The extended Bloch's law in yttrium iron garnet doped with Zn, Ni and Co

The empirical extended Bloch's law about the saturation magnetization behavior as a function of temperature was checked in nanoparticles of yttrium iron garnet doped with zinc, nickel and cobalt. The exponent values from fitting extended Bloch's law with experimental results vary from 1.42 to 9.68, and are different from these expected values; 9/2, 2, 3/2, 3 and 5/2. The discrepancy was associated to the existence of structural defects and moments with frustrated exchange interaction, due to the nanoparticles size and thermal treatment conditions. Other adjustment attempt was performed with a linear term combined to the traditional Bloch's law T-3/2 motivated by the nanometric particles size. This other attempt was unsuccessful showing discrepancy with the experimental results and attributed to the atomic disorder and magnetic frustrations.