Mitglied der HelmholtzGemeinschaft Strength of the effective Coulomb

Mitglied der Helmholtz-Gemeinschaft Strength of the effective Coulomb interaction at metal and insulator surfaces Ersoy Şaşıoğlu, Christoph Friedrich, and Stefan Blügel Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany March 22, 2013

Motivation Atoms Surfaces U = 15 -25 e. V U = ? e. V Bulk U = 2 -5 e. V U March 22, 2013 Folie 2

Coulomb interaction at surfaces U March 22, 2013 Folie 3

Hubbard U from Constrained RPA DFT + Model Hamiltonians DFT (LDA) Model Hamiltonian Sr. VO 3 V Multi-orbital Hubbard model March 22, 2013 Folie 4

Hubbard U from Constrained RPA Partially screened Coulomb interaction: Hubbard U r space r d space d r d EF d d Hubbard U r r Advantages of c. RPA over c. LDA § Elimination of d-d screening channel § The matrix U( ) contains valuable information: March 22, 2013 on-site and off-site U and J frequency dependence F. Aryasetiawan, et al. , Folie 5 Phys. Rev. B 74, 125106 (2006)

FLAPW Realization (c. RPA) Full-Potential Linearized Augmented Plane Wave (www. flapw. de) DFT part GW part FLEUR SPEX Projection of U(r, r‘) onto Wannier basis Wannier 90 E. Sasioglu, C. Friedrich, and S. Blügel, Phys. Rev. B 83, 121101(R) (2011). March 22, 2013 Folie 6

Surface Hubbard U Competing effects at surfaces § Reduced screening volume: U § Electronic structure effects : U Effective surface band narrowing (metals) Surface states (metals, insulators, semiconductor) March 22, 2013 U E. Sasioglu, C. Friedrich, and S. Blugel, Phys. Folie 7 Rev. Lett. 109, 146401 (2012).

Surface Hubbard U fcc Al (3 p) Competing effects at surfaces § Reduced screening volume: U § Electronic structure effects : U Surface band narrowing Volume effect is dominating: March 22, 2013 E. Sasioglu, C. Friedrich, and S. Blugel, Folie 8 Phys. Rev. Lett. 109, 146401 (2012).

Surface Hubbard U bcc Cr (3 d) Competing effects at surfaces § Reduced screening volume: U § Electronic structure effects : U Surface band narrowing Electronic structure effects are dominating: March 22, 2013 Folie 9

Surface Hubbard U 3 d transition metals (100 and 110 surfaces and bulk) Hubbard U Fully screened U U bcc (V, Cr, Mn, Fe) ~30% March 22, 2013 fcc (Sc, Ti, Co, Ni, Cu) ~40% E. Sasioglu, C. Friedrich, and S. Blugel, Phys. Rev. Lett. 109, 146401 (2012). Folie 10

Surface Hubbard U for insulators: Na. Cl (Cl-3 p) Na. Cl 100 surface Na. Cl 110 surface Surface states March 22, 2013 Folie 11

Surface Hubbard U for insulators: Mg. O (O-2 p) Mg. O 100 surface Mg. O 110 surface U = 6. 38 U = 6. 95 U = 7. 08 U = 7. 10 U = 7. 23 U = 7. 18 U = 7. 15 U = 7. 12 U = 7. 11 U = 7. 10 Surface states March 22, 2013 Folie 12

Surface Hubbard U Frequency depence of the Hubbard U: bcc Cr U Competing effects at surfaces § Reduced screening volume: U § Electronic structure effects : U March 22, 2013 ( >3 e. V ) ( <3 e. V ) E. Sasioglu, C. Friedrich, and S. Blugel, Folie 13 Phys. Rev. Lett. 109, 146401 (2012).

Conclusions § Employing the constrained RPA method we have determined the strength of the Hubbard U parameter at metal and insulator surfaces. § We showed that U does not always increase at the surface as commonly expected. It decreases at most of the transition metal surface as well as insulator surfaces with pronounced surface states. § We found that surface states and the effective band narrowing play an important role for the strength of the Hubbard U at surfaces. § At the surface the U parameter depends more strongly on the frequency than in the bulk. Acknowledgments March 22, 2013 Folie 14