Session V22: Focus Session: Fe-based Superconductors - Magnetism and Anisotropy

In Plane Resistivity Anisotropy in iron Chalcogenides

FeTe suffers a bicolinear antiferromagnetic ordering, with a ($\frac{1}{2}$ 0) ordering wave-vector, in contrast to the ($\frac{1}{2}$ $\frac{1}{2}$) ordering wave-vector found in underdoped ``122'' and ``1111'' iron pnictides. At the optimal doping the static ($\frac{1}{2}$ 0) order disappears and a spin resonance at the ($\frac{1}{2}$ $\frac{1}{2}$) wave-vector emerges. Here we report measurements of the in-plane resistivity anisotropy of single crystals of Fe$_{1+\delta}$Te$_{1-x}$Se$_x$ for underdoped and optimally doped compositions. The underdoped compounds were partially detwinned by applying uni-axial strain along the ($\frac{1}{2}$ 0), revealing a larger resistivity along the antiferromagnetic ordering direction. However, for optimal doping uni-axial strain induces the largest resistivity anisotropy along the ($\frac{1}{2}$ $\frac{1}{2}$) direction, similar to the ``122'' family of compounds. This behaviour suggests that in addition to the presence of spin resonance, a divergent nematic susceptibility might be a key feature associated with optimal doping in iron based superconductors.   

The temperature dependence of the conductance anisotropy of the pnictides studied via Monte Carlo simulation of the Spin-Fermion model

The undoped three-orbital ($xz$, $yz$, $xy$) spin-fermion model for the pnictides is studied via Monte Carlo (MC) simulations [1], using both the standard exact diagonalization of the fermionic sector (supplemented by cooling down procedures) developed in the manganite context [2], as well as the truncated polynomial expansion techniques [3]. The magnetic order is found to be the expected $(\pi,0)$ wavevector and the angle-resolved photoemission signal is in good agreement with experiments. The low-temperature conductance reveals the experimentally observed anisotropy between the ferromagnetic and the antiferromagnetic (AFM) directions, with the largest conductance for the AFM case, similarly as observed in recent investigations using the Hartree-Fock approximation to the Hubbard model [4]. The finite temperature MC analysis also produces results in good agreement with transport experiments. [1] S. Liang, G. Alvarez, C. Sen, A. Moreo, and E. Dagotto, submitted for publication. [2] C. Sen, S. Liang, and E. Dagotto, arXiv: 1109.1797 ; and references therein. [3] C. Sen, G. Alvarez, Y. Motome, N. Furukawa, I. A. Sergienko, T. Schulthess, A. Moreo, and E. Dagotto. Phys. Rev. B 73, 224430 (2006). [4] X. Zhang and E. Dagotto, Phys. Rev. B 84 132505 (2011).   

Anisotropy in BaFe$_{2}$Se$_{3}$ single crystals with double chains of FeSe tetrahedra

Since two-dimensional (2D) FePn or FeCh (Pn = pnictogens, Ch = chalcogens) tetrahedron layers are the common structural ingredient in all iron based superconductors, they are probably related to high temperature superconductivity. In order to fully understand the nature of iron-based superconductivity, study of materials containing similar FePn or FeCh tetrahedron as building blocks is of significant interest. BaFe$_{2}$Se$_{3}$ contains one-dimensional (1D) double chains of edge shared Fe-Se tetrahedra along the b-axis, in contrast to iron chalcogenide superconductors which feature two-dimensional (2D) Fe-Se planes. We report the anisotropic physical properties and local crystal structure of Ba$_{1.00(4)}$Fe$_{1.9(1)}$Se$_{3.1(1)}$ single crystals. It shows that BaFe$_{2}$Se$_{3}$ is a semiconductor with a short-range AFM correlation at the room temperature and a long-range AFM order below 255 K. Composition analysis indicates that all crystallographic sites are fully occupied. X-ray absorption near edge structure (XANES) result shows that the valence of Fe is about 1.87+.   

Towards an understanding of magnetic interactions and anisotropies in iron superconductors

The itinerant or strong coupling origin of magnetism in iron pnictides is still unsettled. The localized description generally assumes AF exchange constants satisfying $2J_2>J_1$, with$J_1$ and $J_2$ referring to first and second nearest neighbors respectively. The itinerant picture relies on the nesting of the Fermi surface. Both descriptions reproduce the columnar ordering found experimentally. The role played by the Hund's coupling $J_H$ and the orbital degree of freedom are also highly debated. Orbital ordering has been invoked to explain the anisotropic resistivity and optical conductivity. We make connection between these two pictures by studying the same five-orbital model within Heisenberg and mean field descriptions [1]. We have found that $J_2/J_1$ strongly depends on the charge and orbital filling what results in an unexpected sensitivity of the AF ordering to crystal field parameters. $J_1$ and $J_2$ can become ferromagnetic at large $J_H$. Consistent results are obtained in the mean field description. We also analyze the resistivity and optical conductivity anisotropies and show that they are a consequence of magnetism and not of orbital ordering [2].\\[4pt] [1] M.J. Calder\'on et al, arXiv:1107.2279. E. Bascones et al, PRL 104, 227201 (2010).\\[0pt] [2] B. Valenzuela et al, PRL 105, 207202 (2010).   

Nematic order and its implications to the iron pnictides: pseudogap behavior, orbital order, and magneto-structural phase diagram

We present an electronic model for the emergence of nematic order in the iron pnictides. In particular, we show that the degeneracy of the magnetic ground state, allied to spin fluctuations, gives rise to a state that spontaneously breaks the tetragonal symmetry of the system, but preserves its spin-rotational symmetry. The nematic state displays several anisotropic properties, inducing a weak orbital polarization as well as a small orthorhombic distortion of the lattice. Nematic order also enhances the magnetic fluctuations and facilitates the magnetic phase transition, leading to a joint magnetic and meta-nematic transition, as well as to a pseudogap behavior due to magnetic precursors. Finally, we discuss the characters of the magnetic and structural phase transitions, showing that electron doping tends to split both transitions, whereas pressure and lattice softness tend to make them simultaneous. Our model provides a simple framework to understand the interplay between the different degrees of freedom present in the iron pnictides, shedding light on the primary role played by magnetism in these materials.   

Impurity-Induced Electronic Nematic State in Iron-Pnictide Superconductors

We propose that impurity-induced electronic nematic state is realized above the orthorhombic structure transition temperature $T_S$ in iron-pnictide superconductors [1]. In the presence of strong orbital fluctuations near $T_S$, it is theoretically revealed that a single impurity induces non-local orbital order with $C_2$-symmetry, consistently with recent STM/STS measurements. Each impurity-induced $C_2$ orbital order aligns along a-axis by applying tiny uniaxial pressure along b-axis. In this impurity-induced nematic phase, the resistivity shows sizable in-plane anisotropy ($\rho_b/\rho_a \sim 2$) even above $T_S$, actually observed in various ``detwinned" samples. The present study indicates the existence of strong orbital fluctuations in iron-pnictide superconductors. [1] Y. Inoue, Y. Yamakawa and H. Kontani, arXiv:1110.2401.   

Effect of uniaxial strain on the structural and magnetic phase transitions in BaFe$_2$As$_2$

We report neutron scattering experiments probing the influence of uniaxial strain on both the magnetic and structural order parameters in the parent bilayer iron pnictide compound BaFe$_2$As$_2$. Under the application of modest strain fields along the in-plane orthorhombic b-axis, we observe an upward shift in the onset of both the structural and magnetic phase transition temperatures. Our data show that modest strain fields can affect significant changes in phase behavior simultaneous to the removal of structural twinning effects. As a result, we demonstrate in BaFe$_2$As$_2$ samples detwinned via uniaxial strain that the in-plane C$_4$ symmetry is broken by both the structural lattice distortion and long-range spin ordering at temperatures far above the nominal, strain-free, phase transition temperatures. The relevance of our measurements to earlier transport measurements in detwinned crystals of BaFe$_2$As$_2$ is discussed.   

Anisotropic transport properties of the paramagnetic state of iron-based superconductors

Recent experiments in detwinned iron-pnictide samples have revealed strong anisotropies in the in-plane transport properties of the paramagnetic state. Since these anisotropies cannot be attributed solely to the small orthorhombic distortion of the lattice, it has been proposed that an underlying anisotropic electronic order is at play. One of the candidates is the Ising-nematic order that emerges due to the degeneracy of the magnetic ground state. Here we present a microscopic model for the transport properties of this nematic phase, considering both the elastic scattering by impurities as well as the inelastic scattering by anisotropic spin fluctuations. We show that the interference between these two scattering channels give rise to anisotropic non-Fermi liquid transport properties. In particular, we explain the observed sign of the resistivity anisotropy in electron-doped samples and predict a sign-change for sufficiently hole-doped samples. We also address the suppression of the resistivity anisotropy with sample annealing, as well as its dependence on alkaline-earth substitution. Finally, we discuss the predictions of our model to the thermopower anisotropy.   

Anisotropic magnetoelastic coupling in iron arsenide superconductors: an x-ray diffraction study in high magnetic field

We report high-resolution single crystal x-ray diffraction measurements of underdoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ in pulsed magnetic fields as high as 28 Tesla. Our direct measurements confirm earlier reports of strong and highly anisotropic magnetoelastic coupling in iron arsenides. We observe magnetic field induced de-twinning of orthorhombic samples, and characterize the magnitude of the effect as a function of temperature and field. We identify a range of field and temperature where samples can be 100\% de-twinned by magnetic fields less than 30 Tesla. The effect shows a notable insensitivity to SDW ordering, but varies rapidly in the vicinity of the superconducting transition.   

In-plane structural and electronic anisotropy in de-twinned (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$

The iron-pnictides undergo a tetragonal to orthorhombic structural transition below a doping - dependent temperature $T_s$. In the absence of external stress or strain, the orthorhombic phase is divided into four degenerate, equally populated, ``twin'' structural domains, obscuring direct measurement of in-plane anisotropy. This degeneracy may be broken through mild mechanical stress or strain leaving the sample de-twinned. The properties of detwinned (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ with x=0.1, 0.18 (hole under-doped) were discussed previously [1]. Here we report polarized-light microscopy and AC transport measurements of strain-detwinned (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ with a dopping range from x=0.15 to x=0.35. Our results provide new insight into a region of coexisting magnetic and superconducting order parameters. \\[4pt] [1] J. J. Ying, et al. Phys. Rev. Lett. \textbf{107} 067001 (2011).   

Nematic phase persisting above the superconducting dome of BaFe$_2$(As$_{1-x}$P$_x$)$_2$

Strongly interacting electrons can exhibit novel collective phases, among which the electronic nematic phases are perhaps the most surprising as they spontaneously break rotational symmetry of the underlying crystal lattice. Here, we provide the first thermodynamic evidence in pure crystals of BaFe$_2$(As$_{1-x}$P$_x$)$_2$ that the nematicity develops well above the structural transition and persists to the nonmagnetic superconducting regime, resulting in a new phase diagram strikingly similar to the pseudogap phase diagram in the cuprates. Our highly sensitive magnetic anisotropy measurements using microcantilever torque-magnetometry under in-plane field rotation reveal pronounced two-fold oscillations, which break the tetragonal symmetry. Combined with complementary high-resolution synchrotron X-ray and resistivity measurements, our results consistently identify two distinct temperatures---one at $T^{\ast}$, signifying a true nematic transition, and the other at $T_s (< T^{\ast})$, which we show to be not a true phase transition, but rather what we refer to as a ``meta-nematic transition'', in analogy to the well-known metamagnetic transition in the theory of magnetism.   

Unusual giant negative thermal expansion in La-doped CaFe$_{2}$As$_{2}$ superconducting single crystal

Large negative thermal expansion (NTE), wherein a material substantially shrinks on heating, is a phenomenon that occurs only in very rare materials.\footnote{T. A. Mary et al. Science, \textbf{272}, 90 (1996)}$^,$\footnote{G. D. Barrera et al. J. Phys.: Condens. Matter, \textbf{17}, R217 (2005)} Here we present results on anisotropic and unusually large NTE in single crystalline Ca$_{0.8}$La$_{0.2}$Fe$_{2}$As$_{2}$ (CLFA), a recently discovered high temperature superconducting material. The volume thermal expansion coefficient in CLFA remains negative over the entire measured temperature range and reaches a maximum of $\Omega=-90\times10^{-6}$ K$^{-1}$ near 65 K, which is remarkably large compared to the thermal expansion (TE) of most other materials. Furthermore, we do not observe signatures of any structural transition in the linear TE in the $a$, $b$ and $c$ axes. Our results on TE and heat capacity behavior in the vicinity of superconducting transition temperature ($T_{C}=42.7$ K) indicate non-bulk superconductivity in the sample. The observed large NTE in our sample is attributed to anomalous transverse modes which may vibrate in a quartic potential as in ScF$_{3}$.\footnote{C. W. Li et al. Phys. Rev. Lett., \textbf{107}, 195504 (2011)}   

Lower critical field, anisotropy, and two-gap features of LiFeAs

The magnetic properties of LiFeAs, as single crystalline and polycrystalline samples, were investigated. The lower critical field deduced from the vortex penetration of two single crystals appears to be almost isotropic with a temperature dependence closer to that of two-gap superconductors. The parameters extracted from the reversible magnetizations of sintered polycrystalline samples are in good agreement with those from the single-crystal data.