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2009 SEMICONDUCTORS AND NANOSTRUCTURESOn the trigonal field acting at the Cr 3+ ( 2 E states) in RubyAs the magnetic field breaks the time-reversal symmetry,magneto-optical spectroscopy allows to unravel details intransition-metal ions electronic structure by producing efficientlifts of degeneracy. In particular, interaction betweenelectronic spin and orbital magnetic moments with an appliedmagnetic field B yield a splitting of electronic states,namely the well-known Zeeman effect.Representative results are shown in figure 54. In particular,the observed splitting in very high field above 50 T unveilsthe existence of two parameters ∆ 1 and ∆ 2 ; the deviation ofthe excited state Landé factor from the value of the groundstate factor g 0 (see figure 55). Under high pressure, thesecoefficients exhibit a significant linear increase that unveilsan unexpected increase of the trigonal field under pressure.The relative enhancement of the trigonal field matrix element< k| =< t 2g |V tr |t 2g > is 6.2 × 10 −3 /GPa.In fact there are two contributions to the pressure dependenceof the trigonal crystal-field energy. The first one isexplicit and positive and scales with the trigonal coordinateQ t , whereas the second term depends implicitly on the evolutionof the system sensitivity to the trigonal distortion i.e.on the changes of the coupling parameter with pressure at aconstant Q t value. Crystallographic data under pressure onpure Al 2 O 3 allows to assume that the crystal is homotheticallycontracted and therefore the distortion is reduced as itscales with the a lattice parameter.Figure 54: Typical magneto-photoluminescence spectrum at highpressure (5 GPa) and high field (56 T). Eight major peaks (A-H)are recorded. Logarithmic intensity scale enhances the visibilityof the four weaker peaks (a-h). (b) Zeeman energy splitting fanchart highlighting the two pairs of peaks (BC) and (FG) giving directaccess to ∆ 1 and ∆ 2 the intrinsic splitting factor of the excitedstates related to the trigonal field component.We have reported high-field magneto-optical measurementsunder high pressure on ruby single crystals up to 10 GPaand 56 T [Millot et al., Phys. Rev. B 78, 155125 (2008)].Figure 55: Zeeman splitting of ground state and first excitedstates of ruby. Observed emission lines are described by allowed(solid arrows) and forbidden (dashed arrows) dipolar absorptiontransitionThen the observed variation is consistent with the presentmodel and reflects the increase of the trigonal coupling parameterwith pressure, its dependence being proportional toR −n with n = 5. This value agrees with the exponent derivedfrom crystal-field theory but in the present case is obtainedempirically from magneto-optical spectroscopy, andconstitutes the first experimental evidence of a R −5 law.M. Millot, S. George and J.M. BrotoJ. Gonzalez and F. Gonzalez (DCITIMAC, Santander, Spain)43