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) stefaan.cottenier@ugent.be

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

Slide by K. Schwarz

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

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

electric point charge

electric point charge volume shape

electric point charge N volume shape magnetic moment S

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

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)

Content Definitions magnetic hyperfine interaction electric quadrupole interaction isomer shift summary

S N

N S

S N

S N

S N

S E Energy (units: B) N

S E Energy (units: B) N

S E Energy (units: B) N

S E Energy (units: B) N

S E Energy (units: B) N

E Energy (units: B)

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

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

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

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

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

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

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

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

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)

Content Definitions magnetic hyperfine interaction electric quadrupole interaction isomer shift summary

Force on a point charge:

Force on a point charge: Force on a general charge:

-Q -Q

-Q -Q

-Q -Q

-Q 2

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

 (deg) Energy (units e2/40)

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

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

} 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)

Content Definitions magnetic hyperfine interaction electric quadrupole interaction isomer shift summary

No no  with 

No no  with 

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

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 0.0005 au)

Content Definitions magnetic hyperfine interaction electric quadrupole interaction isomer shift summary

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

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

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

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

Experiments : T. Klas et al., Surf. Science 216 (1989) 270-302 G. Krausch et al., Hyp. Int. 78 (1993) 261-280 H. Haas, Z. Naturforsch. 50a (1994) 407-417 … and many others WIEN2k calculations : PRB 70 (2004) 155418 PRB 70 (2004) 155419

Experiments : T. Klas et al., Surf. Science 216 (1989) 270-302 G. Krausch et al., Hyp. Int. 78 (1993) 261-280 H. Haas, Z. Naturforsch. 50a (1994) 407-417 … and many others WIEN2k calculations : PRB 70 (2004) 155418 PRB 70 (2004) 155419

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

B

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

N S B

N S B

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

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) = …

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

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

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