A GAGG:Ce crystal scintillator contaminated by thorium was used to search for double-$\alpha$ decay of ${}^{224}\mathrm{Ra}$. Considering that the daughter nucleus is ${}^{216}\mathrm{Po}$ with the half-life of 0.144 s, the time-amplitude method was utilized to search for ${}^{224}\mathrm{Ra}$ $2\alpha$ events, which allows for a significant background reduction in the region of the expected effect. No double-$\alpha$ decay events were observed, allowing us to set a lower limit on the decay half-life, $\lim T_{1/2}=64\mathrm{yr}$ at 90% confidence level, which exceeds the theoretical predictions of the symmetric model of $2\alpha$ decay ($T_{1/2}=2.6\mathrm{yr}$).

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• Nuclear decay
• Nuclear structure & decays