Session X22: Focus Session: Fe-based Superconductors - Exchange Coupling Theory

Strong Versus Weak Coupling Pairing in Iron-Based Superconductors

We use the functional renormalization group as well as strong-coupling methods to analyze the phase diagram of several of the iron-based superconductors. As in the previous studies by F. Wang, D.H. Lee et. al., we observe a nodeless sign-changing order parameter to be favored over a sizable part of the parameter space, but the physics quickly develops peculiarities depending on the doping, shape, size and orbital content of the Fermi surfaces in the different superconducting compounds. Using several new one-body models available in the literature (due to Kuroki, Graser and Raghu), we analyze the orbital content of the superconducting gap, which should be observable in spin-polarized ARPES experiments. We find that the effective theory of the Iron-based superconductors is a $J_1-J_2$ model in orbital space with $J_2> |J_1|$ and antiferromagnetic, and analyze the behavior of the physical properties such as superconducting gap for systems ranging from electron overdoped $(K, Cs)Fe_{2?x}Se_x$ to hole-doped $ K_{x}Ba_{1-x}Fe_2As_2$.   

Hund's metal physics in iron-based superconductors

The role of Hubbard U and Hund's J in a material depends on the energy scale of the crystal field splitting. In transition metal oxides, the crystal field splitting is usually considerably larger than Hund's J thus Hubbard U plays the dominating role. However, the crystal field splitting in iron-based superconductors is substantially smaller and the physics in this family is governed primarily by Hund's rule. In this talk, we will show that the combination of density functional theory and dynamic mean field theory properly incorporates the Hund's physics as well as realistic band structure thereby is well suited to capture and predict a wide range of physical properties and their trends in iron pnictides and chalcogenides, such as optical conductivity, x-ray spectroscopy, Fermi surface, magnetic ordering and moments, spin excitations, effective masses and so on. We will demonstrate two important mechanisms operating in this family, namely, Hund's blocking and Kinetic frustration. The importance of electronic correlation caused by the Hund's physics and its relation to various experimental observations will also be discussed.   

Consistent theory of magnetism and superconductivity in iron pnictides

We show that iron pnictide systems possess unusual quantum spin fluctuations which strongly affect their magnetic properties and may be relevant in the mechanism of superconductivity. These fluctuations represent highly non-linear aharmonic excitations and have both transversal and longitudinal components which may contribute differently to the observed properties. From the point of view of magnetism, these fluctuations are responsible for the stability of the observed magnetic ground states, and thus determine the spin-wave spectra. The anharmonic character of the excitations under consideration provides a strong coupling with electron degrees of freedom which may be relevant for the appearance of high-temperature superconductivity. We discuss a mechanism of superconductivity related to spin fluctuation which uses the same pool of fluctuations to explain the Cooper pairing. Theory predicts some correlations between superconductivity temperature and magnetic characteristics and they seem to be in agreement with the available experimental data for pnictides and selenides. We discuss also other materials where one can expect a similar behavior.   

Giant spin zero-point fluctuations in iron superconductors

We analyze the strength of quantum spin fluctuations in novel iron superconductors. By using linear response calculations and the density functional approach, we show that many of these materials can be classified as highly responsive magnetic materials with very strong non-linear quantum spin fluctuations. Furthermore, by using the newly developed theory of magnetic instabilities in systems with strong spin zero-point motion, we show that the inclusion of fluctuations dramatically improves an agreement with the experiment for systems such as CaFe$_{2}$As$_{2}$, LiFeAs and FeSe, while for FeTe, the results are less affected by fluctuations. We demonstrate how spin fluctuations influence the criteria of local magnetic moment and long range magnetic order existence. In addition to iron superconductors, several other groups of materials with possible giant quantum spin fluctuations are identified.   

Spectral and magnetic properties of the iron-based superconductors: The role of electronic correlation

Electronic correlation plays a subtle role in Fe-based superconductors. In fact, due to the presence of several moderately correlated bands close to the Fermi level, one observes the formation of localized magnetic moments driven by the Hund's exchange interactions, which takes place, however, in a mainly metallic background (``Hund's metal'' [1]). This physical scenario provides the key to understand [2,3] the discrepancies observed between experimental estimates of the magnetic moments in the magnetically ordered phase and those obtained via standard LSDA calculations. The magnitude of the discrepancy observed in different compounds would be hence related to the efficacy of the metallic screening, which is decreasing when going from the 1111 (e.g., LaFeAsO) to the 122 class, and eventually to the 11 materials (like FeTe). Also important to be considered for the interpretation of the ARPES experiments and of the symmetry of the superconducting pairing within the Hund's exchange scenario is the interplay between the electronic correlations and the details of the band-structure of the specific compound considered.\\ \\ \noindent [1] K. Haule and G. Kotliar, NJP {\bf 11} 025021 (2009). [2] P. Hansmann, {et al.}, PRL {\bf 104}, 197002 (2010). [3] A. Toschi, {et al.} in preparation   

{\it Ab initio} Evidence of Strong Correlation Associated with Mott Proximity in Iron-Based Superconductor

Recently discovered iron-based superconductors have attracted much interest because of their high superconducting critical temperatures ($T_{c}$). Although it is believed that electron correlations play key roles in the unconventional high-$T_{c}$ superconductivity, their roles are not fully understood yet. To clarify electron correlation effects from a microscopic point of view, we study the {\it ab initio} low-energy effective models for iron-based superconductors by using multi-variable variational Monte Carlo (mVMC) method. From the {\it ab initio} calculations, we show that the iron-based superconductors found around $d^6$ configuration (namely, five Fe 3$d$ orbitals filled by 6 electrons on average) are under the umbrella of an unexpectedly large-scale dome of correlated-electron matter centered at the Mott insulator at $d^5$ (namely, half filling). This proximity of the large-dome of strong electron correlations yields a variety with bad insulating (or incoherent metallic) states, quantum criticality of antiferromagnetism, orbital fluctuations and differentiations arising from interplay between the Hund's rule coupling and Mott physics.   

Two-orbital quantum spin model of magnetism in the iron pnictides

We study a two-orbital spin model to describe $(\pi,0)$ stripe antiferromagnetism in the iron pnictides. The ``double-spin'' model has an on-site Hunds's coupling and inter-site interactions extending to second neighbors on the square lattice. Using a variational method based on a cluster decomposition, we optimize wave functions with up to $8$ cluster sites (up to $2^{16}$ variational parameters). We focus on the anomalously small ordered moments in the stripe state of the pnictides. To account for it, and large variations among different compounds, we show that the second-neighbor cross-orbital exchange constant should be ferromagnetic, which leads to ``partially hidden'' stripe order. In a different parameter region, we confirm a canted state previously found in spin-wave theory.   

Spin waves of 2D $J_1$-$J_2$ model and single hole dynamics via nearest neighbor hole hopping

We study the two dimensional $J_1$-$J_2$ model using the spin wave approximation and find the spin wave modes at different values of parameter $\lambda$=$J_2/J_1$. Competing antiferromagnetic ($\pi,\pi$) and ($\pi,0$) (or, ($0,\pi$)) orders preferred by the $J_1$ and $J_2$ terms respectively creates frustration in such a system and the spin wave excitations about different vacuum states are observed for different values of $\lambda$. We investigate the stability of different zero spin deviation states as $\lambda$ is varied from 0 to 1.5. We discuss the band folding of the super-lattice structure that appears with the emergence of the $J_2$ term and study the different spin wave modes that the system inherits. Dynamics of a foreign hole put in such a system is studied using a $t$-$J_1$-$J_2$ model and the hole spectra obtained by solving the Dyson's equation self-consistently within the non-crossing approximation are compared with the ARPES spectra from the newly discovered FeAs superconducting compounds.   

An unified minimum effective model of magnetism in iron-based superconductors

Since 2008, many new families of iron-based high temperature (high-Tc) superconductors have been discovered. Unlike all parent compounds of cuprates that share a common antiferromagnetically (AF) ordered ground state, those of iron-based superconductors exhibit many different AF ordered ground states, including collinear-AF (CAF) state in ferropnictides, bicollinear-AF (BCAF) state in 11-ferrochalcogenide FeTe, and block-AF vacancy (BAFv) order state in 122-ferrochalcogenide K0.8Fe1.6Se2. While the universal presence of antiferromagnetism suggests that superconductivity is strongly interrelated with magnetism, the diversity of the AF ordered states obscures their interplay. Here we show that all magnetic phases can be unified within an effective magnetic model. This model captures three incommensurate magnetic phases as well, two of which have been observed experimentally. The model characterizes the nature of phase transitions between the different magnetic phases and explains a variety of magnetic properties, such as spin-wave spectra and electronic nematism. Most importantly, by unifying the understanding of magnetism, we cast new insight on the key ingredients of magnetic interactions which are critical to the occurrence of superconductivity.   

Spin dynamics of the J1-J2 Model with Biquadratic Spin Interactions for the Paramagnetic Phase of the Iron Pnictides

The parent compounds of the iron pnictides are bad metals, and are hence interpreted as being located at the boundary of localization and itinerancy. As such, the effective exchange interactions will naturally include more than two spin components. Here we study the $J_1-J_2$ antiferromagnetic Heisenberg model with a biquadratic spin-spin coupling $-\kappa (\vec{S}_i \cdot \vec{S}_j)^2$ to explore the spin excitations in the paramagnetic phase of the iron pnictides which has a $(\pi,0)$ collinear antiferromagnetic ground state. By using the modified spin wave theory and Schwinger Boson mean field theory, we determine the spin dynamics at finite temperatures. We show that a moderate biquadratic coupling $\kappa$ can induce sizable anisotropy in the spin excitation spectrum. The calculated dynamical structure factor $S(\vec{q},\omega)$ shows anisotropic elliptic features near $(\pi,0)$, which expand with increasing frequency ($\omega$), in a way that agrees with recent experiment on BaFe$_2$As$_2$ above its Neel transition temperature (L.~W.~Harriger {\it et.al}, PRB {\bf 84}, 054544, 2011).   

Dimensional crossover in the quasi-two-dimensional Ising-O(3) model

We present results of our Monte Carlo simulation of the Ising-O(3) model on the two-dimensional (2D) and quasi-2D lattices. This model is an effective classical model for the stacked square-lattice $J_1$-$J_2$ Heisenberg model where the nearest neighbor ($J_1$) and next-nearest neighbor ($J_2$) couplings are frustrated and we assume that $J_2$ is dominant. We find an Ising ordered phase where the O(3) spins remain disordered in a moderate quasi-2D region. There is a single first order transition for a sufficiently large 3D coupling in agreement with a renormalization group treatment. The subtle region where the single transition splits into two transitions is also discussed and compared against recent measurements of two very close transitions in BaFe$_2$As$_2$. Our results can provide a qualitative explanation on the experiments on ferropnictides, namely observed sequence and orders of the structural and magnetic transitions, in terms of the ratio between the inter-layer and intra-layer coupling.   

Are Spinwaves Glue for Cooper Pairs in Iron-Pnictide High-T$_{\rm c}$ Superconductors?

We study the 2-orbital t-J model over the square lattice via Schwinger-boson-slave-fermion mean-field theory and by exact numerical diagonalization of two holes over a 4$\times$4 grid. The two orbitals in question are the degenerate $d\pm = 3d_{(x\pm iy)z}$ ones, which maximize the Hund's Rule coupling. The mean-field theory predicts the existence of a quantum critical point (QCP) that separates a commensurate spin-density-wave (cSDW) metal at strong Hund's Rule coupling from a hidden half metal at weak Hund's Rule coupling. Holes in the hidden half metal hop through a $\nwarrow_{d+}\searrow_{d-}$ spin background without much hopping across orbitals. Mean-field theory further predicts a critical spin-wave spectrum that shows hidden low-energy excitations at zero momentum, and that shows observable low-energy excitations at cSDW momenta. We find that the virtual exchange of such spin-waves by mobile holes can be attractive, and that it can result in the formation of hole pairs. We seek to corroborate this by exact diagonalization of two holes in the 2-orbital t-J model.