peter blaha - tu wiensusi.theochem.tuwien.ac.at/events/ws2019/blaha-hyperfine.pdf · peter blaha...
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Hyperfine interactionsMössbauer, PAC and NMR Spectroscopy:
Quadrupole splittings, Isomer shifts, Hyperfine fields (NMR shifts)
Peter BlahaInstitute of Materials Chemistry
TU Wien
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Definition of Hyperfine Interactions
hyperfine interactions=
all aspects of nucleus-electron interactions which go beyond an electric point charge for a nucleus
and ismeasured at the nucleus
(affects the nucleus)
===> information about nucleus and the electron (spin) density around it
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description of the nucleus:
electric point charge (Z/r)
nucleus with volume, shape and magnetic moment
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How to measure hyperfine interactions ?
NMRNQRMössbauer spectroscopyTDPAC
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Electric Hyperfine-Interaction
between nuclear charge distribution () and external potential
Taylor-expansion at the nuclear position dxxVxE n )()(
ijji
ji
ii i
dxxxxxx
V
dxxxx
V
ZVE
)()0(21
)()0(
2
0
direction independent constant(monopole interaction)
electric field xnuclear dipol moment (=0)
electric fieldgradient xnuclear quadrupol moment Q
higher terms neglected
nucleus with charge Z, but not a sphere (I>1/2)
( V00(r) n(x) )
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Mössbauer effect:
•Recoil-free, resonant absorption and emission of -rays by a nucleus. 1958 by Rudolf Mößbauer ( Nobelprice 1963)
•The decay of a radioactive nucleus produces a highly excited isotope of a neighboring element (Z-1).
•This isotope can get into its ground state by emission of -photons (recoil-free, otherwise E-loss; requires a “solid”, no phonon excitation; the “source”) !.
•The nucleus in the “probe” can absorb this photon (of eg. 14.4 keV), but the nuclear level splitting will be slightly modified by the chemical environment of the probe (only by ~ 10 neV !!!). Bring them in resonancewith the Doppler effect (mm/s) !
•The most important isotopes are: 57Fe, Sn, Sb, Te, I, W, Ir, Au, Eu and Gd.
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Electric monopole interaction
Mössbauer Isomer Shift : integral over nuclear radius of electron density x nuclear charge nuclear radii are different for ground and excited state
)0()0(
)0()0(
/~~22
QA
QAQA
QA
RR
smmneVEE
bcc Fe
(57Fe)=-0.24 mm/s a03
large (0) neg. IS
Fe2+, Fe3+,…
:RTOxxx = (0)
14keV
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Quadrupole interaction
ij
ij QVE21
Q(57Fe)=0.16 barn
cc
bc
ac
cb
bb
ab
ca
ba
aa
VVV
VVV
VVV
zz
yy
xx
VV
V00
0
0
00
0 zzyyxx VVV
|Vzz| ≥ |Vyy| ≥ |Vxx|
//////
zz
xxyy
VVV
jiij xx
VV
)0(2
similarity transformation
with
EFG characterized by principal component Vzzand asymmetry parameter
31
21 2
zzeQVQS
Vij: traceless 3x3 tensor of electric field gradient EFG
(2nd derivative of V(0))
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First-principles calculation of EFG
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ij
ij QVE21
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theoretical EFG calculations
alinterstiti.....
.)(;;ˆ)(
:iondecomposit orbital
alinterstiti)(
)()(
)(
:iondecomposit spatial
,,,.,2020
320
int
33
2033
203
320
*
ddzz
ppzzzz
mmllnk
nkml
nklm
spherezz
erstitalsphere
LMLMLM
zz
VVV
contrdsddpprdYr
drr
rV
rdr
Yrrdr
YYrrd
rYrV
We write the charge density and the potential inside the atomic spheres in a lattice-harmonics expansion
jiijc
LMLMLM xx
VVrdrr
rrVrYrr
)0(;)()();ˆ()()(2
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theoretical EFG calculations
222 )(211
)(211
.....
3
3
zyzxzyxxyd
ddzz
zyxp
ppzz
ddzz
ppzzzz
dddddr
V
pppr
V
VVV
• EFG is proportial to differences of orbital occupations ,e.g. between px,py and pz.
• if these occupancies are the same by symmetry (cubic): Vzz=0• with “axial” (hexagonal, tetragonal) symmetry (px=py): =0
In the following various examples will be presented.
interstitial
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EFG (1021 V/m2) in YBa2Cu3O7
Site Vxx Vyy Vzz Y theory -0.9 2.9 -2.0 0.4 exp. - - - - Ba theory -8.7 -1.0 9.7 0.8 exp. 8.4 0.3 8.7 0.9 Cu(1) theory -5.2 6.6 -1.5 0.6 exp. 7.4 7.5 0.1 1.0 Cu(2) theory 2.6 2.4 -5.0 0.0 standard LDA calculations give exp. 6.2 6.2 12.3 0.0 good EFGs for all sites except Cu(2) O(1) theory -5.7 17.9 -12.2 0.4 exp. 6.1 17.3 12.1 0.3 O(2) theory 12.3 -7.5 -4.8 0.2 exp. 10.5 6.3 4.1 0.2 O(3) theory -7.5 12.5 -5.0 0.2 exp. 6.3 10.2 3.9 0.2 O(4) theory -4.7 -7.1 11.8 0.2 exp. 4.0 7.6 11.6 0.3
K.Schwarz, C.Ambrosch-Draxl, P.Blaha, Phys.Rev. B42, 2051 (1990) D.J.Singh, K.Schwarz, K.Schwarz, Phys.Rev. B46, 5849 (1992)
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EFG in YBa2Cu3O7
Interpretation of the EFG at the oxygen sites
px py pz Vaa Vbb Vcc
O(1) 1.18 0.91 1.25 -6.1 18.3 -12.2
O(2) 1.01 1.21 1.18 11.8 -7.0 -4.8
O(3) 1.21 1.00 1.18 -7.0 11.9 -4.9
O(4) 1.18 1.19 0.99 -4.7 -7.0 11.7
ppp
zz rnV 3
1)(
21
yxzp pppn
Asymmetry count EFG (p-contribution)
EFG is proportional to asymmetric charge distributionaround given nucleus
Cu1-d
O1-py
EF
partly occupied
y
x
z
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Cu(2) and O(4) EFG as function of r
EFG is determined by the non-spherical charge density inside sphere
Cu(2)
O(4)
drrrdrr
YrVYrr zzLM
LMLM )()()()( 20320
final EFG
r
r r
rr
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EFG contributions:
Depending on the atom, the main EFG-contributions come from anisotropies (in occupation or wave function) semicore p-states (eg. Ti 3p much more important than Cu 3p) valence p-states (eg. O 2p or Cu 4p) valence d-states (eg. TM 3d,4d,5d states; in metals “small”) valence f-states (only for “localized” 4f,5f systems)
usually only contributions within the first nodeor within 1 bohr are important.
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LDA problems in Cuprates
Undoped Cuprates (La2CuO4, YBa2Cu3O6) are nonmagnetic metals instead of antiferromagnetic insulators
Both, doped and undoped cuprates have a “planar Cu” – EFG which is by a factor of 2-3 too small
We need a method which giver a better description of correlated 3d electrons: can LDA+U fix these problems ??
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Magn. moments and EFG in La2CuO4
LDA+U gives AF insulator with reasonable moment
U of 5-6 eV gives exp. EFG
GGAs “mimic” a Uof 1-2 eV(EV-GGA more effectivethan PBE, but very bad E-tot !!)
AMF FLL
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EFG: Sensitivity to the DFT-functional
(for this set of compounds)
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Magnetic hyperfine interaction
Zeman - interaction between magnetic moment I of the nucleus and the external magnetic field B (at the nucleus, produced by the spin-polarized e-
in a FM)
)0()0( B
B proportional to thespindensity at the nucleus
B often proportional tothe magnetic momentof an atom in a solid.
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magnetic fields at nucleus:
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Magnetic fields at the nucleus:
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How to do it in WIEN2k:
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Verwey transition in YBaFe2O5
charge ordered (CO) phase: valence mixed (VM) phase:Pmma a:b:c=2.09:1:1.96 (20K) Pmmm a:b:c=1.003:1:1.93 (340K)
Fe2+ and Fe3+ form chains along b contradicts Anderson charge-ordering conditions with minimal electrostatic
repulsion (checkerboard like pattern) has to be compensated by orbital ordering and e--lattice coupling
ab
c
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DOS: GGA+U vs. GGAGGA+U GGA
insulator, t2g band splits metallic single lower Hubbard-band in VM splits in CO with Fe3+ states lower than Fe2+
insulator metalGGA+U
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Difference densities =cryst-atsup
CO phase VM phaseFe2+: d-xzFe3+: d-x2
O1 and O3: polarized toward Fe3+
Fe: d-z2 Fe-Fe interactionO: symmetric
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Mössbauer spectroscopy
CO
VM
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Isomer shift: charge transfer too small in LDA/GGA
CO
VM
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Hyperfine fields: Fe2+ has large Borb and Bdip
CO
VM
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EFG: Fe2+ has too small anisotropy in LDA/GGA
CO
VM
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conversion of exp. data to EFGs
Mössbauer: {e Q Vzz(1+2/3)1/2} / 2 ; (E ) / c (e Q c Vzz) / 2 E Q(57Fe)=0.16 b; E =14410 eV
Vzz [1021 V/m2] = 6 * [mm/s]
NMR: vQ = (3 e Q Vzz) / {2 h I (2 I – 1)} I .. nuclear spin quantum n.
Vzz [1021 V/m2] = 4.135 1019 vQ [MHz] / Q [b] Q(49Ti)=0.247 b