Structural, electronic, and magnetic properties of CoFeVGe-based compounds: Experiment and theory

Heusler alloys are interesting materials for research due to their various novel properties, which are useful in advancing modern technology.¹ While a wide range of interesting properties such as high perpendicular magnetic anisotropy,² shape memory effect,³ topological magnetic order,⁴ and magnetocaloric effect⁵ have been observed in Heusler alloys, half-metallic and spin-gapless semiconducting properties have attracted increasing attention.⁶ In principle, half-metals and spin-gapless semiconductors have ability to produce fully (100%) spin polarized currents because of the nature of their electronic band structure, which is metallic for one spin channel and insulating for the opposite spin channel.^6–8 For room temperature spintronic applications, these materials need to show robust half-metallicity at room temperature, which is possible in magnetic materials exhibiting high Curie temperature much above room temperature.⁹ Many half-metallic Heusler alloys have been found to show this behavior and their magnetic and electronic properties can be tuned as desired by adjusting the elemental composition, applying mechanical strain, etc.^10–12 For example, we recently showed that half-metallicity can be induced in a half-Heusler alloy CrMnSb by chemical substitution, which results in a modification of the lattice parameter.^13,14

Heusler alloys crystallize mainly in cubic structure. The completely ordered quaternary Heusler alloys crystalize in cubic Y type (XX′YZ) structure (prototype LiMgPdSn).¹ However, this structure is prone to various types of disorders such as L2₁, B2 and A2. When X and X′ atoms mix in the lattice, the alloy assumes L2₁ type structure, whereas B2 type structure results from mixing of Y and Z atoms. The A2 disorder results from a random mixing of all atoms (X, X′, Y, and Z). These disorders are typically detrimental to the magnetic and spin-electronic properties of Heusler alloys.¹⁵ 

In this work, we present our combined experimental and theoretical investigations on the magnetic and electronic properties of CoFeVGe and related alloys Co_1.25Fe_0.75VGe, Co_0.75Fe_1.25VGe, and CoFe_0.75VGe. Xiong et al. have shown using first principles calculation that CoFeVGe exhibits half-metallic properties in its Y structure but we have not found any experimental report in the literature yet.¹⁶ 

We have prepared CoFeVGe, Co_1.25Fe_0.75VGe, Co_0.75Fe_1.25VGe, and CoFe_0.75VGe bulk alloys using arc-melting and high-vacuum annealing. First, highly pure (99.99%) metal pieces with proper weight ratio were cut from corresponding commercially available pellets and melted on a water-cooled Cu hearth of an arc furnace in an argon environment. The arc-melted ingots were then annealed in a tubular vacuum furnace (∼10⁻⁷ torr) at 600 °C for 48 hours to further homogenize the samples. The crystal structures of the samples were analyzed using Rigaku MiniFlex600 x-ray diffractometer with Cu-Kα source (λ = 1.54 Å), and magnetic properties were measured using a Quantum Design VersaLab magnetometer.

All calculations are performed with the Vienna ab initio simulation package (VASP),¹⁷ within the projector augmented-wave method (PAW)¹⁸ and generalized-gradient approximation (GGA) of Perdew, Burke, and Ernzerhof.¹⁹ The cut-off energy of the plane waves was set to 500 eV, and the integration method by Methfessel and Paxton with a 0.05 eV width of smearing was used.²⁰ The total energy and electronic structure calculations were performed with the energy convergence criteria of 10⁻⁶ eV. The Brillouin-zone integration was performed with a k-point mesh of 12 × 12 × 12, for a 16-atom cubic cell. Some of the results and figures were obtained using the MedeA^® software environment.²¹ Most of the calculations were performed using Extreme Science and Engineering Discovery Environment (XSEDE) resources located at the Pittsburgh Supercomputing Center (PSC),²² and the resources of the Center for Functional Nanomaterials (CFN) at Brookhaven National Laboratory (BNL).

Figure 1 shows calculated element- and spin-resolved density of states of CoFeVGe (a), CoFe_0.75VGe (b), Co_0.75Fe_1.25VGe (c), and Co_1.25Fe_0.75VGe (d). Calculated lattice constants, magnetization, and spin polarization values are shown in the corresponding figures. All four considered compounds have lowest energy in the regular cubic Heusler structure in which the magnetic alignment is ferromagnetic. The main contribution to the total magnetization comes from Co and Fe, with the local magnetic moments of ∼1.1 µ_B/Co, and 0.8 µ_B/Fe. The magnetic moment of V is small (∼0.1 µ_B per atom), while Ge is non-magnetic.

Our calculations indicate that CoFeVGe, Co_1.25Fe_0.75VGe, and Co_0.75Fe_1.25VGe are highly spin polarized, with spin polarization values of over 80%, as shown in Figs. 1(a), 1(c), and 1(d). Here, the spin polarization is calculated as $P=N↑EF−N↓EFN↑EF+N↓EF$⁠, where $N↑↓EF$ is the spin-dependent density of states at the Fermi level, E_F.²³ Even though the calculated spin-polarization values of CoFeVGe, Co_1.25Fe_0.75VGe, and Co_0.75Fe_1.25VGe are large, these materials are not half-metallic, mainly due to the presence of the minority-spin vanadium states around Fermi level (see Fig. 1). However, the large calculated spin polarization shows that these materials have potential for spintronic applications. The calculated spin polarization of CoFe_0.75VGe in regular cubic structure is only 61%, i.e. reducing the content of Fe without increasing Co results in reduced spin polarization.

Figure 2 shows the x-ray diffraction patterns recorded on the powder samples of Co_1.25Fe_0.75VGe, CoFeVGe, CoFe_0.75VGe and Co_0.75Fe_1.25VGe alloys at room temperature. The XRD patterns can be indexed with the cubic Heusler structure with disorder. The absence of superlattice peaks (111) and (200) suggests that the samples have A2 type disorder. In addition, the patterns of CoFe_0.75VGe and Co_0.75Fe_1.25VGe show weak peaks from unknown impurity.

Figure 3(a) shows the thermomagnetic curves M(T) recorded at 1 kOe on Co_1.25Fe_0.75VGe, CoFeVGe, CoFe_0.75VGe and Co_0.75Fe_1.25VGe alloys. There is a smooth transition on the M(T) curves of all these alloys at their Curie temperatures. The parent alloy CoFeVGe has a Curie temperature (T_C) of 288 K which is slightly below the room temperature. Increasing Fe content at the cost of Co has decreased the Curie temperature. The T_C of Co_0.75Fe_1.25VGe is 238 K. However, the T_C can be increased by reducing Fe content either keeping Co concentration constant or increasing it. The Curie temperature of Co_1.25Fe_0.75VGe and CoFe_0.75VGe are slightly above room temperature, namely 305K and 306K, respectively. However, the magnetization of Co_1.25Fe_0.75VGe shows very slow decrease at the Curie temperature similar to that of a disordered ferrimagnetic material and also the magnetization has decreased drastically as compared to those of the other samples.

Figure 3(b) shows the isothermal magnetization curves M(H) of CoFeVGe, CoFe_0.75VGe and Co_0.75Fe_1.25VGe alloys recorded at 100 K. All three alloys show very small coercivities with saturation magnetizations of 42 emu/g, 35 emu/g, and 39 emu/g for CoFeVGe, CoFe_0.75VGe and Co_0.75Fe_1.25VGe, respectively. The saturation magnetization of the cobalt rich sample Co_1.25Fe_0.75VGe (not shown in Fig. 3(b)) which shows ferrimagnetic like transition at the Curie temperature is very small (1.5 emu/g) as compared to those of other three samples. The saturation magnetizations 42 emu/g, 39 emu/g and 35 emu/g of three samples CoFeVGe, Co_0.75Fe_1.25VGe and CoFe_0.75VGe follow the trend predicted by theory (1.98 µ_B/f.u., 1.68 µ_B/f.u., and 1.45 µ_B/f.u.). However, Co_1.25Fe_0.75VGe which is predicted to have the highest magnetization (2.21 µ_B/f.u.) among the studied samples shows the smallest magnetization of 1.5 emu/g. Although all studied samples are disordered, the presence of excess cobalt in Co_1.25Fe_0.75VGe has shown unique magnetic behavior inconsistent with our theoretical prediction.

We have investigated the electronic, structural, and magnetic properties of CoFeVGe, Co_1.25Fe_0.75VGe, Co_0.75Fe_1.25VGe, and CoFe_0.75VGe bulk alloys. Our first principles calculations suggest that all four alloys show ferromagnetic order, where CoFeVGe, Co_1.25Fe_0.75VGe, and Co_0.75Fe_1.25VGe are highly spin polarized with spin polarization values of over 80% but the spin polarization of CoFe_0.75VGe is only 61%. The samples prepared using arc-melting and annealing have crystallized in a cubic structure with A2 type disorder. The experimental (theoretical) saturation magnetizations of CoFeVGe, Co_0.75Fe_1.25VGe, and CoFe_0.75VGe and are 42 emu/g (1.98 µ_B/f.u.), 39 emu/g (1.68 µ_B/f.u.), 35 emu/g (1.45 µ_B/f.u.) respectively, but that of Co_1.25Fe_0.75VGe is only 1.5 emu/g irrespective of the predicted high value of 2.21 µ_B/f.u. The observed magnetic and electronic band properties indicate that the investigated materials have the potential for near room temperature magnetic applications desiring low magnetization and high spin polarization.

This research is supported by the National Science Foundation (NSF) under Grant Numbers 2003828 and 2003856 via DMR and EPSCoR. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. This work used the XSEDE Regular Memory (Bridges 2) and Storage (Bridges 2 Ocean) at the Pittsburgh Supercomputing Center (PSC) through allocation TGDMR180059, and the resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, and the Scientific Data and Computing Center, a component of the Computational Science Initiative, at Brookhaven National Laboratory (BNL) under Contract No. DE-SC0012704.

The authors have no conflicts to disclose.

Parashu Kharel: Conceptualization (lead); Writing – original draft (equal). Zachary Lehmann: Data curation (lead); Formal analysis (equal). Gavin Baker: Data curation (equal). Lukas Stuelke: Data curation (equal). Shah Valloppilly: Data curation (equal); Writing – review & editing (supporting). Paul M. Shand: Funding acquisition (equal); Writing – review & editing (equal). Pavel V. Lukashev: Data curation (equal); Funding acquisition (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.