1. 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,
4 Department of Physics, University of Ottawa, Ottawa, Canada
5 Applied Computer Science Division, Institute of Technology,
A contribution to MSMS-2010, , Liptovský Ján, Slovakia

2. Superconducting Materials

3. Fe-based Superconducting Families
LaFeAsOF BaFe2As LiFeAs FeSe
~55K ~40K ~20K ~10K

4. Fe-Se phase diagram
The following phases form close to the FeSe stoichiometry:
1) tetragonal P4/nmm structure similar to PbO, called β-FeSe (or α-FeSe)
2) hexagonal P63/mmc structure similar to NiAs, called δ-FeSe
3) hexagonal phase Fe7Se8 with two different kinds of order, i.e., 3c (α-Fe7Se8) or 4c (β-Fe7Se8)
A tetragonal P4/nmm phase transforms into Cmma orthorhombic phase at about 90 K,
and this phase is superconducting with Tc ≈ 8 K.

5. Crystal structure of -FeSe
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 ?

6. Fe1.05Se

7. Fe1.05Se

8. 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

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

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

11. Hyperfine magnetic field is equal to applied external magnetic field.
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.

12. Calculation methods
Density Functional Theory (DFT) has been applied in the spin-dependent Local Density Approximation (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 phonon densities
of states (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.

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

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

15. Recoilless fraction for IRON
Cmma phase (orthorhombic)

16. Second order Doppler shift on IRON (SOD)

17. Expected spectrum due to the recoilless fraction anisotropy

18. Phonon dispersion relations at null pressure and for the ground state

19. TRANSITION TO THE METALLIC STATE FROM THE FERROMAGNETIC INSULATING
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.

20. Fermi level is marked by the vertical line.
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.

21. A transition to the metallic state
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

22. THANK YOU FOR YOUR ATTENTION
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 during transition
from tetragonal to orthorhombic phase. 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.
THANK YOU FOR YOUR ATTENTION