Table Of ContentSpin-Peierls-like transition in AFe As (A=Ba, Sr)
2 2
D. Hou,1,2 Q. M. Zhang,1 Z. Y. Lu,1 and 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
9 superconductors of the new structural family, undergoes a spin-Peierls-like phase transition at low
0 temperature. Thecouplingbetweenthephononsandfrustratedspinsisprovedtobethemaincause
0 of the structural transition from the tetragonal to orthorhombic phase. These results well explain
2 themagnetic andstructuralphasetransitions in AFe2As2(A=Ba,Sr)recently observedbyneutron
scattering.
n
a
J PACSnumbers: 74.25.Jb,71.18.+y,74.70.-b,74.25.Ha
2
1
Introduction The recent discovery of iron-based high- tions have suggested that the frustrated superexchange
] transition temperature (high-Tc) superconductors[1] has interactions between Fe ions induces the collinear stripe
n invokedgreatresearchinterests insimilar materialswith antiferromagnetic ground state [10, 14], on the other
o
Fe-As layers. Currently, the focuses are mainly on two hand the main cause of the structural phase transition,
c
- kinds of structures: the first is iron arsenide-oxides with as well as its correlationto the magnetic one, is not well
r P4/nmms space group [2, 3, 4], represented by the par- understood so far.
p
u ent compound LaFeAsO;and the second is ternary iron- Let us start with the frustrated J J Heisenberg
1 2
s arsenide compound with body-centered I4/mmm space −
model to describe the nearest neighbor and next-nearest
.
at group[5, 6, 7] , represented by the parent compound neighborsuperexchangeinteractionsamongtheFeatoms
BaFe As [5]. Those compounds show similar structural
m 2 2 bridged by As atoms, which can be described as [10]
and magnetic properties. At room temperature, they all
-
d lay in non-magnetic, high-symmetric state, with Fe-As
n layersseparatedbyLa-OlayersorBalayersrespectively. H =J1 X S~i S~j +J2 X S~i S~j, (1)
· ·
o With the decrease of temperature, LaFeAsO undergoes <ij> ≪ij≫
c
a slight structural transition from the tetragonal to or-
[
thorhombic phase at Ta = 150K, followed by the ap- where<ij >and ij denotethesummationoverthe
1 pearance of a magnetic SDW(spin-density wave) state nearestandthe ne≪xt-ne≫arestneighborsrespectively. The
v
5 at 134K[8], while BaFe2As2 experiences a similar struc- groundstate ofthe frustratedJ1−J2 spin-halfmodelon
2 tural and magnetic transition simultaneously at about a square lattice at zero temperature has been studied by
5 Ta = 140K [9]. At the magnetic SDW state, they all several groups in the literature and the main results are
1 form a collinear stripe-ordering magnetic ground-state, summarizedas follows [15, 16]: (1) In the absentof frus-
1. withthenearestFeatomsaligninganti-ferromagnetically tration(J2 =0),itsgroundstatehaslong-rangeN´eelor-
0 alongonecrystalaxisinFe-Asplane,whileferromagnet- der;(2)Withtheincreaseoffrustration(J /J ),aphase
2 1
9 ically parallel to the other axis[8, 9, 10, 11]. By doping transition from N´eel order to a spin-liquid phase occurs;
0
withelectronorholecarriers,thestructuretransitionand (3) If further increasing the frustration,a collinear order
:
v the SDW state are both suppressed, and the supercon- emerges at J /J &0.55, with the nearest spins aligning
2 1
Xi ductivity emerges at 52K[12] and 38K[13] respectively. anti-ferromagneticallyalong one axis while ferromagnet-
Thus there exists a competition between magnetism and ically parallel to the other.
r
a superconductivityinthesecompounds,butthesubtlede-
AccordingtotheDFTcalculationinRef.10,J almost
1
tails such as the pairing mechanism are far from clear.
equals to J for Fe-As superconductors. In this sense,
2
As that in high-T cuprates, revealing the mecha- theDFT andmodelcalculationsconsistentlyexplainthe
c
nism ofsuperconductivity ofiron-basedsuperconductors collinearmagneticorderofthe parentcompounds. How-
highly requires understanding the electronic, structural ever, the ground state given by J J model is twofold
1 2
−
and magnetic properties of parent compounds first. The degenerate with the π/2 rotational symmetry, which is
structural and magnetic phase transitions seem to be not in agreement with the orthorhombic structure ob-
common features in these Fe-As based superconductors, served in experiments. It indicates that the pure spin
thus revealing the sources of these transitions and the modelisnotsufficienttoaccountforthestructuralphase
possible connections between them may lead to better transition. WeherebysuggesttoextendJ J modelby
1 2
−
understandings of the experimental observations. Some evolving the spin-phonon coupling. For examples, when
first-principles density functional theory (DFT) calcula- adiabatic phonons are considered, the model should be
2
modified as,
K
H = X[J1(1−α1yij)S~i·S~j + 21yi2j]
<ij>
K
+ X [J2(1−α2yij)S~i·S~j + 22yi2j] (2)
≪ij≫
where y = ~u ~u with ~u denoting the in-plane dis-
ij j i i
| − |
placement of atom i, α is the spin-phonon coupling con-
FIG. 1: (color online) Structure of BaFe2As2, from left to
stant. The ground state (at T = 0) of above model was
right: conventional cell in I4/mmm space group, primitive
calculated with a spin-wave approximation in recent lit- non-magnetic cell and primitivestripe-ordering cell
erature and a Peierls-like transition from a tetragonal
to an orthorhombic phase was found at large frustration
(J2/J1 &0.5)[17]. ResultFromsymmetryanalysis,theRamanphononof
In this letter, motivated by the modelanalysis,we use nonmagnetic AFe As with I4/mmm space group con-
2 2
the first-principles density functional calculations com- sists of four modes: the A and E for As, the B and
1g g 1g
bined with varying temperature Raman experiments to E forFe. ThevibratingdirectionsinA andB modes
g 1g 1g
study the ground state of AFe As (A=Ba, Sr). We areperpendiculartotheFe-Aslayer,whilethatofE par-
2 2 g
prove that the spin-Peierls-like phase transition is the allel to the Fe-As layer. After cooling down to the tran-
very mechanism of the structural transition at T in the sitiontemperature T , the crystalstructure changesinto
a a
parent compounds of iron-based superconductors. orthorhombic F/mmm space group, and the magnetism
Method The calculation was done using a plane- appears almost at the same temperature. In this space
wave based method[18] with local spin density approx- group, the Eg modes split into B2g and B3g modes, and
imation (LSDA) and generalized gradient approxima- A1g mode for As changes into Bg mode. The calculated
tion (GGA) of Perdew-Burke-Ernzerh(PBE)[19] for the Raman modes, as listed in Table 1, are in good agree-
exchange-correlation potentials. The density-functional ment with symmetry analysis. All of the modes have
perturbation theory (DFPT) was used to calculate been found and assigned from atomic displacements.
the Γ-point phonons. Firstly, the electronic proper- The Raman modes of SrFe As have been measured
2 2
ties of AFe As (A=Ba,Sr) were calculated to deter- in Ref.20 but only for nonmagnetic state reported. By
2 2
mine the electronic ground state, using experimental comparing our calculated phonon frequencies with the
cell parameters[5] and energy-minimized internal atomic experimentalvalues,wefindasystematicfrequencyshift
positions. Different magnetic configurations, namely ( 20cm−1) of the calculated values towards higher
∼
thenonmagnetic,squareanti-ferromagneticandcollinear value region (see Table 1) due to the temperature ef-
anti-ferromagnetic were considered[10]. The ground fect. That is to say, the DFPT theory deals with the
states of both BaFe As and SrFe As are found to be ground-stateproblems,whichinthis casecorrespondsto
2 2 2 2
collinear anti-ferromagnetic with a slight structure tran- a non-magneticstate at T =0K,while the Ramanspec-
sition, which is in agreement with previously reported trawasmeasuredatroomtemperature,asaconsequence,
results. Forthephononcalculations,wefocusonthenon- the corresponding experimental values are lower.
magnetic high-temperature state and the collinear anti- Sincethestrongspin-phononinteractionisthebasisof
ferromagneticgroundstate atlow temperature. Here we the suggested mechanism of spin-Peierls-likephase tran-
adoptthetriclinicprimitiveunitcellsasshowninFig.1, sition, we must verify this point first, by calculating the
inwhichthestructuretransitionalterstheanglebetween change of the Raman modes in nonmagnetic state with-
x and y crystal axes from 90◦ to 89.6◦. outthemagnetictransitionbutwiththestructuraltran-
The Raman measurements were performed with a sition. In that case, the calculated Raman modes and
triple-grating monochromator (Jobin Yvon T64000), frequenciesalmostremainunchangedforbothBaFe As
2 2
whichworkswithamicroscopicRamanconfiguration. A and SrFe As , with frequency shifts (or splits) less than
2 2
50 objective microscopic lens with a working distance 3 cm−1. This suggests that the slight structure transi-
×
of 10.6mm, is used to focus the incident lighton sample tion has limited effects on the electronic properties and
andcollectthescatteredlightfromsample. Thedetector Ramanphonons. Ourtentativecalculationsalsogivesus
isaback-illuminatedCCDcooledbyliquidnitrogen. An another valuable information: the E mode of Fe atom
g
solid-state laser (Laser Quantum Torus 532) with high- experiences a frequency splitting as a resultof the struc-
stabilityandverynarrowwidthoflaserline,isusedwith tural transition, which consists with the fact that the
an excitation wavelength of 532 nm. The laser beam of structure distortion mainly appears in Fe-As layer and
3 mW was focused into a spot of less than 10 microns in changes the nearest neighbor Fe-Fe distances slightly, so
diameter on sample surface. that the nearest neighbor Fe-Fe distances are no longer
3
equal in the orthorhombic crystal axes directions.
Table 1: Raman phonon frequencies of AFe As (A=Ba,Sr) in the non-magnetic state (marked as N) and in the
2 2
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 SrFe As , and 290K and 100K for BaFe As . The
2 2 2 2
atomic displacements are for the collinear anti-ferromagnetic state.
Atom Raman Mode SrFe As -N SrFe As -C BaFe As -N BaFe As -C Displacement
2 2 2 2 2 2 2 2
(cm−1) Cal. (Exp.) Cal. (Exp.) Cal. (Exp.) Cal. (Exp.) of Atoms, C
As E (B ) 138.9 96.1 140.2 86.8 As(x), Fe(y)
g 2g
As E (B ) 138.9 126.3 140.2 125.6 As(y), Fe(x)
g 3g
As A (B ) 207.6 183.4 205.7 177.8 As(z)
1g g
Fe B (B ) 219.5(206) 219.3(213) 224.0(206) 214.2(212) Fe(z)
1g 1g
Fe E (B ) 301.2 262.4 293.6 252.0 Fe(y), As(x)
g 2g
Fe E (B ) 301.2 289.0 293.6 281.1 Fe(x), As(y)
g 3g
We are now on the position to elucidate the changes
of the Raman modes due to spin-phonon interactions
at the magnetic ground state. Our calculations on
the electronic structure verify that the magnetic ground
state of AFe As (A=Ba,Sr)is a collinearstripe-ordering
2 2
anti-ferromagnetic one. The Fe spins align parallel
along the shorter axis in Fe-As layer and anti-parallel ky
along the longer one, as observed by neutron diffraction M
measurement[9], which is similar to that of LaFeAsO[8].
To correctly illustrate this magnetic configuration, the ky’ kx’
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 kx
× ×
thenearestFe-Fedirections. Bydoublingthecrystallat-
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
distortionfromtetragonalto orthorhombicnotshownin
the figure). It is clear that original M(π, π, 0) points
folddowntothenewΓ(0,0,0)point. Thustheobtained
Γ point phonon modes in SDW state doubly contain the
informationfrombothoriginalΓandMpoints. Onlythe FIG. 2: Reciprocal space of BaFe2As2 in non-magnetic(solid
modes corresponding to Γ point are picked up according lines) and stripe-ordering(dashed lines) state.
to the atomicdisplacements, whichareshownin Table 1
(marked as C). For the purpose of comparison, we also
show the measured Raman phonons at different temper- our DFT calculations, which directly support the mech-
atures before and after the magnetic transitions in the anism of the spin-Peierls-like phase transition at Ta in
table. The calculated phonon frequencies are found very AFe2As2(A=Ba,Sr). Letuselaboratethispointinmore
closetotheexperimentalvalues,whichfurtherprovesthe details as follows:
reliance of our phonon calculations. Firstly, by comparing the changes of B3g and B2g fre-
quencies of Fe atoms (seen in Table 1), one can see that
As shown in Table 1, accompanied with the onset of the former only reduces 12cm−1 for both BaFe As and
2 2
magnetism, almost all of the Raman phonon frequencies SrFe As while the latter reduces 41cm−1 for BaFe As
2 2 2 2
softened to lower values, specifically some of them (As- and39cm−1 forSrFe As (GPS).Thedifferencebetween
2 2
B and Fe-B ) show a giant phonon softening (GPS). these two modes is the involved Fe atoms vibrating in
2g 2g
The GPS of Raman phonon modes is the main result of different direction - along x and y crystal axis respec-
4
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∗
Electronic address: [email protected]
