Gutzwiller Theory of Band Magnetism in LaOFeAs

We use the Gutzwiller variational theory to calculate the ground-state phase diagram and quasiparticle bands of LaOFeAs. The $\mathrm{Fe}3d\mathrm{\text{−}}\mathrm{As}4p$ Wannier-orbital basis obtained from density-functional theory defines the band part of our eight-band Hubbard model. The full atomic interaction between the electrons in the iron orbitals is parametrized by the Hubbard interaction $U$ and an average Hund’s-rule interaction $J$. We reproduce the experimentally observed small ordered magnetic moment over a large region of ($U,J$) parameter space. The magnetically ordered phase is a stripe spin-density wave of quasiparticles.

Figure 1

$\mathrm{Fe}3d\mathrm{\text{−}}\mathrm{As}4p$ band structure (in eV) of LaOFeAs along the high-symmetry lines of the 2D Brillouin zone containing one formula unit per cell. Left: DFT [8] (dashed lines) and GT (solid lines) in the PM phase for $(U,J)=(8,0.6)\mathrm{eV}$. The bands are lined up at the Fermi level ($E=0$). Right: GT bands in the PM (dashed lines) and SDW (solid lines) phases in the Brillouin zone folded along the line $\frac{1}{2}\overline{\Gamma }\overline{Y}\mathrm{\text{−}}\frac{1}{2}\overline{X}\overline{M}$. High-symmetry points and the directions $x,y$ and $X,Y$ are defined in Fig. 2. Dominant orbital and spin characters are indicated. Spin-$\uparrow$ are minority and spin-$\downarrow$ are majority spin states [8].

Figure 2

PM Fermi surface. Left: DFT. Right: GT for $(U,J)=(8,0.6)\mathrm{eV}$. The lower and upper case coordinate systems used to designate the orbitals are shown.

Figure 3

Local $d$-charge distribution $p(n)$ (left) and local spin distribution $p(s)$ (right) for the PM GT with $(U,J)=(8,0.6)\mathrm{eV}$ and for the PM single-particle wave function $|{\Psi }_0⟩$.

Figure 4

GT ordered magnetic moment as a function of $U$ for various values of $J/U$. Our characteristic parameter set is at $J/U=0.075$ (filled squares). Full symbols: Full atomic Hamiltonian; open symbols: restricted atomic Hamiltonian with density-density interactions only. Inset: Ground-state phase diagram as a function of $U$ and $J$. In the SDW metal, we also show lines for constant magnetization, $m=0.4{\mu }_B$ and $m=0.5{\mu }_B$, respectively.

Figure 5

Ordered moment as a function of $I=J+0.017\mathrm{U}$ for various values of $J/U$ in GT (diamonds), and the inverse susceptibility in DFT ${\chi }_{\mathrm{DFT}}^{-1}=\Delta /m(\Delta )$ (dots). The ordered moment given by spin-DFT (generalized gradient approximation) is reproduced by $I_{\mathrm{DFT}}=0.82\mathrm{eV}$ [8].