Role of multiorbital effects in the magnetic phase diagram of iron pnictides

We elucidate the pivotal role of the band structure's orbital content in deciding the type of commensurate magnetic order stabilized within the itinerant scenario of iron pnictides. Recent experimental findings in the tetragonal magnetic phase attest to the existence of the so-called charge and spin ordered density wave over the spin-vortex crystal phase, the latter of which tends to be favored in simplified band models of itinerant magnetism. Here we show that employing a multiorbital itinerant Landau approach based on realistic band structures can account for the experimentally observed magnetic phase, and thus shed light on the importance of the orbital content in deciding the magnetic order. In addition, we remark that the presence of a hole pocket centered at the Brillouin zone's $\mathrm{M}$ point favors a magnetic stripe rather than a tetragonal magnetic phase. For inferring the symmetry properties of the different magnetic phases, we formulate our theory in terms of magnetic order parameters transforming according to irreducible representations of the ensuing $D_{4h}$ point group. The latter method not only provides transparent understanding of the symmetry-breaking schemes but also reveals that the leading instabilities always belong to the $\{A_{1g},B_{1g}\}$ subset of irreducible representations, independently of their $C_2$ or $C_4$ nature.

Figure 1

Eigenvalues of the inverse magnetic propagator as a function of electron filling at the transition temperature $T_{\mathrm{SDW}}$. A zero eigenvalue indicates a magnetic transition. Two distinct features are clear: The leading instability is well separated from subleading instabilities. The eigenvalues cluster into two groups; the group nearest $\lambda =0$ consists of instabilities leading to order parameters with real matrix elements in orbital space. In contrast the group around $\lambda =10$ is characterized by imaginary matrix elements for the order parameters.

Figure 2

Leading instabilities for the free energy in Eq. (19). The magnetic structures obtained are shown in the top panel; note that the $C_4$ orders have $|{\mathbf{M}}_X|=|{\mathbf{M}}_Y|$ as required by the free energy. The dots signify the microscopically obtained values of the quartic coefficients for $U=0.85\mathrm{eV}$ and $J=U/4$ as a function of filling for a step size of $\delta \langle n\rangle =0.01$. The evolution of the third independent quartic coefficient, $\beta$, is shown in the bottom panel as a function of doping. Finally we note that in the absence of SOC, only the relative orientation of ${\mathbf{M}}_X$ and ${\mathbf{M}}_Y$ is fixed by the free energy.

Figure 3

(a) Fermi surface for $\langle n\rangle =5.95$ in the paramagnetic phase. Magnetism is driven by nesting between the hole pockets at $\mathrm{\Gamma }=(0,0)$ and $\mathrm{M}=(\pi ,\pi )$, and the electron pockets at $\mathrm{X}=(\pi ,0)$ and $\mathrm{Y}=(0,\pi )$. (b) Fermi surface for $\langle n\rangle =6$ where the $\mathrm{M}$ pocket has been removed as described in the text.

Figure 4

(a) Orbital weight $v_X^{ab}$ at the magnetic transition for the FS shown in Fig. 3, with $U=0.85\mathrm{eV},J=U/4$, and $\langle n\rangle =5.95$, yielding an MS phase. Note that the off-diagonal elements between $x^2-y^2$ and $z^2$ are small but nonzero. (b) Orbital weight $v_X^{ab}$ at the magnetic transition for the FS shown in Fig. 3, with $U=1.2\mathrm{eV},J=U/6$, and $\langle n\rangle =6$, where the $\mathrm{M}$ pocket has been removed, hence resulting in a CSDW phase.

Figure 5

Leading instabilities for the band structure of Ref. [27] with $U=0.85\mathrm{eV}$ and $J=U/4$. The color corresponds to the type of magnetic order parameter at the transition and is the same as the one in Fig. 2, red is the CSDW phase, blue is the magnetic stripe phase, and green is the SVC phase. As the free energy analysis with only quartic coefficients is only valid in the vicinity of the phase transition, the region of the phase diagram deep in the magnetic phase is intentionally left blank.

Figure 6

Leading instabilities for $U=0.95$ eV and $J=U/4$ supplemented by Hartree-Fock calculations for specific doping values confirming the existence of a secondary transition to an SVC phase at lower temperatures.

Figure 7

Phase diagrams for the parameters $U=1.2\mathrm{eV}$ and $J=U/6$. (a) Leading instability for the original band structure is shown and the system exhibits an MS phase throughout. (b) Leading instability in the case of an absent hole pocket at M. The MS phase of the original case is replaced with a CSDW phase, while the transition temperature is reduced due to the change in nesting properties of the Fermi surface. The gray area denotes regions of incommensurate magnetism.