Microscopic interpretation of magnetic ordering and critical slowing down in potassium ferrate

Abstract

Experimental M\"ossbauer results are reported for the antiferromagnet ${\mathrm{K}}_{2}$Fe${\mathrm{O}}_{4}$ from 0.16 to 4.2 K which show significant spin-relaxation effects. The data are analyzed using the Clauser-Blume theory of stochastic spin relaxation, applied to the case spin $S=1$. This analysis yields the N\'eel temperature ${T}_{N}=3.60$ K, and verifies the crystal-field parameters $D=0.11$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and $E=0.02$ ${\mathrm{cm}}^{\ensuremath{-}1}$ in the presence of significant spin-fluctuation effects. The analysis also shows that, except in the critical region, the strength of the relaxation mechanism is temperature independent, indicating that the spin-spin interaction is the dominant relaxation mechanism in this temperature range. In the region of 3.60 K, the spin-relaxation rate is observed to decrease by a factor of 700, showing the critical slowing down of the iron ions' spin fluctuations in the critical region. Additionally, to fit the data between 3.50 and 3.70 K, it is necessary to include contributions from a range of values of reduced magnetization and relaxation rate. These results are discussed in terms of a proposed model including critical fluctuations.