Contents - Max-Planck-Institut für Physik komplexer Systeme

2.27 Itinerant Magnetism in Iron Based Superconductors
JOHANNES KNOLLE, ILYA EREMIN, RODERICH MOESSNER
Introduction. The ferropnictide (FP) superconductors
have captured the imagination of the condensed
matter physics community, not least because of their remarkably
high critical temperature of up to Tc ≈ 56K.
Like their brethren, the cuprate high-Tc materials, they
are quasi two-dimensional layered materials, and their
parent compounds are antiferromagnetically ordered
below 150K. Also, upon doping of either electrons or
holes into the FeAs layers, magnetism is supressed and
superconductivity emerges. It has by now become clear
that superconductivity is not mediated by phonons [2].
However, there are important differences to the
cuprates. The FPs are always metallic, even in the magnetically
ordered phase. Moreover, the order parameter
has an unusual extended s-wave (s ± ) symmetry.
These facts immediately pose a broader set of questions,
beyond “Why is Tc so high?”. Firstly and foremostly,
what is the minimal model which can account
for the magnetic properties, such as nature of the ordering
and excitations? Secondly, how can one probe
the special features arising from the multiband nature
and the unusual order parameter in the FPs? This latter
question is in part motivated by measurements of
spectroscopic imaging-scanning tunneling microscopy
(SI-STM), which claimed the presence of “nematic ordering”
in the FPs [3].
Indeed, one of the central attractions of FP physics
is the rapid availability of many types of experimental
data, and here we therefore focus on two of these:
firstly, neutron scattering and secondly, SI-STM.
Figure 1: The Fermi surface topology of iron based superconductors
for the BZ based on one iron per unit cell. The two nesting vectors
Q1 and Q2 are shown.
The magnetic structure of FPs is of the QAF = (π,0)
type with ferromagnetic chains in one direction and
antiferromagnetic chains in the other one. The Fermi
surface (FS), shown in Fig.1, consists of two hole-like
pockets at the center of the Brillouin zone (BZ) and
electron-like elliptical pockets at the (±π,0) and (0, ±π)
points. By looking at the Fermi surface topology we
observe that the special nesting wave vector Q2 corresponds
to the magnetic wave vector QAF. At first
sight, both nesting vectors Q1 and Q2 are similar under
a 90 degree rotation and the following natural question
arises: How does the system choose the magnetic odering
QAF = Q2 over the other vector Q1? We have constructed
a minimal four band model with input parameters
from experiments [4], and in a general Ginzburg-
Landau mean-field treatment of the inter- and intraband
interactions we showed that the free energy of the
system is minimized if only one of the vectors is chosen
[5]. Having understood the selection of the magnetic
order from our itinerant starting point we have
computed different observables to make a connection
with available experiments.
Ω (meV)
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0
-1.5
-1.0 -0.5 0 0.5 1.0 1.5
(2π,0) (π,π)
Figure 2: Spin wave dispersion in energy-momentum space together
with experimental data. Starting at the ordering wave vector (π, 0)
the imaginary part of the spin susceptibility is plotted for two perpendicular
directions. This shows the anisotropy of the spin wave
velocities.
Spin Waves. Due to the broken spin rotational
symmetry in the antiferromagnetic phase, Goldstone
modes, namely spin waves, appear as low-energy fluctuations
transverse to the magnetic ordering. They
can be directly probed via inelastic neutron scattering
(INS). For FPs, the INS experiments had only been analyzed
by models of local moments, which however are
not obviously well suited for metallic systems. Therefore,
by computing the spin waves via a self-consistent
mean-field plus random phase approximation, we provided
an alternative explanation of the measurements
94 Selection of Research Results
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