Session R39: Fe-based Superconductors: Nematicity II

Magnetically induced in-plane susceptibility and resistivity anisotropies in BaFe$_{2}$As$_{2}$ and FeSe

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 [1]. The resistivity anisotropy and its corresponding elastoresistivity exhibit very similar diverging behavior as those obtained from piezo-stack experiments [2]. 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 contrast to the large resistivity anisotropy above T$_{N}$ , the anisotropy of the in-plane magnetic susceptibility develops largely below T$_{N}$. Using an itinerant model, we show that the susceptibility anisotropy is determined by spin-orbit coupling and the orientation of the magnetic moments in the magnetically ordered phase. Similar results, however with opposite signs, are found for FeSe, suggesting that the nematic transition in FeSe is also of magnetic origin. [1] M. He et al., arXiv:1610.05575v2 (2016). [2] J.-H. Chu et al.,Science 337, 710 (2012).   

Rare region effects on the Ising-nematic quantum phase transition

The phase diagrams of several correlated electronic systems display an unusual type of electronic liquid-crystalline order, called Ising-nematic, in which the electronic degrees of freedom spontaneously break the tetragonal symmetry of the system. Here, we investigate theoretically the impact of rare regions, characteristic of disordered systems with random dilution, on the Ising-nematic quantum phase transition promoted by the partial melting of a density-wave phase. Although long-range Ising-nematic order takes place in droplets of all sizes, the onset of the transition and the character of the transition (i.e. second-order or first-order) depend on the size of the droplet. After averaging over the droplets, we find that the first-order quantum Ising-nematic transition of the clean system is smeared and behaves essentially as a second-order transition. We attribute this behavior to an effective dimensional crossover, and discuss the experimental implications of our findings.   

Coupled nematic-magnetic quantum phase transitions in the presence of isotropic quenched disorder: a renormalization-group study

Recent elastoresistance measurements in iron-based superconductors revealed a puzzling interplay between disorder and nematic quantum criticality. Theoretically, in the case in which nematic order is promoted by magnetic fluctuations in an itinerant system, renormalization group calculations of the appropriate low-energy model predict a simultaneous first-order nematic-magnetic quantum phase transition, and, consequently, the absence of a nematic quantum critical point. Here, we investigate how these results are affected by the presence of isotropic quenched disorder, which is manifested as a random-mass term in the low-energy model. By combining the replica trick and the renormalization group approach, we investigate the existence of nematic fixed points, and discuss whether disorder can promote a second-order nematic quantum phase transition that is split from the magnetic quantum phase transition.   

Elasto-Scanning Tunneling Microscopy - New Insights into the nature of Electronic Nematicity in the Pnictides

Mechanical strain is a powerful technique for tuning electronic interactions in quantum materials. In particular, strain affects nematic order in the same way that magnetic field affects ferromagnetic order. Here, we report a new experimental scanning probe technique that provides atomic-resolution insight into the effect of strain on electronic structure. We use this technique to study the coupling between strain and electronic nematicity in the iron pnictide superconductors. We show that while true long range nematic order in the pnictides is established at the tetragonal to orthorhombic structural transition temperature, the dominant effects on the electronic structure are associated with the magnetic phase transition. We complement this technique with temperature and doping dependent measurements of ordered domains across the phase diagram which show that strong nematic fluctuations persist all the way to the overdoped end of the superconducting dome, and that the strength of electronic nematic order in the pnictide NaFeAs is intimately connected to magnetic correlations.   

Nematic superconducting state in iron pnictides near optimal hole doping

Nematic order often breaks the tetragonal symmetry of iron-based superconductors~\footnote{R. M. Fernandes, A.V. Chubukov and J. Schmalian, \textbf{Nat. Phys.} 10, 97 (2014)}. It arises from regular structural transition or electronic instability in the normal phase. Recently, a nematic superconducting state was observed which is not accompanied by a symmetry breaking of tetragonal lattice or the onset of magnetic order. Measurements of the angular dependence of the in-plane magnetoresistivity of single-crystalline thin samples of Ba$_{0.5}$K$_{0.5}$Fe$_{2}$As$_{2}$ in vicinity of T$_c$ found large twofold oscillations with the rotation of the applied magnetic field in the basal plane~\footnote{ J. Li, et al., submitted to \textbf{P. N. A. S.} (2016)}. Here we present the explanation of this unusual phenomenon on the basis of microscopic description of the superconducting state of these samples. We show that the nematic superconductivity arises from the weak mixture of the quasi-degenerate s$_\pm$ and d$_{x^2-y^2}$ components of the superconducting condensate, most probably induced by a weak anisotropy of stresses inherent to single-crystalline films.   

New experimental results concerning the nematic state in Fe-based superconductors

The nature of the nematic state in FeSe and Ba122 systems is studied using a variety of experimental probes. In particular, we use a new technique, in which a considerable uniaxial strain is applied to the crystals by glueing them to a substrate with a large anisotropic thermal expansion, to measure the in-plane anisotropy of the uniform magnetic susceptibility and the resistivity under large strains [1]. We discuss the scaling of these quantities for both Ba122 and FeSe. Further, we study the shear-modulus response of the C4-reentrant phase in Na - doped Ba122 using a three-point bending technique. Surprisingly, we still find a sizeable nematic susceptibility in this phase, which further increases upon entering the superconducting state, in strong contrast to the behavior of optimally doped crystals. This is likely related to the strong competition between superconductivity with the double-Q state, as our previous studies have shown [2,3]. Finally, we study the coupling between nematicity and superconductivity of FeSe crystals using thermal expansion, magnetostriction and heat capacity. Surprisingly, the orthorhombic distortion is enhanced by superconductivity in S-substituted FeSe [4]. Heat capacity data point to a nodal superconducting gap structure. [1] M. He, L. Wang, F. Ahn, F. Hardy, T. Wolf, P. Adelmann, J. Schmalian, I. Eremin, and C. Meingast, arXiv:1610.05575. [2] A. E. Boehmer, F. Hardy, L. Wang, T. Wolf, P. Schweiss, and C. Meingast, Nat. Commun. 6, 7611 (2015). [3] L. Wang, F. Hardy, A. E. Boehmer, T. Wolf, P. Schweiss, and C. Meingast, PRB 93, 014514 (2016). [4] L. Wang, F. Hardy, T. Wolf, P. Adelmann, R. Fromknecht, P. Schweiss, and C. Meingast, physica status solidi (b) 1-6 (2016), 10.1002/pssb.201600153.   

Nematic fluctuations and resonance in iron-based superconductors

The spontaneous appearance of nematicity, a state of matter that breaks rotation but not translation symmetry, is ubiquitous in many iron based superconductors (Fe SC), and has relevance for the cuprates as well. Here I will review recent electronic Raman scattering experiments which report the presence of critical nematic fluctuations in the charge channel in the tetragonal phase of several Fe SC systems. In electron doped Co-BaFe$_{\mathrm{2}}$As$_{\mathrm{2}}$ (Co-Ba122), these fluctuations extend over most of the superconducting dome. Their associated nematic susceptibility shows Curie-Weiss behavior, and its doping dependence suggests the presence of a nematic quantum critical point near optimal T$_{\mathrm{C}}$ [1,2] Similar nematic fluctuations are also observed in FeSe despite the absence of magnetic order, raising the question of the link between nematicity and magnetism in Fe SC [3]. In FeSe I will further contrast the evolution of nematic fluctuations under isoelectronic S substitution and hydrostatic pressures up to 8 GPa, with only the former showing evidence for a nematic quantum critical point. In the superconducting state of Co-Ba122, I will show that a resonance emerges in the Raman spectra near the nematic quantum critical point. This nematic resonance is a clear fingerprint of the coupling between nematic fluctuations and Bogoliubov quasiparticles, and can be thought as the nematic counterpart of the spin resonance observed in neutron scattering experiments [4]. [1] Y. Gallais et al. Phys. Rev. Lett. 111, 267001 (2013) [2] Y. Gallais and I. Paul, C. R. Phys. 17, 133 (2016) [3] P. Massat at al. PNAS 113, 9177 (2016) [4] Y. Gallais et al. Phys. Rev. Lett. 116, 017001 (2016)   

Effect of nematic order on the low-energy spin fluctuations in detwinned BaFe$_{1.935}$Ni$_{0.065}$As$_2$

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,$\pi$) 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 at (0,$\pi$) happens just below $T_s$, suggesting strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.   

Short-ranged spin correlations and electronic nematicity in the pnictides: theoretical framework and application to elasto-scanning tunneling microscopy data

The origin of electronic nematic order in iron-based superconductors is a hotly debated topic, with potential implications for superconducting pairing mechanism in these and other systems. Scanning tunneling microscopy experiments on Co-doped NaFeAs performed in the presence of elastic strain generated by piezoelectric devices reveal a rich temperature and doping dependence of the anisotropy of the electronic states both in real-space and momentum-space. Here, we argue that these observations are consistent with modest symmetry-breaking strain fields inducing unidirectional large-amplitude magnetic fluctuations even in the paramagnetic state. We present a theoretical model describing these effects and their coupling to low-energy electronic states, and discuss the constraints imposed by the experimental data on the character of the magnetic fluctuations.   

Intertwined superconducting and nematic orders in NaFe$_{1-x}$Ni$_x$As without antiferromagnetic order

We use neutron scattering to study antiferromagnetic (AF, $T_{\rm N}$) and tetragonal-to-orthorhombic structural ($T_{\rm s}$) phase transitions in NaFe$_{1-x}$Ni$_x$As. Compared to BaFe$_{2-x}$$TM_x$As$_2$ ($TM =$ Co, Ni) and NaFe$_{1-x}$Co$_x$As, AF order in NaFe$_{1-x}$Ni$_x$As remains commensurate and long-range upon approaching optimal superconductivity while exhibiting strong competition with superconductivity. For NaFe$_{0.987}$Ni$_{0.013}$As with $T_{\rm s}\approx 33$ K, $T_{\rm N}\approx 20 K$, and $T_{\rm c}\approx 15$ K, we find that while magnetic order is completely suppressed by superconductivity below $T_{\rm r}\approx 10$ K, the suppression of lattice orthorhombicity stops abruptly below $T_{\rm r}$. These results demonstrate that orthorhombicity only indirectly competes with superconductivity through coupling with the magnetic order parameter and there is no structural re-entry into the tetragonal phase in NaFe$_{1-x}$Ni$_x$As. The lack of direct coupling between superconductivity and the lattice in the absence of magnetic order is similar to that observed in FeSe, suggesting the nematic order and associated lattice distortions in these compounds are intertwined rather than competing with superconductivity.   

The relationship between static and dynamic nematic susceptibility studied by low-energy Raman spectroscopy

The critical nematic fluctuations are widely observed in many iron-based superconductors and are related to the superconductivity [1]. Both Raman susceptibility and elastic shear modulus $C_{66}$ show evidence of XY quadrupolar nematic fluctuations near the nematic instability. However, while the dynamic Raman response and the static $C_{66}$ data exhibit apparent different temperature dependence, similar critical temperatures were derived from both measurements [2,3]. Here we measure and analyze ultra-low frequency Raman susceptibility in BaFe$_2$As$_2$, which we compare to the $C_{66}$, and demonstrate consistency between the dynamic and static nematic susceptibilities, with accounting for the ultra-low frequency spectral weight in the Raman response, which was missed in the prior studies. [1] H.-H.Kuo \textit{et al}., Science \textbf{352}, 958 (2016). [2] Y.Gallais \textit{et al}., Phys.Rev.Lett. \textbf{111}, 267001 (2013). [3] A.E.Bohmer \textit{et al}., Phys.Rev.Lett. \textbf{112}, 047001 (2014).