Amalia Coldea. c/a. Oxford University. KITP, Santa Barbara, Jan

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1 Topological changes of the Fermi surface and the effect of electronic correlations in iron pnictides Amalia Coldea Oxford University c/a KITP, Santa Barbara, Jan 2011

2 Collaborators Antony Carrington, Caroline Andrew, Jon Fletcher, A. Bangura H. H. Wills Physics Laboratory, University of Bristol, UK Ian Fisher, James Analytis, Jiun-Haw Chu, Hsueh-Hui Kuo Geballe Laboratory for Advanced Materials, Stanford University, USA S. Kasahara, H. Shishido, K. Hashimoto, T. Shibauchi, Y. Matsuda Department of Physics, Kyoto University, Japan Ross McDonald National High Magnetic Field Laboratory, Los Alamos National Laboratory, USA Alix McCollam High Magnetic Field Laboratory, Nijmegen, The Netherlands D. Vignolles, C. Proust, B. Vignolle Laboratoire National des Champs Magnetiques Intenses, Toulouse, France

3 Phase diagrams: cuprates vs pnictides pseudogap Bad metal AFM ordering - Mott-insulator; Strong electronic correlations; pseudogap; Cu 2+ -O 2p 3d x2-y2 single band; AFM ordering Bad metals; small carrier density ; Fe 2+ -As 3- (d 6 ); all five d orbitals important; high density of states N(EF), prone to magnetic instabilities; Doiron-Leyraud et al, Nature, (2007) C. Lester et al, Phys. Rev. B 79, (2009)

4 Effect of chemical pressure: P substitution suppression of magnetism and the presence of superconductivity through chemical substitutions: As replaced by P, or Fe replaced by 4d and 5d elements: Rh, Ir and Pd; other examples SrFe 1-x Ru x As 2, LaFeAs 1-x P x O and EuFe 2 As 2-x P x. S. Jiang, et al., arxiv: (2009) S. Kasahara et al., PRB 81,

5 Criticality determined by As/P substitution CeFeAs 1 x P x O: Fe Ru QCP1 QCP2 suppression of magnetism by chemical substitution As/P, unique role of P- doping in suppressing the d-electron correlations. J. Dai et al., PNAS, 106, 4118 (2009) Y. Luo, et al., arxiv: (2009)

6 Plan of my talk Quantum oscillations to determine the Fermi surface and comparison with band structure calculations LaFePO T c ~ 6K the superconducting LaFePO; role of nesting ; Role of dimensionality on the Fermi surface: the case of SrFe 2 P 2; Fermi surface shrinking and enhanced correlations in BaFe 2 (As 1-x P x ) SrFe 2 P 2 c/a=3.04 Topological change of the Fermi surface with c/a ratio: the case of CaFe 2 P 2. Conclusions 122 CaFe 2 P 2 c/a=2.65

7 Quantum oscillations map out the Fermi surface oscillations of the density of states in magnetic field; F=(ħ / 2π e) A(E F ) A (E F ) k-space microscopy : 0.1% IBZ; 3D map of the Fermi surface; bulk probe; no sensitive to surface effects like ARPES; Shoenberg, Magnetic oscillations in metals, (1984)

8 Lifshitz-Kosevich formalism Temperature - low temperatures Finite scattering time clean samples Superconducting state random vortex lattice extracted parameters: quasiparticle effective mass m* (band renormalization near the Fermi energy), scattering rates ~ T D =ħ / (2pk B t), spin-splitting factor g * m*/m b =(1+λ el-ph )(1+ λ el-el ) ~ 1+ λ el-ph + λ el-el Shoenberg, Magnetic oscillations in metals, (1984)

9 Torque measurements with AFM cantilevers B 50 μm The resistance of the active piezocantilevers (SEIKO) is measured with respect to that of the dummy using a conventional ac Wheatstone bridge circuit.

10 High magnetic field and low temperatures magnet probe Night shifts 3 He 4 He pumps Low temperatures (0.3 K < T <4K), high magnetic fields (0 < B < 55 T) at NHMFL, Tallahassee, USA, Nijmegen, The Netherlands and Toulouse, France; rotation in field (-90 0 < θ <90 0 );

11 Bulk superconductivity in LaFePO 4.00 T c =6.3 K 0.20 ρ (mωcm) T (K) 1.00 ρ (RT)/ρ(10 K) ~ T (K) High residual resistivity ratio: ~ 85; low H c2 ; Anomaly in specific heat: bulk superconductor; non-magnetic; 0.07 μ B /Fe; reversible signal - weak pinning; anisotropy ~10 ; J. Analytis, et. al., arxiv: (2008) C. Andrew, PhD Thesis (2010)

12 Superconducting order parameter with line nodes in LaFePO Δλ ~ T ± Clean superconductor: Superfluid density show linear dependence down to 100 mk suggesting the presence of nodes in the symmetry of the superconducting gap; J. Fletcher, et. al., PRL 102, (2009) New J. Phys. 11, (2009)

13 de Haas-van Alphen effect in LaFePO 0.75 T=0.35 K θ =31 o 4x10-4 θ =31 o Sample B torque (Ω) H c2 H c2 τ ~ B 2 θ =94 o torque (Ω) 2x x x B (T) x10-2 α 1 α 2 B (T) high B: normal state; oscillations periodic in inverse field, de Haas-van Alphen effect. τ ~ B 2 characteristic to a paramagnet; a simple corrugation of the Fermi cylinder leads to a beat pattern in the magnetization. FFT (amplitude) 4x10-2 2x β 1 β 2 A.I. Coldea et al., PRL, 101, (2008) F (T)

14 Torque (a.u.) de Haas-van Alphen effect in LaFePO F=(ħ / 2π e) A(E F ) Different frequencies correspond to extremal areas of the Fermi surface perpendicular to the applied magnetic field for a particular orientation; A.I. Coldea et al., PRL, 101, (2008)

15 Fermi surface warping and Yamaji angle H H β 2 β 1 α 2 α 1 F(θ )=F(0) / cosθ Quasi-two dimensional cylinder; ΔF α /F α ~ 4%; ΔF β /F β ~23 %; At Yamaji angles all Fermi surface cross sections have equal areas; their magnetization contributions interfere constructively=peak effect. K. Yamaji, J. Phys. Soc. Jpn. 58, 1520 (1989)

16 Significant c-axis c warping: of the Fermi surface 3D Fermi surfaces in 1111 compounds pnictides overdoped cuprates organics LaFePO ΔF α /F α ~ 4%; ΔF β /F β ~23 %; ρ c /ρ ab ~10 Tl 2 Ba 2 CuO 6+δ ΔF/F < 1%; ρ c /ρ ab ~10 3 ΔF/F < 1.3%; ρ c /ρ ab ~10 4 N. Hussey et al., Nature 425, 814 (2003); M. Kartsovnik et al., Chem. Rev., 104, 5737 (2004)

17 band 4 band 5 S. Lebègue, Phys. Rev. B 75, (2007) Conduction FeP layer Band structure of LaFePO: spaghetti 3D d z2 hole pocket at Z most susceptible to P position and doping; band 1 Electron pockets centred at M point: dxz, dyz h e e h h Hole pockets centred at Γ point:dxz,dyz bands 2 and 3

18 dhva data versus band structure calculations dhva Frequency F (kt) β 2 β 1 ε δ dhva Frequency F (kt) h e band 1 band 2 band 3 band 4 band 5 e e M α 2 α γ θ (degrees) θ (degrees) electronic branches show similar dispersion to the experimental α and β pockets; no experimental branch matches the weak dispersion due to the 3D hole pocket;

19 dhva Frequency F (kt) δ β 2 β 1 Band shifting and charge balance ε α 2 α γ θ (degrees) dhva Frequency F (kt) θ (degrees) Electron bands shifted by ΔE=+85 mev (band 5), +30 mev (band 4); hole bands all shifted by ΔE=-53 mev; Charge imbalance ~0.034 el/fu; ~1.7% oxygen deficiency in LaFePO. h e band 2 band 3 band 4 band 5 e h M Γ

20 Shrinking of the Fermi surface in LaFePO Q experimental observation of upward shift of the electron bands and of a downward shift of the hole band may be evidence of dominance of interband scattering (nesting); L. Ortenzi et al., PRL 103, (2009).

21 Moderate mass enhancement in LaFePO FFT Amplitude (a.u.) ΔB = T 710 T 985 T T 1335 T T (K) (el-el + el-ph) the effective masses between m e for both electrons and holes; moderate mass enhancement for the electronic bands;

22 Electronic contribution to the specific heat 3D E F lies just above a peak in the DOS, which leads to a rapidly decreasing DOS with energy. γ exp_powder ~7-12 mj/mol K 2 ; γ dhva = 6 mj/mol K 2 ; (mev) Assuming 4 quasi-two dimensional cylinders with m*~2 m e ; 3D pocket absent?

23 Quasiparticle scattering rates in LaFePO T =0.35 K Torque (a.u.) k F is the orbitally averaged Fermi wavevector for the particular Fermi surface orbit; l α ~1300 Ǻ inelastic quasiparticle mean free-path (small and large angle scattering from impurities) mean free path: electrons l α ~1300 Ǻ and l β ~ 800 Ǻ; scattering for hole ~ factor 2 larger;

24 K. Kuroki et al. Phys. Rev. B 79, (2009) S. Gaser et al., arxiv (2010) Relevance of the orbital character of bands T =0.35 K Torque (a.u.) k F is the orbitally averaged Fermi wavevector for the particular Fermi surface orbit; l α ~1300 Ǻ inelastic quasiparticle mean free-path (small and large angle scattering from impurities) mean free path: electrons l α ~1300 Ǻ and l β ~ 800 Ǻ; scattering for hole ~ factor 2 larger;

25 Effect of chemical pressure: P substitution BaFe 2 As 2 BaFe 2 P 2 Low temperature Fermi surface of BaFe 2 As 2 W. Xie, PRB 79, (2009) S. Kasahara et al., PRB 81,

26 Reconstructed Fermi surface in the AFM phase PM SrFe 2 As 2 S. Sebastian et al., J. Phys.: Cond. Mat. 20 (2008) AFM BaFe 2 As 2 J. Analytis et al., arxiv: (2009)

27 Quantum oscillations in SrFe 2 P 2 SrFe 2 P 2 is non-magnetic and non-superconducting with bond angle o (away from a perfect tetrahedron with ) Electronic bands α and β shows the largest amplitude; the least affected by scattering (if masses the same); J.G. Analytis et al., PRL 103, (2009)

28 Fermi surface of SrFe 2 P 2 Electronic bands in very good agreement with band structure calculations; band shifts still needed. Nesting? J.G. Analytis et al., PRL 103, (2009)

29 Fermi surface of SrFe 2 P 2 holes electrons Moderate mass enhancement sheet dependent and anisotropy in scattering; Nesting strongly diminished-strongly warped cylinders and a three-dimensional hole pocket; some nesting may be possible along k z ; J.G. Analytis et al., PRL 103, (2009)

30 Evolution of Fermi surface in BaFe 2 (As 1-x P x ) 2 l=800å T c ~25 K T c ~30 K l=150å oscillations observed for materials with Tc = 0 25 K; T max =30 K for x = 0.33; H. Shishido et al., PRL 104, (2010)

31 Evolution of electronic pockets in BaFe 2 (As 1-x P x ) 2 Two electron cylindrical Fermi surfaces; Volume: Decrease with decreasing x (no doping); H. Shishido et al., PRL 104, (2010)

32 Fermi surface shrinking in BaFe 2 (As 1-x P x ) 2 S. Kasahara et al., PRB 81, (2010)

33 Enhancement of the effective mass in BaFe 2 (As 1-x P x ) 2 H. Shisido et al., JPSJ 74, 1103 (2005) Outer electron cylinder λ el-ph~0.25 Increase of effective mass due to manybody interactions; Decrease of T F T F = hef m* k B γ expr ~18 mj/mol K 2 (x=0.38); (arxiv: ) Quantum critical behavior?

34 Spin fluctuations in BaFe 2 (As 1-x P x ) 2 ρ =ρ 0 +AT α S. Kasahara et al., PRB 81, (2010) Antiferromagnetic spin fluctuations close to QCP 1/T 1 T~1/(T+θ) Y. Nakai, et al. arxiv: (2010) H. Shishido et al., PRL 104, (2010)

35 Enhanced nesting towards maximum Tc? BaFe 2 As 2 x~0.63 (T c ~ 9 K) BaFe 2 P 2 One further HEAVY hole pocket observed; inner electron pocket and inner hole pocket have similar sizes ; shrinking of the electronic bands; J.G. Analytis et al., PRL 105, (2010)

36 ARPES studies in BaFe 2 (As 1-x P x ) 2 (x=0.38) h h e e Mass enhancement for all orbits varies between one quasi-two dimensional electron and hole pockets have similar size and shape inplying good nesting but they have different orbital character (d xz/yz for hole and d xy for the electron sheet) so weak contribution to the spin susceptibility; T. Yoshida et al., arxiv: (2010)

37 Significant pnictogen bonding affects FS SrFe2P2 c/a=3.04 CaFe2P2 Small spacer between Fe layers enhances P-P bonding. c/a=2.65

38 Effect of applied pressure in pcnitides CaFe 2 As 2 CaFe 2 A 2 under pressure has a transition to a non-magnetic collapsed tetragonal (ct) state; ~ 10% decrease in the c-axis and a ~2% increase in the a-axis; c/a=3 in the tetragonal phase to c/a=2.65 in the ct phase; Superconductivity present under non-hydrostatic conditions (uniaxial pressure); A.I. Goldman et al., Phys. Rev. B 79, (2009) D. A. Tompsett, G. G. Lonzarich,arxiv: (2009)

39 Effect of chemical pressure: small c/a ratio c/a=2.65 c/a=2.59 Band structure calculations predict: CaFe 2 P 2 is a close structural analogue of the collapsed tetragonal non-magnetic phase of CaFe 2 As 2 and shows a similar Fermi surface; single electron and hole sheets highly three-dimensional in character ; A.I. Coldea et al., PRL, 103, (2009)

40 Quantum oscillations in CaFe 2 P 2 CaFe 2 P 2 θ=-15 o a b θ=0 o B (T) torque measurements in 45 T at 0.4 K; series of different frequencies corresponding to various extremal areas on the Fermi surface; A.I. A.I. Coldea et et al., al., PRL, arxiv 103, (2009)

41 Quantum oscillations in CaFe 2 P 2 good agreement between the band structure calculations and experimental data; no band shifts required. identical mass enhancement on both electron and hole pockets ~1.5; topological change of the Fermi surface;. A.I. A.I. Coldea et et al., al., PRL, arxiv 103, (2009)

42 SC The strength of electronic correlations Mass enhancement: 1+ λ λ LaFePO m*/m b ~2. 2 inner electron pocket outer electron pocket 1.54 BaFe 2 (As 1-x P x ) 2 m*/m b ~ 3 for electron pockets ~2 Non SC CaFe 2 P 2 BaFe 2 P 2 m*/m b ~1.5 electron/hole pockets m*/m b ~1.5 electron pockets m*/m b =(1+λ el-ph )(1+ λ el-el ) ~ 1+ λ el-ph + λ el-el electron-phonon coupling λ th el-ph ~0.25 for Fe-pnictides electron-electron interactions (nesting, spin fluctuations) λ el-el ~ Magneto-elastic coupling large pnictide polarizability: Kulic et al., arxiv: L. Boeri, Physica C 469, 628 (2009)

43 Summary Fermi surface of 122 compounds extremely sensitive to structural effects (c/a ratio uniaxial pressure?). For small spacer layer or large d orbitals Fermi surface topology is strongly modified (in particular for the hole bands); Anisotropic scattering: hole pockets affected much more by impurity scattering as compared to the electron pockets; orbitals? Shrinking of the Fermi surface as compared with the band structure calculations electronic correlations; Enhanced effective masses and increased FS nesting in LaFePO and BaFe 2 (P 1-x As x ) strength of electronic correlations;