Through analysis of variable-temperature neutron powder-diffraction data, we present solutions for the magnetic structures of ${\mathrm{SrMn}}_7{\mathrm{O}}_{12}$, ${\mathrm{CdMn}}_7{\mathrm{O}}_{12}$, and ${\mathrm{PbMn}}_7{\mathrm{O}}_{12}$ in all long-range ordered phases. The three compounds were found to have magnetic structures analogous to that reported for ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$. They all feature a higher-temperature lock-in phase with commensurate magneto-orbital coupling and a delocked multi-k magnetic ground state where incommensurate magneto-orbital coupling gives rise to a constant-moment magnetic helix with modulated spin helicity. ${\mathrm{CdMn}}_7{\mathrm{O}}_{12}$ represents a special case in which the orbital modulation is commensurate with the crystal lattice and involves stacking of fully and partially polarized orbital states. Our results provide a robust confirmation of the phenomenological model for magneto-orbital coupling previously presented for ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$. Furthermore, we show that the model is universal to the $A^{2+}$ quadruple perovskite manganites synthesized to date and that it is tunable by selection of the $A$-site ionic radius.

We report new results of a ⁵⁷ Fe Mössbauer study of hyperfine magnetic interactions in the layered multiferroic 3 R -AgFeO ₂ 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 ⁵⁷ Fe the nuclei below T _N1 ≈ 14 K indicates that 3 R -AgFeO ₂ 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 ⁵⁷ Fe 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 (Δ H _anis ≈ 30 kOe) which is related with a local intra-cluster (FeO ₆ ) 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 (FeO ₆ ) clusters. Analysis of different mechanisms of spin and hyperfine interactions in 3 R -AgFeO ₂ and its structural analogue CuFeO ₂ points to a specific role played by the topology of the exchange coupling and the oxygen polarization in the delafossite-like structures.

New results of 57 Fe Mössbauer studies on BiFeO 3 powder sample performed at various temperatures above and below magnetic phase transitions point T N ≈ 640K are reported. We have performed self-consistent calculations of the lattice contributions to the EFG tensor, taking into account dipole moments of the O 2− and Bi 3+ ions. Low-temperature 57 Fe Mössbauer spectra recorded at T < T N were analyzed assuming an anharmonic cycloidal modulation of the Fe 3+ magnetic moments. The cycloidal modulation of the iron spin was described with the elliptic Jacobi function sn[(±4K(m)/λ)x,m] . The good fit of the experimental spectra was obtained for the anharmonicity m = 0.44 ± 0.04 (T = 4.9K) resulting from the easy-axis magnetic anisotropy.

The paper reports results of the ${}^{57}\mathrm{Fe}$ Mössbauer measurements on an $\mathrm{F}{\mathrm{e}}_3\mathrm{P}{\mathrm{O}}_4{\mathrm{O}}_3$ powder sample recorded at various temperatures, including the point of magnetic phase transition $T_{\mathrm{N}}\approx 163\mathrm{K}$. The spectra measured above $T_{\mathrm{N}}$ consist of a quadrupole doublet with high quadrupole splitting of ${\mathrm{\Delta }}_{300\mathrm{K}}\approx 1.10\mathrm{mm}/\mathrm{s}$, emphasizing that $\mathrm{F}{\mathrm{e}}^{3+}$ ions are located in crystal positions with a strong electric-field gradient (EFG). To predict the sign and orientation of the main components of the EFG tensor, we calculated the EFG using the density-functional-theory approach. In the temperature range $T<T_{\mathrm{N}}$, the experimental spectra were fitted assuming that the electric hyperfine interactions are modulated when the $\mathrm{F}{\mathrm{e}}^{3+}$ spin $\left(\mathit{S}\right)$ rotates with respect to the EFG axis, and with the emergence of spatial anisotropy of the hyperfine field $H_{\mathrm{hf}}\propto \tilde{\mathit{A}}·\mathit{S}$ at ${}^{57}\mathrm{Fe}$ nuclei. These data were analyzed to estimate the components of the anisotropic hyperfine coupling tensor $\left(\tilde{\mathit{A}}\right)$. The large anharmonicity parameter, $m\approx 0.94$, of the spiral spin structure results from easy-axis anisotropy in the plane of the iron spin rotation. The temperature evolution of the hyperfine field $H_{\mathrm{hf}}\left(T\right)$ was described by the Bean-Rodbell model, which takes into account that the exchange magnetic interactions are a strong function of the lattice spacing. The obtained Mössbauer data are in qualitative agreement with previous neutron-diffraction data for a modulated helical magnetic structure in strongly frustrated $\mathrm{F}{\mathrm{e}}_3\mathrm{P}{\mathrm{O}}_4{\mathrm{O}}_3$.

Following the trend of finding better thermoelectric materials among synthetic analogs of copper–chalcogenide minerals, we have synthesized iron-bearing colusites of a general formula Cu_26−xFe_xV₂Sn₆S₃₂. They crystallize in the cubic space group P-43n with the unit cell parameter increasing linearly with the iron content. At a low iron concentration, the crystal structure features disorder manifested by an anti-site effect and a shift of a part of the tin atoms from their ideal positions, which is absent for higher iron contents. The magnetization and ⁵⁷Fe/¹¹⁹Sn Mössbauer studies showed that, for x = 1, iron is present as Fe³⁺, whereas for x > 1, Fe²⁺ and Fe³⁺ coexist. Additionally, weak antiferromagnetic interactions between iron atoms and fast on the ⁵⁷Fe Mössbauer time scale (10⁷–10⁹ s⁻¹) electron transfer between adjacent Fe²⁺ and Fe³⁺ centers were revealed. Thermoelectric studies showed that iron-bearing colusites are p-type semiconductors with low thermal conductivity stemming from their complex crystal structure and structural disorder. The highest ZT of 0.78 at 700 K was found for the x = 1 iron content, where iron is present as Fe³⁺ only.