  Ferrofluids containing magnetic nanoparticles represent a special class of
magnetic materials due to the added freedom of particle tumbling in the fluids.
We studied this process, known as Brownian relaxation, and its effect on the
magnetic properties of ferrofluids with controlled magnetite nanoparticle
sizes. For small nanoparticles (below 10 nm diameter) the N\'eel process is
expected to dominate the magnetic response, whereas for larger particles,
Brownian relaxation becomes important. Temperature- and magnetic
field-dependent magnetization studies, differential scanning calorimetry, and
AC susceptibility measurements were carried out for 6, 8, 10.6, and 13.5 nm
diameter magnetite nanoparticles suspended in water. We identify clear
fingerprints of the Brownian relaxation for the sample of the large diameter
nanoparticles as both magnetic and thermal hysteresis develop at the water
freezing temperature, whereas the samples of small diameter nanoparticles
remain hysteresis-free down to the magnetic blocking temperature. This is
supported by the temperature-dependent AC susceptibility measurements: above
273 K, the data show a low-frequency Debye peak, which is characteristic of the
Brownian relaxation. This peak vanishes below 273 K.
