Ilya EREMIN (Ruhr-Uni. Bochum): Selection of magnetic order and magnetic excitations in the metallic SDW state of ferropnictides

OUTLINE:
(I) Introduction
(II) Peculiarities of the SDW state in the itinerant scenario
(III) Spin excitations

I. Introduction
Cu-oxides vs. Fe-pnictides - similarities in the (T-doping) phase diagram. Proximity to AFM phase is important in both cases. However, unlike CuO2, all regions of FeAs phase diagram are metallic.

Two somewhat contradictory observations:

• Metallic transport in Ba-122 (N. Kurita, PRB'09): below T_Neel, the resistivity is metallic [Remark from the audience: for samples prepared in Sn-flux, the resistivity is known to go up, not down, below T_Neel.]
• well-defined Fe-moments, with spin waves inside the ordered phase.
  

I will present the itinerant scenario, leaving aside the alternative scenario (local moments).


II. Peculiarities of the SDW state: itinerant scenario

Nesting properties:
\eps_holes(k) = - \eps_el(k+Q),
with Q=(pi,pi) an AFM ordering wave-vector (in a 2-Fe unit cell convention).
Nesting provides a boost for SDW, with susceptibility \chi(Q,w) diverging as log(w/Ef).

Below T_Neel: \sqrt{2} x \sqrt{2} order with Q=(pi,pi).

Unfolding the bands to an extended BZ corresponding to 1-Fe unit cell. In this unfolded picture, there are 2 nesting wave-vectors: Q1=(0,pi) and Q2=(pi,0). Two vector order parameters with Delta_1 and Delta_2. Two sublattice order parameters: (Delta_1 + Delta_2) and (Delta_1 - Delta_2). How do we know which of the two orders is selected?

Simplest model: 1 hole and 2 electron pockets [in the unfolded 1-Fe BZ]
I. Eremin and A. Chubukov, PRB 81, 024511 (2010)

Only 1 equation, from which \Delta_1 and \Delta_2 SDW components cannot be both determined: only |\Delta_1|^2 + |\Delta_2|^2 is fixed. The absolute values and the angle can vary!
Result: very degenerate ground state: O(6) degeneracy, 5 Goldstone modes
(more degenerate than the purely magnetic J1-J2 model).

Nesting is not perfect. Pockets are elliptic, introducing a positive term (mx-my)^2, resulting in the term ~C|\Delta_1|^2 |\Delta_2|^2. This term comes from charge-charge interactions (and won't be there in the purely magnetic J1-J2 model).
As a result of this term, the ground state is either \Delta_1 = 0 or \Delta_2 = 0.
To summarize:
- no need to appeal to qu. fluctuations
- charge fluctuations are crucial to determine the order parameter.

NOTE:
One of the electronic pockets decouples from the problem, so that even for arbitrarily strong interaction, there will always remain an ungapped electron pocket at the Fermi level, resulting in a metallic state even inside the SDW phase!

Inclusion of the 4th (hole) pocket: the picture remains basically unchanged, with the same type of the magnetic order.
[Proviso: However, for U>Ucr, both \Delta_1 and \Delta_2 may become non-zero, resulting in a stripe order that will be distorted.]

Comparison with ARPES:
one electron pocket does indeed survive at the Fermi level (Dresden group ARPES: V. Zabolotnyy et al, Nature'2009)

III. AFM excitations
J. Knolle, I.Eremin, A.Chubukov, R. Moessner, PRB 81, 140506 (2010).

Now that we determined the ground state, let us consider excitations.
Compute transverse spin susceptibility -> spin waves.

If nesting is complete -> continuum is gapped, Goldstone modes only near (0,pi) and (pi,0). No Landau damping as long as the energy is below the size of the SDW gap.

If ellipticity is included -> finite continuum, with present Landau damping. Well-defined spin waves around Q1=(pi,0), but only diffuse paramagnons around (0,pi).
Results in anisotropic spin wave velocity along x- and y- directions, even though the underlying interactions are isotropic.

CONCLUSIONS:

• ellipticity of the electron pockets and the e-e interaction at (pi,pi) stabilize the metallic AFM state with (0,pi) or (pi,0) order
• well-defined spin excitations near Q, with anisotropic spin velocities in x- and y-direction
  
• AFM state is always metallic with more FS crossings than in the normal state. In the folded BZ, (0,0) and (pi,pi) are not equivalent.
  
• no correspondence to the J1-J2 model in strong coupling limit

QUESTIONS:

Q: A. Chubukov: What if there is coupling to the lattice?
A: Depending on the scenario, either SDW is of electronic origin, and structural transition follows. OR, the structural transition leads to spin nematic phase ( see Fernandez, arXiv:0911.3084).

Q: M. Vojta: Can Dirac points develop in the pnictides? Can you comment on this?
A: In Vishvanath's picture, the Dirac point can develop due to q-dependent interaction. However in our picture, accidental Dirac points can appear.
Z. Tesanovic's comment: unlike Vishvanath et al, there is also a possibility of a topologically protected Dirac point (only arises in pure xz,yz (2 band) models).

Q. Yu Lu: 1) what is the size of the moment?
2) above the magnetic transition, how do you explain the linear-T behaviour of
susceptibility (R. Klingeler et al, )?
A: 1) the moment of order 0.6 bohr-magneton, and depends on how much of the Fermi surface is gapped.
2) non-analytic, linea-T, corrections to susceptibility can arise due to proximity to SDW. See Korshunov, I. Eremin PRL 102 (2009).

Q: Rafael Fernandez: Do you need orbital physics to explain the spin excitation dispersion, or is it enough to only consider spin physics?
A: no comment. Perhaps.