⁵⁷Fe Mössbauer study of unusual magnetic structure of multiferroic 3R-AgFeO₂

We report new results of a ⁵⁷Fe Mössbauer study of hyperfine magnetic interactions in the layered multiferroic 3R-AgFeO₂ demonstrating two magnetic phase transitions at T _N1 and T _N2. The asymptotic value β ^*  ≈  0.34 for the critical exponent obtained from the temperature dependence of the hyperfine field H _hf(T) at ⁵⁷Fe the nuclei below T _N1  ≈  14 K indicates that 3R-AgFeO₂ shows quasi-3D critical behavior. The spectra just above T _N1 (T _N1  <  T  <  T  ^*  ≈  41 K) demonstrate a relaxation behavior due to critical spin fluctuations which indicates the occurrence of short-range correlations. At the intermediate temperature range, T _N2  <  T  <  T _N1, the ⁵⁷Fe Mössbauer spectra are described in terms of collinear spin-density-waves (SDW) with the inclusion of many high-order harmonics, indicating that the real magnetic structure of the ferrite appears to be more complicated than a pure sinusoidally modulated SDW. Below T  <  T _N2  ≈  9 K, the hyperfine field H _hf reveals a large spatial anisotropy (ΔH _anis  ≈  30 kOe) which is related with a local intra-cluster (FeO₆) spin-dipole term that implies a conventional contribution of the polarized oxygen ions. We proposed a simple two-parametric formula to describe the dependence of H _anis on the distortions of the (FeO₆) clusters. Analysis of different mechanisms of spin and hyperfine interactions in 3R-AgFeO₂ and its structural analogue CuFeO₂ points to a specific role played by the topology of the exchange coupling and the oxygen polarization in the delafossite-like structures.