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Noncollinear magnetic ground state of PrFeAsO
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2011 EPL 93 17003
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EPL, 93 (2011) 17003
Noncollinear magnetic ground state of PrFeAsO
J. Liu , B. Luo , R. Laskowski
1 School of Physics, Huazhong University of Science and Technology - Wuhan 430074, China
2 Technische Universit¨at Wien - Getreidemarkt 9/165TC, A-1060 Vienna, Austria, EU
3 International Center of Materials Physics, The Chinese Academy of Science - Shengyang 110015, China
received 13 April 2010; accepted in ﬁnal form 18 December 2010published online 28 January 2011
PACS 74.25.Jb – Electronic structure (photoemission, etc.)PACS 74.70.Dd – Ternary, quaternary, and multinary compounds (including Chevrel phases,
borocarbides, etc.)
Abstract – Noncollinear magnetic investigations of the ground state in PrFeAsO have beenperformed by the density-functional theory. We calculated the total energy and made structureoptimization, and the electronic density of states of PrFeAsO was analyzed. There are threediﬀerent magnetic structures in PrFeAsO deﬁned by experiments. Based on these magneticstructures, we studied four collinear and four noncollinear cases. The ground state is found totake the ordering proposed by Zhao, in which the FeAs plane is of stripe antiferromagnetism andPr spins are perpendicular to Fe spins. The electronic density of states indicates that for PrFeAsOthe increase of the electron Coulomb interaction leads to a decrease in conductivity.

Antiferromagnetism is relevant to high-temperature
Kimber et al. proposed the collinear magnetic model,
superconductivity because copper oxide and iron arsenide
where both Fe and Pr spin ordering are within the ab-plane
superconductors arise from electron- or hole- doping
in the two-left, one-right magnetic structure [5]. Accord-
of their antiferromagnetic parent compounds [1,2]. If
ing to Kimber's structure, we constructed two kinds of
magnetism is important for the superconductivity of
collinear solutions CM1 and CM2. Pr spins are aligned
these materials, it is essential to get the correct magnetic
antiferromagnetically along the b-axis in the CM1 solu-
ground state of their parent compounds. The neutron
tion (see ﬁg. 1(a)) and are aligned ferromagnetically in the
powder diﬀraction has deﬁned the crystal structure and
CM2 solution (ﬁg. 1(b)). Simultaneously a rather compli-
the magnetic ordering of the RFeAsO system, which
cated noncollinear magnetic structure was shown by Zhao
shows a structural phase transition from tetragonal
et al. [6], where the Pr spins align along the c-axis, trios
to orthorhombic with decreasing temperature [3–8].

of spins are coupled ferromagnetically, and adjacent trios
However, it is found that at very low temperature there
align antiferromagnetically. This noncollinear magnetic
exits strong magnetic coupling between the rare-earth
structure is called NCM1 in our work (ﬁg. 1(c)). Finally,
elements, and they form antiferromagnetic ordering in
Maeter et al. reported a new noncollinear magnetic struc-
the RO layer, meanwhile their spins are coupled with iron
ture diﬀerent to NCM1, which is called NCM2 [7]. In
spins. The Fe spin structure is supposed to be the same
NCM2 Pr spins order within the ab-plane and Fe spins
as that arranged above the magnetic phase transition
make an acute angle with the ab-plane (ﬁg. 1(d)).

temperature when data ﬁtting. Hence it needs more
The two-dimensional electronic structure in the iron-
investigations to help deﬁne the iron spins ordering and
arsenide compound has been analyzed by many groups,
the rare-earth element spin ordering in the ground state.

but there are few reports about the three-dimensional
PrFeAsO is one parent compound of the iron arsenide
electronic-structure calculations including the rare-earth
family, and it has a transition temperature of up to 52 K
magnetic-moment direction. With the unconstrained
with oxygen partially replaced by ﬂuorine. Three groups
method, we deﬁned the Pr spin ordering and Fe spin
have worked on determining the magnetic structure of
ordering in the ground state. The lattice parameters
PrFeAsO and their results are totally diﬀerent. First,
were taken from refs. [6,9], and we made a
All calculations were performed by the WIENNCM
code [10,11], the Perdew-Burke-Ernzerh of 96 GGA
J. Liu et al.

other [13–15]. The stripe antiferromagnetic ordering isobserved by experiments [16–18]. In order to comparewith experiments and other theoretical work, we alsoconsidered the checkboard antiferromagnetic ordering. Weused checkboard ordering instead of stripe ordering in theabove four solutions and got the corresponding solutionsof CM1-FeC, CM2-FeC, NCM1-FeC and NCM2-FeC.

(The magnetic structure of CM1-FeC is similar to CM1,but the FeAs plane takes a checkboard ordering, see
ﬁg. 1(e).) Only two kinds of antiferromagnetic orderingare discussed in the NCM structure, for the experimentsand previous theoretical calculations both indicate anti-ferromagnetic ordering is more stable than other orderings(ferromagnetic, nonmagnetic and paramagnetic) [19,20].

Table 1 gives the energy of each conﬁguration. The
energy value in the CM1 case is set to zero; the other casesare given as the energy diﬀerences relative to the CM1case (energy values reserve four decimal places). Fromtable 1, it can be seen that two kinds of noncollinearmagnetic models are more stable than the collinear
magnetic models. When the Coulomb repulsion is consid-ered into Pr and Fe ions, NCM1 is the ground state andNCM2 is the metastable state. On three diﬀerent on-siteCoulomb interactions, NCM1 keeps the lowest energy.

In NCM1 the Fe spin shows stripe antiferromagneticordering within the ab-plane and the Pr spin plane isperpendicular to the Fe spin plane. Both NCM1 andNCM2
structures. Moreover the energy results indicate that in
noncollinear magnetic structure the stripe ordering is
more stable than the checkboard ordering, because the
NCM1 case and NCM2 case have lower energy than theNCM1-FeC case and NCM2-FeC case, respectively. If the
Fig. 1: (a) (Colour on-line) The collinear magnetic structure of
Coulomb repulsion is not considered, NCM2 takes the
the CM1 case; (b) the CM2 case; (c) the noncollinear magneticstructure of NCM1 case; (d) the NCM2 case; (e) the CM1-FeC
lowest energy. The X-ray absorption (XAS) and resonant
case. The red arrows indicate the magnetic-moment directions
inelastic X-ray scattering (RIXS) for 122 and 1111 Fe
of the magnetic ions. Light-green balls indicate Fe ions, green
pnictides show qualitative similarity to the Fe metal,
balls indicate Pr ions, red balls indicate O ions and purple balls
therefore the cases which included Coulomb interaction
indicate As ions.

are in accord with the actual conditions [12,21].

Using the unconstrained approach, the magnetic struc-
ture can be optimized according to the charge density.

exchange-correlation potential was used. Atomic sphere
The orientation of the spins is described using spherical
radii were set to 2.04, 2.39, 2.12 and 2.30 a.u. for O, Fe, As
coordinates. Each magnetic moment is symbolized by a
and Pr, respectively. We used a 4 × 4 × 4 k-point sampling
vector R(ρ, θ, ϕ), so that θ corresponds to the angle in the
of the Brillouin zone. The unconstrained approach was
basal plane, and ϕ is the angle relative to the c-axis (z-
adopted in order to lower the total energy and optimize
direction). In the optimization of the magnetic structure,
the magnetic structure. The RKmax value was set to Pr spins and Fe spins are found to make small changes in θ
7.0. Within GGA+U calculations, the eﬀective Coulomb
but give a relative large deﬂection in ϕ. The modiﬁcation
interaction value was set to 2 eV, 4 eV and 5 eV for Fe
for θ is no more than ±0.5◦, this means that the magnetic
ions and 4 eV, 6 eV and 7 eV for Pr ions, respectively [12].

ordering is quite stable within the ab-plane. Table 2 lists
Energy convergence and charge convergence were attained
the average ϕ deﬂection angles (between ρ- and c-axis) in
CM1, NCM1 and NCM2. From table 2 we can see that
The two interpenetrating square antiferromagnetic
the NCM1 case almost keeps the original magnetic struc-
orderings (checkboard ordering and stripe ordering) in
ture after optimization: both in GGA and GGA+U, Pr
the FeAs plane have been proposed by theoretical works,
deﬂection is no more than ±2◦ and Fe deﬂection is no
for the Fe-Fe eﬀective nearest-neighbor and next-nearest-
more than ±1◦. A larger alteration occurred to the NCM2
neighbor magnetic interactions are comparable to each
case: within GGA, ϕ deﬂection of Pr spin up to ±11.5◦
Noncollinear magnetic ground state of PrFeAsO
Table 1: Energies for each conﬁguration of PrFeAsO. The unit of the energy is Ry.

Table 2: Optimization results of magnetic structure: the average ϕ deﬂection angles in the CM1 case, NCM1 case and NCM2case.

The average ϕ deﬂection angles (◦)
and Fe deﬂection is ±3.4◦; within GGA+U, Pr deﬂection interaction the Fe moment is 2.59 µB and 2.99 µB foris between ±5.66◦ and ±5.13◦, Fe deﬂection is between 4.41 a.u. and 4.69 a.u. Fe-As bonds, respectively [27–29].

±0.4◦ and ±0.08◦. It tells us Pr spins are straying from However the Pr moment keeps 1.90 µB during the increase
the ab-plane and approaching the c-axis, and the trend of volume and it is not sensitive to the Pr-O bonds.

is weakened with the increase of the electronic correla-
Figure 2 illustrates the optimized results of energy and
tions. The same tendency is also found in the CM1 case.

For this reason, the optimization results prove that the
Finally, the electronic density of states (DOS) of the
NCM1 magnetic model is more stable than others. Within
NCM1 case is given (see ﬁg. 3). In ﬁg. 3, PrFeAsO
the GGA+U method we get Fe and Pr moments of about
indicates the metallic property within GGA; the Fe 3d
2.83 µB/Fe and 1.96 µB/Pr using the experimental lattice. band and Pr 4f band are continuous across the FermiThe calculated Fe moments do not reduced in noncollinear
level. While within GGA+U, the Fe 3d band and Pr
magnetic calculation or spin orbital coupling compared
4f band split and move away from the Fermi level, the
with other people's work [22–26].

distance between the split bands and the Fermi level
We also performed the volume optimization, this time
depends on the eﬀective Coulomb repulsion value. The
the spin direction of Pr and Fe were constrained. There
results of the DOS are in agreement with other theoret-
are two cases: 1) without considering on-site Coulomb
ical calculations [20,30,31], which perform the electronic-
interaction, 2) with Ueﬀ = 2 eV for the Fe ion and Ueﬀ = structure calculation for PrFeAsO within LDA or GGA.

4 eV for the Pr ion. When the on-site Coulomb interac-
If the electronic correlations are weak enough in Fe ions,
tion is not included, the lowest total energy occurs at
the FeAs plane will be metallic or easily conductive in
about V /Vexp = 5%, the lattice parameters are obtained the excited state [21]. CM1, CM2, NCM2 and NCM1with a = 8.738 ˚
A. If the eﬀec-
have a similar DOS under one Coulomb interaction, that
tive Coulomb interaction are set to 2 eV and 4 eV for
is to say, the Pr spin direction does not much aﬀect the
Fe and Pr ions, respectively, the structure can be stabi-
density of states at the Fermi level. In ﬁg. 3(a), Fe has a
lized in V /Vexp = 9% by the lattice parameters a = 8.848 ˚
few similar peaks with Pr between –2 eV and 2 eV, hence
A. Additionally, the Fe magnetic
there exits a magnetic coupling between the FeAs plane
moment is sensitive to the Fe-As bonds, with Coulomb
and the PrO plane. We believe that the magnetoelastic
J. Liu et al.

Fig. 2: (Colour on-line) The energy and magnetic moment for volume optimization.

Fig. 3: (Colour on-line) Density of states of the NCM1 case. (a) The DOS without Coulomb interaction. (b) The DOS withCoulomb interaction (U − J = 2 eV for Fe and U − J = 4 eV for Pr).

volume eﬀect reported in ref. [5] originates from both
NCM1 in which the Pr spin is perpendicular to the Fe
Pr spin density waves and Fe spin density waves. The
spin and the FeAs plane takes stripe antiferromagnetic
superconducting isotropy of PrFeAsO1−y suggests a ordering. Another noncollinear magnetic structure NCM2quasi–three-dimensional
is considered for metastable states. We found that the Pr
spin direction does not much aﬀect the density of states
tions conﬁrm it also has a three-dimensional magnetic
at the Fermi level. The Fe magnetic moment is sensitive
structure [32].

to the Fe-As bonds but the Pr moment is not sensitive to
In conclusion, this work has investigated four collinear
the Pr-O bonds. The conductivity of PrFeAsO is mainly
and four noncollinear magnetic structures in PrFeAsO.

depending on the electronic correlation interaction, if the
Total energy calculation, magnetic structure optimization
electronic correlations are weak enough, the PrFeAsO will
and volume optimization deﬁne the magnetic ground state
show metallic character or semi-metallic character.

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Source: http://www.cms.tuwien.ac.at/media/pdf/publications/epl_93_1_17003_2011.pdf

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