1. Theory of Magnetic Moment in Iron Pnictides (LaOFeAs) Jiansheng Wu (UIUC), Philip Phillips (UIUC)
and A.H.Castro Neto (BU) arxiv:

2. Purpose:
Explain the experimental results in LaOFeAs (arXiv: ):
E1: Stripe type anitferromagnetism ;
E2: Small magnetic moment 0.35 μB ;
E3: Magnetic moments lie in xy plane, 860 to c axis .

3. using the ordinary Hund’s rule, we have two configurations
Why the experimental results are so striking?
using the ordinary Hund’s rule, we have two configurations
NO way to get magnetic moment of 0.35 μB !

4. A hint
As 4p-Fe 3d hybridisation is crucial

5. spin-orbit+
pd hybridization+
crystal field

6. Three ingredients when we consider the new way to arrange electrons in For As-Fe band:
Spin-orbits interaction,
No trivial spin up/down degeneracy;Some levels are not spin eigenstates. (New eigenstates:)
d-band p-band

7. p-d hybridization: Crystal field:
delocalization of 3p electrons
(in α or β basis Vpd is the following, Δp ,Δd are spin-orbit splitting);
Crystal field:
lower the energy of mz=0 orbits for p and d bands (the crystal field is the followings, δp ,δd are crystal splitting:)

8. Magnitude of parameters
(a) Energy levels, (b) hopping matrix elements, on-site interactions, (c) intra-band interaction and (d) spin components as a function of hybridization M. Shown in the inset of (c) is the on-site interaction U2 as a function of the crystal field (monoclinic distortion).

9. New way to arrange electrons in For As-Fe band:
(by diagonalizing the above Hamiltonian)
Sketch of the energy levels of the Fe 3p and As 4p hybridized levels after the inclusion of spin-orbit coupling, p-d hybridization, and the monoclinic crystal field distortion.
Only the Γ15 p-levels of Fe hybridize with the As 4p levels. The Γ12 levels remain non bonding.
Each of the hybridized levels is doubly degenerate, though not an eigenstate of Sz.The only hybridized level which is an eigenstate of Sz is E0. The lowest-energy configuration of the spins in E0 and E2 is indicated. As a result, only the x-y component produces a non-zero moment.

10. The final picture itinerant
Strong on-site interaction U2 make electrons on E2 antiferromagnetic.
Interaction between spin “up” on E2 and spin up on E0 make them favour the above configurations. Then their z-components almost cancel.
itinerant

11. Conclusion 1) & 2) explain E2 and E3; 3) explains E1.
1) z-component of spin is vanishingly small 0.05 μB due to cancellation of z-component of spins on E0 and E2
(M. A. McGuire, et al. arXiv: ).
2) xy component of spin on E2 is 0.32 μB
3) due to strong on-site interaction on E2, spins on E2 form antiferromagetic Fe-As-Fe bands.
1) & 2) explain E2 and E3;
3) explains E1.