Magnetic and Ising quantum phase transitions in a model for isoelectronically tuned iron pnictides

Considerations of the observed bad-metal behavior in Fe-based superconductors led to an early proposal for quantum criticality induced by isoelectronic P for As doping in iron arsenides, which has since been experimentally confirmed. We study here an effective model for the isoelectronically tuned pnictides using a large-$N$ approach. The model contains antiferromagnetic and Ising-nematic order parameters appropriate for $J_1-J_2$ exchange-coupled local moments on an Fe square lattice, and a damping caused by coupling to itinerant electrons. The zero-temperature magnetic and Ising transitions are concurrent and essentially continuous. The order-parameter jumps are very small, and are further reduced by the interplane coupling; consequently, quantum criticality occurs over a wide dynamical range. Our results reconcile recent seemingly contradictory experimental observations concerning the quantum phase transition in the P-doped iron arsenides.

Figure 1

(a) Illustration of the $J_1-J_2$ model on a square lattice. The staggered magnetizations ${\stackrel{\rightharpoonup }{m}}_A$ and ${\stackrel{\rightharpoonup }{m}}_B$ are defined on two interpenetrating Néel square lattices. (b) Schematic phase diagram proposed for the P-doped iron arsenides [3]. P doping increases $w$, the spectral weight of the coherent itinerant electrons. The yellow dot denotes the tuning parameter $w_c$ for the QCP. The purple solid line and the green dashed one respectively mark the AF and structural transitions.

Figure 2

The evolution of the Ising order parameter ${\mathrm{\Delta }}_I$ (a) and the collinear AF order parameter $\sigma$ (b) vs the control parameter at different damping rates $[\mathrm{\Gamma }=\gamma /\left(c^{1/2}{\mathrm{\Lambda }}_c\right)]$ at a relatively large anisotropy $\epsilon \approx 0.27$, with fixed values of the normalized interactions $a_I$ and $a_0$. Each order parameter is normalized so that its value deep in the ordered phase is 1. The transition is very weakly first order, with jumps in the order parameters (insets) that are very small and decrease with damping: already for relatively small damping rate, the jump is on the order of ${10}^{-6}$ (and ${10}^{-3}$) for the nematic (and AF) order parameter.