Influence of the critical Fe atomic volume on the magnetism of Fe-rich metallic glasses evidenced by pressure-dependent measurements

Despite the intensive studies for decades, it is still not well understood how qualitatively different magnetic behaviors can occur in a narrow composition range for the Fe-rich Fe-transition metal (TM) amorphous alloys. In this study of amorphous $\mathrm{F}{\mathrm{e}}_{100\ensuremath{-}x}\mathrm{Z}{\mathrm{r}}_{x}$ ($x=7$, 9, 12) metallic glasses, normal ferromagnetism (FM) is found at 12 % Zr where only the FM-paramagnetic (PM) transition is observed at the Curie temperature, ${T}_{C}$. In contrast, spin-glass (SG)-PM transition at a temperature, ${T}_{g}$, called SG temperature, is only observed at 7 % Zr, while in the transient re-entrant composition range $(x=8\ensuremath{-}11)$, an SG-FM transition at a temperature, ${T}_{f}$, called spin-freezing temperature, is also observed at low temperature besides the normal FM-PM transition at ${T}_{C}$. In order to understand this unusual behavior, a detailed characterization of pressure (atomic volume), composition, and temperature dependence of the magnetic properties is coupled with high pressure synchrotron x-ray diffraction determination of the pressure dependence of the atomic volume. The results on $\mathrm{F}{\mathrm{e}}_{100\ensuremath{-}x}\mathrm{Z}{\mathrm{r}}_{x}$ ($x=7$, 9, 12) are compared to those obtained for the FM $\mathrm{C}{\mathrm{o}}_{91}\mathrm{Z}{\mathrm{r}}_{9}$ metallic glass not showing any kind of anomalous magnetic properties. It is confirmed that the unusual behavior is caused by a granularlike magnetic structure where weakly coupled magnetic clusters are embedded into a FM bulk matrix. Since the mechanism of the magnetization reversal was found to be of the curling type rather than homogeneous rotation, the energy barrier determining the blocking temperature of the clusters is calculated as AR, where A is the exchange constant and R is the cluster size, in contrast to the usual characterization of the energy barrier by KV where K is the anisotropy energy and V is the cluster volume. The volume fraction of the FM part is a fast changing function of the bulk composition: Almost 100% FM fraction is found at 12 % of Zr while no trace of real FM is observed at 7 at % Zr. The driving force of this surprising magnetic character is the atomic volume: The lower the Zr content, the higher is the fraction of Fe atoms with compressed atomic volume having low magnetic moment. The percolation of their network separates the clusters from the FM bulk. The complex magnetic behavior of the Fe-rich Fe-Zr amorphous system at low temperatures can thus be interpreted with the only assumption of a cluster-size distribution and a weak coupling of the clusters to the FM matrix. The introduction of this coupling is able to explain the opposite pressure dependence of ${T}_{g}$ and ${T}_{f}$. The threshold atomic volume in the low magnetic moment regions is found to be comparable to the atomic volume characteristic to the low-spin limit of the face-centered-cubic Fe alloys. The extensive literature results on the anomalous magnetism for various Fe-rich Fe-TM amorphous alloys and especially for the Fe-rich Fe-Zr glassy system are also found to be in agreement with this granular magnetic behavior.