Structural Origin of the Anomalous Temperature Dependence of the Local Magnetic Moments in the ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ Family of Materials

We report a combination of Fe $K\beta$ x-ray emission spectroscopy and density functional reduced Stoner theory calculations to investigate the correlation between structural and magnetic degrees of freedom in ${\mathrm{CaFe}}_2{({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$. The puzzling temperature behavior of the local moment found in rare earth-doped ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ [H. Gretarsson et al., Phys. Rev. Lett. 110, 047003 (2013)] is also observed in ${\mathrm{CaFe}}_2{({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$. We explain this phenomenon based on first-principles calculations with scaled magnetic interaction. One scaling parameter is sufficient to describe quantitatively the magnetic moments in both ${\mathrm{CaFe}}_2{({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$ ($x=0.055$) and ${\mathrm{Ca}}_{0.78}{\mathrm{La}}_{0.22}{\mathrm{Fe}}_2{\mathrm{As}}_2$ at all temperatures. The anomalous growth of the local moments with increasing temperature can be understood from the observed large thermal expansion of the $c$-axis lattice parameter combined with strong magnetoelastic coupling. These effects originate from the strong tendency to form As-As dimers across the Ca layer in the ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ family of materials. Our results emphasize the dual local-itinerant character of magnetism in Fe pnictides.

Figure 1

(a) Temperature dependence of the $c$-axis lattice parameter in ${\mathrm{CaFe}}_2{({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$. Both $x=0$ (black open circles) and $x=0.033$ (red open triangles) samples go through tetragonal to orthorhombic-phase transition ($T_O$) around 165 and 130 K, respectively. In the $x=0.055$ (blue open squares) an abrupt transition into collapsed-tetragonal phase is seen at 80 K ($T_{\mathrm{CT}}$). (b) The temperature dependence of the IAD values for the same samples derived from their XES spectra. On the right-hand side is the magnetic moment of Fe ($M$) derived as described in text. Data for ${\mathrm{Ca}}_{0.78}{\mathrm{La}}_{0.22}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (black stars) [24] are also shown for comparison.

Figure 2

Magnetic moment $M$ of ${\mathrm{Ca}}_{0.78}{\mathrm{La}}_{0.22}{\mathrm{Fe}}_2{\mathrm{As}}_2$ as a function of the DFT-RST scaling parameter $s$ for different temperatures (solid lines). The horizontal dashed lines show the experimental values of the magnetic moment for different temperatures taken from Ref. [24]. Best agreement with experimental values is obtained using $s=0.85$ (gray vertical line).

Figure 3

Magnetic moment as a function of temperature in the DFT-RST calculations using $s=0.85$ (diamonds) compared with the experimental data (squares) of (a) ${\mathrm{Ca}}_{0.78}{\mathrm{La}}_{0.22}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (Ref. [24]) and (b) ${\mathrm{CaFe}}_2({\mathrm{As}}_{0.945}{\mathrm{P}}_{0.055}{)}_2$. The hollow circles indicate conventional LSDA results (equivalent to DFT-RST with $s=1.00$). See also Ref. [47] and the Supplemental Material for additional discussion [25].