5.3 Experimental Techniques
5.3.1 Measuring Electron Polarisation
The SiV0 has D
3d symmetry [146], S = 1 and a positive zero-field splitting (D) of 942 MHz at 300 K [80, 70]. This results in ground state splitting into ms =
−1,0,+1 states. An ensemble of randomly orientated SiV0 centres results in an
EPR spectra with four pairs of lines, each arising from an ensemble of centres at one of the four equivalent h111i orientations. The field position of the lines depends on the angle between the symmetry axis h111i and the magnetic field direction. When the field direction is along one of the h111i type directions one pair of lines is created by the centres parallel to the field. The three other pairs of lines now appear on top of each other as they make the same angle to the field direction, 109◦. In the absence of preferential orientation and microwave power saturation this gives EPR signals with ratios 1:3:3:1 for a dark spectrum. In the light, electron spin polarisation will cause an increase in absorption and emission from the defects which are parallel to the magnetic field. An example of such a spectra is shown in figure 5.3.
As can be seen from figure 5.3 the two outermost lines are much larger than the others; one in emission and one in absorption. This sample was illuminated during this scan and this has the effect of enhancing the population of the ms = 0 level. The difference between an illuminated and an unilluminated scan can be seen in figure 5.4. The inset in this figure shows a higher population in the ms = 0 level when the centre is polarised which causes absorption and emission into the ms = +1 level and ms = −1 level respectively, and hence an increase in these
Figure 5.3: Spectra of an ensemble of polarised silicon vacancy centres. Data taken at 100 K with illumination from a 532 nm laser diode. The field direction is parallel toh111i. The red arrows mark the two pairs of three equivalent sites which are 109◦ to the field direction. The two outermost lines arise from the one site whose symmetry axis is parallel to the field, shown in more detail in the graphs at either side.
lines. It is also clear from these spectra that spin polarisation efficiency is highly dependent on orientation within the magnetic field as it is only the outermost lines (those with symmetry axis parallel to the magnetic field) which show a large change under electron spin polarisation.
For the results presented in this chapter the degree of electron spin polarisation had to be quantified in order to discover which wavelengths of light were most efficient at generating spin polarisation.
Calculating the Electron Spin Polarisation
The electron spin polarisation was measured by comparing the pair of EPR lines which belong to the same orientation; the one with its symmetry axis parallel to the magnetic field direction. The lines were fitted and their intensity was calculated. This was compared to the EPR line’s intensity without illumination in order to quantify the degree of enhancement. At most temperatures below room temperature the unilluminated cw EPR lines were microwave power saturated. This meant with the spectrometers available it was not possible to use a low enough microwave power that the transitions could relax at a sufficient rate to keep the spin populations at equilibrium values. This was especially true at liquid
Figure 5.4: EPR signal without illumination at 292 K (red) and with illumination at 10 K (blue). The inset shows spin levels of the SiV0 ground state in both the unpolarised (where the ms = 0→ +1 transition creates the low field line and the
ms =−1→ 0 transition creates the high field line) and polarised state (where the
ms= 0→+1 transition creates the low field line and thems=−1←0 transition
creates the high field line). Not a true representation of line width due to over modulation. Image after [145].
numbers had been determined the electron spin polarisation percentage can then be calculated by comparing the light and dark occupation probabilities of the po- larised level, the ms = 0 level. The assumption is made, for the purpose of this calculation, that the ms = ±1 states have equal populations. At the fields at which these measurements were taken (∼3000 G) thems= +1 is the highest spin level,ms= 0 is the middle and ms =−1 is the lowest. This can be surmised from the sign of the zero-field splitting [80]. For a spectrum like figure5.4 the low field line arises from absorption in the ms = 0→+1 transition and the high field line arises from emission in the ms =−1←0 transition.
The spin occupation probabilities of the levels in the dark can be calculated using Boltzmann statistics and are labelled pd−1, pd0 and pd+1 respectively. It is assumed that, as demonstrated in equation 5.2, the total population of the ground state is not changing; the defect concentration is remaining the same and not transferring into a long lived excited state.
pd−1+pd0+pd+1 = 1 (5.2) The energies of the different levels are given by E+1, E0 and E−1. The energy
separations between the different spin levels can thus be calculated;0,+1 =E+1−
E0 and−1,0 =E0−E−1. The dark occupation probabilities are given by equations
5.3, 5.4 and 5.5. pd−1 = 1 Z (5.3) pd0 = exp(−−1,0/kBT) Z (5.4) pd+1 = exp(−(ε0,+1+ε−1,0)/kBT) Z (5.5)
Z is the partition function and is given by equation 5.6. Z = 1 +exp − −1,0 kBT +exp −(−1,0+0,+1) kBT ! (5.6) The difference in occupation probabilities is given by η. The EPR intensities are proportional to η as this gives a likelihood of transition. In equation 5.7 and 5.8 the subscript +1,0 indicates the transition of the low field line and 0,−1 of the high field line.
η+1,0 =p0−p+1 (5.7)
η0,−1 =p−1−p0 (5.8)
In order to calculate the occupation probabilities in the light,ηlmust be calculated. Thus the ratio of the occupation probability differences is equal to that of the EPR intensities in the light and dark, as given by equation 5.9.
ηl ηd =
Il
Id (5.9)
However,Id is unknown because at low temperatures microwave power saturation causes the signal to become unquantifiable as discussed previously. It is known at room temperature where microwave power saturation does not occur. The theoretical dark intensity can be calculated, as shown in equation 5.10, by using the intensity at room temperature and the occupation probability differences, as calculated previously using Boltzmann statistics.
Id T IRTd = ηd T ηRTd (5.10)
The theoretical occupation probability difference can then be calculated from the intensity of the EPR line in the light using equation 5.11.
ηlT =ηTdI l T Id T =ηRTd I l T Id RT (5.11) Using equations5.2,5.7, 5.8and5.11 the theoretic occupation probabilities in the light can now be calculated using the light and dark intensities. This is shown in equations 5.12, 5.13 and 5.14. pl+1 = 1 3 1−2 ηdRT ITl Id RT ! +1,0 − ηRTd I l T Id RT ! 0,−1 (5.12)
ξ= p l 0−pd0 pd +1+pd−1 ×100% (5.15)
Once the percentage electron spin polarisation can be calculated, for different of wavelengths, temperatures and samples, it can be compared.