Theory meets experiment: insights into structure and magnetic properties of Fe$_{1-x}$Ni$_{x}$B alloy

We studied the structural and magnetic properties of the solid solution Fe$_{1-x}$Ni$_{x}$B through theoretical and experimental approaches. Powder X-ray diffraction, X-ray Pair Distribution Function analysis, and energy dispersive X-ray spectroscopy reveal that the Fe$_{1-x}$Ni$_{x}$B solid solution crystallizes in the $\beta$-FeB structure type up to x = 0.6-0.7 and exhibits anisotropic unit cell volume contraction with increasing Ni concentration. Magnetic measurements showed a transition from ferromagnetism to paramagnetism around x = 0.7. For x = 0.5, the low (< 0.3 $\mu_{B}$) magnetic moments suggest itinerant magnetism despite the relatively high Curie temperature (up to 225 K). Theoretical calculations indicated different types of magnetic orderings depending on the Fe/Ni atomic order, with the antiferromagnetic state being stable for ordered FeNiB$_{2}$, whereas the ground state is ferromagnetic for the disordered alloy. Calculations also predicted the coexistence of low- and high-spin states in Fe atoms around the composition with x=0.5, in line with the experimental evidence from $^{57}$Fe M\"ossbauer spectroscopy. The two magnetically distinct Fe sites for x = 0.3, 0.4, and 0.5 observed by $^{57}$Fe M\"ossbauer spectroscopy can also be interpreted as two magnetically different regions or clusters that could affect the critical behavior near a quantum magnetic transition based on a potential ferromagnetic quantum critical point identified computationally and experimentally near x=0.64. This work highlights the complex interplay between structure and magnetism in Fe$_{1-x}$Ni$_{x}$B alloys, suggesting areas for future research on quantum critical behavior.