Pressure-Induced Invar Behavior in ${\mathrm{Pd}}_3\mathrm{Fe}$

Synchrotron x-ray diffraction (XRD) measurements, nuclear forward scattering (NFS) measurements, and density functional theory (DFT) calculations were performed on $L{1}_2$-ordered ${\mathrm{Pd}}_3\mathrm{Fe}$. Measurements were performed at 300 K at pressures up to 33 GPa, and at 7 GPa at temperatures up to 650 K. The NFS revealed a collapse of the ${}^{57}\mathrm{Fe}$ magnetic moment between 8.9 and 12.3 GPa at 300 K, coinciding with a transition in bulk modulus found by XRD. Heating the sample under a pressure of 7 GPa showed negligible thermal expansion from 300 to 523 K, demonstrating Invar behavior. Zero-temperature DFT calculations identified a ferromagnetic ground state and showed several antiferromagnetic states had comparable energies at pressures above 20 GPa.

Figure 1

Volume-pressure data obtained from synchrotron x-ray diffraction measurements (symbols) and the fit of the data to the Weiss-like equation of state [15] (line).

Figure 2

Nuclear forward scattering spectra from ordered ${\mathrm{Pd}}_3^{57}\mathrm{Fe}$ showing an abrupt decrease of the hyperfine magnetic fields in the material around 12 GPa.

Figure 3

Volume-temperature data for ${\mathrm{Pd}}_3^{57}\mathrm{Fe}$ (diamonds) and Au (squares) obtained from externally heating the diamond anvil cell at an approximately constant pressure of 7 GPa. The ${\mathrm{Pd}}_3^{57}\mathrm{Fe}$ shows practically no thermal expansion up to 523 K. The solid and dashed lines are guides for the eye.

Figure 4

Magnetic moments at the Fe site (left), and charge at the Fe site (right) versus the lattice constant of ${\mathrm{Pd}}_3\mathrm{Fe}$ from DFT calculations. Antiferromagnetic refers to the AFM-I structure (see text). The solid and dashed lines are guides to the eye.