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 analogue 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 SR relaxation
and high-field 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 analogues the
high-temperature rates appear to be fully determined by electron spin-lattice relaxation processes.