  Uncovering neutrinoless double beta decay (0$\nu$2$\beta$) is crucial for
confirming neutrinos' Majorana characteristics. The decay rate of
0$\nu\beta\beta$ is theoretically uncertain, influenced by nuclear matrix
elements that vary across nuclides. To reduce this uncertainty, precise
measurement of the half-life of neutrino-emitting double beta decay
(2$\nu$2$\beta$) in different nuclides is essential.
  We have launched the PIKACHU (Pure Inorganic scintillator experiment in
KAmioka for CHallenging Underground sciences) project to fabricate high-purity
Ce-doped Gd$_{3}$Ga$_{3}$Al$_{2}$O$_{12}$ (GAGG) single crystals and use them
to study the double beta decay of $^{160}$Gd. Predictions from two theoretical
models on nuclear matrix element calculations for 2$\nu$2$\beta$ in $^{160}$Gd
show a significant discrepancy in estimated half-lives, differing by
approximately an order of magnitude. If the lower half-life estimation holds
true, detecting 2$\nu$2$\beta$ in $^{160}$Gd could be achievable with a
sensitivity enhancement slightly more than an order of magnitude compared to
prior investigations using Ce-doped Gd$_2$SiO$_5$ (GSO) crystal. We have
successfully developed GAGG crystals with purity levels surpassing previous
standards through refined purification and selection of raw materials. Our
experiments with these crystals indicate the feasibility of reaching
sensitivities exceeding those of earlier studies. This paper discusses the
ongoing development and scintillator performance evaluation of High-purity GAGG
crystals, along with the anticipated future prospects of the PIKACHU
experiment.
