Linearly-polarized magnetic dipole (MD) scattering as intense as Rayleigh scattering is reported in transparent garnet crystals and fused quartz through a magneto-electric interaction at the molecular level. Radiation patterns in quartz show the strongest optical magnetization relative to electric polarization ever reported. As shown in an accompanying paper, quantitative agreement is achieved with a strong-field, fully-quantized theory of magneto-electric (M-E) interactions in molecular media. The conclusion is reached that magnetic torque enables 2-photon resonance in an EH* process that excites molecular librations and accounts for the observed upper limit on magnetization. Second-order M-E dynamics can also account for unpolarized scattering from high-frequency librations previously ascribed to first-order collision-induced or third-order, all-electric processes.