MÖSSBAUER SPECTROSCOPY OF IRON-BASED
SUPERCONDUCTOR FeSe
A. Błachowski 1 , K. Ruebenbauer 1 , J. Żukrowski 2 , J. Przewoźnik 2 ,
K. Wojciechowski 3 , Z.M. Stadnik 4 , and U.D. Wdowik 5
1 Mössbauer Spectroscopy Division, Institute of Physics,
Pedagogical University, Cracow, Poland
2 Solid State Physics Department, Faculty of Physics and Applied Computer Science,
AGH University of Science and Technology, Cracow, Poland
3 Department of Inorganic Chemistry, Faculty of Material Science and Ceramics,
AGH University of Science and Technology, Cracow, Poland
4 Department of Physics, University of Ottawa, Ottawa, Canada
5 Applied Computer Science Division, Institute of Technology,
Pedagogical University, Cracow, Poland
A contribution to MSMS-2010, 31.01-05.02.2010, Liptovsk ý Ján, Slovakia

La
As OF
1
1 1
Ba
2
As
2
1
2
Li
1
1
As Fe Se
1 1

The following phases form close to the FeSe stoichiometry:
1) tetragonal P4/nmm structure similar to PbO, called β-FeSe (or α-FeSe)
2)
3) hexagonal P6
3
/mmc structure similar to NiAs, called δ-FeSe hexagonal phase Fe
7
Se
8 with two different kinds of order, i.e., 3c
(α-Fe
7
Se
8
) or 4c
(β-Fe
7
Se
8
)
A tetragonal P4/nmm phase transforms into Cmma orthorhombic phase at about 90 K, and this phase is superconducting with T c
≈ 8 K.


Aim of this contribution is to answer two questions concerned with tetragonal/orthorhombic FeSe:
1) is there electron spin density (magnetic moment) on Fe ?
2) is there change of electron density on Fe nucleus during transition from P4/nmm to Cmma structure ?

Fe
1.05
Se
A synthesis was carried at 750°C for 6 days in evacuated silica tube.
Subsequently the sample was slowly cooled with furnace to room temperature.
Resulting ingot was powdered and annealed at 420°C for 2 days in evacuated silica tube and subsequently quenched in the ice water.
Experimental
1) Powder X-ray diffraction pattern was obtained at room temperature by using
Siemens D5000 diffractometer.
2) Magnetic susceptibility was measured by means of the vibrating sample magnetometer (VSM) of the Quantum Design PPMS-9 system.
3) Mössbauer spectra were collected in the temperature 4.2 K, in the range
75–120 K with step 5 K and in the external magnetic field up to 9 T.

Fe
1.05
Se

Magnetic susceptibility measured upon cooling and subsequent warming in field of 5 Oe
- point A - spin rotation in hexagonal phase
- region B - magnetic anomaly correlated with transition between orthorhombic and tetragonal phases
- point C - transition to the superconducting state

tetragonal phase transition orthorhombic orthorhombic orthorhombic and superconducting
Change in isomer shift S
↓
Change in electron density
 on Fe nucleus

S = +0.006 mm/s
↓
 ρ
= –0.02 electron/a.u.
3

tetragonal phase transition orthorhombic orthorhombic orthorhombic and superconducting
T (K)
120
105
90
75
4.2
S (mm/s)
0.5476(3)
0.5529(3)
0.5594(3)
0.5622(3)
0.5640(4)
Δ (mm/s)
0.287(1)
0.287(1)
0.286(1)
0.287(1)
0.295(1)

(mm/s)
0.206(1)
0.203(1)
0.198(1)
0.211(1)
0.222(1)
Quadrupole splitting Δ does not change
- it means that local arrangement of Se atoms around Fe atom does not change during phase transition

Mössbauer spectra obtained in external magnetic field aligned with γ-ray beam
Hyperfine magnetic field is equal to applied external magnetic field.
Principal component of the electric field gradient (EFG) on Fe nucleus was found as negative.

Calculation methods
D ensity F unctional T heory ( DFT ) has been applied in the spin-dependent L ocal D ensity A pproximation ( LDA ) with the periodic boundary conditions . The suite VASP was used.
Atomic positions were relaxed in order to obtain MINIMUM binding energy. Calculations have been performed in the ground state of the respective phase – eventually applying hydrostatic pressure .
Super-cells were chosen to be large enough to account for the realistic atomic forces.
Subsequently atoms were displaced in the directions set by the local symmetry and atomic forces were calculated by the gradient method obtaining another energy MINIMUM for the distorted compound.
Atomic forces were used to calculate phonon dispersion relations and subsequently p honon d ensities o f s tates ( DOS ) by using PHONON suite.
THERE IS NO NEED TO INTRODUCE ELECTRON CORRELATION IN TETRAGONAL
AND ORTHORHOMBIC PHASES IN ORDER TO GET STABLE CONFIGURATIONS.
SUCH CORRELATIONS ARE NECESSARY IN THE HEXAGONAL PHASE (EITHER INSULATING OR
METALLIC) IN ORDER TO GET STABILITY. ONE HAS TO INTRODUCE HUBBARD POTENTIAL ON IRON.
Mössbauer spectra were calculated by means of the MOSGRAF suite.

PHONON DYNAMICS IN TETRAGONAL/ORTHORHOMBIC PHASE
Total density of the phonon states versus pressure for the orthorhombic phase (DOS)

Binding and vibrational energy per chemical formula versus hydrostatic pressure in the ground state

Recoilless fraction for IRON
Cmma phase (orthorhombic) f
 exp[ -q
2  x
2 
]

Second order Doppler shift on IRON (SOD)
SOD
 
 v
2 
2 c

Expected spectrum due to the recoilless fraction anisotropy

Phonon dispersion relations at null pressure and for the ground state

Energy gap and magnetic moment in the hexagonal phase (ground state)
TRANSITION TO THE METALLIC STATE
FROM THE FERROMAGNETIC INSULATING
STATE IS CLEARLY SEEN
Some spurious magnetic moment seems to survive in the metallic state.

Total electron spin density versus energy for the Cmma phase at null pressure
Spin-up and spin-down states are plotted separately in red and green colors, respectively.
Fermi level is marked by the vertical line.
This is obviously non-magnetic metallic system.

Corresponding electron spin density versus energy for the hexagonal phase at various pressures
A transition to the metallic state with very small magnetic moment per unit cell is clearly seen at high hydrostatic pressure

Conclusions
1.
There is no magnetic moment on iron in the P4/nmm and Cmma phases.
It converges to null upon iterating energy to minimum.
This result is in perfect agreement with the experimental data .
2.
The electron density on iron nucleus is lowered by 0 .
02 electron / a.u.
3 from tetragonal to orthorhombic phase.
during transition
3.
There is no significant energy change while going from P4/nmm to Cmma phase or vice versa.
We accounted for binding and vibrational energy (calculated for the ground state , i.e., in the harmonic approximation). Due to the fact that one does not observe any magnetic energy some puzzle remains.
Namely, we do not understand what kind of force is driving this transition (nuclear hyperfine energy is too small for the purpose). Maybe the low temperature phase is not Cmma . Some other symmetry has been proposed as well, e.g. monoclinic .
One has to bear in mind that calculations have been made for the stoichiometric phase, but it seems that one needs quite stoichiometric compound to get superconducting state.
4.
Antiferromagnetic insulating hexagonal phase undergoes transition to the metallic phase
(probably hexagonal) at hydrostatic pressure being in fair agreement with the experimental data [Medvedev et al.
, Nature Materials ]. The latter phase might have some spurious magnetic moment
– insufficient for the ordering except at extremely low temperatures.
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