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We report a combination of Fe K$\beta$ x-ray emission spectroscopy and$ab$-intio calculations to investigate the correlation between structural andmagnetic degrees of freedom in CaFe$_{2}$(As$_{1-x}$P$_{x} $)$_{2}$. Thepuzzling temperature behavior of the local moment found in rare earth-dopedCaFe$_{2}$As$_{2}$ [\textit{H. Gretarsson, et al., Phys. Rev. Lett. {\bf 110},047003 (2013)}] is also observed in CaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$. Weexplain this phenomenon based on first-principles calculations with scaledmagnetic interaction. One scaling parameter is sufficient to describequantitatively the magnetic moments in both CaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ ($x=0.055$) and Ca$_{0.78}% $La$_{0.22}$Fe$_{2}$As$_{2}$ at alltemperatures. The anomalous growth of the local moments with increasingtemperature can be understood from the observed large thermal expansion of the$c$-axis lattice parameter combined with strong magnetoelastic coupling. Theseeffects originate from the strong tendency to form As-As dimers across the Calayer in the CaFe$_{2}$As$_{2}$ family of materials. Our results emphasize thedual local-itinerant character of magnetism in Fe pnictides.

Structural origin of the anomalous temperature dependence of the local magnetic moments in the CaFe$_{2}$As$_{2}$ family of materials