We perform a microscopic theoretical study of the generic properties of competing magnetic phases in iron pnictides. As a function of electron filling and temperature, the magnetic stripe (single-Q) order forms a dome, but competing non-collinear and non-uniform double-Q phases exist at the foot of the dome in agreement with recent experiments. We compute and compare the electronic properties of the different magnetic phases, investigate the role of competing superconductivity, and show how disorder may stabilize double-Q order. Superconductivity is shown to compete more strongly with double-Q magnetic phases, which can lead to re-entrance of the C2 (single-Q) order in agreement with recent thermal expansion measurements on K-doped Ba-122 crystals.PACS numbers: 74.70.Xa, 74.62.En, In correlated materials in general, and unconventional superconductors in particular, a microscopic understanding of the magnetism is of paramount importance. Generally, this is because a proper description of the relevant exchange mechanism in these materials is intimately tied to their basic electronic properties. More specifically, it is additionally shown within a wide class of models that the nature of the magnetic fluctuations may be closely linked to the emergence of the superconducting condensate. 1-3Focussing on the iron-based superconductors, the prevalent magnetic structure consists of collinear magnetic stripe (MS) order with in-plane moments oriented antiferromagnetic (ferromagnetic) along the a (b) axis of the orthorhombic Fe lattice as shown in Fig. 1(a). Thus, this configuration of moments singles out the Q 1 = (π, 0) ordering vector (1Q), i.e. M(r) = M 1 exp(iQ 1 · r). An obvious question, however, is why the system does not take advantage of the enhanced susceptibility at both Q 1 and Q 2 = (0, π) to form other magnetic phases, e.g. double-Q (2Q) phases consisting of superpositions of ordering at Q 1 and Q 2 with M(r) = l=1,2 M l exp(iQ l ·r). This question has been studied theoretically mainly using various effective field theories restricted to the vicinity of the magnetic transition temperature T N .4-7 These works have identified two competing magnetic structures of the 2Q type: 1) an orthomagnetic (OM) non-collinear phase with nearest neighbor moments at right angles as shown in Fig. 1(b), and 2) a collinear non-uniform spin and charge ordered (SCO) phase as shown in Fig. 1(c). The favorable magnetic order depends delicately on the band structure, doping level, and interactions. 4-7Experimentally, the dominating magnetic order in the iron pnictides is the 1Q MS state. This phase lowers the C 4 symmetry of the high-T tetragonal phase to orthorhombic C 2 , and causes an associated splitting of the crystal Bragg peaks due to magneto-elastic coupling. Recently, several experiments have, however, reported the discovery of magnetic order without an associated structural splitting, i.e. in the tetragonal phase, 8,9 which has been taken as indirect evidence for a magnetic driven structural transition in the case of 1Q M...

We consider the role of potential scatterers in the nematic phase of Fe-based superconductors above the transition temperature to the (π, 0) magnetic state but below the orthorhombic structural transition. The anisotropic spin fluctuations in this region can be frozen by disorder, to create elongated magnetic droplets whose anisotropy grows as the magnetic transition is approached. Such states act as strong anisotropic defect potentials that scatter with much higher probability perpendicular to their length than parallel, although the actual crystal symmetry breaking is tiny. We calculate the scattering potentials, relaxation rates, and conductivity in this region and show that such emergent defect states are essential for the transport anisotropy observed in experiments.

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The understanding of disorder has profoundly influenced the development of condensed matter physics, explaining such fundamental effects as, for example, the transition from ballistic to diffusive propagation, and the presence of quantized steps in the quantum Hall effect. For superconductors, the response to disorder reveals crucial information about the internal gap symmetries of the condensate, and thereby the pairing mechanism itself. The destruction of superconductivity by disorder is traditionally described by Abrikosov-Gorkov (AG) theory, [1,2] which however ignores spatial modulations and ceases to be valid when impurities interfere, and interactions become important. Here we study the effects of disorder on unconventional superconductors in the presence of correlations, and explore a completely different disorder paradigm dominated by strong deviations from standard AG theory due to generation of local bound states and cooperative impurity behavior driven by Coulomb interactions. Specifically we explain under which circumstances magnetic disorder acts as a strong poison destroying high-T c superconductivity at the sub-1% level, and when non-magnetic disorder, counter-intuitively, hardly affects the unconventional superconducting state while concomitantly inducing an inhomogeneous full-volume magnetic phase. Recent experimental studies of Fe-based superconductors (FeSC) have discovered that such unusual disorder behavior seem to be indeed present in those systems.For cuprates, heavy-fermions, and FeSC the study of disorder currently constitutes a very active line of research, motivated largely by the fact that these systems are made superconducting by "chemical disordering" (charge doping), but also boosted by controversies of the correct microscopic model, and a rapid development of local experimental probes. [3][4][5] Focusing on multiband FeSC, disorder studies have proven exceptionally rich and strongly material dependent.[6] Scanning tunneling spectroscopy found a plethora of exotic atomicsized impurity-generated states, [7][8][9][10] NMR and neutrons observed clear evidence of glassy magnetic behavior, [11,12] and µSR discovered magnetic phases generated by non-magnetic disorder. [13,14] The resulting complex inhomogeneous phases and their properties in terms of thermodynamics and transport constitute an important open problem in the field.Here, we present a theoretical study of correlationdriven emergent impurity behavior of both magnetic and nonmagnetic disorder in unconventional s± multi-band superconductors. For the case of magnetic disorder, we find that correlations anti-screen the local moment, and significantly enhance the inter-impurity RudermanKittel-Kasuya-Yosida (RKKY) exchange interactions by inducing non-local long-range magnetic order which operates as an additional competitor to superconductivity. This results in an aggressive T c suppression rate where superconductivity is wiped out by sub-1% concentrations of disorder. This mechanism explains the "poisoning effect" discovered in ...