Novel Magnetic Block States in Low-Dimensional Iron-Based Superconductors

Inelastic neutron scattering recently confirmed the theoretical prediction of a $\uparrow \uparrow \downarrow \downarrow$-magnetic state along the legs of quasi-one-dimensional iron-based ladders in the orbital-selective Mott phase (OSMP). We show here that electron doping of the OSMP induces a whole class of novel block states with a variety of periodicities beyond the previously reported $\pi /2$ pattern. We discuss the magnetic phase diagram of the OSMP regime that could be tested by neutrons once appropriate quasi-1D quantum materials with the appropriate dopings are identified.

Figure 1

Schematic representation of (a) the orbital-selective Mott phase and (b) $\pi /2$-block spin state. (c) Interaction $U$ and (d) filling $n$ dependence of the total magnetic moment $⟨S_{\ell }^2⟩$ and orbital-resolved occupation numbers $n_{\gamma }$ of the two-orbital Hubbard model Eq. (1), using $L=48$ sites. In (d), the black dashed line represents the largest possible magnetic moment $S_{\max }^2$. (e) Momentum distribution function $n_0(q)$ of the $\gamma =0$ orbital. Points indicate $q_{\mathrm{der}}^0$, the position of the maximum in $d{n}_0(q)/dq$. (f) $n$ dependence of the position of the maximum of the spin structure factor $q_{\max }^S$. Block OSMP is denoted as a colored area. In (f) we also present the position of the orbital $\gamma =0$ Fermi vector calculated via $2k_F^0=\pi n_0$ and via $2q_{\mathrm{der}}^0$.

Figure 2

(a) Static structure factor $S(q)$ for various fillings $n$ at fixed $U=W$, for the two-orbital Hubbard (lines) and generalized Kondo-Heisenberg (points) models, both using $L=48$ sites ($L=72$ for $n=2.75$, see text for details). Real-space correlation functions $⟨{\mathbf{S}}_{\ell }·{\mathbf{S}}_{L/2}⟩$ of the two-orbital Hubbard model and sketches of the spin alignment are also presented at the top. (b) Interaction vs filling magnetic phase diagram of the generalized Kondo-Heisenberg model on $L=48$ sites. The dashed shaded area represents the region where the mapping is not valid. BI, MI, PM, AFM, FM stands from band insulator, Mott insulator, paramagnet, antiferromagnet, and ferromagnet, respectively.

Figure 3

(a),(b) Finite-size scaling of (a) the spin structure factor maximum $S(q_{\max }^S)$ and (b) position of $q_{\max }^S$, calculated for $U/W=1$ using the generalized Kondo-Heisenberg model. Arrows in (b) represent the $L\to \infty$ limit $\pi n_0$. (c)–(f) $U$ dependence of $S(q)$ for $n=2.50$ and 2.66. Lines (circles) represent results using the two-orbital Hubbard model (generalized Kondo-Heisenberg model) and $L=48$ sites. Dashed horizontal lines represent $2k_F=\pi n$. (g) $U$ dependence of $q_{\max }^S$ for the two-orbital Hubbard model (lines) and generalized Kondo-Heisenberg model (circles) at fillings $n=2.33$, 2.50, and 2.66. The dashed shaded area represents the region where the mapping is not valid.

Figure 4

(a) $n$ dependence of $S(q_{\parallel },0)$ (bonding component) at $U=W_L$ using the two-orbital Hubbard ladder (lines) and the generalized Kondo-Heisenberg (points) models, both on $L=48$ sites (24 rungs). The inset depicts the antibonding component $S(q_{\parallel },\pi )$. Schematics of the spin configurations are also presented. (b) Filling $n$ dependence of $q_{\max }^{S\parallel }$, $2k_F^{0\parallel }=2\pi n_0$, and $2q_{\mathrm{der}}^{0\parallel }$. Block OSMP appears as a colored area. (c) Momentum distribution function $n_0(q_{\parallel },0)$ of the $\gamma =0$ orbital in the bonding $q_{\perp }=0$ sector. The legend is the same as in (a).