Pressure-induced magnetic moment abnormal increase in Mn2FeAl and non-continuing decrease in Fe2MnAl via first principles

The magnetism of Fe2MnAl and Mn2FeAl compounds are studied by first principles. Evolutions of magnetic moment of Fe2MnAl display distinct variation trends under pressure, showing three different slopes at different pressure intervals, 0~100 GPa, 100~250 GPa, 250–400 GPa, respectively, and the moment collapses finally at 450 GPa. The magnetic moment of Mn2FeAl shows an increasing tendency below 40 GPa and decreases subsequently with pressure, and collapses ultimately at about 175 GPa. Such non-continuing decrease of Fe2MnAl originates from the unusual charge transfer of Fe and Mn and bond populations rearrangement of Fe-Fe and Mn-Fe, whereas the distinct moment evolution of Mn2FeAl is attributed to the complicated distributions of bond populations. The half-metallicity of the compounds can be maintained at low pressure, below about 100 GPa in Fe2MnAl and 50 GPa in Mn2FeAl. The magnetic moment collapse process didn’t induce volume and bond length anomalies in the two compounds, the unique anomaly is the elastic softening behaviour in elastic constant c44 and shear (G) and Young’s (E) moduli of Fe2MnAl at 270 GPa, where the second moment collapse occurs.

The presence of nanotechnology requires more novel materials with extraordinary physical properties. Half-metallic heusler magnetic compounds can play a key role in the field of microdevice as it shows metallic properties in one of its spin orientations while an evident energy gap is formed in the other spin orientation. The number of heusler family is more than 1000 members and nearly all of them crystalline similar to that of binary semiconductors 1 . The general chemical formula can be classified into two different styles, half-(semi-) or full-heusler structures.
Recently, half-metallic (XYZ) characteristic has been reported in full-Heusler (X 2 YZ) alloys, including Co 2 YZ, Mn 2 YZ, Fe 2 YZ, Cr 2 YZ, and V 2 YZ 2-5 , where X and Y are transition metal elements and Z is a sp element, in which Fe-(Mn-)containing compounds attract much attention due to the complicated magnetic behavior of Fe and Mn element. Fe 2 MnAl exhibits Cu 2 MnAl-type structure (Fm m 3 , 225#) and Mn 2 FeAl has the Hg 2 CuTi-type structure (F m 43 , 216#). However, the detailed magnetic moment evolution under pressure for the typical Fe-(Mn-)containing compounds are still unknown, in particular for the key role of the on-site coulomb term in this kind of compounds.
In this paper, two representative compounds Fe 2 MnAl and Mn 2 FeAl are deeply studied under pressure by first principles. Our comprehensive calculations confirmed the crucial role of on-site coulomb term in the investigation of electronic structures, whereas such influence is not sensitive in the macroproperty calculations. In addition, we also systematically simulated the magnetic moment evolution with volume variations and found

Computational Methods
Spin-polarized geometric and electronic relaxations are performed by the projector augmented wave method 6 . The exchange correlation is calculated using generalized gradient approximation perdew-burke-ernzerh function (GGA-PBE) 7 . The k meshes 8 9 × 9 × 9 is used for the first Brillouin zone integration. Energy cutoff 450 eV is set for plane wave basis. The on-site Coulomb term U is selected for Fe (U = 2.0 eV) and Mn (U = 0.8 eV). The exchange integral J = 1.1 eV is also carefully selected. The self-consistent convergence of the energy is at 5.0 × 10 −7 eV/atom. Electronic properties. Our thorough test found that it is necessary to introduce the on-site coulomb term U and J during the calculation of electronic properties, otherwise the band structures at spin-down orientation will cross the Fermi level, as is shown in Fig. 4, in which the left panel is the density of states (DOS) but the right one is the energy band at G point of the Brillouin zone of Fe 2 MnAl near Fermi level in the spin-down orientation. According to the definition of spin polarization given 19  To further illustrate the nature of electronic structures, we simulate the total and atomic DOS, as are shown in Figs 5 and 6. Deep analysis to the DOS for the two compounds found that d states of Fe and Mn distributed mainly at the both sides of Fermi level, with an energy range of −4.5~5 eV, in which Mn displays stronger magnetism than Fe owing to its less overlap between spin-up and spin-down channels. The DOS profile also clearly reflects the strong magnetism of Mn and weak magnetism of Fe. Furthermore, both the two compounds formed potential valleys at Fermi level, implying the extreme stability of the compounds, as is reflected in the moment collapse process.

Results and Discussion
The two different kinds of Mn atoms in Mn 2 FeAl, named Mn(A) and Mn(B), presenting almost opposite charge probability distributions in the whole space, namely, charges located at spin-up channel distribute mainly at Fermi level, whereas charges located at spin-down channel distribute mainly at low-energy zone in Mn(A), which is just opposite  in Mn(B) atom. The substantial discrepancy of spin-up and spin-down charge location is the origin of the higher magnetism collapse pressure. Mn(B) bonds with more Al and thus accumulates more charges at lower energy zone, which is obviously larger than that of Mn(A) in Mn 2 FeAl, as are also the cases for their Fermi-level values. In particular, Mn(A) exhibits a peak at Fermi level but Mn(B) and Fe locate at the steep hill, both of which make the charge transfer easier with respect to that of Fe 2 MnAl, consisting with the fact of its lower magnetism collapse pressure. Cr ion moment collapse process has been deeply discussed in         wide pressure range and increase again after the moment collapse. The DOS profiles of Fe and Mn clearly reflected their individually magnetic contributions to the total crystal structure. Both Fe d states, comprising of spin-up and spin-down components, distribute mainly at higher energy level, whereas Mn spin-up d states contribute mainly at lower energy level. Generally, both Fe d states shift towards lower energy level side under pressure, as is also the case in Mn. In fact, both Fe d states present highly delocalized features at 100 GPa below Fermi level, whereas this is not true in Mn, indicating that Mn also plays a key role to the total magnetism at high pressure.
The moment direction of Fe is changed at about 25 GPa in Fe 2 MnAl, and its magnitude keeps almost unchanged between 50 GPa and 400 GPa, with a value of about 0.15 μ B . The magnetism collapse process is highly correlated with the mulliken charge and bond population distributions, through which many evident evidences can be clearly seen, such as a strong indicator of charge transfer tendency is seen at the first collapse pressure 100 GPa, as are also the cases of 250 and 400 GPa, respectively.
The total moment curve of Mn 2 FeAl shows a peak at about 40 GPa, which is similar with the variation tendency of Mn (

Conclusions
The present investigation demonstrates that the