Magnetic properties of the Zn Fe 2 O 4 spinel

Using neutron diffraction (ND), muon-spin rotation/relaxation ($\ensuremath{\mu}\mathrm{SR}$), and $^{57}\mathrm{Fe}$ and $^{67}\mathrm{Zn}$ M\"ossbauer spectroscopy (MS) we investigated magnetic properties of the normal spinel Zn${\mathrm{Fe}}_{2}$${\mathrm{O}}_{4}$. Inversion is below limits of detection in samples which were slowly cooled from 1200 \ifmmode^\circ\else\textdegree\fi{}C to room temperature. Below ${T}_{N}=10.5$ K the spinel exhibits long-range antiferromagnetic order (LRO). However, already at temperatures of about $T\ensuremath{\approx}10{T}_{N}$ a short-range antiferromagnetic order (SRO) develops which extends through \ensuremath{\approx}70% of the sample volume just above ${T}_{N}$. Below ${T}_{N}$ antiferromagnetic SRO and LRO coexist. At 4.2 K still \ensuremath{\approx}20% of the sample are short-range ordered. The regions exhibiting SRO are very small (\ensuremath{\approx}3 nm). Their fluctuation rates as estimated from $\ensuremath{\mu}\mathrm{SR}$ are in the GHz range. For this reason the SRO above ${T}_{N}$ remains hidden in MS and is only seen in ND and $\ensuremath{\mu}\mathrm{SR}$ with their more appropriate time windows. Although the physical origin of the SRO remains an enigma, our experiments show that it is not caused by partial inversion but rather is an intrinsic property of Zn${\mathrm{Fe}}_{2}$${\mathrm{O}}_{4}$. Modern ab initio cluster calculations successfully describe the magnetic hyperfine field as well as the electric field gradient tensor at the Fe site as seen by MS.