Size-dependent magnetic ordering and spin dynamics in DyPO4 and GdPO4 nanoparticles

Low-temperature magnetic susceptibility and heat-capacity measurements on nanoparticles (d? 2.6 nm) of the antiferromagnetic compounds DyPO4 (TN=3.4 K) and GdPO4 (TN=0.77 K) provide clear demonstrations of finite-size effects, which limit the divergence of the magnetic correlation lengths, thereby suppressing the bulk long-range magnetic ordering transitions. Instead, the incomplete antiferromagnetic order inside the particles leads to the formation of net magnetic moments on the particles. For the nanoparticles of Ising-type DyPO4 superparamagnetic blocking is found in the ac susceptibility at ?1 K, those of the XY-type GdPO4 analog show a dipolar spin-glass transition at ?0.2 K. Monte Carlo simulations for the magnetic heat capacities of both bulk and nanoparticle samples are in agreement with the experimental data. Strong size effects are also apparent in the Dy3+ and Gd3+ spin dynamics, which were studied by zero-field muon spin rotation (?SR) and high-field 31P-nuclear magnetic resonance (31P-NMR) nuclear relaxation measurements. The freezing transitions observed in the ac susceptibility of the nanoparticles also appear as peaks in the temperature dependence of the zero-field ?SR rates, but at slightly higher temperatures, as to be expected from the higher frequency of the muon probe. For both bulk and nanoparticles of GdPO4, the muon and 31P-NMR rates are for T?5 K dominated by exchange-narrowed hyperfine broadening arising from the electron spin-spin interactions inside the particles. The dipolar hyperfine interactions acting on the muons and the 31P are, however, much reduced in the nanoparticles. For the DyPO4 analogs the high-temperature rates appear to be fully determined by electron spin-lattice relaxation processes.