Noncollinear full-potential studies of -Fe
Elisabeth Sjo
¨
stedt and Lars Nordstro
¨
m
Condensed Matter Theory Group, Physics Department, Uppsala University, S-75121 Uppsala, Sweden
Received 17 January 2002; published 24 July 2002
Accurate density functional calculations have been performed for the fcc-based frustrated antiferromagnet
-Fe. Several competing collinear as well as noncollinear magnetic structures have been considered: ferro-
magnetism, 1 k,2 k,3 k, and double-layered antiferromagnetism, as well as noncommensurate helices. In
contrast to standard noncollinear methods, our scheme treats the magnetization density as a vector field which
is free to change in both magnitude and direction throughout space. The noncollinear method is implemented
in the alternative linearization of the full-potential augmented-plane-wave method, closely related to the con-
ventionally linearized method, but computationally more efficient. The most stable magnetic structure of -Fe
is found to vary sensitively with volume. At the experimental volume a =6.82 a.u., the moments are ordered
in a collinear double-layered antiferromagnetic structure, while the ground state is almost degenerate between
two different helices of different equilibrium volumes a =6.63 a.u. and a =6.61 a.u., respectively. The ob-
tained results are analyzed and compared with earlier calculations and existing experiments. For instance, we
notice that the results are altered when we introduce an atomic moment approximation in our calculations.
DOI: 10.1103/PhysRevB.66.014447 PACS numbers: 75.25.+z, 71.15.Mb
I. INTRODUCTION
The high-temperature fcc phase of iron, -Fe, has at-
tracted much interest due to its elusive magnetic character.
There are also practical implications since many important
iron alloys, such as the Invar alloys and several high-quality
stainless steels, are fcc ordered.
In 1989 Tsunoda
1
managed to stabilize precipitates of
-Fe inside an fcc Cu matrix. They could then explore the
magnetic properties of three-dimensionally constrained clus-
ters of -Fe, each one spherically shaped with a mean diam-
eter of 50 nm. Interestingly enough, the ground state was
found to be a helical spin density wave, or a spin spiral SS,
with a wave vector
q
expt
= 0.10,0,1
2
a
. 1
Here a is the lattice constant of the conventional fcc Cu cell
(6.822 a.u.), inherited by the iron precipitates. This wave
vector nearly yields a type-I antiferromagnetic AF system,
cf. q
AF
=(0,0,1)2 / a .
From a theoretical point it is unclear what magnetic
ground state -Fe is predicted to have, since there is an un-
usual large spread in earlier published results. The first spin-
spiral calculations performed for -Fe were presented by
Mryasov et al.
2
in 1991. Using the linearized muffin-tin or-
bital LMTO method they investigated ordering vectors in
the X
direction of the fcc Brillouin zone BZ, where the q
vector is equivalent to a ferromagnetic FM structure, and
the ordering vector X represents a type-I AF structure. They
found that the magnetic ground state depends on the filling
of 3 d electrons, with -Fe lying at a crossing point between
the FM and AF regions in a magnetic phase diagram of 3 d
metals in fcc lattices. They also showed how the magnetic
structure of -Fe could be changed from FM into different
SS structures by lowering the lattice parameter from
7.11 a.u. down to 6.81 a.u. For the smaller volumes, the
energy of the SS approached that of the AF solution. The
lowest energy was found for the smallest volume examined,
at a SS having q vector
q
A
= 0,0,0.6
2
a
. 2
The same ordering vector was obtained in the calculations
performed by Uhl et al.
3
later the same year. They used the
augmented spherical wave ASW method and included also
q vectors along XW
. Antropov et al.
4
let the directions of the
magnetic moments evolve freely in an LMTO calculation,
using a supercell with 32 atoms. They confirmed that the
magnetic configuration was extremely sensitive to volume
changes. Their results changed quantitatively when the local
spin density approximation LSDA was replaced by a gen-
eralized gradient approximation GGA but the trend was the
same, going from more complex orderings at small volumes
( a 6.78 a.u. and a 6.69 a.u. for the LSDA and GGA,
respectively into a double-layered AF structure for increas-
ing volumes. For larger volumes ( a 7.05 and a
6.90 a.u.), the structure preferred the FM state. James
et al.
5
performed LMTO calculations where they compared
the total energy as function of the volume for a large number
of AF orderings in -Fe. Using the LSDA they found a more
complex ordering of the moments at smaller volumes a
6.78 a.u., with the global minimum at a =6.55 a.u.
Again, the double-layered AF structure became the most
stable for increasing volumes.
In their paper from 1996, Ko
¨
rling and Ergon
6
reproduced
the SS structure of ordering vector q
A
for a lattice constant
a =6.80 a.u. using the LMTO method with LSDA. How-
ever, when introducing the GGA into their calculations, they
stabilized a new SS with an ordering vector at W,
q
B
= 0.5,0,1
2
a
. 3
PHYSICAL REVIEW B 66, 014447 2002
0163-1829/2002/661/01444710/$20.00 ©2002 The American Physical Society 66 014447-1