Session Q39: Focus Session: Iron Based Superconductors: Theory III

The physics of coupled spin-orbital degrees of freedom and Fe pnictides

Motivated by neutron scattering experiments on Fe pnictides, we study the thermodynamic properties and finite-temperature spin dynamics of a model Hamiltonian with coupled quantum Heisenberg-spin and Ising-orbital degrees of freedom. The model system undergoes a phase transition to an orbitally ordered state at a temperature set by short-range magnetic order. The behavior of the specific heat and the order-parameter suggests that the transition is continuous and of second order, belonging to the 2D Ising universality class. The onset of orbital excitations and fluctuations causes a rapid scrambling of the spin spectral weight away from coherent spin-waves, leading to a sharp increase in uniform magnetic susceptibility just below the phase transition. The experimental consequences of this model are in qualitatively good agreement with the observed behavior in the Fe-pnictide materials.   

Nodeless and Nodal Gaps in Iron-Based Superconductors

We use the functional renormalization group method to analyze the phase diagram of the iron-based superconductors. As in the previous studies by F. Wang, D.H. Lee et. al., we observe a nodeless sign- changind order parameter to be favored over a sizable part of the parameter space. We however also find several regions in which nodes develop on the electron Fermi pockets leading to a large quasiparticle density that gives rise to power laws in experimental observables. We analyze the dependence of the superconducting gap on the out-of plane momentum and investigate the possibility of line-nodes in the superconducting order parameter. Using several new 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 also show that effective, Fermi-surface models of iron-based superconductors miss important properties of the superconducting gap. We find that the effective theory of the Iron-based superconductors is a J1-J2 model in orbital space with J2> |J1| and antiferromagnetic.   

Symplectic-N, the t-J1-J2 model, and the iron-based superconductors

Symplectic-$N$ has proven to be a useful large $N$ technique for spin Hamiltonians, and here we extend it to treat charge fluctuations by introducing symplectic Hubbard operators. Requiring that the anti-commutator of two symplectic Hubbard operators generate a symplectic spin flip yields a large $N$ generalization of Wen and Lee's $SU(2)$ slave boson Hubbard operators[1]. As a test application to the iron-based superconductors, we solve the symplectic $t-J_1-J_2$ model, motivated by the observation that a 45 degree rotation of the extended s-wave order parameter gives an $s_{\pm}$ order parameter. [1] X.G. Wen and P. Lee, {\it Phys. Rev. Lett.} {\bf 76}, 503-506 (1996).   

Superconductivity in the Fe-Pnictides - From first principle calculations to effective RG studies

The functional Renormalization Group (fRG) is used to determine the superconducting (SC) mechansim in the ferropnictides, with the main emphasis on distiguishing universal and material-specific aspects. To this end we use a five-band d-orbital whose interactions, in contrast to earlier fRG studies, are not taken as scalar model parameters, but calculated ``a priori'' from constrained RPA calculations. We universally find a SC pairing instability, driven by inter-Fermi surface (FS) scattering and resulting in a sign-changing s+- wave order parameter. However, the gap anisotropy is shown to be dependent on material-specific orbital parameter deviations not only by the ``non-interacting'' (i.e. LDA) part of the d-orbital Hamiltonian, but also by self-energy corrections.   

How close is LaOFeAs to Mott transition? A model Hamiltonian calculation within the Gutzwiller approximation

Using a five-band tight binding model for LaOFeAs we study the role of electron correlations on the low energy electronic structure. The phase boundaries between a metallic state and Mott insulating phases are determined as a function of Coulomb repulsion U and Hund's coupling J for a total number of six d-electrons. For realistic values of U and J LaOFeAs is found to be on the metallic side of the phase boundary. In addition we give a number of spectroscopic signatures that can be used to determine whether the electronic excitations of the metallic state are affected by the vicinity to a Mott transition. These results elucidate the role of strong electron correlations in FeAs-based systems.   

Interorbital Pairing and its Physical Consequences in Iron Pnictide Superconductors

We study interorbital pairings of iron pnictide superconductors within a minimal two-orbital tight-binding model. We find that in real space, a set of self-consistently determined pairing order parameters forms two sublattices with a relative phase of $\pi$ and the pairing symmetry is $d_{x^{2}-y^{2}}\sim \cos k_{x}-\cos k_ {y}$. In momentum space, it corresponds to the $\eta$ pairing proposed by C. N. Yang [Phys. Rev. Lett. \textbf{63}, 2144 (1989)], with nonzero momenta of Cooper pairs. One physical consequence of this type of pairing is the existence of a significant amount of zero energy (gapless) states around the Fermi surface even in the absence of disorder, which contradicts current experiments thus excluding such a pairing in iron pnictide superconductors.   

Effective Hamiltonian to describe the magnetic properties of Fe-pnictides

We discuss an effective Hamiltonian to describe the super-exchange interaction of electrons from two or more different d orbitals of the same Fe site which prefer different types of antiferromagnetic (AF) ordering. Namely, we consider a case where the relationship between nearest neighbor and next nearest neighbor AF couplings is such that the spins occupying the first orbital prefer a columnar AF order while for spins of the second orbital the familiar $(\pi,\pi)$ AF ordering is preferred. In such cases there is frustration introduced by the Hund's rule coupling. Using spin-wave theory and exact diagonalization we have studied the case of such orbitals coupled through Hund's rule. We will discuss the phase diagram of this system and the consequences of our results for the magnetic properties of the Fe-pnictides.   

Nearly unfrustrated stripe antiferromagnetism in the pnictides as a consequence of orbital ordering induced by degenerate double exchange

We propose a local-itinerant theory to explain the anisotropic electronic and magnetic properties of the iron pnictides. The localized spins are described by an isotropic, strongly frustrated $J_1$-$J_2$ Heisenberg model, forming a $(\pi,0)$ stripe antiferromagnetic ground state. We further introduce a strong Hund's coupling between the local moments and the itinerant bands of the degenerate $d_{xz}$ and $d_{yz}$ orbitals. Due to the kinetic energies gained by hopping along the ferromagnetic direction, the electrons form an orbitally ordered nematic state. By calculating the spin-wave dispersion in the presence of both superexchange and double exchange, we find that the orbital order leads to a stabilization of the stripe antiferromagnetism and to a dramatic increase of the spin-wave energies at $(\pi,\pi)$ of the competing N\'eel order. The spectra are in good agreement with recent neutron scattering data and suggest a strong anisotropy of the magnetic exchanges on the level of an effective spin-only model.   

Orbital current density wave order in iron pnictides

In this work we investigate properties of orbital current density wave phases, which are competing with spin density wave states in multiband Fe-pnictide systems. A self-consistent mean field study of t-U-V model Hamiltonian shows that the orbital current density wave phase becomes a ground state within realistic parameter ranges. It turns out that the orbital current density wave state induces abrupt changes of the electron band structure. We also discuss various physical properties of the orbital current density wave state and experimental means to detect it.   

Phase Transitions in a spin-orbital model for the Iron Pnictides

We study the finite temperature phase transition of a spin-orbital Hamiltonian (arXiv:09034408) that could describe the striped magnetic order in the Iron Pnictide materials. The model consists of an Ising like orbital variable with a classical Heisenberg spin variable on a 2D square lattice. The exchange constants for the Heisenberg spins depend on the Ising variables and lead to a strong coupling between spins and orbitals. We use a Monte Carlo algorithm with feedback parallel tempering to study the phase transition. In the model, the orbital phase transition occurs at $T_c=0.447J$ with critical exponents $\nu =1.01 \pm .02$ amd $\gamma =1.74 \pm .03$ consistent with the Ising universality $^{[1]}$. We characterize the heat capacity and orbital susceptibility for the system and study magnetic properties of the system at $\vec q = 0$ and at the ordering wave vector. \\[4pt] [1] C.-C. Chen et al. Phys Rev B 80, 180418 (R), (2009)   

Where are the extra electrons in Co and Ni-substituted BaFe$_{2}$As$_{2}$?

In the literature, the substitution of Co or Ni for divalent Fe in pnictides is frequently referred to as an electron doping. Chemical intuition on the other hand, advocates the isovalent nature of the substitution with little effect on the electron density distribution in the rest of the material in a dilute limit. Here we report on the results of a detailed density functional study of a periodic impurity model of various substitutes in BaFe$_{2}$As$_{2}$. By integrating the total occupied density of states, we demonstrate that the number of electrons situated inside the muffin-tin sphere of the substitute is consistent with isovalent substitution. This suggests that Fermi surface changes seen in the angle-resolved photoemission spectroscopy measurements are mainly due to impurity scattering rather than ``electron doping''.   

Electronic Structures of Parent Compounds of Iron Pnictides: Study Using a Five-Orbital Model

We investigate the electronic structures of the parent compounds of iron pnictides, LaOFeAs, BaFe2As2 and SrFe2As2, based on a three-dimensional five-orbital Hubbard model. The ground state of this model is studied via a spin-density-wave (SDW) mean-field approximation. For these compounds, a metallic SDW ground state with a $(0,\pi)$ magnetic order is found to be stabilized within an intermediate Hubbard U coupling regime. The value of U can be determined by comparing the magnetic moment with neutron scattering experiments. Motivated by recent ARPES experiments, we get the hopping and interaction parameters, determine the Fermi surface, and calculate the single electron spectral function. We show that the shape of the Fermi surface given by the five-orbital model is consistent with those found in recent ARPES experiments.   

Pairing Operators in Multiorbital Systems

The discovery of high-$T_c$ superconductivity in the pnictides highlights the need to understand how superconductivity arises in multiorbital systems. In a simple two orbital model we discuss how strong hybridization between orbitals may lead to both intra and interband pairing [1]. Next a three orbital model for the pnictides is considered where hybridization between the As $p$ orbitals and three of the Fe 3$d$ orbitals is described via the Slater-Koster approach [2]. Spin-singlet pairing operators allowed by lattice and orbital symmetries are constructed and indexed. It is found that the only fully gapped and purely intraband spin-singlet pairing operator arises if the electrons in different orbitals couple with equal strength to the source of pairing. Other pairing operators are discussed as well, including $S_{\pm}$. Spectral functions are calculated in both investigations to guide experimental work.\\[4pt] [1] A. Moreo {\it et. al.}, Phys. Rev. {\bf B80}, 104507 (2009). \\[0pt] [2] M. Daghofer {\it et al.},arXiv:0910.1573v1.   

Effect of P-doping in FeAs compounds

We studied the effect of quenched disorder on the magnetic transition of the frustrated J1-J2 Heisenberg model. It was shown that the model qualitatively explains the experimental behavior of the antiferromagnetic (AF) transition with increasing phosphorus substitution of arsenic in CeFeAsPO. [1] We assume that the introduction of P atoms reduces the effective magnetic interaction strength along both parallel and diagonal iron-iron bonds. When the bond dilution reaches the critical point, the percolation occurs and the system enters the disordered state from the magnetically ordered antiferromagnet. Both the Ising and Heisenberg cases are studied. We find that the P-dependence of the iron AF ordering temperature and the magnetic moment are close to the experimental data. Implications of this effect on superconductivity are also discussed.\\[4pt] [1] C. de la Cruz et al. arXiv:0907.2853   

Magnetic and orbital ordering in models for pnictides

While the shape of the Fermi surface (FS) obtained with the local density approximation (LDA) can be reproduced with two orbitals, three orbitals are needed to produce the degeneracy of the hole pockets. We discuss a three-orbital model including the $xz$, $yz$, and $xy$ iron orbitals, which qualitatively reproduces the shape and orbital composition of the FS obtained for undoped pnictides by LDA. Since this model is not at half filling, orbital order becomes a possibility in addition to various magnetic phases. We use a mean-field approach and the Variational Cluster Approach to investigate orbital and magnetic order depending on the interaction parameters $U$ and $J$. With increasing Coulomb repulsion $U$, four different regimes arise: {\it (1)} paramagnetic metal, {\it (2)} magnetic metal with $(\pi,0)$ spin order, {\it (3)} metal with $(\pi,0)$ spin order as well as alternating orbital order, and {\it (4)} magnetic and ferro-orbital ordered insulator. We discuss the spectral density and the FS and compare our findings to mean-field results for models with all five iron-$d$ orbitals. M. Daghofer, A. Nicholson, A. Moreo, and E. Dagotto, arXiv:0910.1573