The characteristics of the four-wave-mixing signal of Cr3+ ions were measured for host crystals of Gd3Sc2Ga3O12, Gd3Ga5O12, (Gd,Ca)5(Ga,Mg,Zr) 2Ga5O12, and La3Lu2Ga3O12. Signal strengths and decay times were measured as functions of laser-beam crossing angles and temperature. The results are used to determine the properties of radiationless decay and energy-transfer processes in these samples. By comparing the characteristics of the 4T2-2E radiationless relaxation process among these and previously investigated Cr3+-doped laser crystals, it is shown that the ratio of the intersystem-crossing relaxation rate to the internal conversion relaxation rate decreases as the strength of the crystal field of the host material decreases. The properties of energy migration among the Cr3+ ions in the different host materials is found to depend on the average separation of the Cr3+ ions, the strength of the crystal field, and the electron-phonon interactions. © 1990 The American Physical Society.