Magnetic properties of Fe-doped MnAl

Electronic and magnetic properties of L10-ordered FexMn1−xAl alloys (x=0, 0.0625, 0.125, 0.1875, 0.5) are investigated by first-principle supercell calculations. Pristine MnAl exhibits robust ferromagnetism involving the dense-packed Mn atoms in (001) planes of the tetragonal structure. Iron substitution for Mn significantly deteriorates the magnetization of the alloy. The reduction is a dilution effect, caused by the relatively small Fe moment of about 1.9 μB per atom, as compared to the Mn moment, which exceeds 2.4 μB. By contrast, 50% Fe substituted for Mn (x=0.5) yields a magnetocrystalline anisotropy enhancement of about 40%. Both the magnetization reduction and the anisotropy enhancement mainly arise due to the change in dxy and dzx minority density of states (DOS) at the Fermi level. 88 digitalcommons.unl.edu Ma g n e t i c p r o p e r t i e s o f fe-d o p e d Mnal 89 perature increases with increasing Fe concentration, confirming that Fe doping strongly affects the structural and magnetic properties of MnAl alloys. In this work, we use first-principle calculations to study the effect of Fe substitution on the magnetic properties of MnAl alloys. Our results demonstrate that Fe substitution for Mn in τ-phase MnAl enhances the magnetic anisotropy energy but decreases the saturation magnetization. 2. Computational details The calculations are performed using a frozen-core fullpotential projected augumented wave (PAW) method [16], as implemented in the Vienna ab-initio simulation package (VASP) [17]. The electronic exchange and correlation effect are described within the generalized-gradient approximation (GGA), using the functional proposed by Perdew et al. [18]. The energy cutoff of the plane wave basis set is taken as 450 eV. For all the calculations, the experimental lattice parameter of MnAl is used (a=3.93 Å, c=3.56 Å) and energy convergence is set at 10−6. The optimized value of cut-off energy is taken to be 450 eV. Figure 1 shows the supercell used in the calculations, which consists of 32 atoms. In our calculations, we assume that Fe substitutes for Mn, as suggested by the reported atomic radii of 1.43 Å for Al, 1.26 Å for Mn, and 1.27 Å for Fe [19]. The electronic structure, magnetic moment and magnetic anisotropy of FexMn1−xAl alloys (x=0.0625, 0.1250, 0.1875, 0.500) are calculated. To compute the magnetic anisotropy energy, 512 k-points are used in the irreducible part of Brillouin zone. The convergence of energy with respect to the number of k-points has been carefully checked, with the finding that 512 k-points are sufficient to calculate the magnetic anisotropy energy accurately. 3. Results and discussion Table 1 shows the calculated average moments of Fe, Mn and Al as well as the total magnetic moments for all investigated MnAl stoichiometries. In pure L10-ordered MnAl, the calculated moments of Mn and Al atoms are 2.44 μB and −0.061 μB, respectively, indicating antiferromagnetic coupling between Mn and Al sublattices. The experimental saturation magnetization of Fe-free MnAl, 0.7 T is lower than the calculated magnetization (1.0 T), very likely due to Mn antisite disorder. In Table 1, the off-stoichiometric compositions Mn15FeAl16, Mn14Fe2Al16, Mn13Fe3Al16 and FeMnAl2 correspond to Fe concentrations of 6.25%, 12.5%, 18.75% and 50%, respectively. Table 1 shows that the total magnetic moment of the supercell becomes smaller as the Fe concentration increases. However, in contrast to the situation manifest in Fe-substituted MnBi thin films [22], the experimentally-confirmed Curie temperature enhancement supports the absence of antiferromagnetic interatomic exchange between Fe and Mn. In fact, we have found a local magnetic moment value of 1.9 μB for Fe (somewhat reduced from the bulk value of 2.2 μB per Fe atom) and Mn is 2.45 μB. This indicates that the moment reduction is a “dilution” effect, caused by the substitution of Fe for Mn. Further insight into the origin of Fe and Mn magnetic moment is provided by the computed densities of states (DOS). Figure 2 shows the total densities of states of MnAl and Fe0.5Mn0.5Al. Compared to MnAl, the states of Fe0.5Mn0.5Al are shifted to lower energies which is a band-filling effect. Since Fe has one electron more than Mn which enhances the minority DOS in the vicinity of the Fermi level. This results in the reduction of magnetic moment in Fe0.5Mn0.5Al compared to MnAl. Figure 3 shows the element-specific partial densities of states (PDOS) in Fe0.5Mn0.5Al. We find almost completely filled majority d bands for both Fe and Mn atoms whereas the minority bands are partially occupied (strong ferromagnetism). The d bands of Fe and Mn strongly hybridize, and the exchange splitting of Fe DOS is smaller than that of Mn, resulting in a smaller magnetic moment per Fe atom and a reduced total magnetic moment. For all compositions, there is also some negative contribution to the magnetic moment due to the p-electrons of Al atom. At the Fermi level, the minority DOS (↓) is much larger than the majority DOS (↑). This means that additional Fe substitution for Mn would yield extra d electrons that go predominantly into the minority band and further reduce the overall magnetization. This approximately linear dependence of the total moment on the Fe concentration is also evident from Table 1. The magnetic anisotropy energies of MnAl and FexMn1−xAl are calculated by comparing the energy differences between in-plane and perpendicular magnetization directions. The Figure 2. Calculated total DOS for MnAl and Fe0.5Mn0.5Al. Positive and negative values on the vertical axis indicates the density in majority and minority spin states, respectively. The arrows indicate the predominant character of the peaks. Figure 1. Typical FexMn1−xAl supercell structures: (a) x=0.0625 and (b) x=0.125. Table 1. Total magnetic moments, average atomic magnetic moments and magnetic anisotropy energies of the investigated Fe–Mn–Al. Total 〈Fe〉 〈Mn〉 〈Al〉 K1 (μB) (μB) (μB) (μB) (meV/supercell) Mn16Al16 38.06 – 2.44 −0.061 4.855 Mn15FeAl16 37.608 1.886 2.445 −0.06 5.047 Mn14Fe2Al16 37.023 1.885 2.443 −0.059 5.189 Mn13Fe3Al16 36.754 1.924 2.455 −0.058 5.416 Mn8Fe8Al16 34.008 1.899 2.461 −0.056 6.968 90 Ma c h a n d a e t a l. i n Jo u r n a l o f Ma g n e t i s M a n d Ma g n e t i c Ma t e r i a l s 365 (2014) calculated magnetic anisotropy for bulk L10-MnAl is 0.62 meV/unit cell, or K1=1.77 MJ/m3. This is in agreement with previous theoretical and experimental results [7, 20, 21]. Notably the calculated magnetic anisotropy energy is 1.5 MJ/ m3 using an LMTO method [20]. Iron substitution in MnAl enhances the anisotropy up to 2.5 MJ/m3 for Mn8Fe8Al16, as shown in the last row of Table 1. This is because an Fe atom has one extra 3d electron compared to Mn and the magnetic anisotropy strongly depends on the number of electrons in the system. In Ref. [23] and [24] it has been argued that the magnetic anisotropy increases with the number of valence electrons, reaching a maximum for 8 valence electrons and decreasing towards the end of the series. In Mn and Fe the valence electron configuration is 3d54s2 and 3d64s2 with the total number of valence electrons 7 and 8, respectively. However, such rules are very crude, and the magnetocrystalline anisotropy generally oscillates as an atomicstructure-dependent function of the d-band filling [25–27]. An alternative way of rationalizing the trend found for magnetic anisotropy in MnAl is second-order perturbation theory [28]. In this approximation, the anisotropy is caused by matrix elements or coupling of the spin–orbit interaction between occupied and unoccupied states and is inversely proportional to the energy difference between occupied and unoccupied k states, K1~1/(Eo−Eu). The partial DOS of Figure 3 shows that the majority states are almost fully occupied, so that the anisotropy is mainly determined by coupling between the minority states, with a smaller contribution attributed to matrix elements between majority and minority states. The shapes of Mn DOS in MnAl and in Fe0.5Mn0.5Al are very similar, but there is a small difference in the position of peaks. Near the Fermi level, where the Eo−Eu is smallest, the DOS is larger for Fe0.5Mn0.5Al than for MnAl, corresponding to an enhanced number of states that contribute to the anisotropy in the Fe-modified compound. There are virtually no dx−y states at the Fermi level for either compound, but the other subbands, especially dyx and dzx, lies at the Fermi level and therefore contributes to anisotropy. Figure 4 illustrates this situation by showing the partial DOS for the dzx band in both compounds. It is instructive to discuss how atomic-scale disorder is described by various theoretical approaches. Let us consider an equiatomic AB alloy where A atoms (yellow) and B atoms (red) have on-site atomic energies of ±Eo, respectively, Figure 5(a). The simplest approach to disorder is the virtual-crystal approximation (VCA), where the on-site potential is averaged over all A and B atoms, as illustrated in Figure 5(b). This approach is trivial from the viewpoint of density of states, which is assimilated to that of a monatomic metal, as in the closely related rigid-band model [29]. The shortcomings of this approximation can be seen very easily by considering the limit of large on-site energy splittings Eo, where the “red” B atoms have much lower energies than the “yellow” A atoms. In this limit, the interatomic hopping integral |t| is much smaller than Eo, and the DOS effectively splits into two bands or narrowly-spaced level groups centered around ±Eo, in striking contrast to a single band corresponding to Figure 5(b). A major improvement is provided by the coherent-potential approximation (CPA), where the alloy behavior is deduced by properly distinguishing between A and B atoms on any given site but treating the neighboring atoms as an effective medium [29–31]. In terms of Figure 5, the CPA amounts to a weighted average between A atoms (c) and B atoms (c), very similar to the mean-field approximation in statistical physics but requiring a more complicated treatment of the individual electron states. The present supercell approach is an advanced but potentially time-consuming method. A small chunk of material—for example the bright 3×3 region in Figure 5(a)—is repeated periodically. This makes it possible to exploit the Bloch theorem and the accuracy of the calculation (including the resolution of the chemical concentration) is limited by the supercell size only. Compared to the CPA, supercell calculations have the advantage of correctly describing cluster-localization effects [30, 32]. An example of such a cluster is the dark region of six low-energy B or “red” atoms in the top-left corner of Figure 5(a). If the AB alloy is filled with electrons, then the first electrons go into “red” or B clusters, where they benefit from both the low on-site energy and from the freedom to hop around in B-metal mini regions. This hopping effect is poorly described in single-site approximations such as the CPA [30, 32]. In the present paper, the biggest supercell contain 16 formula units of MnAl. This makes it possible to resolve defect concentrations with a resolution of about 3%. For one Fe atom per supercell, there is only one non-equivalent configuration Figure 1(a). For two Fe atoms per unit cell, there are 7 nonequivalent configurations, as previously analyzed for isostructural Fe–Co–Pt [33]. Figure 1(b) shows one of these configurations, where the defected atoms are nearest neighbors and exhibit a hopping contribution that is not accurately described Figure 3. Spin-polarized majority (↑) and minority (↓) d-band densities of states (DOS) of MnFeAl2 relative to the Fermi level. The inset shows the sand p-band DOS of Al. Figure 4. Partial DOS for the dzx bands in MnAl and Fe0.5Mn0.5Al. Ma g n e t i c p r o p e r t i e s o f fe-d o p e d Mnal 91 by the CPA. For higher concentrations, the ensemble averaging becomes time-consuming, but it is then possible to exploit the self-averaging of the electronic structure [29] of the considered alloys.