1. hyperfine interactions (and how to do it in WIEN2k)
Stefaan Cottenier
Department of Materials Science and Engineering
hyperfine interactions (and how to do it in WIEN2k)

3. Slide by K. Schwarz

4. nuclear point charges interacting with electron charge distribution
Slide by K. Schwarz

5. Definition : hyperfine interaction =
all aspects of the nucleus-electron interaction that go beyond the nucleus as an electric point charge.

6. electric point charge

7. electric point charge
volume
shape

8. electric point charge N
volume
shape
magnetic moment S

9. How to measure hyperfine interactions ?
NMR
NQR
Mössbauer spectroscopy
TDPAC
Laser spectroscopy
LTNO
NMR/ON
PAD …

10. How to measure hyperfine interactions ?
NMR
NQR
Mössbauer spectroscopy
TDPAC
Laser spectroscopy
LTNO
NMR/ON
PAD …
This talk:
Hyperfine physics
How to calculate with WIEN2k
NOT :
What are these useful for ? (touched in final slides)

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

14. S N

15. N S

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

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

27. interaction energy (dot product) :
nuclear property
electron property
(vector)
(vector) S N
interaction energy (dot product) :

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

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

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

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

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

37. Force on a point charge:
Force on 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
Energy (units e2/40)
e.g. I = 1
m=1

45. interaction energy (dot product) :
nuclear property
electron property
(tensor – rank 2 )
(tensor – rank 2 )
interaction energy (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 

53. interaction energy (dot product) :
nuclear property
electron property
(scalar )
(scalar ) R
interaction energy (dot product) :

54. How to do it in WIEN2k ? Isomer shift calculations
In regular scf file:
:RTOxxx
= electron density near the nucleus of atom xxx (i.e. at the first radial mesh point, typically au)

55. Content Definitions magnetic hyperfine interaction
electric quadrupole interaction
isomer shift
summary

56. rank nuclear property  electron property
(dot product) R 1 B 2

57. How to measure hyperfine interactions ?
NMR
NQR
Mössbauer spectroscopy
TDPAC
Laser spectroscopy
LTNO
NMR/ON
PAD …

58. rank nuclear property  electron property
(dot product) R 1 B 2

59. rank nuclear property  electron property
(dot product) R 1 B 2

60. Experiments :
T. Klas et al., Surf. Science 216 (1989)
G. Krausch et al., Hyp. Int. 78 (1993)
H. Haas, Z. Naturforsch. 50a (1994)
… and many others
WIEN2k calculations :
PRB 70 (2004)
PRB 70 (2004)

61. Experiments :
T. Klas et al., Surf. Science 216 (1989)
G. Krausch et al., Hyp. Int. 78 (1993)
H. Haas, Z. Naturforsch. 50a (1994)
… and many others
WIEN2k calculations :
PRB 70 (2004)
PRB 70 (2004)

62. rank nuclear property  electron property
(dot product) 1 2 R B

64. B

65. S N NMR chemical shift (‘isotropic’ = scalar):
How does the magnetic hyperfine field change upon an externally applied magnetic field ? N S B

66. N S B

67. N S B

68. S N B NMR chemical shift (‘anisotropic’ = tensor) :
How does this change depend on the orientation of the applied field ?

69. exercise
Calculate magnetic hyperfine field, electric-field gradient and intranuclear electron charge density for all three inequivalent Fe-sites in ferromagnetic Fe4N, with and without spin-orbit coupling:
Vzz = …
(0) = …

71. rank nuclear property  electron property
(dot product) 1 2 R B

73. What matters here is the potential at the nucleus, not the field or the gradient.

74. What matters here is the non-zero dimension of the nucleus, not its asphericity.