  We developed a simple small-scale experiment to measure the beta decay
spectrum of $^{3}$H. The aim of this research is to investigate the presence of
sterile neutrinos in the keV region. Tritium nuclei were embedded in a
1$\times$1$\times$1 cm$^3$ LiF crystal from the $^6$Li(n,$\alpha$)$^3$H
reaction. The energy of the beta electrons absorbed in the LiF crystal was
measured with a magnetic microcalorimeter at 40 mK. We report a new method of
sample preparation, experiments, and analysis of $^3$H beta measurements. The
spectrum of a 10-hour measurement agrees well with the expected spectrum of
$^3$H beta decay. The analysis results indicate that this method can be used to
search for keV-scale sterile neutrinos.
