Low spin moment due to hidden multipole order from spin-orbital ordering in LaFeAsO
Francesco Cricchio, Oscar Grånäs, and Lars Nordström
Department of Physics and Astronomy, Uppsala University, P.O. Box 516, 751 20 Uppsala, Sweden
Received 21 January 2010; revised manuscript received 1 March 2010; published 13 April 2010
An antiferromagnetic AF low-moment solution, 0.35
B
/ Fe, is found in the case of LaOFeAs for an
intermediately strong Coulomb interaction U of 2.75 eV. This solution is stabilized over a large moment
solution due to the gain in exchange energy in the formation of large multipoles of the spin magnetization
density. The multipoles are of rank four and can be understood as a type of spin-orbital ordering. Parallels can
be drawn to the stabilization of the AF order in, e.g., CaCuO
2
.
DOI: 10.1103/PhysRevB.81.140403 PACS numbers: 75.25.-j, 74.70.Xa, 75.10.Lp
With the discovery of the iron pnictide layered supercon-
ductors in 2008,
1
a hope was quickly raised that these mate-
rials would finally lead to an understanding of the elusive
mechanism of the superconductivity of the high-T
C
cuprates.
Indeed there are many common features; the fact that the
parent compound is antiferromagnetic AF, the central role
played by a transition-metal layer, the fact that the AF order
quickly disappears with doping and then is overtaken by a
strong superconducting state. However, fairly soon some dif-
ferences were also discovered. While the main electrons in
the cuprates are correlated and close to an insulating state, in
the iron pnictides they seems to be at most moderately cor-
related and metallic.
2,3
This difference between the two types
of materials is also manifested by the fact that density-
functional theory DFT based calculations of the undoped
iron pnictides obtain the correct metallic AF order while in
the undoped cuprates they falsely lead to a nonmagnetic me-
tallic state. When a correlation term is added to the DFT
Hamiltonian, local-density approximation plus added Cou-
lomb U interaction formalism LDA+ U, an AF insulating
phase is obtained.
4
However, with the increasing number of
DFT studies, it has been clarified that DFT has problems also
for the iron pnictide parent compounds, although of different
nature.
5
The calculations systematically predict unusually
bad Fe-As bonding distances and overestimate the ordered
AF spin moment, which is 0.35
B
in LaOFeAs.
6
In fact,
state-of-the-art DFT calculations in the generalized gradient
approximation GGA give spin moments of the order
2.0–2.5
B
,
5,7
i.e., an overestimation by at least a factor 5.
In this Rapid Communication we perform LDA+ U calcu-
lation for the AF parent compound LaOFeAs. The obtained
results show that, for realistic U parameters, a low spin mo-
ment solution is stabilized due to polarization of higher mul-
tipole moments of the spin density. These terms can be ana-
lyzed as a spin-orbital ordering among mainly the xz and yz
d orbitals at the Fe sites. It is also found that the calculated
equilibrium distance between the Fe plane and the As planes
is in good agreement with the experimental value.
6
Finally
we make a comparison with the LDA+ U solution for an
undoped cuprate, CaCuO
2
, which reveals a striking similar-
ity in the role played by magnetic multipoles.
The electronic structure is calculated within the full-
potential augmented plane wave plus local orbital method as
implemented in the ELK code.
8
The LDA+ U approach is
applied following the same methodology as described in Ref.
9 with Yukawa screening
10
and around mean-field double
counting while the GGA Ref. 11 is used for the DFT part.
The AF Brillouin zone BZ is sampled with 10 10 6 k
points uniformly spaced. The calculations are done for the
crystal parameters of the experimental high-temperature te-
tragonal structure,
6
except when optimizing the internal z
As
parameter. The parameter governing the number of aug-
mented plane waves R|G
+ k
|
max
is set to 8.0, where R is the
Fe muffin-tin radius and G
are the reciprocal-lattice vectors.
There have been several attempts to estimate the magni-
tude of the Coulomb interaction U in this compound. The
results stretch all the way from fairly large values of 4 eV
leading to strong correlation,
12
through moderate values of
3–4 eV Ref. 13 and 2.7 eV,
14
down to less than 2 eV.
15
As
has been discussed,
13,14
part of the disagreement stems from
the different choices of band manifolds that are allowed to
interact with this Coulomb interaction. If one performs a
downfolding to a subset of Fe d states the effective Coulomb
interaction has to be decreased too, otherwise the correlation
effect is overestimated. In the present study we will vary U
between 0 and 4 eV, where the U = 0 eV case corresponds to
a pure GGA calculation, since all Slater parameters are
screened with the same Yukawa screening length.
9
In this
approach the Hund’s rule exchange parameter J varies auto-
matically between 0 and 1 eV, with, e.g., J =0.86 eV for U
=2.75 eV which is very close to the values obtained by a
constrained DFT approach,
14
J = 0.79 and U =2.7 eV.
The total energy as a function of the spin moment, as
obtained by constraining the staggered spin moments
16
of the
stripe ordered AF state, and as a function of U, is displayed
in Fig. 1. In agreement with earlier studies
5
the GGA curve
U =0 has a clear deep minimum at m = 2.2
B
. This mini-
mum moves slightly to larger moments by increasing U.
However, when the spin moment is constrained in the scan
for other solutions, we can observe that a second solution
starts to develop at a smaller moment. At U 2 eV this has
evolved to a local minimum, which becomes the global mini-
mum for U 2.5 eV, a value close to the estimated one.
14
At
the largest values of the Coulomb parameter also an interme-
diate minimum is formed. Hence there are several competing
metastable states found, among which the low-moment solu-
tion is most stable in the case of LaOFeAs and for U
2 eV. It is a nontrivial task to find all stable solutions but
these are the states we have found after systematic searches.
In addition we have verified the low- and large-moment so-
PHYSICAL REVIEW B 81, 140403R2010
RAPID COMMUNICATIONS
1098-0121/2010/8114/1404034 ©2010 The American Physical Society 140403-1