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, 31.01-05.02.2010, Liptovský Ján, Slovakia

Superconducting Materials

Fe-based Superconducting Families LaFeAsOF BaFe2As2 LiFeAs FeSe 1111 122 111 11 ~55K ~40K ~20K ~10K

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.

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 ?

Fe1.05Se

Fe1.05Se

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

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 = +0.006 mm/s ρ = –0.02 electron/a.u.3 orthorhombic orthorhombic and superconducting

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

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.

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.

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)

Second order Doppler shift on IRON (SOD)

Expected spectrum due to the recoilless fraction anisotropy

Phonon dispersion relations at null pressure and for the ground state

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.

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.

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

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