Магнетизм в железосодержащих сверхпроводниках: взаимодействие магнитных, орбитальных и решеточных степеней свободы

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1 Магнетизм в железосодержащих сверхпроводниках: взаимодействие магнитных, орбитальных и решеточных степеней свободы Ilya Eremin Theoretische Physik III, Ruhr-Uni Bochum Work done in collaboration with: A.V. University of Wisconsin, Madison R. University of Minnesota J. KIT Karlsruhe. J. Knolle, R. MPI Physik komplexer Systeme, Dresden

2 Superconductivity reaches the iron age Iron pnictides first high-temperature superconductors since the cuprates! stone age copper age iron age

3 Iron-based superconductors Layered materials: transition metal (Fe) plus pnictogen (nitrogen group, such as As) Ba Fe As BaFe As

4 Iron-based superconductors Layered materials: transition metal (Fe) plus pnictogen (nitrogen group, such as As) T c =8K (55K for Sm) Kamihara et al JACS (008) Ren et al Chin. Phys. Lett. (008) T c =38K Rotter et al. PRL (008) Ni et al Phys. Rev. B 008 (single xtals) T c =18K Wang et al Sol. St. Comm. 008 T c =8K Hsu et al PNAS 008 No arsenic!

5 Iron-based superconductors: what are the common electronic features?

6 Electronic-structure calculations LaFePO Lebegue 007 (T c =6K) LaFeAsO Singh & Du 008 (T c =6K) Band structures for materials nearly identical! Hole pocket near, electron pocket near M D!

7 Electronic-structure: multiorband structure Fe 3d 6 4 holes per site multiband structure. chemical potential lies in the gap LaFeAsO Crystalline electric field of the tetrahedra is weak All 5 Fe d-orbitals are near the Fermi level

8 Hole pockets near (0,0) Electron pockets near () Comparison with other materials La-1111 Ba-1 FeTe courtesy of I. Mazin

9 ARPES NdFeAs(O 1-x F x ) (x=0.1) A. Kaminski et al. Ba06K04FeAs H. Ding et al. dhva LaFePO A. Coldea et al, LiFeAs A. Kordyuk et al Hole pockets near (0,0) Electron pockets near ()

10 Multiorbital structure Mutiorbital and multiband physics: several d-orbitals close to E F L. Boeri, O.V. Dolgov, and A.A. Golubov, PRL 101, (008)

11 Iron-Pnictides: typical phase diagram disorder, pressure magnetic, structural, and superconducting order

12 Iron pnictides: structural and magnetic transitions I) Structural Transition II) Magnetic Transition 1/1111/111 FeTe Not in this talk! DFT correctly Transitions reproduces are simultaneous (or even predicts) for FeTe and correct almost magnetic for and structural parent 1 s, ground but states, structural but transition requires magnetism first in 1111 s as a prior condition and doped for 1 s distortion

13 Outline - Selection of the magnetic stripe order within itinerant picture - Ising nematic degree of freedom - Manifestation of the nematic state: structural and orbital instabilities

14 Iron pnictides: phase diagram magnetic and structural transition lines follow closely each other correlated phases! The systems are metals in the normal state study magnetism in the system with no local moments a-priori rich phase diagram with hidden degeneracy selection of the magnetic order and resulting interaction with the structural degrees of freedom

15 Magnetism in ferropnictides: strong coupling description Ising nematic M 1 M 0 Ch. Henley, PRL 6, 056 (1989) F. Krüger et al., PRB 79 (009); W. G. Yin, C. C. Lee, and W. Ku, PRL 105 (010)

16 Iron pnictides: band structure disconnected Fermi surfaces Fe ions per unit cell hole pocket review: Paglione & Greene, Nature Phys (010) electron pockets unfolded BZ (1 Fe atom) k kq Q 0, Q1,0

17 The model: from orbital to the band description S. Graser et al New J. Phys. 11, (009) u 1 u 4 u 3 A.V. Chubukov, D. Efremov, and I. Eremin, PRB (008)

18 Fermi surface in the unfolded BZ - two nesting wave vectors Q 1 =(0,) andq =(,0) - two vector SDW order parameters - two sublattice order parameters

19 Simplest model to solve: hole and electron pockets - sets the value of the total order parameter but does not specify or - the ground state degeneracy is even larger than in the J 1 -J model of localized spins O(6) degeneracy [5 Goldstone modes] (0, ) or(,0) are two of many possibilities

20 Simplest model to solve: 1 hole and electron pockets U 7 - to add the interaction (densitydensity) between electron pockets - Electron pockets are elliptic, Positive (m x -m y ) U 6 U 8 <0 U 4 or I. Eremin and A.V. Chubukov, PRB 81, (010) (0, ) or (,0) is selected! no need for quantum fluctuations in itinerant picture - charge fluctuations are crucial

21 Ising nematic order and magnetism A state that breaks Z symmetry but remains paramagnetic spontaneous tetragonal symmetry breaking Z O(3) symmetry breaking symmetry breaking disordered state Ising nematic state S i S Electronic nematic phase the point-group symmetry from C 4 (tetragonal) to C (orthorhombic), is equivalent to the orthorhombic phase nematic is used to emphasize that the phase transition is of purely electronic origin I. Eremin, EPFL, 16 May 01 ix S i S i y magnetic state S i 0

22 How to treat the Ising nematic order in the itinerant picture - Ising variable: [ R. Fernandes et al., PRL 105 (010)] M 1 M 0 Ising nematic transition M M 1 1 X Y General procedure: introduce two bosonic fields Partition function as an integral over Grassmann variables

23 How to treat the Ising nematic order in the itinerant picture decouple the quartic term in fermionic operators using the Hubbard- Stratonovich transformation Expand Seff in powers of X and Y and obtain the Ginzburg- Landau type of action

24 Itinerant approach to the nematic state Y X r G G 0, k X, k uspin k u 1 k G, k G X, k G G 1 i, k Y, k Finite ellipticity in k hole pocket g 1 G, k X, k Y, k k G G 0 Away from perfect nesting: F mag r0 1 u 4 1 g 4 1

25 Itinerant approach to the nematic state To consider the possibility of a nematic state, we need to include fluctuations F mag -1 mag q 1 u 4 1 g nematic order parameter

26 Itinerant approach to the nematic state Equation of state for the nematic order parameter: F 0 3 mag g q 1 0 solution already in the paramagnetic phase, when the magnetic susceptibility is large enough 1 magnetic fluctuations nematic order

27 Itinerant approach to the nematic state Magnetic fluctuations become stronger around one of the ordering vectors in the paramagnetic phase nematic Q 0, transition Q1,0 x and y directions become inequivalent: tetragonal symmetry breaking Fernandes, Chubukov, Eremin, Knolle, Schmalian, PRB (01)

28 Ising nematic transition triggers structural transition magneto-elastic coupling: a a b b H magel k c X, k c X, k c Y, k c Y, k nematic transition OR Structural transition driven by magnetic fluctuations

29 Ising nematic transition triggers orbital order Distinct orbital content of different Fermi pockets leads to orbital order (Fe configuration: 3d 6 ) orb Fernandes, Chubukov, Eremin, Knolle, Schmalian, PRB (01) See also: M. Daghofer, A. Nicholson, and A. Moreo, Phys. Rev. B 85, (01)

30 Ising nematic transition triggers orbital order explains the experimentally observed sign of the orbital splitting in BaFe As Yi et al, PNAS (011)

31 Nematic order enhances magnetic fluctuations Strong increase of the magnetic correlation length at the nematic transition magnetic transition nematic transition T T S

32 Nematic order enhances magnetic fluctuations NMR reveals the enhancement of magnetic fluctuations at the nematic transition NaFeAs Fernandes, Chubukov, Eremin, Knolle, Schmalian, PRB (01) Ma et al, PRB (011)

33 Phase diagrams for the magnetic and structural transitions magnetic fluctuations give rise to enhances nematic order transitions naturally follow each other

34 Magnetic and Ising nematic transition temperatures Fernandes, Chubukov, Eremin, Knolle, Schmalian, PRB u g - Ising nematic order introduces orbital polarization - magnetic correlation length jumps to a larger value at the nematic transition

35 Two-component order parameter: combination (,0) and (0,) E C gr X Y or - Ginzburg-Landau description: transition to the two-component phase if C becomes negative G. Giovanetti. et al Nature Commun., 98 (011); I. Eremin and A.V. Chubukov, PRB 81, (010); P.M.R. Brydon, J. Schmiedt, and C. Timm, PRB 84, (011) - non-linear effects inside SAF phase => phase transition at T N <T N1

36 Magnetic mean-field phase diagram saddle-point equations free energy analysis Slight hole doping, 1% Finite ellipticity Ellipticity doping

37 Magnetic mean-field phase diagram: experimental situation 1) Ba 1 x Na x Fe As Neutron and X-ray diffraction S. Avci et al., arxiv: ) Ba 1 x K x Fe As under pressure: Resistivity measurements new phase E. Hassinger et al., PRB 86, (01)

38 Iron-based superconductors: Magnetism: - shows rich phase diagram with hidden magnetic frustration (selection of the magnetic order, preemptive Ising nematic instability) - contains beside striped AF order also C 4 symmetric phase with two-component order parameter - particular aspects of the itinerant physics are important and decisive for comparison with experiment I. Eremin, and A. V. Chubukov, PRB 81, (010) J. Knolle, I. Eremin, A.V. Chubukov, and R. Moessner, PRB 81, (R) (010) J. Knolle, I. Eremin, and R. Moessner, PRB 83, 4503 (011) R. M. Fernandes, A. V. Chubukov, J. Knolle, I. Eremin, and J. Schmalian, Phys. Rev. B 85, (01)