First-principles theory of the pressure-induced invar effect in FeNi alloys

The ${\mathrm{Fe}}_{0.64}{\mathrm{Ni}}_{0.36}$ alloy exhibits an anomalously low thermal expansion at ambient conditions, an effect that is known as the invar effect. Other ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}$ alloys do not exhibit this effect at ambient conditions but upon application of pressure even Ni-rich compositions show low thermal expansion, thus called the pressure induced invar effect. We investigate the pressure induced invar effect for ${\mathrm{Fe}}_x{\mathrm{Ni}}_{1-x}$ for $x$ = 0.64, 0.50, 0.25 by performing a large set of supercell calculations, taking into account noncollinear magnetic states. We observe anomalies in the equation of states for the three compositions. The anomalies coincide with magnetic transitions from a ferromagnetic state at high volumes to a complex magnetic state at lower volumes. Our results can be interpreted in the model of noncollinear magnetism which relates the invar effect to increasing contribution of magnetic entropy with pressure.

Figure 1

Visualization of magnetic structures of ${\mathrm{Fe}}_{0.64}{\mathrm{Ni}}_{0.36}$ at three atomic volumes, from top to bottom: 12.46, 11.57, 11.18 ${\AA }^3$. Magnetic transition begins at 11.57 ${\AA }^3$. Gold and silver spheres represent Fe and Ni, respectively.

Figure 2

Histograms of spin-pair correlation functions for ${\mathrm{Fe}}_{0.64}{\mathrm{Ni}}_{0.36}$ between neighboring Fe-spins (a) and Ni-spins (b) at several volumes (in ${\AA }^3$). ${\widehat{s}}_i·{\widehat{s}}_j=\text{cos}\left(\theta \right)$. The right y axis gives the atomic volumes in units ${\AA }^3$. Inserted plot shows the average magnetic moment size for noncollinear and collinear calculations in filled in blue circles and red crosses, respectively. Dashed line is experimental equilibrium volume.

Figure 3

Absolute values of local magnetic moments for individual atoms in ${\mathrm{Fe}}_{0.64}{\mathrm{Ni}}_{0.36}$, both Fe and Ni, as a function of atomic volume ${\AA }^3$. Dashed and dotted lines are experimental equilibrium volume and transition volume, respectively.

Figure 4

Visualization of magnetic structures of ${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}$ at three atomic volumes, from top to bottom: 11.18, 10.95, and 10.54 ${\AA }^3$. Magnetic transition begins at 10.95 ${\AA }^3$. Gold and silver spheres represent Fe and Ni, respectively.

Figure 5

Spin-pair correlation functions for ${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}$ between neighboring Fe-spins (a) and Ni-spins (b) at several volumes (in ${\AA }^3$). ${\widehat{s}}_i·{\widehat{s}}_j=\text{cos}\left(\theta \right)$. The right y axis gives the atomic volumes in units ${\AA }^3$. Inserted plot shows the average magnetic moment size for noncollinear and collinear calculations in filled in blue circles and red crosses, respectively. Dashed line is experimental equilibrium volume.

Figure 6

Magnetic moment sizes for all individual atoms in ${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}$, both Fe and Ni, as a function of atomic volume ${\AA }^3$. Dashed and dotted lines are experimental equilibrium volume and transition volume, respectively.

Figure 7

Visualization of the magnetic structures of ${\mathrm{Fe}}_{0.25}{\mathrm{Ni}}_{0.75}$ at three atomic volumes, from top to bottom: 10.54, 9.65, 9.31 ${\AA }^3$. Magnetic transition begins at 9.65 ${\AA }^3$. Gold and silver spheres represent Fe and Ni, respectively.

Figure 8

Spin-pair correlation functions for ${\mathrm{Fe}}_{0.25}{\mathrm{Ni}}_{0.75}$ between neighboring Fe-spins (a) and Ni-spins (b) at several volumes (in ${\AA }^3$). ${\widehat{s}}_i·{\widehat{s}}_j=\text{cos}\left(\theta \right)$. The right y-axis gives the atomic volumes in units ${\AA }^3$. Inserted plot shows the average magnetic moment size for noncollinear and collinear calculations in filled in blue circles and red crosses, respectively. Dashed line is experimental equilibrium volume.

Figure 9

Magnetic moment sizes for all individual atoms in ${\mathrm{Fe}}_{0.25}{\mathrm{Ni}}_{0.75}$, both Fe and Ni, as a function of atomic volume ${\AA }^3$. Dashed and dotted lines are experimental equilibrium volume and transition volume, respectively.

Figure 10

Enthalpy differences between noncollinear and collinear calculations for all three compositions. Dashed lines represent the magnetic transitions in NC calculations.

Figure 11

Equation of state for ${\mathrm{Fe}}_{0.64}{\mathrm{Ni}}_{0.36}$ from NC calculations, collinear calculations, and experiment from Ref. [14]. The dashed line shows the Birch-Murnaghan equation of state fitted to the ferromagnetic data points.

Figure 12

Equation of state for ${\mathrm{Fe}}_{0.5}{\mathrm{Ni}}_{0.5}$ from NC calculations, collinear calculations, and experiment on ${\mathrm{Fe}}_{0.55}{\mathrm{Ni}}_{0.45}$ from Ref. [14]. The dashed line shows the Birch-Murnaghan equation of state fitted to the ferromagnetic data points.

Figure 13

Equation of state for ${\mathrm{Fe}}_{0.25}{\mathrm{Ni}}_{0.75}$ from NC calculations, collinear calculations, and experiment on ${\mathrm{Fe}}_{0.2}{\mathrm{Ni}}_{0.8}$ from Ref. [14]. The dashed line shows the Birch-Murnaghan equation of state fitted to the ferromagnetic data points.