Incongruent melting of terbium aluminum garnet (Tb3Al5O12; TAG) single crystals has the largest Verdet constant, based on the Faraday rotation, among "transparent" materials, even though no practically applicable size of TAG single crystal has yet been grown. To grow TAG single crystals, we designed a hybrid laser floating zone growth machine, in which four CO, gas lasers and four halogen lamps were placed around a pedestal. This is capable of both uniform laser heating and lamp pre-heating. We successfully grew TAG single-crystal rods of 3 mm in diameter, which were suitable for the use in optical devices. The crystals showed a full-width at half-maximum in as little as 27 arcsec by the X-ray rocking curve measurement. The examined growth directions were randomly dispersed under the no-seed utilized growth condition. Several optical property evaluations confirmed successful results for high transmittance qualities and a larger Verdet constant than the conventional Tb3Ga5O12 crystals. (C) 2004 Elsevier B.V. All rights reserved.