hyperfine interactions (and how to do it in WIEN2k)

1. Department of MaterialsScienceand Engineering StefaanCottenier hyperfineinteractions(and how to do it in WIEN2k) stefaan.cottenier@ugent.be

2. http://www.hfinqi.consec.com.au/

3. Slideby K. Schwarz

4. nuclear point chargesinteractingwithelectron charge distribution Slideby K. Schwarz

5. Definition : hyperfineinteraction = all aspects of the nucleus-electroninteractionthat go beyondthe nucleus as anelectric point charge.

6. electricpointcharge

7. electricpointcharge • volume • shape

8. electricpointcharge N • volume • shape • magnetic moment S

9. How to measurehyperfineinteractions ? • NMR • NQR • Mössbauerspectroscopy • TDPAC • Laser spectroscopy • LTNO • NMR/ON • PAD • …

10. How to measurehyperfineinteractions ? • NMR • NQR • Mössbauerspectroscopy • TDPAC • Laser spectroscopy • LTNO • NMR/ON • PAD • … • This talk: • Hyperfinephysics • How to calculatewith WIEN2k • NOT : • What are these usefulfor ? (touched in finalslides)

11. Content • Definitions • magnetic hyperfine interaction • electric quadrupole interaction • isomer shift • summary

14. S N

15. S N

16. S N

17. S N

18. S N

19. S E Energy (units: B) N

20. S E Energy (units: B) N

21. S E Energy (units: B) N

22. S E Energy (units: B) N

23. S E Energy (units: B) N

24. E Energy (units: B)

25. Classical Quantum(=quantization) E m =-1 m =0 Energy (units: B) m =+1 e.g. I =1

26. Classical Quantum(=quantization) E m =-1 m =0 Energy (units: B) m =+1 e.g. I =1 Hamiltonian :

27. nuclearproperty electronproperty (vector) (vector) S N interactionenergy(dot product) :

28. Source of magnetic fields at the nuclear site in an atom/solid Btot = Bdip + Borb + Bfermi+ Blat

29. Bdip = electron as bar magnet Source of magnetic fields at the nuclear site in an atom/solid Btot = Bdip + Borb + Bfermi+ Blat

30. Bdip = electron as bar magnet L r I v -e Morb Borb Source of magnetic fields at the nuclear site in an atom/solid Btot = Bdip + Borb + Bfermi+ Blat • Borb = electron as current loop

31. Bdip = electron as bar magnet L r I v -e Morb Borb 2s 2p Source of magnetic fields at the nuclear site in an atom/solid Btot = Bdip + Borb + Bfermi+ Blat • Borb = electron as current loop • BFermi = electron in nucleus

32. Bdip = electron as bar magnet L r I v -e Morb Borb 2s 2p Source of magnetic fields at the nuclear site in an atom/solid Btot = Bdip + Borb + Bfermi+ Blat • Borb = electron as current loop • BFermi = electron in nucleus • Blat= neighbours as bar magnets

33. How to do it in WIEN2k ? • Magnetic hyperfine field • In regular scf file: • :HFFxxx(Fermi contact contribution) • After post-processing with LAPWDM : • orbital hyperfine field (“3 3” in case.indmc) • dipolar hyperfine field (“3 5” in case.indmc) • in case.scfdmup • After post-processing with DIPAN : • lattice contribution • in case.outputdipan more info: UG 7.8 (lapwdm) UG 8.3 (dipan)

34. Content • Definitions • magnetic hyperfine interaction • electric quadrupole interaction • isomer shift • summary

36. Forceon a point charge:

37. Forceon a point charge: • Forceon a general charge:

38. -Q -Q

39. -Q -Q

40. -Q -Q

41. -Q 2

42. -Q  (deg) Energy (units e2/40) 2 -Q

43.  (deg) Energy (units e2/40)

44.  (deg) m=0 e.g. I = 1 Energy (units e2/40) m=1

45. nuclearproperty electronproperty (tensor – rank 2 ) (tensor – rank 2 ) interactionenergy(dot product) :

46. How to do it in WIEN2k ? Electric-field gradient In regular scf file: :EFGxxx :ETAxxx Main directions of the EFG Full analysis printed in case.output2 if EFG keyword in case.in2 is put (UG 7.6) (split into many different contributions) } 5 degrees of freedom • more info: • Blaha, Schwarz, Dederichs, PRB 37 (1988) 2792 • EFG document in wien2k FAQ (Katrin Koch, SC)

47. Content • Definitions • magnetic hyperfine interaction • electric quadrupole interaction • isomer shift • summary

48. No no with 

49. No no with 