Hyperfine interactions (and how to do it in WIEN2k) [email protected] Department of...

hyperfine interactions(and how to do it in WIEN2k)

[email protected]

Department of Materials Science and Engineering

Stefaan Cottenier

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

Slide by K. Schwarz

Slide by K. Schwarz

nuclear point chargesinteracting with

electron charge distribution

hyperfine interaction

all aspects of the nucleus-electron interaction

that go beyond the nucleus as an electric point charge.

=

Definition :

electricpoint

charge

electricpoint

charge

• volume• shape

N

S

electricpoint

charge

• volume• shape• magnetic moment

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)


• Definitions

• magnetic hyperfine interaction

• electric quadrupole interaction

• isomer shift

• summary

Content

N

S

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

Ener

gy (u

nits

: B)

E

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

Ener

gy (u

nits

: B)

E

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

Ener

gy (u

nits

: B)

E

Classical Quantum(=quantization)

e.g. I =1

m =+1

m =0

m =-1

-1.5

-1

-0.5

0

0.5

1

1.5

0 30 60 90 120 150 180

Ener

gy (u

nits

: B)

E

Classical Quantum(=quantization)

e.g. I =1

m =+1

m =0

m =-1

Hamiltonian :

nuclear property electron property

N

S

(vector) (vector)

interaction energy (dot product) :

Btot = Bdip + Borb + Bfermi + Blat

Source of magnetic fields at the nuclear site in an atom/solid


Bdip = electron as bar magnet




rv

-e

L

Borb

Morb

I

Borb = electron as current loop




rv

-e

L

Borb

Morb

I


BFermi = electron in nucleus

2s

2p




rv

-e

L

Borb

Morb

I


BFermi = electron in nucleus

2s

2p


Blat = neighbours as bar magnets

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)

How to do it in WIEN2k ?

• Definitions



• isomer shift

• summary

Content

• Force on a point charge:

• Force on a point charge:

• Force on a general charge:

-Q

-Q

-Q

-Q

0 30 60 90 120 150 180

-4.05

-4.04

-4.03

-4.02

-4.01

-4.00

-3.99

-3.98

-3.97

-3.96

-3.95

E-tm0

(deg)

Ener

gy (u

nits

e2 /

4 0

)

2

(deg)

Ener

gy (u

nits

e2 /

4 0

)

0 30 60 90 120 150 180

-4.05

-4.04

-4.03

-4.02

-4.01

-4.00

-3.99

-3.98

-3.97

-3.96

-3.95

E-tm0

0 30 60 90 120 150 180

-4.05

-4.04

-4.03

-4.02

-4.01

-4.00

-3.99

-3.98

-3.97

-3.96

-3.95

E-tm0

(deg)

Ener

gy (u

nits

e2 /

4 0

)

m=1

m=0

e.g. I = 1

nuclear property electron property(tensor – rank 2 )


(tensor – rank 2 )


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)

more info:• Blaha, Schwarz, Dederichs, PRB 37 (1988) 2792• EFG document in wien2k FAQ (Katrin Koch, SC)

}5 degrees of freedom

• Definitions



• isomer shift

• summary

Content

0 30 60 90 120 150 180

-4.20

-4.15

-4.10

-4.05

-4.00

-3.95

-3.90

E-tm0E-tmAE-tmB

(deg)

Inte

ract

ion

Ene

rgy

(e2/

4

0)

No no with

nuclear property electron property(scalar )


(scalar )

R

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)

• Definitions



• isomer shift

• summary

Content

rank nuclear property electron property(dot product)

0

1

2

R

B


0

1

2

R

B

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

WIEN2k calculations :PRB 70 (2004) 155418PRB 70 (2004) 155419

B


0

1

2

R

B

N

SNMR chemical shift (‘isotropic’ = scalar):

How does the magnetic hyperfine field change upon an externally applied magnetic field ?

B

N

S

B

N

S

NMR chemical shift (‘anisotropic’ = tensor) :

How does this change depend on the orientation of the applied field ?

exerciseCalculate magnetic hyperfine field, electric-field gradient and intranuclear electron charge densityfor all three inequivalent Fe-sites in ferromagnetic Fe4N, with and without spin-orbit coupling:

Vzz = …(0) = …

B


0

1

2

R

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

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

Hyperfine interactions (and how to do it in WIEN2k) [email protected] Department of...

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Transcript of Hyperfine interactions (and how to do it in WIEN2k) [email protected] Department of...