Emergent magnetic degeneracy in iron pnictides due to the interplay between spin-orbit coupling and quantum fluctuations

Recent experiments in iron pnictide superconductors reveal that, as the putative magnetic quantum critical point is approached, different types of magnetic order coexist over a narrow region of the phase diagram. Although these magnetic configurations share the same wave-vectors, they break distinct symmetries of the lattice. Importantly, the highest superconducting transition temperature takes place close to this proliferation of near-degenerate magnetic states. In this paper, we employ a renormalization group calculation to show that such a behavior naturally arises due to the effects of spin-orbit coupling on the quantum magnetic fluctuations. Formally, the enhanced magnetic degeneracy near the quantum critical point is manifested as a stable Gaussian fixed point with a large basin of attraction. Implications of our findings to the superconductivity of the iron pnictides are also discussed.Comment: 6 pages, 2 figures, published versio

Magnetic phase diagram of the iron pnictides in the presence of spin-orbit coupling: Frustration between C2C_2 and C4C_4 magnetic phases

We investigate the impact of spin anisotropic interactions, promoted by spin-orbit coupling, on the magnetic phase diagram of the iron-based superconductors. Three distinct magnetic phases with Bragg peaks at $(\pi,0)$ and $(0,\pi)$ are possible in these systems: one $C_2$ (i.e. orthorhombic) symmetric stripe magnetic phase and two $C_4$ (i.e. tetragonal) symmetric magnetic phases. While the spin anisotropic interactions allow the magnetic moments to point in any direction in the $C_2$ phase, they restrict the possible moment orientations in the $C_4$ phases. As a result, an interesting scenario arises in which the spin anisotropic interactions favor a $C_2$ phase, but the other spin isotropic interactions favor a $C_4$ phase. We study this frustration via both mean-field and renormalization-group approaches. We find that, to lift this frustration, a rich magnetic landscape emerges well below the magnetic transition temperature, with novel $C_2$, $C_4$, and mixed $C_2$-$C_4$ phases. Near the putative magnetic quantum critical point, spin anisotropies promote a stable Gaussian fixed point in the renormalization-group flow, which is absent in the spin isotropic case, and is associated with a near-degeneracy between $C_2$ and $C_4$ phases. We argue that this frustration is the reason why most $C_4$ phases in the iron pnictides only appear inside the $C_2$ phase, and discuss additional manifestations of this frustration in the phase diagrams of these materials.Comment: 21 pages, 19 figures, published versio

Enhanced nematic fluctuations near an antiferromagnetic Mott insulator and possible application to high-TcT_{c} cuprates

Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays N\'eel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-$d$ and O-$p$ orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the $p$-orbitals inevitably generate a biquadratic coupling between the spins of the $d$-orbitals. The key point revealed by our classical Monte Carlo simulations and large-$N$ calculations is that the biquadratic term favors local stripe-like magnetic fluctuations, which result in an enhanced nematic susceptibility that onsets at a temperature scale determined by the effective Heisenberg exchange $J$. We discuss the impact of this type of nematic order on the magnetic spectrum and outline possible implications on our understanding of nematicity in the cuprates.Comment: 11 pages, 4 figures; includes Supplemental Material (14 pages, 4 figures

Enhanced nematic fluctuations near the Mott insulating phase of high-Tc cuprates

The complexity of the phase diagram of the cuprates goes well beyond its unique high-Tc superconducting state, as it hosts a variety of different electronic phenomena, such as the pseudogap, nematic order, charge order, and strange metallic behavior. The parent compound, however, is well understood as a Mott insulator, displaying quenched charge degrees of freedom and low-energy antiferromagnetic excitations described by the Heisenberg exchange coupling J. Here we show that doping holes in the oxygen orbitals inevitably generates another spin interaction - a biquadratic coupling - that must be included in the celebrated t−J model. While this additional interaction does not modify the linear spin wave spectrum, it promotes an enhanced nematic susceptibility that is peaked at a temperature scale determined by J. Our results explain several puzzling features of underdoped YBa2Cu3O7, such as the proximity of nematic and antiferromagnetic order, the anisotropic magnetic incommensurability, and the in-plane resistivity anisotropy. Furthermore, it naturally accounts for the absence of nematicity in electron-doped cuprates, and supports the idea that the pseudogap temperature is related to strong local antiferromagnetism