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

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

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

Dimensional crossover and cold-atom realization of topological Mott insulators

We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this phase has remained elusive, our proposal shall help to shed some light on this exotic state of matter by paving the way for a controlled experimental investigation in optical lattices.Comment: 4+ pages, 3 figures; includes Supplemental Material (3 pages, 1 figure