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UNTERRICHT
A z
B
C
secular
forbidden
transition
FIG. 16: Principle of three-pulse ESEEM. (A) Electron-nuclear forbidden transitions
occur since the nuclear spin has different quantization axes for the
electron spin α and β states. This is because the hyperfine coupling (magenta)
has different signs for the two states and is comparable to the nuclear Zeeman
interaction (dark blue). When the electron spin is flipped to its β state, the
longitudinal nuclear magnetization for the former α electron spin state is partially
converted to transversal magnetization and starts to precess about the
new quantization axis (green). (B) Level scheme for a system consisting of an
electron spin S = 1/2 (red) and a nuclear spin I = 1/2 (blue). Transitions with
mw frequencies are shown red, transitions with Τ frequencies blue. (C) Pulse
sequence of the three-puIse ESEEM experiment with transition types for one
of the coherence transfer pathways that lead to modulation of the stimulated
echo with nuclear frequencies.
The stimulated echo formed after another delay time Τ is thus
superimposed by a modulation with nuclear frequencies ωα,
and ωβ. The ESEEM spectrum is obtained by subtracting the
unmodulated part of the echo decay, which originates from coherence
transfer pathways with only allowed transitions, and
Fourier transformation of the nuclear frequency oscillations.
IX. BOX 5
A/2
- A/2
- B/2 B/2
electron/nuclear nuclear
/2
coherence
/2
coherence
/2
electron
coherence
T
allowed
transition
I
pseudosecular
x
forbidden
transition
nuclear modulation
of electron spin
echo decay
In order to separate the interaction between two electron spins
from other interactions two mw fi elds with different frequencies
are used to excite them individually (“two color excitation“).
At the observer frequency an echo experiment is performed,
which refocusses all interactions of the observed A spins that
110
allowed electron
forbidden
forbidden
nuclear
nuclear
allowed electron
lead to inhomogeneous line broadening. At a variable time
during the pulse sequence an mw π pulse is applied at the
(different) pump frequency. This pulse exclusively excites another
set of spins (B spins), if the frequency separation is much
larger than both the homogeneous line width of spin packets A
and B and the excitation bandwidth of the pulses.
The local fi eld induced at the A spin by a B spin is thus inverted,
which leads to a shift of tbe resonance frequency of the
A spin, determined by the dipole-dipole coupling (see Fig. 17).
This frequency shift is observed as a modulation of the echo
signal as a function of the position of the pump pulse in the
sequence 15,16 .
For a well defi ned distance r the oscillation frequency is proportional
to r –3 with a proportionality constant that can be computed
from fi rst principles. Exact distance measurements are thus
possible without calibration. For disordered structures the observed
time dependence can be
A
B
BUNSEN-MAGAZIN · 10. JAHRGANG · 3/2008
local field inverted local field
pump
pulse
dd A 2
dd B 2
dd
A
2
dd
B
2
dd B 2
dd
A
2
dd
B
2
dd
A
2
FIG. 17: Principle of the DEER experiment. (A) The π pump pulse inverts the
B spin (red) and thus the local field at the A spin (green). (B) This inversion
causes a transfer of an electron coherence (wavy lines) between the two transitions
belonging to the dipolar doublet of the A spin. The resonance frequency
changes by the dipole-dipole coupling ωdd. An analogous local field inversion
and coherence transfer is effected by the π pulse in the HYSCORE experiment,
with the nuclear spin substituting for the observer A spin and the electron spin
for the pumped B spin.
directly converted into a distance distribution using appropriate
transformations 4,17,18 .