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Physical Review B

Level mixing and anisotropy effect in resonant Raman electron paramagnetic transitions in ruby for B perpendicular to c

Xingye Lu, S. Venugopalan, Hyunjung Kim, Marcos Grimsditch, S. Rodríguez, A. K. Ramdas

Published May 17, 2011• 3 citations
Publisher

Abstract

Doubly resonant Raman electron paramagnetic transitions in ruby (Al${}_{2}$O${}_{3}$:Cr${}^{3+}$) have been investigated using dye laser excitation tuned across the range of the Zeeman components of its well-known ${R}_{1}$ emission line. With magnetic field B normal to c, the optic axis of ruby, it is seen that the Raman electron paramagnetic resonance (EPR) lines exhibit significant intensity enhancements due to the simultaneous occurrence of ``in resonance'' and ``out resonance,'' as visualized in the Kramers-Heisenberg formalism of inelastic light scattering. The specific Raman EPR features observed in the present study, together with their resonances, however, differ markedly from those observed in our previous investigation with $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$. These differences can be traced to level mixing effects within the Zeeman multiplet of the ${}^{4}{A}_{2}$ (ground) state on the one hand, and the negligible value of ${g}_{\ensuremath{\perp}}$ for the $\mathrm{E\ifmmode \bar{}\else \={}\fi{}}$ (excited) state of the ${R}_{1}$ emission line on the other. Furthermore, we note that with B\ensuremath{\perp}c and under resonant conditions, the experimentally observed \ensuremath{\Delta}$m$ $=$ \ifmmode\pm\else\textpm\fi{}1 pair of Stokes and anti-Stokes Raman lines are not connected by time-reversal symmetry.

DOI
10.1103/physrevb.83.195126

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The Zeeman effect of R-absorption lines in ruby was observed in a high pulsed magnetic field up to 520 kOe using an optical multichannel analyzer. The experiment was done under a thermal equilibrium condition ( T =130 K) and the Zeeman line intensity is satisfactorily explained. When a magnetic field is applied perpendicular to the C 3 -axis, the excited \barE and 2\barA states show a level mixing and the observed pattern indicates a clear Paschen-Back effect The observed g // -values of the excited states are -2.49±0.05 and 1.49±0.05 for \barE and 2\barA, respectively. g ⊥ -values for these levels were estimated to be smaller than 0.1 at 500 kOe.
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Laser and microwave fields can be mixed in paramagnetic samples in a coherent Raman process. The radiation scattered in the forward direction contains frequency components at the sum and difference frequency. We consider the details of this scattering process in a static magnetic field, where two types of signals appear: magnetic-resonance transitions give rise to signals at fixed magnetic fields, independent of the laser frequency. Another set of resonances is determined by the optical transition frequencies. These resonances are particularly prominent in samples with narrow optical absorption lines. We derive a comprehensive theory that describes both contributions and compare it with experimental data from the R lines of ruby.
Raman-heterodyne-detected paramagnetic resonance has been used to study the level anticrossing in the 3^{3}3A state of the N-V defect in diamond. The electron-paramagnetic-resonance (EPR) frequencies are well accounted for by a triplet-spin Hamiltonian. Comparison of the EPR spectra with the calculated transition dipole strengths indicates that optical pumping determines, to a large extent, the Raman-heterodyne-signal intensity. Spin alignment in the 3^{3}3A ground state under optical pumping leads to the collapse of the EPR signal at the level anticrossing, where the population is equalized due to the mixing of the spin states. This is substantiated by transient nutation and spin-echo measurements, from which the dipole moment and dephasing time are examined. Laser detuning within the 638-nm zero-phonon line shows that the Raman signal is only detectable when the laser frequency is tuned to the low-energy part of the optical line.
Raman-scattering transitions between the excited states Ē (2E) and 2Ā (2E) of Cr3+ in αAl2O3 are studied, with the laser radiation (λ=514.5 nm) simultaneously serving as an optical pump and a Raman probe. This gives rise to a quadratic dependence of the Raman signal on the intensity of the incident radiation at low laser powers, which tends to become linear at higher power levels due to the onset of saturation effects. An analysis is made of the tensorial symmetry properties of the scattering, based on group-theoretical selection rules as well as on a perturbative expansion in the spin–orbit coupling parameter. In comparing the observed polarized spectra with the results of the theoretical analysis, proper account is taken of the dichroic features of the broad absorption bands in ruby, which affect the pumping process and the accompanying population in the excited state. An alternative method for measuring any asymmetry in the scattering tensor is described and employed, making use of the relation between Stokes and anti-Stokes Raman intensities for a fixed scattering geometry.