Defects in inorganic photorefractive materials and their investigations
Defects in inorganic photorefractive materials and their investigations
Defects in inorganic photorefractive materials and their investigations
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<strong>Defects</strong> <strong>in</strong> <strong>in</strong>organic <strong>photorefractive</strong> <strong>materials</strong> <strong>and</strong> <strong>their</strong> <strong>in</strong>vestigations 7<br />
the last one the hyperf<strong>in</strong>e <strong>in</strong>teraction. Here µ B is the Bohr magneton, B the<br />
external magnetic field vector, g the tensor of the Zeeman <strong>in</strong>teraction, S the<br />
sp<strong>in</strong> operator (2S + 1 is the multiplicity of the lowest level considered), D a<br />
crystal field tensor, I i the sp<strong>in</strong> operator of nucleus i <strong>and</strong> A i the tensor of the<br />
hyperf<strong>in</strong>e <strong>in</strong>teraction. The Hamiltonian usually operates only on the (2S +1)<br />
lowest states <strong>and</strong> is thus called a sp<strong>in</strong>-Hamiltonian.<br />
Fig. 4. Basic schemes for paramagnetic resonance <strong>and</strong> related methods, demonstrated<br />
for one electron sp<strong>in</strong>, S = 1 . 2<br />
EPR: One transition occurs between the m s = ± 1 states, Zeeman - split by a static<br />
2<br />
magnetic field B. Obta<strong>in</strong>ed <strong>in</strong>formation: magnitude <strong>and</strong> angular dependence (symmetry)<br />
of splitt<strong>in</strong>g factor g <strong>and</strong> value of crystal field (for S> 1 only). In general:<br />
2<br />
sp<strong>in</strong> value S, related to defect charge state.<br />
ENDOR: If the electron <strong>in</strong>teracts with one nucleus, assumed to have nuclear sp<strong>in</strong><br />
I = 1 , the <strong>in</strong>dicated additional nuclear splitt<strong>in</strong>gs occur. The double arrow nuclear<br />
2<br />
transitions are detected by changes of the EPR signals (wavy arrows). Information:<br />
nuclear sp<strong>in</strong>(s), nuclear splitt<strong>in</strong>g factor g n <strong>and</strong> the magnitude <strong>and</strong> angular dependence<br />
of the hyperf<strong>in</strong>e <strong>in</strong>teraction.<br />
ODMR via MCD: Optical excitations with left- <strong>and</strong> right-circular polarized light<br />
orig<strong>in</strong>ate from different Zeeman-EPR sublevels, as shown. The EPR transition (wavy<br />
arrow) decreases the population difference of these sublevels. The EPR is detected<br />
by the change of the MCD signal, ∆α = α + − α −. Information: EPR parameters<br />
<strong>and</strong> the optical absorption b<strong>and</strong>s orig<strong>in</strong>at<strong>in</strong>g from the ground state Zeeman levels.<br />
The energy splitt<strong>in</strong>gs described by a Hamiltonian of this type are generally<br />
monitored by unbalanc<strong>in</strong>g a microwave bridge circuit when the supplied<br />
microwave energy matches the energy splitt<strong>in</strong>gs, i.e. when the resonance condition<br />
is fulfilled (Fig. 4). Because the population difference of the levels, ∆n,<br />
behaves as<br />
∆n = tanh(µ B gB/2kT), (2)