Thermalization of nuclear spins in lanthanide molecular magnets

Single molecule magnets distinguish themselves in the field of quantum magnetism through the ability to combine fundamental research with promising applications, the evolution of quantum spintronics in the last decade exemplifying the potential held by molecular based quantum devices. Notably, the read-out and manipulation of the embedded nuclear spin states was used in proof of principle studies of quantum computation at the single molecule level. In this paper we study the relaxation dynamics of the $^{159}$Tb nuclear spins in a diluted molecular crystal by using recently acquired understanding of the nonadiabatic dynamics of TbPc$_2$ molecules. We find that phonon modulated hyperfine interaction opens a direct relaxation channel between the nuclear spins and the phonon bath. We highlight the potential importance of the discovered mechanism for the theory of spin bath and the relaxation dynamics of the molecular spins at crossover temperatures.