ANISOTROPIC TRANSPORT IN THE IRON PNICTIDES

Transcription

1 ANISOTROPIC TRANSPORT IN THE IRON PNICTIDES JÖRG SCHMALIAN AMES LABORATORY AND IOWA STATE UNIVERSITY

2 Collaborators theory Ames: Rafael Fernandes Rutgers: Premala Chandra UCLA: Elihu Abrahams experiment Ames: Sergei Bud ko, Paul Canfield Alan I. Goldman Adam Kaminski Andreas Kreyssig, Rob McQueeney Ruslan Prozorov, Makariy Tanatar ORNL: David Mandrus UT Knoxville: Veerle Keppens

3 PHASE DIAGRAM magnetic + structural order are related orbital order O n xz n yz 0 O ba ba induces magnetic order Ni et al, PRB (008) Fernandes et al, PRB (010) Pratt et al, PRL (009) Pratt et al, PRL (009) F. Krüger et al., PRB 79, (009) R. R.P. Sigh, arxiv: (009) C. C. Chen et al., PRB 8, (010). W. Lv, et al. PRB 8, (010).

4 PHASE DIAGRAM orbital order O n xz n yz 0 O ba ba Yi et al, PNAS (010)

5 PHASE DIAGRAM magnetic + structural order are related Ising nematic order S r iq r Qr e 1 e i 1, 0 or 0, Q 1 Q O 1 Ni et al, PRB (008) Fernandes et al, PRB (010) Pratt et al, PRL (009) Pratt et al, PRL (009) naturally related to magnetic order C. Fang et al., PRB 77, 4509 (008) C. Xu, M. Müller, S. Sachdev, PRB 78, 00501(R) (008). Y. Qi, C Xu, PRB (009) Fernandes et al. PRL 105, (010)

6 MAGNETIC ORDER + S.C. Ni et al, PRB (008) Fernandes et al, PRB (010) Pratt et al, PRL (009) Pratt et al, PRL (009) Fernandes et al, PRB (010)

7 STRUCTURAL ORDER + S.C. Ni et al, PRB (008) Fernandes et al, PRB (010) Nandi, et al, PRL (010) Pratt et al, PRL (009) Pratt et al, PRL (009)

8 ORDER BELOW T C Fernandes et al, PRB (010) Nandi, et al, PRL (010) both order parameters are suppressed below T c magnetic order competes naturally for states at the Fermi surface magnetism is the driving order parameter? mean field calculation for competing order R. M. Fernandes et al. PRB (010) A. B. Vorontsov, M. G. Vavilov, B. A. V. Chubukov PRB (009),

9 ORDER BELOW T C Fernandes et al, PRB (010) Nandi, et al, PRL (010) both order parameters are suppressed below T c magnetic order competes naturally for states at the Fermi surface magnetism is the driving order parameter? no direct coupling between s.c. + structural O.P. needed Tc T N Kim, et al, PRB (in press, 011)

10 ORDER BELOW T C Fernandes et al, PRB (010) Nandi, et al, PRL (010) both order parameters are suppressed below T c magnetic order competes naturally for states at the Fermi surface magnetism is the driving order parameter? suppression of the QCP E. G. Moon, S. Sachdev PRB 8, (010)

11 QUANTUM CRITICALITY BaFe (As 1-x P x ) S. Kasahara et al. Phys. Rev. B 81, (010)

12 QUANTUM CRITICALITY Matsubayashi et al. J. Phys. Soc. Jpn (009) E. Colombier et al. Phys. Rev. B 79, (009) S. Kasahara et al. Phys. Rev. B 81, (010) transport anomaly near the magnetic QCP T 1

13 MAGNETIC STRUCTURE: FRUSTRATED T. Yildirim (008), Q. Si +E. Abrahams PRL (008), C. Xu, M. Müller, S. Sachdev PRB (008) C. Fang, H. Yao, W.-F. Tsai, J-P.Hu, S. A. Kivelson, PRB (008) m 1 m Chandra, Coleman, Larkin, Z PRL (1990) SU Z 0 :90 -rot. m 1 m m m 1 Ising-nematic order parameter m 1 m C 4 -rotation symmetry broken

14 C. Xu, M. Müller, S. Sachdev PRB (008) structural order is induced by Ising - nematic order m 1 m 0, m i 0 0, m 0 i Ising order couples to the lattice orth m 1m structural phase transition is driven by magnetic fluctuations

15 NEMATIC FLUCTUATIONS LATTICE SOFTENING shear distortions cost energy: C 1 s,0 s magneto-elastic coupling: orth C 1 s C 1 s,0 C s,0 nem C s ~ T T s shear modulus static nematic susceptibility

16 Hertz-Millis type description of itinerant systems S i1, 1 4 q, Δ i uδi gδ 1 Δ m 1, 1 MAGNETIC FLUCTUATIONS e iq1 r iqr 1 e, 0 or 0, Q 1 Q Q i q, q x 1 qz 1 q 1 cos i / x z D. S. Inosov, et al. Nature Phys. 6, 178 (010)

17 ANISOTROPIC MAGNETIC FLUCTUATIONS 0, 1 soft mode + 1 massive mode soft modes,0 0,, 0 strong magnetic anisotropies weak anisotropies of the electronic structure

18 RENORMALIZED SHEAR MODULUS C 1 s C 1 s,0 C s,0 nem nem 0 nem 1- g T k, n 0 nem 0 nem spin d z4 k, n Resonant ultrasound spectroscopy (V. Keppens Univ. of Tenn.) R. M. Fernandes, Phys. Rev. Lett. (010) M. Yoshizawa et. al..arxiv:

19 TRANSPORT: RESISTIVITY ANISOTROPY untwinned crystals Chu et al, Science (010) Tanatar et al, PRB (010)

20 TRANSPORT: RESISTIVITY ANISOTROPY b a Chu et al, Science (010) Tanatar et al, PRB (010) δ ort is monotonic in x, transport anisotropy is NOT! FM bonds have higher resistance parent compounds: largest anisotropy is near T N (SDW down folding can t be the entire story)

21 TRANSPORT: RESISTIVITY ANISOTROPY b a Chu et al, Science (010) δ ort is monotonic in x, transport anisotropy is NOT! FM bonds have higher resistance parent compounds: largest anisotropy is near T N (SDW down folding can t be the entire story)

22 ANISOTROPY SEEN IN STM Nematic Electronic Structure in the Parent State of the Iron-Based Superconductor Ca(Fe 1 x Co x ) As T Chuang et al. Science 010;37:

23 ANISOTROPY SEEN IN OPTICS scatt. rate + weight anisotropy A. Dusza et al., Europhys. Lett. 93, 3700 (011). Z. P. Yin, K. Haule, and G. Kotliar, Nat. Phys. 7, 94 (011).

24 SCATTERING BY SPIN-FLUCTUATIONS AND IMPURITIES Scattering by spin-fluctuations is anisotropic and inelastic Scattering by impurities is isotropic and elastic hot spots hs T d / cold regions cr T ARPES Liu, et al, Nature Phys (010)

25 SCATTERING BY SPIN-FLUCTUATIONS AND IMPURITIES Scattering by spin-fluctuations is anisotropic and inelastic Scattering by impurities is isotropic and elastic hot spots hs T d / cold regions cr T clean limit hot spots short-circuited by the cold regions: T dirty limit: hot spots smeared out across the Fermi surface: T 0 d / Hlubina & Rice, PRB (1995) Rosch, PRL (1999)

26 TRANSPORT IN THE NEMATIC PHASE: BOLTZMANN EQUATION ij j k j v k Boltzmann equation: f a, k f 0 a, k i a, k f 0 a, k a, k T-depended changes are small corrections i imp (, k) v i k, k' 1 cos k,k' 1 ij imp i i imp Cinel imp

27 TRANSPORT IN THE NEMATIC PHASE: BOLTZMANN EQUATION ii i i f f T 1 imp N k k' k' 1 k k, k' k, k', T Im k k' k, k' g l n l, l1, k k' only one set of hot spots contributes close to T N velocities at the active hot spots determine the resistivity

28 TRANSPORT IN THE NEMATIC PHASE: RESULTS external strain xx yy 0 0 T T d d / /, hs, / hs X, hs X, / hs sign of the resistivity anisotropy depends solely on the velocities at the hot spots

29 SIGN OF THE RESISTIVITY ANISOTROPY VS. DOPING (ellipticity) yy xx 0 (size mismacth) hole doping electron doping possible change in the sign for hole-doped materials J. J. Ying et al arxiv: (010)

30 b / a Ruslan Prozorov Lunch discussion: Minnesota Meeting electrons (Co-doping) x holes (K-doping)

31 ROLE OF IMPURITIES anisotropy decreases in annealed samples back to Hlubina-Rice

32 CONCLUSIONS m 1 m Ising-nematic scenario driven critical magnetic fluctuations with two degenerate ordering vectors offers a viable approach SU Z m 1 m

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