Session B38: Fe-based Superconductors: Nematicity I

Anisotropic optical response in the electronic nematic phase of iron-pnictides

The ferropnictides harbor a structural tetragonal-to-orthorhombic transition at T$_s$ that may either coincides or precedes a transition into a long-range antiferromagnetic order (AFM) at T$_N$, usually ascribed to a spin-density-wave state. There is an ongoing debate as to whether the dc anisotropy (both in the nematic phase (T$_N$ $<$ T $<$ T$_s$) or in the tetragonal phase above T$_s$ in the presence of an external symmetry breaking field) is primarily determined by the Fermi surface or scattering rate anisotropy. We measure the in-plane optical reflectivity of BaFe$_2$As$_2$ (T$_s$ = T$_N$ = 135 K) over a broad spectral range, covering the energy interval from the far infrared to the ultraviolet, at several combinations of uniaxial pressure, used to detwin the specimen, and temperature. Our goal is to probe the anisotropic response in the real part $\sigma_1(\omega)$ of the optical conductivity, extracted from the reflectivity data via Kramers-Kronig transformations. 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, though, the dc resistivity anisotropy of strained samples is almost exclusively due to stress-induced changes in the Drude weight rather than anisotropy in the scattering rate. This result definitively establishes that the primary effect driving the resistivity anisotropy in the paramagnetic orthorhombic phase is the anisotropy of the Fermi surface [1]. Recent developments within this context on FeSe will be presented as well. [1] C. Mirri et al., Phys. Rev. Lett. 115, 107001 (2015).   

Nematicity and Spin Fluctuations in the Iron Pnictide Superconductors Studied by NMR

The iron pnictide superconductors exhibit rich phase diagrams with both nematic and magnetic ordering as well as unconventional superconductivity. These phases can be probed by As-75 NMR, which is sensitive to both magnetic and quadrupolar degrees of freedom. We show that the spin-lattice relaxation rate probes both the dynamical electron spin susceptibility as well as the dynamical nematic susceptibility in the Ba(Fe,Co)$_2$As$_2$ and BaFe$_2$(As,P)$_2$ system. A ubiquitous feature of the NMR in the doped systems, however, is the presence of glassy relaxation. We show that this behavior is connected to the large nematic susceptibility in these materials, and the presence of quenched random order. We further present new data on detwinned crystals under uniaxial strain, which uncovers the intrinsic anisotropy of the spin fluctuations in the nematic phase.   

A microscopic solution to the magnetic detwinning mystery in EuFe$_2$As$_2$

One of the greatest recent advances in studying nematic phenomena in Fe-based superconductors was the mechanical detwinning of the 122-family compounds. Unfortunately, these techniques generate considerable stress in the investigated samples, which contaminates the results. Recently, we observed that a minuscule magnetic field of the order of 0.1 T irreversibly and persistently detwins EuFe$_2$As$_2$, opening an entirely new avenue for addressing nematicity\footnote{PRL 113,227001 (2014)}. However, further development was hindered by the absence of a microscopic theory explaining this magnetic detwinning. In fact, Eu$^{2+}$ has zero orbital moment and does not couple to the lattice, and its exchange coupling with the Fe sublattice cancels by symmetry. Moreover, further increase of the field to $\sim$ 1 T leads to a reorientation of Fe domains, while even larger fields $\sim$10 T reorient the domains once again. We will present a new microscopic model, based on a sizable biquadratic coupling between the Fe 3$d$ and Eu 4$f$ moments. This model quantitatively explains our old and new magnetization and neutron diffraction data, thus removing the veil of mystery and finally opening the door to full-scale research into magnetic detwinning and nematicity in Fe-based superconductors.   

In-plane resistivity anisotropy in mechanically and magnetic field detwinned single crystals of EuFe$_{2}$As$_{2}$

The in-plane resistivity of EuFe$_{2}$As$_{2}$ (Eu122) shows anomalies at the nematic/magnetic ordering temperature of Fe ions, $T_N^{Fe} \approx$ 190 K, as well as of Eu ions, $T_N^{Eu} \approx$ 19 K. When the crystal is detwinned by mechanical strain, resistivity along the $a-$ orthorhombic direction is lowered at all temperatures $T < T_N^{Fe}$, similar to other parent 122 compounds such as Sr122 and Ba122 [1]. Application of a 3 T in-plane magnetic field below $T_N^{Eu}$ leads to the structural detwinning with $a-$ axis following field direction and persistent up to $T_N^{Fe}$ [2]. On contrary, $a-$ axis direction is fixed in strained samples. \newline\newline [1]E. C. Blomberg et al., Phys. Rev. B 83, 134505 (2011) \newline [2]S. Zapf et al., Phys. Rev. Lett. 113, 227001 (2014) \newline [3]Y. Xiao et al., Phys. Rev. B 81, 220406 (2010)   

Nmr Studies Of Strained Ba(Fe1-xcox)2as2single Crystal

{MNR measurements have been performed on strained ba(fe1-xcox)2as2for x}$=$\sout{\textsc{4.8{\%} around tetragonal-to-orthorhombic phase transition at ts. To ensure that the single crystal was strained, resistivity measurements were done in both strained and unstrained configurations. We report the spin-lattice relaxation rate of as site for hparallel and perpendicular to the a-axis direction and show that spin-lattice relaxation rate is anisotropic which reflects the anisotropic spin fluctuations.}}   

Enhancement of the Magnetic Ordered Moment in Electron-doped BaFe$_2$As$_2$ under Uniaxial Pressure

Many iron superconductors exhibit structural and magnetic phases that break the in-plane symmetry of the iron-pnitogen or iron-chalcogen layers. We developed a new apparatus to apply large and highly controllable in-plane uniaxial stress to these materials along the direction of the orthorhombic distortion at low temperature. Using several complimentary techniques, including DC electrical resistivity, neutron diffraction, and muon spin relaxation, we find that crystalline twinning in BaFe$_{2-x}$Ni$_x$As$_2$ and Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ is completely suppressed and the magnetic ordering temperature increases under modest uniaxial pressure, consistent with the idea that orthorhombicity favors the magnetic phase. Moreover, we find an enhancement of the magnetic ordered moment in the samples near the superconducting regime. We argue these results demonstrate the importance of quantum fluctuations for superconductivity, for which uniaxial stress is a novel probe.   

Nematic Quantum Critical Fluctuations in iron-based superconductor BaFe$_{2-x}$Ni$_x$As$_2$

We have systematically studied the nematic fluctuations in 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 though 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 sizable pressure-dependent resistivity along the (100) direction presents in all doping levels, which is against the simple picture of Ising-type nematic model. The signal along the (100) direction becomes maximum at optimal doping, suggesting that it is associated with nematic quantum critical fluctuations. Our results indicate that thermal fluctuations from striped antiferromagnetic order dominate the underdoped regime along the (110) direction. We argue that either there is a strong coupling between the quantum critical fluctuations and the fermions or more exotically, a higher symmetry may present around optimal doping.   

Nonlinear Elastoresistivity Response in the $A_{1g}$ Symmetry Channel of the Iron Superconductor Ba(Fe$_{0.975}$Co$_{0.025}$)$_2$As$_2$

Elastoresistivity relates changes in resistance of a material to strains that it experiences. Previously we have shown how the $B_{2g}$ component of the elastoresistivity tensor is proportional to the nematic susceptibility, and hence can be used to infer a divergence of the nematic susceptibility approaching the tetragonal-to-orthorhombic structural phase transition in the Fe-based superconductors. In this talk I will introduce a new application of elastoresistance measurements for probing the resistivity response in the $A_{1g}$ symmetry channel. This is not a nematic symmetry; rather, it describes the isotropic response to strains that the material experiences. This technique was performed on a stereotypical iron based superconductor, Ba(Fe$_{0.975}$Co$_{0.025}$)$_2$As$_2$. We find that the response in the $A_{1g}$ channel is nonlinear with a quadratic elastoresistance coefficient that diverges close to the tetragonal to orthorhombic structural transition. I will explain the significance of these measurements and how they fit with our understanding from previous measurements of the $B_{2g}$ elastoresistance response.   

Frustrated magnetism and quantum transitions of nematic phases in FeSe

The iron-based superconductivity has been known to develop near an antiferromagnetic order, but this paradigm apparently fails in the FeSe. The striking puzzle that FeSe displays a nematic order while being non-magnetic has led to competing proposals for the origin of the nematic order. Here we show that the phase diagram of FeSe can be fully described by a quantum spin model with highly frustrated interactions. We perform density matrix renormalization group calculations on a frustrated spin-1 bilinear-biquadratic model on the square lattice, and find three stable phases breaking $C_4$ rotational symmetry, including the antiferromagnetic states with wave vectors $(0,\pi)$ and $(\pi/2,\pi)$, and a $(\pi,0)$ antiferroquadrupolar state. Tuning the ratio of competing interactions, we show quantum transitions from the $(\pi,0)$ antiferroquadrupolar order to the $(\pi,0)$ antiferromagnetic state, either directly or through the $(\pi/2,\pi)$ antiferromagnetic order. Our findings explain the recent dramatic experimental observations of an orthorhombic antiferromagnetic order in the pressurized FeSe, and suggest that superconductivity in a wide range of iron-based materials has a common origin in the antiferromagnetic correlations of strongly correlated electrons.   

Interatomic Coulomb interaction and electron nematic bond order in FeSe

Despite having the simplest atomic structure, bulk FeSe has an observed electronic structure with the largest deviation from the band theory predictions among all Fe-based superconductors and exhibits a low temperature nematic electronic state without intervening magnetic order. We show that the Fe-Fe interatomic Coulomb repulsion $V$ offers a natural explanation for the puzzling electron correlation effects in FeSe superconductors. It produces a strongly renormalized low-energy band structure where the van Hove singularity sits remarkably close to Fermi level in the high-temperature electron liquid phase as observed experimentally. This proximity enables the quantum fluctuations in $V$ to induce a rotational symmetry breaking electronic bond order in the $d$-wave channel. We argue that this emergent low-temperature $d$-wave bond nematic state, different from the commonly discussed ferro-orbital order and spin-nematicity, has been observed recently by several angle resolved photoemission experiments detecting the lifting of the band degeneracies at high symmetry points in the Brillouin zone.   

Strong electronic two-dimensionality and close relationship between spin nematicity and superconductivity in soft-chemistry synthesized (Li,Fe)OHFeSe and FeSe single crystals

We have developed hydrothermal ion-exchange and ion-release routes to synthesize a series of big superconducting (Li,Fe)OHFeSe and FeSe single crystals out of insulating K$_{\mathrm{2}}$Fe$_{\mathrm{4}}$Se$_{\mathrm{5}}$ matrix. In (Li$_{\mathrm{0.84}}$Fe$_{\mathrm{0.16}})$OHFe$_{\mathrm{0.98}}$Se crystal, a common temperature scale $T$* $=$ 120 K has been established. Below $T$*, the normal state electronic behavior becomes highly two-dimensional prior to the superconducting transition and AFM spin fluctuations in the iron plane set in. In FeSe crystals, a spin-nematic order is identified by in-plane angular-dependent magnetoresistance and magnetism measurements, manifested as a rotational symmetry breaking and evident spin frustrations below a characteristic temperature $T_{\mathrm{sn}}$. Remarkably, a universal linear relationship between $T_{\mathrm{c}}$ and $T_{\mathrm{sn}}$ is observed on a series of crystal samples, indicating that the spin nematicity and the superconductivity in bulk FeSe have a common microscopic origin. \textbf{References:} [1] X. Dong et al., \textbf{\textit{JACS}} \textbf{137}, 66-69 (2015). [2] X. Dong et al., \textbf{\textit{PRB}} \textbf{92}, 064515 (2015). [3] D. Yuan et al., \textbf{\textit{Chin. Phys. B}} \textbf{25}, 077404 (2016). [4] D. Yuan et al.,, \textbf{\textit{PRB }}\textbf{94}, 060506R (2016).