Nonlinear temperature variation of magnetic viscosity in nanoscale FeOOH particles

Temperature variations of the magnetization and magnetic viscosity S in 30-Å particles of FeOOH are reported. An average blocking tempeature T${\mathrm{¯}}_{\mathit{b}}$=47 K is determined for this system from the temperature variation of the difference susceptibility between the field-cooled and zero-field-cooled cases. The measured decrease of T${\mathrm{¯}}_{\mathit{b}}$ with applied field is used to determine an average magnetic moment ≃7150${\mathrm{\mu }}_{\mathit{B}}$ per particle. The relaxation data of the magnetization M(t) follow the equation M(t)/M(${\mathrm{\tau }}_0$)=1 -S ln(t/${\mathrm{\tau }}_0$), from which temperature variation of S is determined for the range 2 to 200 K. Below 7 K, S is temperature independent signifying quantum tunneling. Above 7 K, initially S increaes linearly with T, but the variation becomes increasingly nonlinear, reaching an apparent maximum at T${\mathrm{¯}}_{\mathit{b}}$=47 K. The temperature variation of S is characteristic of a phase transition at T${\mathrm{¯}}_{\mathit{b}}$ since the data fits well the equation S=A‖(T-T${\mathrm{¯}}_{\mathit{b}}$)/T${\mathrm{¯}}_{\mathit{b}}$ ${\mathrm{\Vert }}^{\mathrm{-}\nu }$ with A=0.040(0.0076) and ν=1.10(1.29) for T>T${\mathrm{¯}}_{\mathit{b}}$(TT${\mathrm{¯}}_{\mathit{b}}$). An average energy barrier 〈U〉=2140 K and ${\mathrm{\tau }}_0$=5×${10}^{\mathrm{-}12}$ s are also estimated from the analysis of the data.