Magnetic moments evolution in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Mn</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Fe</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>(</mml:mo> <mml:mi mathvariant="normal">P</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Si</mml:mi> <mml:mo>)</mml:mo> </mml:math> single crystals from x-ray emission spectroscopy

First-order magnetoelastic transitions usually involve mechanisms unique to each family of materials. For ${(\mathrm{Mn},\mathrm{Fe})}_{2}(\mathrm{P},\mathrm{Si})$ compounds, it is generally predicted that the unit cell distortion occurring at the ferromagnetic transition leads to a strong electronic reconstruction of the Fe $d$ states accompanied by a notable change in magnetic moment. However, there is no experimental consensus on this mechanism. Here, we use x-ray emission spectroscopy (XES) complemented by first-principles calculations, high-energy resolution fluorescence detected x-ray absorption (HERFD-XAS), and resonant inelastic x-ray scattering (RIXS) experiments, to clarify the nature of the first-order transition in a ${\mathrm{Mn}}_{0.74}{\mathrm{Fe}}_{1.23}{\mathrm{P}}_{0.71}{\mathrm{Si}}_{0.32}$ crystal. HERFD-XAS and RIXS data show a minor evolution of the spectral features in the upper part of the $K$-edge for Mn and Fe, consistent with the calculated $4p$ density of states and fingerprinting the transition. In contrast, no significant evolution of the XES spectra is observed when the transition is crossed. In Fe-rich compositions, the calculations indicate that Fe at the $3g$ site develops a magnetic moment (2.43 ${\ensuremath{\mu}}_{B}$) that is smaller than that of Mn at the $3g$ site (2.93 ${\ensuremath{\mu}}_{B}$), but larger than that of Fe at the $3f$ site (1.48 ${\ensuremath{\mu}}_{B}$). Quantitative XES analysis using the IAD method gives a reasonable agreement with the magnetic moments for different ${(\mathrm{Mn},\mathrm{Fe})}_{2}(\mathrm{P},\mathrm{Si})$ compositions. However, the reduction of the Fe moment predicted by theory (approx. $\ensuremath{-}0.6\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{B}$) is not observed around the transition. This study indicates that the Fe moment collapse at the transition may be weaker than the theoretically predicted value or more gradual in temperature, suggesting a secondary role for this moment instability in the giant magnetocaloric effect of ${(\mathrm{Mn},\mathrm{Fe})}_{2}(\mathrm{P},\mathrm{Si})$ compounds.