Possible half-metallic behavior of ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ Heusler alloys: Theory and experiment

This paper reports a combined experimental and theoretical study of structural, electronic, magnetic, and mechanical properties of quaternary Heusler alloys ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ prepared by arc-melting with Cr concentrations $0\le x\le 1$. Single-phase microstructures are observed for Cr compositions from $x=0.25$ to $x=1$. Lower Cr concentrations are multiphased. X-ray diffraction patterns at room temperature reveal a face-centered cubic crystal structure in all single-phase samples. The low-temperature saturation magnetic moments, as determined from magnetization measurements, agree fairly well with our theoretical results and also obey the Slater-Pauling rule for half-metals, a prerequisite for half-metallicity. All alloys are observed to have high Curie temperatures that scale linearly with the saturation magnetic moments. Relatively high mechanical hardness values are also observed. First-principles calculations also predict a finite band gap in the minority spin channel of the alloys, increasing in size with increasing Cr concentration. Cr substitution brings the Fermi level toward the center of this gap while also increasing the majority spin density of states near the Fermi level. As a whole, ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ shows great promise as a half-metal with 100% spin polarization.

Figure 1

Optical micrograph of ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ annealed at $1000{}^{\circ }\mathrm{C}$ for 15 days followed by slow cooling showing the granular microstructure. The samples were etched for 30 seconds using the Adler etchant.

Figure 2

SEM micrograph of ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ annealed at $1000{}^{\circ }\mathrm{C}$ for 15 days followed by slow cooling showing the granular microstructure.

Figure 3

Experimental XRD patterns of ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ alloy series annealed at $1000{}^{\circ }\mathrm{C}$ for 15 days investigated at room temperature; here, $*$ corresponds to the secondary phase/unknown impurity phase. The first from the bottom is the simulated XRD pattern for ordered ${\mathrm{L}2}_1$ structure of CFG. The relative intensity (y axis) is plotted in log scale so that all the peaks can be seen clearly.

Figure 4

(a) Enlargement of (111) and (200) x-ray diffraction peaks of single-phase samples and (b) the corresponding simulated patterns for the ideal ordered structure.

Figure 5

Rietveld refinement performed on ${\mathrm{Co}}_{1.50}{\mathrm{Cr}}_{0.50}\mathrm{FeGe}$ annealed at $1000{}^{\circ }\mathrm{C}$ for 15 days followed by slow cooling considering first atomic configuration given in Table 1.

Figure 6

Crystal structure in unit cell of (a) CFG and (b) ${\mathrm{Co}}_{1.50}{\mathrm{Cr}}_{0.50}\mathrm{FeGe}$ (I) configuration mentioned in Table 1 assuming ${\mathrm{L}2}_1$ structure. The structures are shown in their ideal, unrelaxed forms.

Figure 7

Variation of lattice parameter with Cr concentration showing linear behavior. The black data point is the reported literature value [30, 36].

Figure 8

(a) The field-dependent magnetization at 1.8 K of ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}(0\le x\le 1)$. The inset shows the enlargement for $x=0.50$. (b) The saturation magnetic moment vs Cr concentration, both the experimental value and the value calculated according to the Slater-Pauling rule for half-metals.The inset shows the Arrot plot for $x=0.50$. The black data points represent reported literature values [30, 36].

Figure 9

(a) Temperature dependence of magnetization at 100 Oe. The inset shows the first-order derivative of magnetization as a function of temperature, the minima of which is used to extract ${\mathrm{T}}_c$. (b) Variation of Curie temperature as a function of saturation magnetic moment.The black data points represents reported literature value [36].

Figure 10

Vickers hardness vs Cr concentration in ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$, all annealed at $1000{}^{\circ }\mathrm{C}$ for 15 days, with imprint of the indenter with radial cracks for $x=0.50$ [bottom right].

Figure 11

Site preference energies (in eV/atom) for different configurations of ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ as a function of Cr concentration created manually. Each data point represents a different configuration given in Table 4 and the color axis indicates the magnetic moment value for each structure.

Figure 12

Spin polarized total DOS for ${\mathrm{Co}}_{2-x}{\mathrm{Cr}}_x\mathrm{FeGe}$ ($x=$ 0, 0.25, 0.50, 0.75, and 1). The blue arrow represents the majority spin channel and red arrow represents minority spin channel. Number of states in each figure is scaled with respect to one formula unit.

Figure 13

Atom-resolved DOS for $x=0.50$. I and II in parenthesis distinguishes the same atom type with different magnetic environment. For simplicity same color is used for minority (lower-half) and majority (upper-half) spin channels in each case.

Figure 14

Crystal structure showing the different magnetic environments in unit cell of $x=0.50$ assuming I configuration in Table 4.