Over the past few years Fe chalcogenides (FeSe/Te) have advanced to the forefront of Fe-based superconductors (FeBS) research. The most intriguing results thus far are for intercalated and monolayer FeSe, however experimental studies are still inconclusive. Yet, bulk FeSe itself remains an unusual case when compared with pnictogen-based FeBS, and may hold clues to understanding the more exotic FeSederivatives. The FeSe phase diagram is unlike the pnictides: the orthorhombic distortion, which is likely to be of a "spin-nematic" nature in numerous pnictides, is not accompanied by magnetic order in FeSe, and the superconducting transition temperature Tc rises significantly with pressure before decreasing. In this paper we show that the magnetic interactions in chalcogenides, as opposed to pnictides, demonstrate unusual (and unanticipated) frustration, which suppresses magnetic, but not nematic order, favors ferroorbital order in the nematic phase and can naturally explain the nonmonotonic pressure dependence of the superconducting critical temperature Tc(P ).While full consensus regarding the mechanism of hightemperature superconductivity in Fe-based superconductors (FeBS) remains elusive, nearly all researchers agree that it is unconventional and that it has a magnetic origin 1,2 . However, there is a divergence of opinions on the nature of the electrons responsible for magnetism. There is an itinerant approach based on calculating the spin susceptibility with moderate Coulomb (Hubbard) and Hund's interactions [3][4][5][6][7][8][9][10] as well as a localized approach where itinerant electrons responsible for conduction and the Fermi surface interact with local spins 11,12 . Finally, there is an increasingly popular description where the electrons have a dual character and provide the local moments, the interaction between them, and the electronic conductivity [13][14][15][16] . Within this picture, FeBS can still be reasonably mapped onto a short-range model of pairwise interactions between the local moments.Following the discovery of the FeBS, there were multiple attempts to map the exchange interactions onto the Heisenberg model. The J 1 -J 2 model on the square lattice 17 with nearest-(J 1 ) and next-nearest-neighbor (J 2 ) exchange couplings was a natural starting point 18-21 , but required dramatically different couplings for ferro-and antiferromagnetic neighbors, J 1a J 1b to reproduce the observed spin waves 22,23 and ab-initio calculations 24 ; it also failed to describe the double-stripe configuration in FeTe 25,26 . The model was extended to include third-neighbor exchange J 3 27 to reproduce the FeTe magnetic ground state. However, only the Ising model has this configuration as a solution, and in the Heisenberg model it is not a ground state for any set of parameters 28,29 . Therefore adding J 3 does not solve the problem. Besides, the J 1a J 1b implies an unphysical temperature dependence of the exchange constants (as T approaches T N , by symmetry J 1a → J 1b ).There were attempts to overcome these pr...

A recently discovered magnetic semiconductor Ba1−xKx(Zn1−yMny)2As2, with its decoupled spin and charge doping, provides a unique opportunity to elucidate the microscopic origin of the magnetic interaction and ordering in dilute magnetic semiconductors (DMS). We show that (i) the conventional density functional theory (DFT) accurately describes this material, and (ii) the magnetic interaction emerges from the competition of the short-range superexchange and a longer-range interaction mediated by the itinerant As holes, coupled to Mn via the Schrieffer-Wolff p−d interaction representing an effective Hund's rule coupling, J eff H . The key difference between the classical double exchange and the actual interaction in DMS is that an effective J eff H , as opposed to the standard Hund's coupling JH , depends on the Mn d−band position with respect to the Fermi level, and thus allows tuning of the magnetic interactions. The physical picture revealed for this transparent system may also be applicable to more complicated DMS systems.Introduction-The carrier-mediated magnetism in DMS [1-5] offers a versatile control of the exchange interaction by tuning the Curie temperature T C through changes in the carrier density [5][6][7][8]. However, despite four decades of intensive work, challenges remain and materials complexity often hinders theoretical understanding. The origin of magnetic ordering [1-3, 5] and paths to higher T C remain strongly debated [3,9,10].

Spin-driven nematicity, or the breaking of the point-group symmetry of the lattice without longrange magnetic order, is clearly quite important in iron-based superconductors. From a symmetry point of view, nematic order can be described as a coherent locking of spin fluctuations in two interpenetrating Néel sublattices with ensuing nearest-neighbor bond order and an absence of static magnetism. Here, we argue that the low-temperature state of the recently discovered superconductor BaTi2Sb2O is a strong candidate for a more exotic form of spin-driven nematic order, in which fluctuations occurring in four Néel sublattices promote both nearest-and next-nearest neighbor bond order. We develop a low-energy field theory of this state and show that it can have, as a function of temperature, up to two separate bond-order phase transitions -namely, one that breaks rotation symmetry and one that breaks reflection and translation symmetries of the lattice. The resulting state has an orthorhombic lattice distortion, an intra-unit-cell charge density wave, and no long-range magnetic order, all consistent with reported measurements of the low-temperature phase of BaTi2Sb2O. We then use density functional theory calculations to extract exchange parameters to confirm that the model is applicable to BaTi2Sb2O. arXiv:1610.06622v1 [cond-mat.str-el]