Two-photon magnetoabsorption experiments are reported for the first time. From the splitting of the 2p excitons of ZnO in a magnetic field of 42 kG the hole masses and the g values for the upper valence bands r 9 and r 7 are deduced, Two-photon spectroscopy has gained growing importance as a spectroscopic method in studying electronic properties in solids. Because of the changed selection rules as compared with ordinary spectroscopy (one-photon absorption), two-photon data yield information on excited states which are commonly forbidden for onephoton transitions.* Two -photon measurements with polarized light allow symmetry assignments to be determined for the different excited states. Much more quantitative information on band parameters (e.g., effective masses, g-values) are expected from two-photon magnetoabsorption, since transitions with Ara= ±2, ±1, and 0 are two-photon allowed, as compared with Am = ±1 and 0 in one-photon absorption. In this Letter we report the first observation of two-photon magneto-optic absorption in ZnO. Because of its rather large band gap (3.5 eV) and its pronounced exciton structure, ZnO is well suited for this kind of experiment. One-photon data 2 ' 3 on ZnO show three well-resolved exciton series, which are interpreted as transitions to S excitons from the three valence bands [symmetry T 7 (A), T 9 (J5), and T 7 (C)] and a T 7 conduction band. The two-photon spectrum looks quite different: It shows very narrow exciton lines close to the corresponding 2s transitions. This is shown for the A and B excitons in Fig. 1. For polarization parallel to the c axis one gets in one-photon absorption the C series and in two-photon absorption again a single pronounced exciton line, 4 which is close to the 2s line in the one-photon spectrum. We interpret the two-photon lines as transitions to 2p excitons. The shift of about 2.5 meV to lower energies as compared with the 8 ( Q 2 i Q_ Q. o o <

Exciton fine structure is measured in hexagonal AgI by two-photon absorption. A detailed assignment of the different P-exciton states is possible using the appropriate polarization configurations. The experimental results can be explained quantitatively taking into account anisotropy as the only perturbation on the hydrogenic series. Using an effective mass Hamiltonian for degenerate valence bands it is shown that the Hd-contributions to the hole kinetic energy are responsible for the mass anisotropy of the A and B series. An expression for the two-photon transition probability in a three-band model using the abovementioned Hamiltonian is derived.Es wird die Feinstruktur der Exzitonenlinien in hexagonalem AgJ mittels Zwei-Photonenabsorption gemessen. Mit Hilfe geeigneter Polarisationskonfigurationen ist eine detaillierte Zuordnung der P-Exzitonenzustande moglich. Die alleinige Berucksichtigung der Anisotropie als Storung der Wasserstoffserie fuhrt zur quantitativen Erklarung der experimentellen Ergebnisse. Von einem Effektive-Masse-Hamiltonoperator fur entartete Valenzbander ausgehend wird gezeigt, daB die Hd-Terme der Lochenergie die Ursache fur die Massenanisotropie der A-und B-Serie sind. Ein Ausdruck fur die Zwei-Photonenubergangswahrscheinlichkeit wird aus obigem Hamiltonoperator im Drei-Bandmodell abgeleitet.

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