomaly at $T_{N}$, reflecting the connection between Fe-As distance and Fe local moment.   

Nematic transition and hidden quantum critical point in iron-pnictide superconductors

A central issue in the physics of iron-based superconductivity concerns the origin of the pairing interaction, in which the importance of the spin and orbital degrees of freedoms has been discussed. Clarifying the anomalies inherent to this system and unveiling their connections to the high-temperature superconductivity are of primary importance. Here, we report our investigations on clean single crystals of BaFe$_2$(As$_{1-x}$P$_x$)$_2$ [1]. The observed quantum critical point (QCP) behaviors as represented by non-Fermi liquid transport [1], effective mass enhancement [2], and a sharp peak in the zero-temperature magnetic penetration depth [3] at a critical doping are discussed. In addition, we discuss the development of electronic nematicity, a unidirectional self organized state which breaks the underlying crystal lattice symmetry. Our highly sensitive magnetic anisotropy measurements, together with high resolution synchrotron X-ray diffraction experiments, indicate that electronic nematicity develops in the normal state, far above the magneto-structural and superconducting transitions, resulting in a new phase diagram of iron-based superconductors. The development of electronic nematicity appears to help the emergence of superconductivity whilst the QCP provides the highest superconducting transition temperature.\\[4pt] [1] S. Kasahara et al., Phys. Rev. B {\bf 81}, 184519 (2010).\\[0pt] [2] H. Shishido et al., Phys. Rev. Lett. {\bf 104}, 057008 (2010).\\[0pt] [3] K. Hashimoto et al., Science {\bf 336}, 1554-1557 (2012).\\[0pt] [4] S. Kasahara, et al., Nature {\bf 486}, 382-385 (2012).   

Electronic anisotropy in Ba(Fe$_{1-x}$Ru$_{x})_{2}$As$_{2}$ revealed by ARPES

One of the central issues in field of iron pnitides is the origin of electronic anisotropy observed by in-plane resistivity measurement and STM quasi-particle interference patterns. It is believed that it is related to magnetism and plays an important role in superconductivity in iron pnictides. It was argued that the split bands in ARPES data are from two orthogonal bands with dominant d$_{xz}$ and d$_{yz}$ characters, demonstrating the in-plane electronic anisotropy. It appears to be consistent with anisotropy observed by other probes. We performed temperature dependent ARPES measurements on an iron pnictide system, Ba(Fe$_{1-x}$Ru$_{x})_{2}$As$_{2}$, to experimentally verify existence of electronic anisotropy and compare the results with those of BaFe$_{2}$As$_{2}$ and Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$.   

Elastic softening of the shear modulus in Fe-based superconductors

A strong softening of the elastic shear modulus C$_{\mathrm{66}}$ has been observed as one approaches the spin-density-wave (SDW) transition in Ba122 from high temperature [1,2]. A smaller softening is still observed for superconducting Co-doped Ba122 crystals, followed by distinct hardening below T$_{\mathrm{c\thinspace }}$[1,2]. This elastic response has been taken as evidence either for electronic-magnetic nematic fluctuations [1], or as evidence for a structural quantum critical point near optimal doping [2]. Here we study the elastic response of various Fe-based superconductors by a recently developed technique based upon a three-point bending experiment in a high-resolution capacitance dilatometer. We measure the temperature dependence of the Young's modulus, which for thin slabs can be shown to be closely related to C$_{\mathrm{66}}$ for a given orientation. This is confirmed by measurements on Co-doped Ba122, for which we find very similar results as previously reported [1,2]. We will report on new measurements of the Young's modulus on other Fe-based Ba122 systems in order to study the universality of the elastic response at the SDW and superconducting transitions. [1] R. M. Fernandes, et al., Phys. Rev. Lett. 105, 157003 (2010). [2] M. Yoshizawa, et al., J. Phys. Soc. Jpn. 81, 024604 (2012).   

Magnetic Origin of Electronic Nematicity in NaFeAs (Part I)

Several experiments have shown that the parent states of the iron pnictides display electronic nematicity at high temperature, where the electronic states spontaneously break the rotational symmetry of the crystal lattice. A common feature displayed by many pnictide systems is a tetragonal to orthorhombic distortion on cooling down the system below $T_{S}$ and a magnetically ordered phase below $T_{SDW}$. In particular, NaFeAs has a structural to orthorhombic transition ($T_{S}$=54K) and a SDW transition ($T_{SDW}$= 39K). This wide temperature difference between transitions makes it an excellent testing ground for the characterization of the electronic states in each one of these regimes. The electronic states of this material can be directly visualized as a function of temperature using atomic-resolution scanning tunneling microscopy/spectroscopy. Real-space images of the electronic states show domains on the micron scale, with a strong unidirectional character persisting to temperatures well above $T_{S}$. These unidimensional features are found to be localized around defects in the system. We will discuss the details of the energy and temperature dependence of these features in both real space and Fourier space, as well as draw differences with the structurally similar LiFeAs.   

Magnetic Origin of Electronic Nematicity in NaFeAs (Part II)

The characterization of possible broken symmetries is essential to understanding high-temperature superconductivity. The electronic states of many iron-based superconductors have been shown to break rotational symmetry, but the origin of this nematicity remains elusive. We use Scanning Tunneling Microscopy (STM) and Spectroscopy (STS) to directly visualize the spatial structure of electronic states in NaFeAs. Intrinsic defects produce unidirectional spectroscopic features that persist to temperatures well above both the spin density wave (SDW) and orthorombic transitions. By comparing our measurements to angle-resolved photoemission spectroscopy (ARPES) data on the same material, we find that these features arise from quasiparticle interference (QPI) in the presence of magnetic order, indicating the primary role of spin interactions in electronic nematicity.   

Nematicity driven by hybridization in the iron-based superconductors

We introduce an effective three-orbital model to study the normal state of the iron-based superconductors. It has both itinerant and localized electrons - the former originate from the d$_{xz}$/d$_{yz}$ iron orbitals, and the latter from the d$_{xy}$ iron orbitals. These distinct degrees of freedom are coupled through hybridization and onsite interactions. On a mean-field level this model has an excitonic instability, driven by the effective delocalization of the d$_{xy}$ electrons. Because of the multiband character of the itinerant Fermi surface the ordered state can spontaneously break the lattice rotation symmetry (and thus is nematic) and generate orbital order. In this scenario the nematic state is induced by the coupling of the d$_{xz}$/d$_{yz}$ with the d$_{xy}$ iron orbitals, rather than the presence of magnetic order, or the proximity to such. We propose this mechanism as an explanation of the tendency towards nematicity observed in several iron-based compounds, and study some of its experimental consequences.   

Nematic state of the pnictides induced by the interplay between the spin, orbital, and lattice degrees of freedom

The nematic state with orthorhombic distortion observed in several iron based superconductors is stabilized in the undoped three-orbital ($xz$, $yz$, $xy$) spin-fermion model [1] via the addition of lattice degrees of freedom. The Monte Carlo simulations show that the electron-phonon coupling is not sufficient to stabilize the experimentally observed lattice distortion. The nematic phase is induced instead by the spin-lattice coupling. The interplay between the coupling strength of the lattice to the magnetic and charge degrees of freedom determines the separation between the structural and the magnetic transitions. Experimental results for the anisotropic behavior of the resistivity and the orbital spectral weight as a function of the temperature are also reproduced by the numerical simulations.[2] [1] S. Liang, G. Alvarez, C. Sen, A. Moreo, and E. Dagotto, Phys. Rev. Lett. 109 047001 (2012) and references therein. [2] S. Liang, A. Moreo, and E. Dagotto, submitted for publication.