Disorder-promotedC4-symmetric magnetic order in iron-based superconductors

Abstract

In most iron-based superconductors, the transition to the magnetically ordered state is closely linked to a lowering of structural symmetry from tetragonal (C4) to orthorhombic (C2). However, recently, a regime of C4-symmetric magnetic order has been reported in certain hole-doped ironbased superconductors. This novel magnetic ground state can be understood as a double-Q spin density wave characterized by two order parameters M1 and M2 related to each of the two Q vectors. Depending on the relative orientations of the order parameters, either a noncollinear spinvortex crystal or a nonuniform charge-spin density wave could form. Experimentally, Mössbauer spectroscopy, neutron scattering, and muon spin rotation established the latter as the magnetic configuration of some of these optimally hole-doped iron-based superconductors. Theoretically, lowenergy itinerant models do support a transition from single-Q to double-Q magnetic order, but with nearly-degenerate spin-vortex crystal and charge-spin density wave states. In fact, extensions of these low-energy models including additional electronic interactions tip the balance in favor of the spin-vortex crystal, in apparent contradiction with the recent experimental findings. In this paper, we revisit the phase diagram of magnetic ground states of low-energy multi-band models in the presence of weak disorder. We show that impurity scattering not only promotes the transition from C2 to C4-magnetic order, but it also favors the charge-spin density wave over the spin-vortex crystal phase. Additionally, in the single-Q phase, our analysis of the nematic coupling constant in the presence of disorder supports the experimental finding that the splitting between the structural and stripe-magnetic transition is enhanced by disorder.

Observation of the magnetic C4 phase in Ca1−xNaxFe2As2

“…Since then, theory has shown that impurity scattering can play a significant role in the stabilization of the C 4 phase. 17 In their work, Hoyer et al show that intraband electron scattering due to crystallographic defects stabilize the C 4 phase at lower doping concentrationsat the begining of the C 4 dome. However, no such effect is found on the higher doped side of the dome in agreement with our observation of mixed phase samples at the onset of C 4 in composition but not at higher consentrations.…”

“…Consequently, it has become the focus of many recent first principle reports to reveal what parameters are causing the sudden reordering of the single-Q C 2 structure into this novel double-Q structure and how this new phase hosts superconductivity. 12,[15][16][17][18][19] Currently, several different proposed models predict the observed C 4 but they do so through different mechanisms which range from expanded itinerant mean field models to impurity scattering stabilization to spin-orbit coupling driven spin anisotropies. 15,17,18 The different models invoke varying assumptions about the underlying physics in these materials and necessarily predict different, sometimes subtlety so, manifestations of the C 4 phase.…”

Order parameter fluctuation and ordering competition in Ba1−xKxFe2As2

“…This C 4 magnetic state is characterized by biaxial magnetic orders [29][30][31][32][33], and the corresponding spin operator is given by S(r) = M X e iQX ·r + M Y e iQY ·r [33,34]. It has been suggested that this double-Q magnetic state has two possible realizations [29][30][31][32][33]35]: a charge-spin density wave (CSDW) in which M X and M Y are collinear; a spin-vortex crystal (SVC) in which M X and M Y are orthogonal.…”

“…Since the largest value of T c of FeSCs is observed at the proximity of tetragonal C 4 magnetic order [22,26], there might exist a quantum critical point (QCP) at certain doping x c in the superconducting (SC) dome [33]. After its discovery, the double-Q structured C 4 SDW state has stimulated a variety of experimental [21,22,[24][25][26][27] and theoretical works [29][30][31][32][33][34][36][37][38][39].…”

“…The observed C4 symmetric SDW state could be either CSDW or SVC. Distinct phases are distinguished by different values of the model parameters [33,34] defined in Eq. (4): (i) g < 0 and w = 0, the system is in PM phase; (ii) g > max(0, −w) represents the C2 symmetric SDW phase (with nematic order); (iii) C4 symmetric magnetic state is of SVC-type if g < 0 and w > 0, and CSDW-type if g < −w and w < 0.…”