  In this work, a first cryogenic characterization of a scintillating
LiAlO$_{2}$ single crystal is presented. The results achieved show that this
material holds great potential as a target for direct dark matter search
experiments. Three different detector modules obtained from one crystal grown
at the Leibniz-Institut f\"ur Kristallz\"uchtung (IKZ) have been tested to
study different properties at cryogenic temperatures. Firstly, two 2.8 g twin
crystals were used to build different detector modules which were operated in
an above-ground laboratory at the Max Planck Institute for Physics (MPP) in
Munich, Germany. The first detector module was used to study the scintillation
properties of LiAlO$_{2}$ at cryogenic temperatures. The second achieved an
energy threshold of (213.02$\pm$1.48) eV which allows setting a competitive
limit on the spin-dependent dark matter particle-proton scattering cross
section for dark matter particle masses between 350 MeV/c$^{2}$ and 1.50
GeV/c$^{2}$. Secondly, a detector module with a 373 g LiAlO$_{2}$ crystal as
the main absorber was tested in an underground facility at the Laboratori
Nazionali del Gran Sasso (LNGS): from this measurement it was possible to
determine the radiopurity of the crystal and study the feasibility of using
this material as a neutron flux monitor for low-background experiments.
