Interplay between magnetism and superconductivity in Fe-pnictides Institute for Physics Problems, Moscow, July 6, 2010 Andrey Chubukov University of Wisconsin

IRON AGE ( B.C.E.) RFeAsO (1111) R = La, Nd, Sm, Pr, Gd AFe 2 As 2 (122) A = Ba, Sr, Ca LiFeAs (111) Fe-Pnictides: Binary componds of pnictogens A pnictogen – an element from the nitrogen group N,P, As,Sb,Bi LaOFeP Fe(SeTe) T c,max =57K (SmFeAsO)

time

Crystal structure 2D Fe-As layers with As above and below a square lattice formed by Fe LaFeAsO Folded BZ Unfolded BZ

Phase diagram: magnetism and superconductivity BaFe 2 (As 1-x P x ) 2 Fernandes et al Matsuda et al Luetkens et al

Pnictides Cuprates Are pnictides similar to cuprates? Parent compounds are antiferromagnets Superconductivity emerges upon doping

Bragg peaks in YBCO 6.15 Tranquada et al Hayden et al Optical and acoustic bands  Heisenberg physics (plus DM…) Sushkov, Silva Neto… PARENT CUPRATES: HEISENBERG MAGNETS

Magnetism in pnictides Spin configuration (  0) or (0,  ) in the unfolded BZ (  ) in the folded BZ C. de la Cruz et al

Effective Heisenberg model Si & Abrahams

Sushkov et al Richter, Honecker …   

( ,0) or (0,  ) --- order from disorder Shender, 1982 J2J2 J1J1 Classicaly (S= infinity) the angle between sublattices is not fixed Quantum fluctuations fix the angle and stabilize (0,  ) or ( ,0) order Two sublattices

Spin-wave dispersion, neutrons: P. Dai et al, Zaliznyak…

All this is surely correct, but…. The pnictides are metals, not insulators

C. de la Cruz et al., Nature 453, 899 (2008)  SR: H.-H. Klauss et al., arXiv: Magnetic moment is rather small

Lynn & Dai Ordered moment

Itinerant magnetism

Collaborators Maxim Vavilov Anton Vorontsov Ilya Eremin

Band theory calculations agree with experiments Band theory calculations agree with experiments Lebegue, Mazin et al, Singh & Du, Cvetkovic & Tesanovic… 2 circular hole pockets around (0,0) 2 elliptical electron pockets around  ) (folded BZ),  or  and  (unfolded BZ) Electron Fermi surface Hole Fermi surface

Dong et al, Korshunov & Eremin, Raghu et al., K. Kuroki et al, … Itinerant description: magnetism comes from nesting

For a perfect nesting, AFM instability occurs already at small U Nesting is a boost for an SDW antiferromagnetism M. Rice (for Cr), V. Cvetkovic and Z.Tesanovic, …. Eremin & Korshunov (  ) in the folded BZ 2k F

TUG-OF-WAR Heisenberg magnetism Itinerant magnetism Abrahams, Bernevig, Haule, Kivelson, Kotliar, Phillips, Sachdev, Si, Sushkov, Xu …. Carbotte, Gorkov, Eremin, Hirschfeld, Kee, Kim, Kuroki, D-H Lee, Maier, Mazin, Moreo, Scalapino, Schmalian, Tesanovic, Vishwanath, …..

Questions for itinerant approach: 1. The actual order is Q 1 = ( ,0) Q 2 = (0,  ) ( ,0) SDW gaps 2. Why the system remains a metal? ( ,  ) folded BZ

Introduce two SDW order parameters 1. Selection of a magnetic order O(6) symmetry perfect nesting Eremin, A.C.

Either W 1 =0, (0,  ) state Or W 2 =0, (  ) state Introduce two SDW order parameters 1. Selection of a magnetic order O(6) symmetry ellipticity perfect nesting non-perfect nesting Eremin, A.C.

The magnetic order selected in itinerant model is the same as in J1-J2 model: ferromagnetism along one direction and antiferromagnetism along the other

How this affects electrons? In an SDW phase the system remains a metal! SDW (0,0) (  ) SDW gap Q1Q1

Q1Q1 Q2Q2 If FS geometry was different (0,  ) insulator

Complications: 1. Interactions are generally angle-dependent, f1f1 f2f2 c Dirac points Vishwanath et al 2. Fermi surfaces are not circular – SDW order does not immediately gap the FSs More FS crossings in the SDW phase than in the paramagnetic phase

Borisenko et al Theory Experiment

Number of Fermi surface crossings Normal state: doubly degenerate hole dispersion doubly degenerate electron dispersion (0,0) (  ) Two Fermi surface crossings near (0,0) and two near (  )

Number of Fermi surface crossings SDW state: Three Fermi surface crossings near (0,0) and three near (  )

Experiment BaFe 2 As 2 Zhou et al Near (0,0) paramagnet SDW phase More FS crossings in the SDW phase

Spin-wave dispersion: Perfect nesting Non-perfect nesting

Spin-wave dispersion (cont’d)

Magnetism and Superconductivity

Phase diagram: magnetism and superconductivity BaFe 2 (As 1-x P x ) 2 Fernandes et al Matsuda et al Luetkens et al Either 1 st order or co-existence

Standard approach: introduce two order parameters and analyze Ginzburg-Landau free energy AB – C 2 >0, co-existence AB – C 2 <0, first order

two-band model Pnictides perfect nesting AB – C 2 =0 if s +- gap AB – C 2 <0 if s ++ gap, no co-existence!

Non-perfect nesting: ellipticity of electron FSs doping (change of sizes of hole and electron pockets) doping ellipticity electron band hole band non-perfect nesting

First-order transition and co-existence are both possible

Even more complex phase diagram as a function of temperature doping Fernandes, Schmalian, et al, Vorontsov, Vavilov, AC

Conclusions Ghost of the Heisenberg J 1 -J 2 model in an AFM metal. Quantum selection of the magnetic order: O(6) degeneracy for perfect nesting, the degeneracy is reduced to O(3) * Z 2 (i.e., to (0,  ) or ( ,0)) once ellipticity of electron pockets is included. The system remains a metal in the antiferromagnetic phase with more FS crossings than in the paramagnetic phase Either co-existence between AFM and SC, or 1 st order transition, depending on how O(6) degeneracy is broken by ellipticity/doping.

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Systems are quasi-2D Lynn & Dai