Interplay between tetragonal magnetic order, stripe magnetism, and superconductivity in iron-based materials

Motivated by experiments in ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ [A. E. Böhmer et al., arXiv:1412.7038], we analyze the type of spin-density wave (SDW) order in doped iron-pnictides and the discontinuities of the superconducting transition temperature $T_c$ in the coexistence phase with SDW magnetism. We find a sequence of transitions, upon lowering the temperature, from the stripe-orthorhombic $\left(C_2\right)$ SDW order to the tetragonal $\left(C_4\right)$ order and then back to the $C_2$ order. We argue that $T_c$ has two discontinuities—it jumps to a smaller value upon entering the coexistence region with the $C_4$ magnetic phase, and then jumps to a larger value inside the SDW state when it crosses the boundary between the $C_4$ and $C_2$ SDW orders. We argue that the agreement with the experimental phase diagram provides a strong indication that the itinerant approach is adequate for weakly/moderately doped iron pnictides.

Figure 1

Schematic phase diagram resulting from our itinerant model (left) and experimental phase diagram of Ref. [14] for ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ (right). Blue lines refer to the (second-order) SC phase transition whereas the green and red lines refer to the (first-order) $C_4\text{−}{C}_2$ and normal-state–SDW phase transitions, respectively. Black lines refer to the first-order SDW phase transitions inside SC phase. The four experimental features (i)–(iv) discussed in the main text are naturally captured by the itinerant model. The precise shapes of the transition lines is nonuniversal and depends on details of the model.

Figure 2

(a) The schematic phase diagram when SC is not included. The dashed (solid) lines give the phase boundary of $C_4$ SDW order in the absence (presence) of higher-order terms in the free energy. (b) The coefficients $g$ and $v$ in Eq. (2) [normalized to their absolute ${\delta }_{\mu }=0$ values, $\left|g\left(0\right)\right|\approx 1.8N_f/{\left(2\pi T\right)}^2$ and $\left|v\left(0\right)\right|\approx 12.6N_f/{\left(2\pi T\right)}^4]$ as functions of ${\delta }_{\mu }/\left(2\pi T\right)$ for ${\delta }_m/\left(2\pi T\right)=1$. Note that $g$ and $v$ change sign twice as ${\delta }_{\mu }/\left(2\pi T\right)$ becomes larger. This behavior is generic for other values of ${\delta }_m/\left(2\pi T\right)$ (see SM).