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Charge Modulations in Fe-Based Superconductors: Insights from Mössbauer Spectroscopy

This paper explores charge modulations in Fe-based superconductors using 57Fe Mössbauer spectroscopy, focusing on topics such as hyperfine interactions, electron charge density, and electric field gradients. It discusses examples like Ba1-xKxFe2As2 and SmFeAsO1-xFx, showcasing various doping and substitution effects. The study provides a comprehensive analysis of how charge modulations influence the electronic structure properties in these materials.

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Charge Modulations in Fe-Based Superconductors: Insights from Mössbauer Spectroscopy

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  1. Charge modulations in Fe-based superconductors as seen by 57Fe Mössbauer spectroscopy A. Błachowski1, K. Komędera1, Z. Bukowski2, K. Rogacki2, K.Z. Takahashi3, T.J. Sato3 1Mössbauer Spectroscopy Laboratory, Institute of Physics, Pedagogical University, Kraków, Poland 2 Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wrocław, Poland 3Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Japan --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Fundamental Aspects of Superconductivity 3rd International Conference on Superconductivity and Magnetism in Selected Systems September 16-21 2018, Zakopane, Poland

  2. to commemorate Prof. Krzysztof Ruebenbauer (1947-2018)

  3. Outline 1. Fe-based superconductors – diversity of doping types 2.57Fe Mössbauer spectroscopy – hyperfine interactions - electron charge density - electric field gradient EFG 3. Charge modulations : CDW and EFGW - CDWs as seen by Mössbauer spectroscopy 4. Examples - Ba1-xKxFe2As2 – hole-doping - SmFeAsO1-xFx – electron-doping - BaFe2(As1-xPx)2 – isovalent-substitution 5. Conclusions

  4. ________”122” Fe-based Superconducting Family________ AFe2As2 (A = Ca, Sr, Ba, Eu) ______________Parent compound______________ BaFe2As2 TSDW = 136 K _________Superconductors_________ Ba1-xKxFe2As2Ba(Fe1-xCox)2As2BaFe2(As1-xPx)2 hole-dopingelectron-dopingisovalent-substitution x = 0.40x = 0.08x = 0.31 Tsc = 38 K Tsc = 24 K Tsc = 31 K Ba1-xKxFe2As2 Ba(Fe1-xCox)2As2  K  Co  P x Rev. Mod. Phys. 87, 855 (2015)

  5. Mössbauer Spectroscopy recoilless nuclear resonance absorption of -rays -ray energy is modulated by the Doppler effect due to the source motion vs. absorber (studied sample) Source (e.g. 57Co/Rh) Absorber (57Fe) Detector 1 mm/s 48neV conversion factor – v +v

  6. Hyperfine Interactions between Nuclei and Electrons  Mössbauer Parameters  Electronic structure properties Hyperfine interactions shift and split nuclear levels in a specific ways --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Electric Monopole Interaction between charge of the nucleus and charge of the electrons Isomer Shift S Electron charge density  S S S 1 mm/s3.4el./Bohr3 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Electric Quadrupole Interaction between nuclear quadrupole moment and EFG from electrons Quadrupole SplittingEQ Electric Field Gradient EFG EFG S EQ EFG1 mm/s5.7 1021V/m2

  7. Charge modulations • Spatial modulation of the electron charge density, seen by the Fe nucleus, • causes the distribution of the isomer shiftS •  • Charge density wave (CDW) • Spatial modulation of the electric field gradientEFG, seen by the Fe nucleus, • causes the distribution of the quadrupole splittingEQ •  • Electric field gradient wave (EFGW) Fe Simplified sketch of modulation incommensurate with the lattice period and the Fe atoms distributed along the lattice (propagation direction of the modulation) experience various hyperfine electric fields.

  8. CDW as seen by Mössbauer Spectroscopy J. Cieślak and S. M. Dubiel, Nuclear Instr. Methods B 101, 295 (1995) Scheme of the construction of the Mӧssbauer spectrum for a sinusoidally shaped CDW: (a) one period of the CDW, (b) partial sub-spectra having the isomer shift proportional to the amplitude of CDW, (c) the overall spectrum as a result of superposition of a partial sub-spectra, (d) histogram of the isomer shift (charge-density) distribution. For CDW one can estimate dispersion (around average value) of the electron charge density  – unbroadened line-width – calibration constant Γ – spectral line-width

  9. Electric field gradient wave (EFGW) as seen by Mössbauer Spectroscopy  - quadrupole coupling constant with 57Fe Mössbauer spectraDistributions of quadrupole splittingShape of EFGW Shape of the EFGW in the wave vector (or phase angle) scale with a smaller or larger amplitude gives a narrower or wider distribution of quadrupole splitting due to varying EFG experienced by the Fe nucleus. It gives additional wide component to the Mössbauer spectrum.

  10. Charge modulations as seen by Mössbauer Spectroscopy Fe Charge modulations causes specific broadening of the Mössbauer spectral line. Γ – Mössbauer (absorber) line-width CDW A = 0.2 mm/s EFGW A = 1 mm/s SDW A = 4 Tesla 5.7 1021V/m2 0.7 el./Bohr3 Broadening ”types”: ”all along” the entire length ;”wings” at the base of peak;”stairs”-like

  11. Ba1-xKxFe2As2 (Tc_max = 38 K) hole-doping our sample : x = 0.4  K Ts– tetragonal-orthorhombic distortion TN– magnetic order Tc– critical temperatures S. Avci et al., Phys. Rev. B 85, 184507 (2012)

  12. 57Fe Mössbauer spectra of theBa0.6K0.4Fe2As2 (TSC = 38 K) acrosstransition to the superconducting state Difference in total molar specific heat coefficients between superconductor and parent compound. Inset shows electronic specific heat coefficient of superconductor. The anomaly in the hyperfine interactions exactly coincides (!) with the peak of the electronic specific heat coefficient.

  13. Ba0.6K0.4Fe2As2 (TSC = 38 K) Mössbauer parameters: S– spectrum shift versus α-Fe Δ0– constant component of quadrupole splitting Γ– absorber line-width Shape of EFGW electric field gradient wave (delectrons density variation) 1 mm/s5.7 1021V/m2 • Dispersion of CDW • charge density wave • (s electrons density variation) • is suppressed by • 0.2 el./Bohr3 within the anomaly region. Charge modulation is sensitive to the transition between normal and superconducting state. It is partially suppressed just below opening of the superconducting gap, and it recovers upon separation of the bosonic states (Cooper pairs) from the rest of the electronic system.

  14. SmFeAsO1-xFx (Tc_max = 55 K) electron-doping our sample : x = 0.09 (Tc = 47 K) Sm Sm

  15. 57Fe Mössbauer spectra of theSmFeAsO0.91F0.09(Tsc ≈ 47 K) across transition to the superconducting state Magnetic susceptibility Resistivity

  16. SmFeAsO0.91F0.09 (Tsc = 47 K) Shape of EFGW electric field gradient wave (delectrons density variation) Mössbauer parameters: S– spectrum shift versus α-Fe Γ– absorber line-width 1 mm/s5.7 1021V/m2 • Dispersion of CDW • charge density wave • (s electrons density variation) • is enhanced by • 0.2 el./Bohr3 within the anomaly region. In this case charge modulations (CDW and EFGW) are enhanced upon superconducting transition and partially recover when the superconducting state is fully developed.

  17. BaFe2(As1-xPx)2 isovalent-substitution x = 0 hPn = 1.36Å x = 0.30 hPn = 1.28Å S. Kasahara et al., Nature 486, 382 (2012) our samples: 0.33,0.53 ,0.70 superconductorsover-doped

  18. BaFe2(As1-xPx)2x = 0.33 Tsc = 27.6 K Magnetic broadening of spectral line  0.30 mm/s  0.35 mm/s  0.35 mm/s  0.35 mm/s Γ – spectral line-width  x = 0.33  x = 0.53  x = 0.70 Traces of magnetic order in superconducting state due to …vicinity of the quantum critical point … or coexistence (?) Magnetic broadening makes impossible registration of possible change in charge modulation

  19. BaFe2(As1-xPx)2x = 0.53 Tsc = 13.9 K    1 mm/s3.8el./Bohr3 Γ – spectral line-width  x = 0.33  x = 0.53  x = 0.70 Oscillations of the spectral line-width vs. temperature due to varying charge modulation. One gets 0.2 el./(Bohr radius)3 electron density oscillation on the iron nuclei across formation of the superconducting state. … and nematic order (?)

  20. Conclusions 1) Mössbauer spectroscopy sees CDWs in Fe-SC. 2) CDWs modulations are perturbed at Tsc-onset and return to the modulations from the normal state below Tsc-offset (R=0). 3) Direction of CDWs perturbation depends on the type of doping. Ba0.6K0.4Fe2As2 Tsc = 38 K SmFeAsO0.91F0.09 Tsc = 47 K (hole doping) (electron doping) EFGW EFGW CDW CDW

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