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We carried out the negative refractive index in the solid medium Er3+:YAlO3 crystal with a L-type four-level scheme proposed for atomic vapour by Thommen and Mandel, and Kastel (Phys. Rev. Lett. 2006 96 053601 and 2007 98 069301) based on quantum interference and electromagnetically induced transparency (EIT). The results show that the frequency band with the negative index is much wider ([?]1 MHz) than reported previously. Usually, Im[n] is always positive, corresponding to absorption, and the figure of merit (FOM, the ratio of real to imaginary, namely |Re[n]/Im[n]|) is only on the order of unity. We achieve FOM = |Re[n]/Im[n]| = 4.6. The corresponding negative Im[n] is related to the stimulated emission of 4I13/2 - 4I15/2 of the rare earth ion Er3+ under external electromagnetic fields. It is concluded that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for the electromagnetically induced negative refractive index material. [ABSTRACT FROM AUTHOR]