Spin-Peierls-like transition in AFe$_2$As$_2$(A=Ba, Sr)

Abstract

From first-principles density functional theory calculations combined with varying temperature Raman experiments, we show that AFe$_2$As$_2$ (A=Ba, Sr), the parent compound of the FeAs based superconductors of the new structural family, undergoes a spin-Peierls-like phase transition at low temperature. The coupling between the phonons and frustrated spins is proved to be the main cause of the structural transition from the tetragonal to orthorhombic phase. These results well explain the magnetic and structural phase transitions in AFe$_2$As$_2$(A=Ba, Sr) recently observed by neutron scattering.

Full text

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arXiv:0901.1525v1 [cond-mat.supr-con] 12 Jan 2009
Spin-Peierls-like transition in AFe2As2(A=Ba, Sr)
D. Hou,1,2Q. M. Zhang,1Z. Y. Lu,1and J. H. Wei1, ∗
1Department of Physics, Renmin University of China, Beijing 100872, P. R. China
2School of Physics, Shandong University, Jinan 250100, P. R. China
(Dated: January 12, 2009)
From first-principles density functional theory calculations combined with varying temperature
Raman experiments, we show that AFe2As2 (A=Ba, Sr), the parent compound of the FeAs based
superconductors of the new structural family, undergoes a spin-Peierls-like phase transition at low
temperature. The coupling between the phonons and frustrated spins is proved to be the main cause
of the structural transition from the tetragonal to orthorhombic phase. These results well explain
the magnetic and structural phase transitions in AFe2As2(A=Ba, Sr) recently observed by neutron
scattering.
PACS numbers: 74.25.Jb, 71.18.+y, 74.70.-b, 74.25.Ha
Introduction The recent discovery of iron-based high-
transition temperature (high-Tc) superconductors[1] has
invoked great research interests in similar materials with
Fe-As layers. Currently, the focuses are mainly on two
kinds of structures: the first is iron arsenide-oxides with
P4/nmms space group [2, 3, 4], represented by the par-
ent compound LaFeAsO; and the second is ternary iron-
arsenide compound with body-centered I4/mmm space
group[5, 6, 7] , represented by the parent compound
BaFe2As2[5]. Those compounds show similar structural
and magnetic properties. At room temperature, they all
lay in non-magnetic, high-symmetric state, with Fe-As
layers separated by La-O layers or Ba layers respectively.
With the decrease of temperature, LaFeAsO undergoes
a slight structural transition from the tetragonal to or-
thorhombic phase at Ta = 150K, followed by the ap-
pearance of a magnetic SDW(spin-density wave) state
at 134K[8], while BaFe2As2experiences a similar struc-
tural and magnetic transition simultaneously at about
Ta = 140K [9]. At the magnetic SDW state, they all
form a collinear stripe-ordering magnetic ground-state,
with the nearest Fe atoms aligning anti-ferromagnetically
along one crystal axis in Fe-As plane, while ferromagnet-
ically parallel to the other axis[8, 9, 10, 11]. By doping
with electron or hole carriers, the structure transition and
the SDW state are both suppressed, and the supercon-
ductivity emerges at 52K[12] and 38K[13] respectively.
Thus there exists a competition between magnetism and
superconductivity in these compounds, but the subtle de-
tails such as the pairing mechanism are far from clear.
As that in high-Tc cuprates, revealing the mecha-
nism of superconductivity of iron-based superconductors
highly requires understanding the electronic, structural
and magnetic properties of parent compounds first. The
structural and magnetic phase transitions seem to be
common features in these Fe-As based superconductors,
thus revealing the sources of these transitions and the
possible connections between them may lead to better
understandings of the experimental observations. Some
first-principles density functional theory (DFT) calcula-
tions have suggested that the frustrated superexchange
interactions between Fe ions induces the collinear stripe
antiferromagnetic ground state [10, 14], on the other
hand the main cause of the structural phase transition,
as well as its correlation to the magnetic one, is not well
understood so far.
Let us start with the frustrated J1− J2 Heisenberg
model to describe the nearest neighbor and next-nearest
neighbor superexchange interactions among the Fe atoms
bridged by As atoms, which can be described as [10]
H = J1
?
<ij>
?Si·?Sj+ J2
?
≪ij≫
?Si·?Sj,(1)
where < ij > and ≪ ij ≫ denote the summation over the
nearest and the next-nearest neighbors respectively. The
ground state of the frustrated J1−J2spin-half model on
a square lattice at zero temperature has been studied by
several groups in the literature and the main results are
summarized as follows [15, 16]: (1) In the absent of frus-
tration (J2= 0), its ground state has long-range N´ eel or-
der; (2) With the increase of frustration (J2/J1), a phase
transition from N´ eel order to a spin-liquid phase occurs;
(3) If further increasing the frustration, a collinear order
emerges at J2/J1? 0.55, with the nearest spins aligning
anti-ferromagnetically along one axis while ferromagnet-
ically parallel to the other.
According to the DFT calculation in Ref. 10, J1almost
equals to J2 for Fe-As superconductors. In this sense,
the DFT and model calculations consistently explain the
collinear magnetic order of the parent compounds. How-
ever, the ground state given by J1−J2model is twofold
degenerate with the π/2 rotational symmetry, which is
not in agreement with the orthorhombic structure ob-
served in experiments. It indicates that the pure spin
model is not sufficient to account for the structural phase
transition. We hereby suggest to extend J1−J2model by
evolving the spin-phonon coupling. For examples, when
adiabatic phonons are considered, the model should be

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modified as,
H =
?
<ij>
[J1(1 − α1yij)?Si·?Sj+K1
2y2
ij]
+
?
≪ij≫
[J2(1 − α2yij)?Si·?Sj+K2
2y2
ij] (2)
where yij= |? uj− ? ui| with ? uidenoting the in-plane dis-
placement of atom i, α is the spin-phonon coupling con-
stant. The ground state (at T = 0) of above model was
calculated with a spin-wave approximation in recent lit-
erature and a Peierls-like transition from a tetragonal
to an orthorhombic phase was found at large frustration
(J2/J1? 0.5)[17].
In this letter, motivated by the model analysis, we use
the first-principles density functional calculations com-
bined with varying temperature Raman experiments to
study the ground state of AFe2As2 (A=Ba, Sr).
prove that the spin-Peierls-like phase transition is the
very mechanism of the structural transition at Tain the
parent compounds of iron-based superconductors.
Method The calculation was done using a plane-
wave based method[18] with local spin density approx-
imation (LSDA) and generalized gradient approxima-
tion (GGA) of Perdew-Burke-Ernzerh (PBE)[19] for the
exchange-correlation potentials. The density-functional
perturbation theory (DFPT) was used to calculate
the Γ-point phonons.Firstly, the electronic proper-
ties of AFe2As2(A=Ba,Sr) were calculated to deter-
mine the electronic ground state, using experimental
cell parameters[5] and energy-minimized internal atomic
positions.Different magnetic configurations, namely
the nonmagnetic, square anti-ferromagnetic and collinear
anti-ferromagnetic were considered[10].
states of both BaFe2As2 and SrFe2As2 are found to be
collinear anti-ferromagnetic with a slight structure tran-
sition, which is in agreement with previously reported
results. For the phonon calculations, we focus on the non-
magnetic high-temperature state and the collinear anti-
ferromagnetic ground state at low temperature. Here we
adopt the triclinic primitive unit cells as shown in Fig. 1,
in which the structure transition alters the angle between
x and y crystal axes from 90◦to 89.6◦.
The Raman measurements were performed with a
triple-grating monochromator (Jobin Yvon T64000),
which works with a microscopic Raman configuration. A
50× objective microscopic lens with a working distance
of 10.6 mm, is used to focus the incident light on sample
and collect the scattered light from sample. The detector
is a back-illuminated CCD cooled by liquid nitrogen. An
solid-state laser (Laser Quantum Torus 532) with high-
stability and very narrow width of laser line, is used with
an excitation wavelength of 532 nm. The laser beam of
3 mW was focused into a spot of less than 10 microns in
diameter on sample surface.
We
The ground
FIG. 1: (color online) Structure of BaFe2As2, from left to
right: conventional cell in I4/mmm space group, primitive
non-magnetic cell and primitive stripe-ordering cell
Result From symmetry analysis, the Raman phonon of
nonmagnetic AFe2As2 with I4/mmm space group con-
sists of four modes: the A1gand Egfor As, the B1gand
Egfor Fe. The vibrating directions in A1gand B1gmodes
are perpendicular to the Fe-As layer, while that of Egpar-
allel to the Fe-As layer. After cooling down to the tran-
sition temperature Ta, the crystal structure changes into
orthorhombic F/mmm space group, and the magnetism
appears almost at the same temperature. In this space
group, the Egmodes split into B2gand B3gmodes, and
A1gmode for As changes into Bgmode. The calculated
Raman modes, as listed in Table 1, are in good agree-
ment with symmetry analysis. All of the modes have
been found and assigned from atomic displacements.
The Raman modes of SrFe2As2 have been measured
in Ref.20 but only for nonmagnetic state reported. By
comparing our calculated phonon frequencies with the
experimental values, we find a systematic frequency shift
(∼ 20cm−1) of the calculated values towards higher
value region (see Table 1) due to the temperature ef-
fect. That is to say, the DFPT theory deals with the
ground-state problems, which in this case corresponds to
a non-magnetic state at T = 0K, while the Raman spec-
tra was measured at room temperature, as a consequence,
the corresponding experimental values are lower.
Since the strong spin-phonon interaction is the basis of
the suggested mechanism of spin-Peierls-like phase tran-
sition, we must verify this point first, by calculating the
change of the Raman modes in nonmagnetic state with-
out the magnetic transition but with the structural tran-
sition. In that case, the calculated Raman modes and
frequencies almost remain unchanged for both BaFe2As2
and SrFe2As2, with frequency shifts (or splits) less than
3 cm−1. This suggests that the slight structure transi-
tion has limited effects on the electronic properties and
Raman phonons. Our tentative calculations also gives us
another valuable information: the Eg mode of Fe atom
experiences a frequency splitting as a result of the struc-
tural transition, which consists with the fact that the
structure distortion mainly appears in Fe-As layer and
changes the nearest neighbor Fe-Fe distances slightly, so
that the nearest neighbor Fe-Fe distances are no longer

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equal in the orthorhombic crystal axes directions.
Table 1: Raman phonon frequencies of AFe2As2(A=Ba,Sr) in the non-magnetic state (marked as N) and in the
collinear anti-ferromagnetic state (marked as C). The Raman modes are in I4/mmm space group corresponding to
the non-magnetic state, while those in the brackets are in P/mmm space group for the collinear anti-ferromagnetic
state.The measurement temperatures are 260K and 87K for SrFe2As2, and 290K and 100K for BaFe2As2. The
atomic displacements are for the collinear anti-ferromagnetic state.
Atom Raman Mode SrFe2As2-N SrFe2As2-C BaFe2As2-N BaFe2As2-C Displacement
(cm−1) Cal. (Exp.) Cal. (Exp.) Cal. (Exp.) Cal. (Exp.) of Atoms, C
AsEg(B2g) 138.996.1
AsEg(B3g) 138.9 126.3
AsA1g(Bg) 207.6183.4
FeB1g(B1g) 219.5(206) 219.3(213)
FeEg(B2g)301.2 262.4
FeEg(B3g) 301.2 289.0
140.2
140.2
205.7
224.0(206)
293.6
293.6
86.8
125.6
177.8
214.2(212)
252.0
281.1
As(x), Fe(y)
As(y), Fe(x)
As(z)
Fe(z)
Fe(y), As(x)
Fe(x), As(y)
We are now on the position to elucidate the changes
of the Raman modes due to spin-phonon interactions
at the magnetic ground state.
the electronic structure verify that the magnetic ground
state of AFe2As2(A=Ba,Sr) is a collinear stripe-ordering
anti-ferromagnetic one.The Fe spins align parallel
along the shorter axis in Fe-As layer and anti-parallel
along the longer one, as observed by neutron diffraction
measurement[9], which is similar to that of LaFeAsO[8].
To correctly illustrate this magnetic configuration, the
nonmagnetic primitive unit cell should be doubled in a-
b plane to include two formula cells. Here we adopt a
√2×√2×1 cell, with x(y) axis rotates 45◦and points to
the nearest Fe-Fe directions. By doubling the crystal lat-
tice, the reciprocal lattice rotates and shrinks to a half,
and the original reciprocal points fold down to the new
points. The folding is illustrated in Fig. 2 (the structure
distortion from tetragonal to orthorhombic not shown in
the figure). It is clear that original M(π, π, 0) points
fold down to the new Γ(0, 0, 0) point. Thus the obtained
Γ point phonon modes in SDW state doubly contain the
information from both original Γ and M points. Only the
modes corresponding to Γ point are picked up according
to the atomic displacements, which are shown in Table 1
(marked as C). For the purpose of comparison, we also
show the measured Raman phonons at different temper-
atures before and after the magnetic transitions in the
table. The calculated phonon frequencies are found very
close to the experimental values, which further proves the
reliance of our phonon calculations.
Our calculations on
As shown in Table 1, accompanied with the onset of
magnetism, almost all of the Raman phonon frequencies
softened to lower values, specifically some of them (As-
B2g and Fe-B2g) show a giant phonon softening (GPS).
The GPS of Raman phonon modes is the main result of
FIG. 2: Reciprocal space of BaFe2As2 in non-magnetic(solid
lines) and stripe-ordering(dashed lines) state.
our DFT calculations, which directly support the mech-
anism of the spin-Peierls-like phase transition at Ta in
AFe2As2(A=Ba, Sr). Let us elaborate this point in more
details as follows:
Firstly, by comparing the changes of B3gand B2gfre-
quencies of Fe atoms (seen in Table 1), one can see that
the former only reduces 12cm−1for both BaFe2As2and
SrFe2As2while the latter reduces 41cm−1for BaFe2As2
and 39cm−1for SrFe2As2(GPS). The difference between
these two modes is the involved Fe atoms vibrating in
different direction - along x and y crystal axis respec-

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tively. In SDW state, the spins on Fe atoms align an-
tiparallel along x (longer) direction, while parallel along
y (shorter) direction. In B2g mode, the vibration direc-
tion of Fe atoms accords with the parallel spin direction,
suggesting an instability of parallel alignment of Fe spins.
Secondly, if assuming yx,y
δy, α1 = α2 = α and K1 = K2 = K in the extend
J1− J2model [see Eq.(2)], one can obtain the collinear
state (ground state) with δx= α(J2− J1)/4K and δy=
α(J2+J1)/4K at sufficient large frustration J2/J1> 0.5
[17]. In consideration of J2 ∼ J1 in AFe2As2, one can
reach δy≫ δx, which consistently explains why the GPS
of Raman modes of Fe atoms mainly happens along y
crystal axis.
Thirdly, the spin-Peierls-like phase transition proved
by the DFT and model analysis here closely relates
to the ”exchange striction” effect that also predicts
symmetry breaking distortions from the magnetoelastic
interaction[21]. That effect is believed to play an impor-
tant role for the origin of the multiferroics, and further-
more, we prove here it may be also related to the high-Tc
superconductivity.
Summary In summary, the consistence of the first-
principles density functional calculations and model anal-
ysis strongly prove that the spin-Peierls-like phase tran-
sition is the very mechanism of the structural transition
at Ta in parent compounds of iron-based superconduc-
tors. We thus conclude that the dominate interactions
in those parent compounds are frustrated spin-spin in-
teraction and spin-phonon interaction. Electron or hole
doping suppresses the ground state of parent compounds
(orthorhombic structural and collinear magnetic phase)
and induces the superconductor state. In order to under-
stand the pairing mechanism for ion-based new supercon-
ductors, one should treat the spin-spin and spin-phonon
interactions on an equal footing.
Supports from the National Natural Science Foun-
dation of China (Grants No. 10604037) and the
National Basic Research Program of China (Grants
No. 2007CB925001) are gratefully acknowledged.
<ij>= δx,y, yx,y
≪ij≫= δx+
∗Electronic address: wjh@ruc.edu.cn
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