Iron pnictides: correlated multiorbital systems Belén Valenzuela Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC) ATOMS 2014, Bariloche Maria José Calderón ICMM-CSIC Madrid Elena Bascones ICMM-CSIC Madrid Gladys León ICMM-CSIC Madrid Luca de Medici CNRS-ESPCI Paris France

Index Introduction: Multiorbital character, magnetism and correlations in iron superconductors. Our work: –Hamiltonian: 5 orbital tight-binding+interactions –Magnetic mean field phase diagram from the mean-field approach. Orbital ordering. –( ,0) mean field phase diagram with orbital differentiation. –Orbital differentiation in optical conductivity ATOMS 2014, Bariloche

K 0.8 Fe 2 Se Electronic structure close to Fermi energy dominated by these planes ATOMS 2014, Bariloche Iron planes Zhang et al, Mod. Phys. Lett.’12

Phase diagram of iron arsenides Phase diagram of Cuprates Mechanism? Non-phonon mediated J. Zhao, et al. Nat.Mat’08 ATOMS 2014, Bariloche

Phase diagram of iron arsenides J. Zhao, et al. Nat.Mat’08 Cuprate phase diagram Metal!: Does it mean correlations are not relevant? Mott insulator Néel ( ,0) Columnar ATOMS 2014, Bariloche (  /2,  /2) double stripe in 11 compound. Sensitivity to doping and pressure Magnetic softness Structural transition follows the magnetic one

Multiorbital system: Atomic view Pnictides: 6 electrons in 5 Fe orbitals in a tetrahedral environment: S=1 (2m B ) S=2 (4m B ) Cuprates: 9 electron in 5 d orbitals in a tetragonal environment: d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 Crystal field  200 meV d x 2 -y 2 d 3z 2 -r 2 d xz, d yz d xy ATOMS 2014, Bariloche Crystal field  O(eV) Kamihara’08

Correlations in iron superconductors ATOMS 2014, Bariloche ARPES experiments Optical conductivity experiments Warning! To study correlations in optical conductivity arguments of one-orbital system (as for cuprates) have been used. Are these arguments valid in a multiorbital system? Quasiparticle bands are observed But mass enhancement around 3

ATOMS 2014, Bariloche Summary of questions: 1. Metallic system means correlations are not important? 2. Origin of the magnetic softness? 3. Can we interpret experiments using the same arguments than for one orbital system? 4. What is the role of the orbital degree of freedom in a correlated system?

Our work: Iron pnictides: Multiorbital correlated systems M.J. Calderón, B.V, E. Bascones, PRB 80, (2009) E. Bascones, M.J. Calderón, B. V., PRL 104, (2010) B. V., E. Bascones, M.J. Calderón, PRL 105, (2010) M.J. Calderón, G. León, B.V, E. Bascones, PRB 86, (2012) M.J. Calderón, B.V., E. Bascones, PRB 86, (2012) B.V., M.J. Calderón, G. León, E. Bascones, PRB 87, (2013) M.J. Calderón, L. De Medici, B. V., E. Bascones arXiv:1407:6935 ATOMS 2014, Bariloche

Microscopic Hamiltonian d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 Spin 2 Introducing on-site interactions: U -> intraorbital repulsion U’ -> interorbital repulsion J -> Hund’s coupling U’=U-2J 6 electrons in 5 d orbitals in a tetrahedral environment with crystal field meV: ATOMS 2014, Bariloche

Tight-binding for five orbitals 2D electron pocket 2D hole pocket Extended Brillouin zone ATOMS 2014, Bariloche Focus on Fe-pnictogen planes, square lattice, Fe unit cell Five Fe d-orbitals; pnictogen included through hoppings; direct (Fe-Fe) + indirect (Fe-pnictogen-Fe) hoppings Symmetry of the orbitals considered through Slater-Koster: 4 parameters to describe the hoppings (pd, dd 1, dd 1,dd 1 ) Straightforward change of pnictogen position (angle )

Tight-binding for five orbitals: angle dependence of the hoppings MJ Calderon, B.V, E Bascones PRB’09 High sensitivity to the As position and not-intuitive hoppings terms Experimental range ATOMS 2014, Bariloche

Magnetism: Mean field theory J’=J and U’=U-2J H because of rotational symmetry We calculate the magnetic U-J/U phase diagram applying mean field theory to the complete Hamiltonian. We allow for ferroorbital order. Ansatz: Intraorbital mean field terms ATOMS 2014, Bariloche

Magnetism: Mean field phase diagram ATOMS 2014, Bariloche E. Bascones, M.J. Calderón, B. V., PRL’10 M.J. Calderón, G. León, B.V., E. Bascones, PRB’12 Insulator-metal transition driven by Hund’s coupling: Hund’s metal!

Magnetism: Mean field phase diagram ATOMS 2014, Bariloche E. Bascones, M.J. Calderón, B. V., PRL’10 M.J. Calderón, G. León, B.V., E. Bascones, PRB’12 Low magnetic moment with Hund’s rule violated Like in 1111 and 122 compounds Columnar ordering comes with orbital ordering Like in 11 compounds Recents experiments find this order with doping With hole doping there is a change from ( ,0) to (  ) and phase separation. Magnetic softness!

100 vs 50 mev Competition between phases: Magnetic softness To understand these phases key parameters are the hopping and the crystal field in a tetrahedral environment ATOMS 2014, Bariloche d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 ( ,0) dominates the phase diagram

( ,0) magnetism: Orbital differentiation ATOMS 2014, Bariloche xy and yz orbitals are gapped, zx, x 2 -y 2, 3z 2 -r 2 are itinerant M.J. Calderón, B. V., E. Bascones, PRB’12 With hole doping the orbital differentiation region dominates: Correlations become more important with hole-doping xy and yz go to half-filling with increasing interactions and become gapped U Orbital ordering Half-filled

Orbital differentiation in the paramagnetic state ATOMS 2014, Bariloche Yu&Si PRB’12 Insulator-metal transition with Hund’s coupling Hund’s metal. Orbital differentiation region with xy localized Proposed scenario by de Medici et al. PRL’14: Unified vision for cuprates and iron superconductors ARPES, quantum oscillations and C v observe increasing correlations and orbital differentiation with hole-doping in KFe 2 As 2 Slave-spin and DMFT also find Hund’s metal, correlations increasing with hole doping in the PM state and orbital differentiation

Orbital differentiation in the PM phase in optical conductivity: interband transitions ATOMS 2014, Bariloche B.V., M.J. Calderón, G. León, E. Bascones, PRB’13 M.J. Calderón, L. De Medici, B.V., E. Bascones, arXiv: Renormalization included within slave-spin mean field formalism-> Z m Renormalized Interband transitions contribute at low energy. The effect is more drammatic with hole doping. Be careful with the sum-rule!

Conclusions (partial) 1. Metallic system means correlations are not important? Not necessarily! Hund’s metal. Correlations are enhanced doping with holes. 2. Origin of the magnetic softness? Key: Tetrahedral crystal field, As-Fe angle and non trivial hoppings 3. Can we interpret experiments using the same arguments than for one orbital system? No! Careful is needed to properly account for the orbital degree of freedom 4. What is the role of the orbital degree of freedom in a correlated system? Orbital ordering, orbital differentiation, … ATOMS 2014, Bariloche

Outreach webpage about superconductivity in Spanish

Orbital reorganization in the Hartree-Fock phase diagram x 2 -y 2 3z 2 -r 2 ( ,0) in x 2 -y 2 configuration (  ) in 3z 2 -r 2 configuration M.J. Calderón, G. León, B. V., E. Bascones, PRB’12

Exchange constants for iron pnictides ATOMS 2014, Bariloche x 2 -y 2 & 3z 2 -r 2 configurations In the 3z 2 -r 2 configuration  ordering is preferred since the direct hopping t x x2-y2 contributes to AF J 1 -> superexchange wins. J 1 & J 2 becomes FM at large J H /U. M.J. Calderón, G. León, B. V., E. Bascones, arXiv: (2011) |J 2 |<!J 1 /2|  again!

Strong coupling limit ATOMS 2014, Bariloche We map into a Heisenberg model using 2º order perturbation theory and study 3 fillings 5 e -, 6 e - & 7 e - per iron site. 5 e - per iron site Atomic limit: We restrict to S=5/2 (keeping just Sz= ±5/2) states d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 ! |J 2 |<!J 1 /2| 

Exchange constants for iron pnictides: Comparison between x2-y2 & 3z2-r2 configuration ATOMS 2014, Bariloche The boundary between  and  depend on the crystal field  x2-y2 -  3z2-r2. Competition between phases. Magnetic softness x 2 -y 2 3z 2 -r 2 M.J. Calderón, G. León, B. V., E. Bascones, prb’12

Strong coupling limit EMRS 2011 fall, Poland Undoped pnictides: 6 e - per Fe site Atomic limit: We restrict to S=2 (keeping just Sz= ±2) states (they dominate de Hartree-Fock phase diagram at large U) Due to the small crystal field splitting (0.05eV) we consider x 2 - y 2 & 3z 2 -r 2 configuration x 2 -y 2 configuration 3z 2 -r 2 configuration d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2 d xy d xz, d yz d 3z 2 -r 2 d x 2 -y 2

Exchange constants: Dependence on Fe-As-Fe angle ATOMS 2014, Bariloche U=5eV, J H =0.22U M.J. Calderón, G. León, B. V., E. Bascones, prb’12 Because hoppings depend on the angle J 1 and J 2 also depend on the angle

Reasoning from the strong coupling point of view to understand the LM The low moment phase is stabilized because crossed hoppings are as big as direct hoppings and also very anisotropic: Release frustration Q=( ,0)

Orbital ordering in the band structure for U=2.2 eV and J=0.07U

Phase separation JH/U=0.22 U n

Magnetism: Mean field phase diagram ATOMS 2014, Bariloche In the mean field description there is a DS phase charge modulated instead of FM. But strong coupling analysis also points to DS instability at high J H 7 electrons 5 electrons M.J. Calderón, G. León, B. V., E. Bascones, arXiv: (2011)

Anisotropy and nematicity Nematic scenario: the anisotropy is also present in the paramagnetic state Chu et al. Science’10 and many other experiments Fe More metallic Less metallic ATOMS 2014, Bariloche Fernandes et al. Nat. Phys’14 In pnictides: is it orbital driven anisotropy or magnetically driven anisotropy? Nematicity has also been found in cuprates but the origin is probably different

Anisotropy in the magnetic state, orbital ordering?

We also calculate the Drude ratio with the Kubo formula and get the same result. We assume the scattering rate is isotropic Drude weight ratio ATOMS 2014, Bariloche

Experimental signs of anisotropy and orbital ordering are anticorrelated, from our approximation OO is not responsible of the resistivity anisotropy found in experiments. Anisotropy is instead dependent on the topology of the Fermi surface. B. V., E. Bascones, M.J. Calderón, PRL 105, (2010) Is orbital order responsible of resistivity anisotropy? ATOMS 2014, Bariloche ( ,0) Magnetism Orbital ordering D x /D y Anisotropy found in experiments Opposite anisotropy n yz <n zx Maximum orbital ordering

Magnetic reconstruction as origin of the conductivity anisotropy D x /D y J H /U Anisotropy linked to topology and morphology of the Fermi Surface. Experimental anisotropy in general for low moment. B. Valenzuela, EB, M.J. Calderón, PRL 105, (2010) D x /D y = 0.72D x /D y = 1.34 D x /D y = 0.52 D x /D y = 1.09

Sensitivity of the anisotropy to the angle  ATOMS 2014, Bariloche D x /D y Regular tetrahedron Squashed tetrahedron This indicates that probably the anisotropy Dx/Dy>1 is not universal for all compounds and may vary with pressure and doping. Magnetic softness. B. V., G. León, M.J. Calderón, E. Bascones, PRB’13 D x /D y

Iron pnictides: Crystal structure High Tc SC based on As-Fe layers Tetrahedral environment Cuprates crystal structure: High Tc SC based on Cu-O layers Tetragonal environment Kamihara’08 ATOMS 2014, Bariloche