  Lithium magnesium molybdate (Li$_2$Mg$_2$(MoO$_4$)$_3$) crystals were grown
by the low-thermal-gradient Czochralski method. Luminescence properties of the
material (emission spectra, thermally stimulated luminescence, dependence of
intensity on temperature, phosphorescence) have been studied under X-Ray
excitation in the temperature interval from 8 K to 400 K, while at the same
being operated as a scintillating bolometer at 20 mK for the first time. We
demonstrated that Li$_2$Mg$_2$(MoO$_4)_3$ crystals are a potentially promising
detector material to search for neutrinoless double beta decay of $^{100}$Mo.
