Mössbauer study of the magnetic transition in $\epsilon$-Fe$_2$O$_3$ nanoparticles using synchrotron and radionuclide sources

Nuclear $\gamma$-resonance experiments with energy and time resolved detection are carried out with $\epsilon$-Fe$_2$O$_3$ nanoparticles and a $^{57}$Co(Rh) laboratory Mössbauer source of $\gamma$ radiation and a $14.4125$ keV synchrotron radiation source on the ID18 beamline (ESRF) in the temperature range of $4$–$300$ K. Both methods show a tremendous increase in the hyperfine field in tetrahedrally coordinated iron positions during the magnetic transition in the range of $80$–$150$ K. As a result, the splitting of the quantum beat peaks in the nuclear scattering spectra is observed in the time interval of $20$–$170$ ns with a periodicity of $\sim 30$ ns. In addition, the first quantum beat is slightly shifted to shorter times. A correlation between the quadrupole shift and the orbital angular momentum of iron in $\epsilon$-Fe$_2$O$_3$ nanoparticles is found. The magnetic transition leads to the rotation of the magnetic moment in the tetrahedral positions of iron around the axis of the electric field gradient by an angle of $44^\circ$.