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&lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-ordered MnAl shows a high magnetic moment of 2.4 &lt;i&gt;μ&lt;sub&gt;B&lt;/sub&gt;&lt;/i&gt;/&lt;i&gt;f.u&lt;/i&gt;. and magnetocrystalline anisotropy constant (&lt;i&gt;K&lt;/i&gt;) of 1.5 MJ/m&lt;sup&gt;3&lt;/sup&gt; [1,2]. The magnetocrystalline anisotropy and spin direction can be tuned by either the axial ratio &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; or substituting the Mn of MnAl by transition metals. Sakuma calculated &lt;i&gt;K&lt;/i&gt;&lt;sub&gt;u&lt;/sub&gt; of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-ordered equiatomic MnAl as a function of the axial ratio &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; ranging from 0.60 to 1.2 by first-principles calculation [1]. It was found that the spin direction changes to the out-of-plane direction (uniaxial) from the in-plane direction at &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; = 0.7071 by changing the magnetocrystalline anisotropy sign to positive from negative. The calculated magnetocrystalline anisotropy constant is 1.5 MJ/m&lt;sup&gt;3&lt;/sup&gt; at &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; = 0.9058. Sakuma used the lattice constants of &lt;i&gt;a &lt;/i&gt;=3.93 Å and &lt;i&gt;c &lt;/i&gt;=3.56 Å measured at 300 K in his first-principles calculations.&lt;br/&gt;On the other hand, Manchanda &lt;i&gt;et al&lt;/i&gt;. have performed the first-principles calculation on Fe-substituted&lt;i&gt; L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-ordered MnAl to investigate magnetocrystalline anisotropy constant and found that Fe increases the magnetocrystalline anisotropy constant to 2.5 MJ/m&lt;sup&gt;3&lt;/sup&gt; from 1.5 MJ/m&lt;sup&gt;3 &lt;/sup&gt;of non-substituted MnAl. However, the total magnetic moment decreased, and the spin direction did not change [3]. Neither Sakuma nor Manchanda reported the Curie temperature for various &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; MnAl and Fe-substituted MnAl and relaxed the studied MnAl system.&lt;br/&gt;In this paper, we have systematically investigated the effects of transition metals (Fe, Co, Ni) on magnetization, magnetocrystalline anisotropy, and Curie temperature of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-ordered MnAl.&lt;br/&gt;We used the WIEN2k package based on density functional theory (DFT) and the full-potential linearized augmented plane wave (FPLAPW) method to conduct the first-principles calculations [4]. All calculations used 19 × 19 × 27 k-point mesh generating 1400 k-points in the irreducible part of the Brillouin zone to obtain electronic structures of Mn&lt;sub&gt;0.5&lt;/sub&gt;TM&lt;sub&gt;0.5&lt;/sub&gt;Al (TM = Mn, Fe, Co, and Ni). Each TM has the following valence electrons (&lt;i&gt;n&lt;/i&gt;): 7 for Mn (3&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;5&lt;/sup&gt; 4&lt;i&gt;s&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;), 8 for Fe (3&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;6&lt;/sup&gt; 4&lt;i&gt;s&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;), 9 for Co (3&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;7&lt;/sup&gt; 4&lt;i&gt;s&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;), and 10 for Ni (3&lt;i&gt;d&lt;/i&gt;&lt;sup&gt;8&lt;/sup&gt; 4&lt;i&gt;s&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;). After having relaxed &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-ordered Mn&lt;sub&gt;0.5&lt;/sub&gt;TM&lt;sub&gt;0.5&lt;/sub&gt;Al (TM = Mn, Fe, Co, and Ni), we obtained the lattice constants, volumes, and &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; ratios in Table 1. It is found that the &lt;i&gt;c&lt;/i&gt;/&lt;i&gt;a&lt;/i&gt; ratio and volume decrease with an increase in &lt;i&gt;n&lt;/i&gt; from 7 (Mn) to 10 (Ni) in Table 1.&lt;br/&gt;Figure 1 shows the density of states (DOS) for Mn&lt;sub&gt;0.5&lt;/sub&gt;TM&lt;sub&gt;0.5&lt;/sub&gt;Al (TM = Mn, Fe, Co, and Ni) with spin configuration. DOS significantly changes with the TM substitution. It is striking that Ni-substituted MnAl shows the ferrimagnetic spin configuration, as seen in Fig. 1(d). However, the ferromagnetic spin configuration is set in Mn&lt;sub&gt;0.5&lt;/sub&gt;TM&lt;sub&gt;0.5&lt;/sub&gt;Al (TM = Mn, Fe, and Co). As summarized in Table 1, the total magnetic moment decreases as the valence electron increases in the order of Ni, Co, and Fe.&lt;br/&gt;In order to calculate the &lt;i&gt;K&lt;/i&gt; of the Mn&lt;sub&gt;0.5&lt;/sub&gt;TM&lt;sub&gt;0.5&lt;/sub&gt;Al system, the magnetocrystalline anisotropy energy (MAE) was calculated using the total energy difference between &amp;lt;001&amp;gt; and &amp;lt;100&amp;gt; spin configurations (Δ&lt;i&gt;E&lt;/i&gt; = &lt;i&gt;E&lt;/i&gt;&lt;sub&gt;&amp;lt;001&amp;gt;&lt;/sub&gt; - &lt;i&gt;E&lt;/i&gt;&lt;sub&gt;&amp;lt;100&amp;gt;&lt;/sub&gt;). The Fe substitution leads to a significant increase in &lt;i&gt;K&lt;/i&gt; from 1.34 MJ/m&lt;sup&gt;3&lt;/sup&gt; to 2.98 MJ/m&lt;sup&gt;3&lt;/sup&gt;. &lt;sup&gt; &lt;/sup&gt;When either Co or Ni replaces Fe, the &lt;i&gt;K&lt;/i&gt; becomes negative and is -0.3 MJ/m&lt;sup&gt;3&lt;/sup&gt; for Co or -0.18 MJ/m&lt;sup&gt;3&lt;/sup&gt; for Ni in Table 1. This implies the magnetization (Co, Ni) direction changes to the in-plane direction from the out-of-plane direction, &lt;i&gt;i.e&lt;/i&gt;., uniaxial (Mn and Fe). Curie temperature (&lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;) was calculated by the mean-field approximation (MFA). The &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; dramatically decreases from 685 K(Mn) to 20 K(Ni). Alloying the MnBi with transition elements could tune the spin direction and magnetocrystalline anisotropy of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-ordered MnAl. However, magnetization and Curie temperature are negatively affected by the alloying. We will discuss all these findings in detail in this presentation.&lt;br/&gt;&lt;br/&gt;* This work was supported in part by the E. A. “Larry” Drummond Endowment at the University of Alabama.

**References:**

[1] A. Sakuma, &lt;i&gt;J. Phys. Soc. Jpn.&lt;/i&gt; 63, 1422 (1994)&lt;br/&gt;[2] J. H. Park, Y. K. Hong, &lt;i&gt;et al&lt;/i&gt;., &lt;i&gt;J. Appl. Phys&lt;/i&gt;. 107, 09A731 (2010)&lt;br/&gt;[3] P. Manchanda, et al., &lt;i&gt;J. Magn. Magn. Mater&lt;/i&gt;, 365, 88-92 (2014)&lt;br/&gt;[4] Blaha, P. and Schwarz, K., WIEN2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz Techn. Universität Wien, Vienna, Austria, 2001)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aecee2e75cceaee3a872a555081225de.jpg)
Table 1. Lattice parameters and magnetic properties of &lt;i&gt;L&lt;/i&gt;1&lt;sub&gt;0&lt;/sub&gt;-Mn&lt;sub&gt;0.5&lt;/sub&gt;TM&lt;sub&gt;0.5&lt;/sub&gt;Al (TM = Mn, Fe, Co, Ni).

![](https://assets.underline.io/uploads/markdown_image/1/image/8c515420a3e4c27b6c54c6fa18f1b9d9.jpg)
Figure 1. Density of states (DOS) for (a) MnAl, (b) Mn&lt;sub&gt;0.5&lt;/sub&gt;Fe&lt;sub&gt;0.5&lt;/sub&gt;Al, (c) Mn&lt;sub&gt;0.5&lt;/sub&gt;Co&lt;sub&gt;0.5&lt;/sub&gt;Al, and (d) Mn&lt;sub&gt;0.5&lt;/sub&gt;Ni&lt;sub&gt;0.5&lt;/sub&gt;Al based relaxed lattice constants.

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 Tuning Spin and Magnetocrystalline Anisotropy of L10-ordered MnAl with Transition Metal Elements (TM = Mn, Fe, Co, Ni)*

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L10-ordered MnAl shows a high magnetic moment of 2.4 μB/f.u. and magnetocrystalline anisotropy constant (K) of 1.5 MJ/m3 [1,2]. The magnetocrystalline anisotropy and spin direction can be tuned by either the axial ratio c/a or substituting the Mn of MnAl by transition metals. Sakuma calculated Ku of L10-ordered equiatomic MnAl as a function of the axial ratio c/a ranging from 0.60 to 1.2 by first-principles calculation [1]. It was found that the spin direction changes to the out-of-plane direction (uniaxial) from the in-plane direction at c/a = 0.7071 by changing the magnetocrystalline anisotropy sign to positive from negative. The calculated magnetocrystalline anisotropy constant is 1.5 MJ/m3 at c/a = 0.9058. Sakuma used the lattice constants of a =3.93 Å and c =3.56 Å measured at 300 K in his first-principles calculations. On the other hand, Manchanda et al. have performed the first-principles calculation on Fe-substituted L10-ordered MnAl to investigate magnetocrystalline anisotropy constant and found that Fe increases the magnetocrystalline anisotropy constant to 2.5 MJ/m3 from 1.5 MJ/m3 of non-substituted MnAl. However, the total magnetic moment decreased, and the spin direction did not change [3]. Neither Sakuma nor Manchanda reported the Curie temperature for various c/a MnAl and Fe-substituted MnAl and relaxed the studied MnAl system. In this paper, we have systematically investigated the effects of transition metals (Fe, Co, Ni) on magnetization, magnetocrystalline anisotropy, and Curie temperature of L10-ordered MnAl. We used the WIEN2k package based on density functional theory (DFT) and the full-potential linearized augmented plane wave (FPLAPW) method to conduct the first-principles calculations [4]. All calculations used 19 × 19 × 27 k-point mesh generating 1400 k-points in the irreducible part of the Brillouin zone to obtain electronic structures of Mn0.5TM0.5Al (TM = Mn, Fe, Co, and Ni). Each TM has the following valence electrons (n): 7 for Mn (3d5 4s2), 8 for Fe (3d6 4s2), 9 for Co (3d7 4s2), and 10 for Ni (3d8 4s2). After having relaxed L10-ordered Mn0.5TM0.5Al (TM = Mn, Fe, Co, and Ni), we obtained the lattice constants, volumes, and c/a ratios in Table 1. It is found that the c/a ratio and volume decrease with an increase in n from 7 (Mn) to 10 (Ni) in Table 1. Figure 1 shows the density of states (DOS) for Mn0.5TM0.5Al (TM = Mn, Fe, Co, and Ni) with spin configuration. DOS significantly changes with the TM substitution. It is striking that Ni-substituted MnAl shows the ferrimagnetic spin configuration, as seen in Fig. 1(d). However, the ferromagnetic spin configuration is set in Mn0.5TM0.5Al (TM = Mn, Fe, and Co). As summarized in Table 1, the total magnetic moment decreases as the valence electron increases in the order of Ni, Co, and Fe. In order to calculate the K of the Mn0.5TM0.5Al system, the magnetocrystalline anisotropy energy (MAE) was calculated using the total energy difference between &lt;001&gt; and &lt;100&gt; spin configurations (ΔE = E&lt;001&gt; - E&lt;100&gt;). The Fe substitution leads to a significant increase in K from 1.34 MJ/m3 to 2.98 MJ/m3. When either Co or Ni replaces Fe, the K becomes negative and is -0.3 MJ/m3 for Co or -0.18 MJ/m3 for Ni in Table 1. This implies the magnetization (Co, Ni) direction changes to the in-plane direction from the out-of-plane direction, i.e., uniaxial (Mn and Fe). Curie temperature (TC) was calculated by the mean-field approximation (MFA). The TC dramatically decreases from 685 K(Mn) to 20 K(Ni). Alloying the MnBi with transition elements could tune the spin direction and magnetocrystalline anisotropy of L10-ordered MnAl. However, magnetization and Curie temperature are negatively affected by the alloying. We will discuss all these findings in detail in this presentation. * This work was supported in part by the E. A. “Larry” Drummond Endowment at the University of Alabama.

**References:**

[1] A. Sakuma, J. Phys. Soc. Jpn. 63, 1422 (1994) [2] J. H. Park, Y. K. Hong, et al., J. Appl. Phys. 107, 09A731 (2010) [3] P. Manchanda, et al., J. Magn. Magn. Mater, 365, 88-92 (2014) [4] Blaha, P. and Schwarz, K., WIEN2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz Techn. Universität Wien, Vienna, Austria, 2001)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aecee2e75cceaee3a872a555081225de.jpg)
Table 1. Lattice parameters and magnetic properties of L10-Mn0.5TM0.5Al (TM = Mn, Fe, Co, Ni).

![](https://assets.underline.io/uploads/markdown_image/1/image/8c515420a3e4c27b6c54c6fa18f1b9d9.jpg)
Figure 1. Density of states (DOS) for (a) MnAl, (b) Mn0.5Fe0.5Al, (c) Mn0.5Co0.5Al, and (d) Mn0.5Ni0.5Al based relaxed lattice constants.

technical paper

In this work, SEM image analysis and fractal dimension calculations are carried out on the fractures obtained under the same conditions for N50-type with high remanence, 30EH-type with high coercivity, and isotropic commercial Nd-Fe-B permanent magnets. It is further proved that the fractal dimensions of the fractures parallel and perpendicular to the c-axis for Nd-Fe-B permanent magnets are different. In other words, there is anisotropy in fractal dimension. In addition, it was discovered for the first time that the difference between the fractal dimensions D⊥ and D∥ of N50-type magnet with high remanence is large, and the difference between the fractal dimensions D⊥ and D∥ of the 30EH-type magnet with high coercivity is small, indicating that both remanence and coercivity are sensitive parameters with the microstructure. The difference in the fractal dimension of the fracture will provide new insights for studying the relationship between the magnetic properties and the microstructure of permanent magnetic materials. The anisotropic fractal dimension of the fracture will serve as a new performance parameter in the research of Nd-Fe-B permanent magnets. Keywords: Nd-Fe-B, Fractal dimension, Anisotropy, Performance parameter Introduction The magnetic properties of permanent magnets are closely related to the microstructure. However, researchers have seldom focused on the fractal characteristics of fractures in Nd-Fe-B permanent magnets. In fact, it is significant to study the fractal dimension of the fractured microstructure of permanent magnets with statistical self-similarity. Zhu et al. [1] reported the line-measuring dimension of fracture cracks of N50-type permanent magnets, and pointed out that the fractal dimension perpendicular to the c-axis and parallel to the c-axis has some anisotropic trends, but the difference in anisotropy is not obvious. In this work, N50-type, 30EH-type, and isotropic magnets are selected as the research objects. The anisotropic characteristics in fractal dimension of permanent magnets fractures parallel and perpendicular to the c-axis are explored. Experimental N50-type, 30EH-type, and isotropic commercial Nd-Fe-B permanent magnets were selected as the research specimens. A Zeiss field emission scanning electron microscope (FE-SEM) was used to observe the fracture morphology of all samples. The fractal dimensions of the fractures were calculated by the method of box counting dimension based on the image processing function of MATLAB. Results and Discussion The fractal dimensions of different types of magnet fractures parallel and perpendicular to the c-axis are summarized in Fig. 1. The difference ΔD between the fractal dimension D⊥ and D∥ of N50-type and 30EH-type magnets are 0.0856 and 0.0311, respectively. However, there is almost no difference in the fractal dimension of the isotropic magnet. In a word, the fractal dimension of the magnet oriented by the magnetic field has obvious anisotropy. The fractal dimension can be used as a research method to prove the anisotropy of magnets. The internal microstructure of magnet has a great influence on the magnetic parameters such as remanence, coercivity, and maximum energy product. Comparing the difference in fractal dimensions between N50-type and 30EH-type magnets, it can be found that N50-type magnet with higher remanence has larger anisotropic fractal dimensions, while 30EH-type magnet with higher coercivity has smaller anisotropic fractals dimension. The difference in ΔD of different magnets is inherently related to remanence and coercivity, which indirectly indicates that remanence and coercivity are sensitive parameters of microstructure. Conclusions The calculation on fractal dimensions of the fractures for the N50-type and 30EH-type commercial Nd-Fe-B permanent magnets along different crystalline axes demonstrates that the fractal dimensions of the fracture of the permanent magnet are anisotropic. So that the fractal dimension of the fracture can be used as a method to characterize the anisotropy of Nd-Fe-B magnet, which specifically characterizes whether the magnet has anisotropy, the magnitude of remanence and coercivity, and even the level of magnetic properties.

**References:**

[1] M.G. Zhu, W. Li, Y.K. Fang, et al. Fractal study for the fractured surface of Nd-Fe-B permanent magnets. J. Appl. Phys. 2011, 109, 07A706.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/18fb790553f6c2980aa53ad0431aab56.jpg)
Figure 1 Fractal dimensions of fractures parallel and perpendicular c-axis for different types of magnets

 Anisotropic Fractal Dimension of Nd-Fe-B Permanent Magnets Fracture Surface

The world is progressively shifting from a fossil-fuel-based energy-and-transportation system to more environmentally friendly and energy-efficient technologies. The transport sector currently presents a quarter of Europe's CO2 emissions. The European "Green Deal", presented in December 2019, aims at reaching net-zero greenhouse gas emissions by 2050. The emergence of electric vehicles and electricity production from renewable sources like wind power are necessary steps towards resolving contemporary environmental issues like climatic changes and air pollution in larger cities. However, the state-of-the-art traction motors and wind turbine generators often depend on Nd-Fe-B magnets to provide the strong and constant magnetic fields required to convert electrical to mechanical energy and vice versa. The rapid growth of the market for electric vehicles and advancements in green technologies development are inevitably related to the increasing demand for Nd and other rare-earth (RE) elements (RE = Nd, Pr, Dy, Tb). The rare-earth elements are considered most critical for Europe due to the high supply risk and their impact on the economy. Less than 1 % of all magnets are recycled after the magnet-containing device has been put out of use. It is thus necessary to develop cost-effective and sustainable reprocessing routes for end-of-life (EOL) permanent magnets. The hydrogen decrepitation (HD) of sintered magnets, combined with jet-milling, is used to obtain anisotropic Nd-Fe-B powders for further processing [1]. However, each reprocessing step exposes the material to oxidation, limiting its potential for the processing of high-coercivity magnets. Moreover, an increase in the oxygen content reduces the amount of the secondary Nd-rich phases, which can hinder the densification and evolution of microstructure during sintering when conventional powder metallurgy approaches are considered. Spark-plasma sintering (SPS) is a pulsed-current-activated, pressure-assisted sintering technique characterised by fast sintering kinetics. The technique exploits the Joule heating effect to consolidate a powder compact under non-equilibrium conditions. SPS offers a high potential for the net-shape manufacture of dense sintered bodies from various materials [2]. Recently, an SPS route was provided as an alternative to the conventional sintering of Nd-Fe-B jet-milled powders. By exploiting the SPS-specific sintering mechanisms, it is possible to densify such material without risking extensive grain growth or oxidation [3]. We have taken the spark-plasma sintering approach to synthesise anisotropic, fully-dense magnets from a heavily-oxidised Nd-Fe-B jet-milled powder. The powder that could not be sintered by conventional methods was obtained through hydrogen decrepitation and jet-milling of a magnet scrap and contained 0.8 wt.% of oxygen. Small additions of Nd-Cu eutectic alloy (up to 5 wt.%) were beneficial for developing the hard-magnetic properties in bulk magnets. We studied the effect of the sintering parameters such as heating rate and dwell time on magnetic properties and microstructure formation. The as-sintered samples' intrinsic coercivity exceeded 1000 kA/m, and the properties could be further tuned with post-sinter annealing.

**References:**

[1] A. Walton, H. Yi and N. A. Rowson, Journal of Cleaner Production, Vol. 104, p.236-241 (2015) [2] O. Guillon, J. Gonzalez Julian and B. Dargatz, Advanced Engineering Materials, Vol. 16, p.830-849 (2014) [3] T. Tomše, Z. Samardzija and L. Scherf, Journal of Magnetism and Magnetic Materials, Vol. 520, p.166504 (2020)

**Images:**

 Anisotropic Nd-Fe-B Magnets Prepared from Recycled Jet-Milled Powders with Spark-Plasma Sintering Technique

Some rare-earth intermetallic compounds are superior in magnetic properties such as saturation magnetization and magnetocrystalline anisotropy, and are suitable for permanent magnetic materials. This is due, at least in part, to the orbital magnetic moment of the 4f shell, and also to its interaction with the crystal field. Thus it is important to know the 4f orbital magnetic moment of rare-earth ions in those compounds in order to theoretically search for novel permanent magnets. However, first-principles calculations based on density functional theory (DFT) still have a problem with the treatment of 4f orbital magnetic moments: even for 3d transition metals, they are often underestimated in DFT calculations. Therefore some additional corrections such as the so-called DFT+U method [1] [2] or the self-interaction correction (SIC) are necessary to describe the strongly correlated 4f electronic states adequately. Of course, comparison with experimental inputs is inevitable to validate these corrections. A suitable material to study the 4f orbital magnetic moment with reference to experimental information is SmFe12 with ThMn12 structure [3] [4]. This is due to its relatively simple crystal structure, and also the abundance of recent detailed experimental results, as it has received renewed attention as a promising candidate for new permanent magnet materials in the last few years. Of course it is well known that this system is thermodynamically unstable, but also that Ti substitution for Fe can stabilize the crystal structure. In the resulting crystal structure, the volume of the so-called interstitial region is larger than in other well-known rare-earth intermetallics such as Nd2Fe14B or SmCo5. Thus we can expect that the 4f electrons of Sm ions are well localized enough to form the well-defined 4f orbital magnetic moment. We calculate the electronic structure of SmFe12 and orbital moment of the Sm ions with the DFT+U method (GGA+U). In the frame work of the first-principles method, we have to investigate ground state properties, however, the DFT+U method sometimes might converge to metastable states [5]. Therefore, we examine several initial conditions and investigate the properties of a possible ground state. In present study, we use three initial conditions to approach the true ground state. The initial conditions are reflected in the orbital potential for 4f states of the Sm ions, the matrix elements of which are specified by the magnetic quantum number m. First one is set so that m=3,2,1,0,-1 states are occupied (Condition 1). Second one is set so that m=3,2,1,0,-2 states are occupied (Condition 2). The final one is set so that mainly m=3,2,1,0,-2 states are occupied, however, these states include the hybridization between different m reflecting four-fold symmetry (Condition3). We tested these conditions and search the true ground states. According to the calculated U dependence of the orbital moment and total energy shown in Figure 1, the third one (Condition 3) yields the lowest energy regardless of the U value. The calculated orbital moment of the Sm ions is about 3.0μB which is smaller than the maximum value expected from 4f5 configuration regardless of the U value. This implies that the orbital moment of the Sm ions is partially quenched due to the crystal field. The calculated 4f charge density has the four-fold symmetry which reflects the symmetry of the crystal. The calculated total, f-partial, and m-resolved f-partial density of states (DOS) are shown in Figure 2 (a) and (b). In Figure 2 (a), DOS is mainly composed by the Fe states and the down spin Sm f-states are well localized below the fermi level. Increasing U value, the gap between upper and lower Hubbard part of Sm f states becomes larger. In our calculation, we have confirmed that the anti-parallel spin configuration between Fe and Sm becomes stable. From the calculated f-partial density of states in Figure 2 (b), m=3,2,1,0,-2 states are mainly occupied. It yields the orbital moment roughly 4.0μB. In addition, hybridized states between m=3 and m=-1, m=2 and m=-2, and m=1 and m=-3 are also realized according to the initial condition. These states cause the reduction of the orbital moment from 4.0μB to 3.0μB due to the partial quenching of the orbital moment. In our DFT+U calculation, the quenching of the orbital moment is predicted, the comparison with the experimental data such as XMCD is expected. For future work, we are going to investigate the effect of the quenching of the orbital moment to magnetocystalline anisotropy energy.

**References:**

[1] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. Rev. B., Vol. 44, p. 943 (1991). [2] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B., Vol. 52, p. 5467 (1995). [3] Y. Hirayama et al., Scripta Mater., Vol. 138 p.62-65 (2017). [4] Y. Harashima et al., JPS Conf., Proc. 5 011021 (2015). [5] P. Larson, I. I. Mazin, D. A. Papaconstantopoulos, Phys. Rev. B., Vol. 67, p. 214405 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5996e56e128ba38c565fd1cb782b50a.jpg)
The U dependence of the calculated (a) orbital moment and (b) total energy including spin-orbit coupling. Bule, red and black plots correspond to the initial conditions Condition1, Conditon2 and Condition3 (see text). The magnetization axis is set (001) direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/90fadae7780a3329e44ab8a1e7d70d88.jpg)
The calculated density of states (DOS) of SmFe12 with U=0.8 Ryd and J=0.0615 Ryd. (a) Black line corresponds to total DOS and red line corresponds to Sm f-partial DOS. (b)Sm f-partial DOS and m-resolved Sm f-partial DOS. The magnetization axis is set the (001) direction with spin-orbit coupling.

 Theoretical investigation of the orbital moment of the Sm ions in SmFe12 with the GGA+U method.

Magnetic binary alloys with a CuAu-I type chemically ordered face centered tetragonal (fct) structure, mainly known as L10 structure, have attracted a special attention in the last decades due to their peculiar physical properties and excellent chemical stability, which arise from the particular arrangement of the atoms that alternate in composition along the c-axis direction of the fct unit cell [1]. Among the L10 alloys, ferromagnetic (e.g. FePt, FePd, CoPt, CoPd, NiPt, MnAl, FeNi) and antiferromagnetic (e.g. MnPt, MnPd, MnNi, CrPt) nanostructured materials are of particular interest in view of their potential applications in many technological fields. The extraordinary high uniaxial magnetic anisotropy of L10 FePt(Pd) and CoPt makes such alloys of particular importance for next generation ultra-high density magnetic recording media, magnetic hyperthermia and catalysis. High-anisotropy L10 MnAl and FeNi alloys are excellent and cost-effective alternative to materials containing rare-earths and other critical elements for both permanent magnets and spintronic applications. Many studies have been carried out to find the optimum conditions for the preparation of L10-ordered alloys that are commonly obtained by post-deposition high-temperature treatments for a few hours in order to favour the conversion from the chemically disordered fcc (A1) phase into the chemically ordered fct (L10) phase. However, in the last decade advanced chemical synthesis strategies have been proposed, allowing highly-ordered L10 magnetic alloys to be synthesized at a much milder conditions than usual; this is the case of the Pre-ordered Precursor Reduction (PPR) method [2] where the desired MPt phase (M=Fe, Co, Ni) is obtained by a thermal decomposition in a reductive atmosphere of a pre-ordered M(H2O)6PtCl6 crystalline precursor salts consisting of alternating planes of pure Me and Pt atoms, which mimic the atomic structure in the alloy (fig.1). Among the characterization techniques applied to investigate the structural properties at the local-scale, XAS is an effective tool to probe the chemical environment around an absorber element, and to get information on the average structural features of the materials, thus being complementary to conventional X-ray diffraction techniques. Due to its peculiar characteristics, i.e. selectivity and high sensitivity, Extended X-ray Absorption Fine Structure (EXAFS) analysis represents the main technique to investigate the local properties in many systems whose behaviour is strongly affected by the atomic arrangement, as in the case of the L10 chemically ordered alloys, where the degree of chemical order influences significantly the final magnetic properties. In this paper, recent studies based on a combination of ex-situ and in-situ X-ray Absorption Spectroscopy (XAS) experiments suitably set-up to describe the local environment around the metals during the synthesis processes of different L10 alloys are presented. In particular, by comparing PPR-synthetised L10 alloys by means of EXAFS, X-ray diffraction results, TGA-DTA analysis and magnetic measurements, we could firstly formulate a general and comprehensive explanation of the process at the basis of the thermal treatment that brings to the reduced alloys with such a high ordering degree (S&gt;0.9). This allows a greater control on the synthesis method, which can be exploited, by properly choosing the starting salt, to synthesize other binary alloys, such as L10-FeNi, L10-MnAl and L10-MnPt that are of great interest for many technological applications but extremely challenging to be obtained.

**References:**

[1] A. Cebollada et al., Magnetic nanostrucures, H. Nalwa (Ed), American Scientific Publishers, 2002, ch. 3, p.93 (2002) [2] G. Varvaro et al., Journal of Alloys and Compounds, Vol. 846, p.643 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/225649da53a9d40f988d2901d8077c61.jpg)
Fig. 1. Schematic illustration of the Pre-ordered Precursor Reduction strategy.

 Correlation between Atomic Ordering and Magnetic Properties in L10 Alloys INVITED

High-performance permanent magnets are needed for a large number of applications, especially ‘green’ energy conversion, such as electric motors and windmills, which require them in extremely large quantities. At the same time, the heavier rare-earth elements which are necessary for obtaining the good magnetic characteristics of these materials (such as Pr, Nd, Sm, Tb, or Dy), are often mined with methods that leave an environmental footprint, quite expensive, and are rapidly decreasing in availability. We are using a high-throughput and data-mining approach to the search of rare-earth free permanent magnets by filtering through a large number of known structures from ICSD database [1]. Using a full-potential linear muffin-tin orbital method with the relativistic formulation as implemented in the RSPt electron structure code [2] we calculate the magnetic moment (M), magnetic anisotropy energy (MAE), and Curie temperature, looking for the materials with high M &gt;1 T, uniaxial MAE &gt;1 MJ/m3, and Tc &gt;300 K to identify the suitable replacement for rare-earth containing materials. To test the method, we investigated the materials containing a 3d-, a 5d-, and one extra element of the periodic table and found several candidates that have characteristics suitable for a good permanent magnet (Pt2FeCu, Pt2FeNi, W2FeB2, etc). Based on this result we have also proposed two new materials, not existing in ISCD database - Pt2FeCo and Pt2CoNi [3]. The second run was performed for the materials that contain at least two 3d- metals (with no restriction on the number of elements). Based on this run, new material was found (that had not been used as a permanent magnet before) and consequently synthesized, that has the high magnetization, MAE, and Tc. Hence, a new class of rare-earth-free permanent magnets has been proposed. We would like to acknowledge the financial support of the SSF and SNIC for the computation resources.

**References:**

1. http://www2.fiz-karlsruhe.de/icsd_home.html 2. John M. Wills et al., arXiv:cond-mat/9912173 (1999) 3. A. Vishina, O. Yu. Vekilova, T. Björkman, A. Bergman, H. C. Herper and O. Eriksson Phys. Rev. B 101, 094407 (2020)

**Images:**

 High-throughput and Data-mining Search for Rare-earth-free Permanent Magnets

Hard magnetic nanocomposites, consisting of a fine mixture between a large magneto crystalline anisotropy phase and a large magnetization phase, are attractive materials both for integration of hardness-tuned magnets in microsystems and for building next-generation high performance permanent magnets for energy conversion technologies. Instead of relying on the hypothetical discovery of new hard magnetic compound, this approach is based on the mastering of the microstructure in a mixture of already known magnetic phases. Theoretical descriptions predicted a potential energy product of 1 MJ/m3, which is twice as large as the one of best Nd2Fe14B magnets produced today [1]. However, exploiting their full potential has appeared to be very challenging since the first reports on exchange spring structures in the 90’s. Indeed, calculations pointed out the absolute necessity to confine the softer phase in nano-sized grains, smaller than twice the domain wall width of the hard phase. In parallel, to maximize the magnetization, the hard phase volume fraction should be restricted to the minimum needed to develop enough coercivity. These requirements cannot be obtained with conventional process for mass scale material fabrication. In this context, investigations of model systems in films can give insights about the interplay between the nanoscale microstructure and the magnetic properties [2]. In particular, the degree of interdiffusion at the soft-hard interface is expected to significantly impact the magnetization reversal but is difficult to address experimentally. Here we focus on the impact of a graded soft-hard interface on magnetic properties. To do so, we recently prepared Co@FePt transition metal-based nanocomposite (NC) films from mass-selected low energy cluster beam deposition technique (MS-LECBD) of Co clusters, in situ embedded in FePt matrix independently produced by alternative electron gun evaporation on the same substrate [3,4,5]. The Co cluster inclusions can be selected in size prior to their deposition, between 1 and 10 nm. The cluster to matrix volume ratio is adjusted controlling the thickness of each Co, Fe, Pt individual layers. The as-prepared Co clusters have been observed by transmission electron microscopy (TEM) and found to crystallise in magnetically soft fcc phase. In this study, we focused on 8 nm Co clusters. The Co to FePt volume fraction was varied from 0 to 50%. Post-deposition annealing of the whole stack is a crucial step to drive the initial Fe and Pt multilayers to the high-magnetic anisotropy L10 phase. However, this inevitably comes with partial intermixing at the interface between the clusters and the matrix. We systematically compared the nanoclusters-based film with same stoichiometry and alloyed films (NF), obtained by sequential evaporation of Co, Fe, Pt thin and continuous layers. Local atomic structures have been thoroughly investigated using polarization-dependent hard x-ray absorption and element-specific spectroscopies (EXAFS, XLD). Transmission electron microscopy (TEM) equipped with energy-dispersive x-ray spectroscopy (EDX) was used to explore the local chemical profile of the composite films (figure 1). The macroscopic magnetic properties were measured in a Superconducting quantum interference device (SQUID) magnetometer together with local and element specific characterisations using circular dichroism (XMCD). We demonstrate the persistence of soft and hard regions and rule out the fully diluted hypothesis. Magnetic measurements (figure 2) showed a very different behaviour upon annealing between NF and NC films. Using a combinatorial approach, we investigated the coercive magnetic field decay when increasing the Co content. The magnetic coercivity is found to be systematically higher in the NC samples, over the whole range of studied composition. EXAFS spectra fitting and numerical modelling of the diffusion mechanism show that magnetically soft Co-rich inclusions remain after annealing, even at the high temperature required to obtain the L10 phase of the matrix. In the case of multilayer nanofilms with Co thin layers, the diffusion leads to homogeneous alloying. Local XMCD revealed the evolution of spin and orbital moments of Fe and Co as a function of the composition, further distinguishing the NC system with respect to fully homogeneous alloy. Studying these materials in model systems synthesised by nanofabrication routes provides interesting insights into the interplay between the microstructure and the magnetic performances in view to develop mass-scale production of such materials. This work is supported by the ANR collaborative project "SHAMAN": Soft in Hard MAgnetic Nanocomposites (2017-2020).

**References:**

1. Skomski R. and Coey J. M. D. Phys. Rev. B 48, 15812 (1993). 2. Balasubramanian B. et al, Scientific reports 4, 6265 (2014) 3. Tournus F. et al, Journal of Magnetism and Magnetic Materials, vol. 323, p. 1868 (2011) 4. Liu Y. et al, Appl. Phys. Lett. 99, 172504 (2011) 5. Paleo C. et al, Interplay between local structure and magnetic properties of graded exchange-coupled Co@FePt nanocomposite films. Phys. Rev. B 7 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/854d17b4235dd33402f5177028c56401.jpg)
Energy-dispersive x-ray images of a FePt/Co cluster/FePt sample on a Si3N4 substrate, along with the scanning transmission electron microscopy-annular dark-field (STEM-ADF) image.

![](https://assets.underline.io/uploads/markdown_image/1/image/8ac33347c0e0ae0e397c52a2e4bb7528.jpg)
Hysteresis loops at 300 K for two samples with the same Co content and a L10-FePt sample without Co. The NC sample has higher saturation magnetization than the bare L10-FePt ref., which is brought by the Co but retains a sizeable coercivity, whereas the NF is magnetically soft. Inset: Dependence of the coercive field μ0Hc on the Co content for the NF and NC.

 Fcc-Co Clusters in L10-FePt Matrix as Graded-Interface Magnetic Nanocomposite

Low-temperature phase (LTP) MnBi has the hexagonal NiAs structure and retains its ferromagnetic phase up to 613 K [1]. Above 613 K, some Mn atoms from the octahedral sites diffuse into the trigonal-bipyramidal sites, resulting in the antiferromagnetic coupling between Mn at the octahedral and Mn at the trigonal-bipyramidal interstitial sites. Therefore, the magnetic moment sharply drops before reaching the Curie temperature (Tc) of 720 K. Spin reorientation of LTP MnBi occurs at about 90 K from ab-plane (0 - 90 K) to c-axis (T &gt; 90 K) [2]. The spin orientation and magnetocrystalline anisotropy of LTP MnBi can be tuned by partially replacing Bi of MnBi with the third element. Sakuma et al. have performed first-principles calculations on Sn-doped MnBi (MnBi1-xSnx) and found that the Ku increases to about 3 MJ/m3 at x = 0.1 from - 0.5 MJ/m3 at x = 0 and then remains unchanged up to x = 0.3, and TC is 580 K for x = 0 [3]. These calculated Ku and TC for x = 0 are much larger and lower than experimental -0.2 MJ/m3 and 720 K, respectively. Sakuma et al. did not relax MnBi1-xSnx (x &gt; 0) to estimate lattice constants, but used the lattice constants (x = 0) for MnBi1-xSnx (x &gt; 0). Therefore, the calculated Ku and magnetic moment for x &gt; 0 would be inaccurate. In this study, hexagonal crystal structures of LTP MnBi and Sn-doped MnBi in Fig. 1 were used. The LTP MnBi unit cell has two Mn atoms at the octahedral 2a sites of (0, 0, 0) and (0, 0, 1/2) and two Bi atoms at the 2c sites of (1/3, 2/3, 1/4) and (2/3, 1/3, 3/4) [4]. We have relaxed MnBi1-xSnx (x = 0, 0.5) unit cell to obtain lattice constants a and c. Doped Sn decreases the a and c from 4.287 and 6.118 Å for x = 0 to 3.954 and 5.456 Å for x =0.5, respectively. Accordingly, the volume and c/a ratio also decrease from 97.37 Å3 and 1.43 (x = 0) to 73.87 Å3 and 1.38 (x = 0.5), respectively. These relaxed lattice constants (x = 0) are in good agreement with the experimental lattice constants [5, 6]. The WIEN2k package based on density functional theory (DFT) and using the full-potential linearized augmented plane wave (FPLAPW) method was used to conduct the first-principles calculations [7]. In order to calculate spin-polarization and spin-orbit coupling, we used the DFT within the local-spin-density approximation (LSDA) and 19 × 19 × 27 k-point mesh generating 1400 k-points in the irreducible part of the Brillouin zone. Figure 2 shows density of states for MnBi1-xSnx (x = 0, 0.5). The net magnetic moments per formula unit is 3.613 μB/f.u. for x = 0 and 2.517 μB/f.u. for x = 0.5. The net magnetic moment decreases as the Sn concentration increases. The corresponding saturation magnetization in the unit of Tesla (T) monotonically decreases to 0.794 from 0.865 T as the Sn concentration increases to x = 0.5. Calculated magnetic moment of 3.613 μB/f.u., Ku of -0.2 MJ/m3 and TC of 711 Ku for x = 0 are in good agreement with the previously reported results [8]. We will present Ku and magnetic moment as a function of Sn concentration and discuss the discrepancy between Sakuma’s results and this work.

**References:**

[1] A. F. Andersen, Acta Chemica Scandinavica 21, 1543 (1967). [2] Michael A. McGuire, Huibo Cao, Bryan C. Chakoumakos, and Brian C. Sales, Phys. Rev. B 90, 174425 (2014). [3] Akimasa Sakuma, Yuki Manabe, and Yohei Kota, Journal of the Physical Society of Japan 82, 073704 (2013). [4] http://materials.springer.com/isp/crystallographic/docs/sd_1823960, 2020 (accessed 11 November 2020). [5] B. W. Roberts, Phys. Rev. 104, 607 (1956) [6] Wenyong Zhang et al., APL Mater. 7, 121111 (2019) [7] P. Blaha, et al., WIEN2K: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universitat, Wien, Austria, 2001) [8] J. Köhler et al., J. Phys.: Condens. Matter 8, 8681(1996)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/153d31d85f39c335487004e072bb1ff7.jpg)
Fig. 1. Crystal structure for (a) MnBi and (b) MnBi0.5Sn0.5

![](https://assets.underline.io/uploads/markdown_image/1/image/1e46ae3b4980f8fe52a17d3b94569416.jpg)
Fig. 2. Density of states for (a) MnBi and (b) MnBi0.5Sn0.5

 Tuning Magnetic Anisotropy of MnBi Permanent Magnet with Sn*

[Introduction] Hard magnetic materials with high Ku, low Ms, and low α have attracted much attention to MRAM application. MnAl alloy with L10 (Pearson symbol: tP4, prototype: CuAu) phase and Mn3Ge alloy with D022 (Pearson symbol: tI8, prototype: Al3Ti) phase have (Ku, Ms, α) = (1.5×107 erg/cm3 [1], 500 emu/cm3 [2], 0.006-0.0175 [3,4]) and (1.2×107 erg/cm3, 100 emu/cm3 [5], 0.03 [6]), respectively. However, these phases are metastable and crystallographic phases other than L10 or D022 may be involved in Mn-Al and Mn-Ge films [3,5]. The formation of ordered phases is delicately influenced by the film composition. In the present study, Mn-Al and Mn-Ge films are prepared by using a molecular beam epitaxy system with a reflection high-energy electron diffraction (RHEED) facility, which can reveal the crystallographic property during film formation. The effects of composition on the structural and magnetic properties are investigated. [Experimental Procedure] 20-nm-thick MnxAl100-x and MnyGe100-y (at. %) films were formed on Cr(001) single-crystal underlayers at 300 °C. The Mn contents, x and y, were varied from 40 to 100 at. %. The crystal structure and the crystallographic orientation relationship between film and underlayer were determined by RHEED. The order degrees of L10 and D022 phases were estimated by XRD. The surface morphology was observed by AFM. The magnetization curves were measured by VSM. [Results and Discussion] Fig. 1(a) shows the RHEED patterns observed for Mn-Al films with different compositions. Diffraction patterns from L10(001) and A12(001) surfaces [Fig. 1(b-1)] are overlapped for the films with x ≤ 50, which involves the L10-MnAl stoichiometry (x = 50), as shown for example in Fig. 1(a-1). Although metastable L10 phase is formed, A12 (Pearson symbol: cI58, prototype: α-Mn) phase is coexisting with L10 phase in the films. Diffraction pattern from only L10(001) surface [Fig. 1(b-2)] is observed for the films with Mn-rich compositions of x = 58-72, as shown in Fig. 1(a-2). The result shows that L10(001) single-crystal films with the c-axis perpendicular to the substrate surface are successfully obtained. The formation of L10 ordered phase is promoted by using Mn-rich compositions. However, the order degree determined by XRD (not shown here) decreases with increasing the Mn content. With further increasing the Mn content (x = 80-100), diffraction pattern from only A12(001) surface is recognized. Fig. 1(c) summarizes the compositional dependence on crystal structure. Fig. 1(d) shows the crystallographic orientation relationships of L10(001) and A12(001) crystals with respect to Cr(001) underlayer, which are also determined by RHEED. Fig. 1(e) shows the RHEED patterns observed for Mn-Ge films. Diffraction pattern from D022(001) surface [Fig. 1(f-2)] is obtained for the films with y = 68-75 including the D022-Mn3Ge stoichiometry (y = 75). Metastable D022(001) single-crystal films are epitaxially grown on the Cr underlayers. For the films with Mn-rich compositions of y = 83-100, diffraction pattern from A12(001) surface [Fig. 1(f-3)] is recognized, similar to the case of Mn-Al films. For the films with Ge-rich compositions of y = 43-60, diffraction pattern from (001) single-crystal surface with simple cubic structure (Pearson symbol: cP, lattice parameter: a = 0.85 nm) [Fig. 1(f-1)], which does not exist in the bulk Mn-Ge phase diagram, is appearing. In order to determined the crystal structure, characterization by neutron diffraction is necessary. The crystal structures and the epitaxial orientation relationships of Mn-Ge films are summarized in Figs. 1(g) and (h), respectively. Figs. 2(a) and (b) show the compositional dependences on surface roughness values (Ra) of Mn-Al and Mn-Ge films. Flat surfaces with Ra ≤ 0.3 nm are realized for the Mn-Al films with x = 58-72 and the Mn-Ge films with y = 68-75 which are respectively composed of L10 and D022 phases. Fig. 2(c) shows the magnetization curves mesured for Mn-Al films. The Mn58Al42 film consisting of L10 phase shows strong perpendicular magnetic anisotropy [Fig. 2(c-2)]. The magnetization does not saturate at 10 kOe. The magnetic property is apparently reflecting the magnetocrystalline anisotropy of L10 phase. Isotropic magnetization curves are observed for the Mn65Al35 film [Fig. 2(c-3)], though the Mn65Al35 film is consisting of only L10 phase. The reason is due to an influence of low order degree. The Mn50Al50 film also shows isotropic magnetic property due to an influence of coexistence of L10 and A12 phases. Fig. 2(d) shows the magnetization curves of Mn-Ge films composed of only D022 phase. These films do not show perpendicular magnetic anisotropies, since the order degrees are not so high. In the present study, L10-MnAl and D022-Mn3Ge films are prepared under similar experimental conditions. Although flat surfaces which are required for practical applications are realized for both MnAl and Mn3Ge films, strong perpendicular anisotropy is observed only for a MnAl film. The present study shows that it is important achieving a high order degree in addition to obtaining a single phase of L10 or D022 in order to enhance strong perpendicular magnetic anisotropy.

**References:**

[1] A. Sakuma: J. Phys. Soc. Jpn. 63, 1422 (1994). [2] J. H. Park, Y. K. Hong, S. Bae, J. J. Lee, J. Jalli, G. S. Abo, N. Neveu, S. G. Kim, C. J. Choi, J. G. Lee: J. Appl. Phys. 107, 09A731 (2010). [3] M. Hosoda, M. Oogane, M. Kubota, T. Kubota, H. Saruyama, S. Iihama, H. Naganuma, Y. Ando: J. Appl. Phys. 111, 07A324 (2012). [4] S. W. Mao, J. Lu, L. Yang, X. Z. Ruan, H. L. Wang, D. H. Wei, Y. B. Xu, J. H. Zhao: Chn. Phys. Lett. 37, 058501 (2020). [5] A. Sugihara, S. Mizukami, Y. Yamada, K. Koike, T. Miyazaki: Appl. Phys. Lett. 104, 132404 (2014). [6] S. Mizukami, A. Sugihara, S. Iihama, Y. Sasaki, K. Z. Suzuki, T. Miyazaki: Appl. Phys. Lett. 108, 012404 (2016).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fbfc920f2d2586f3826ea2aaa1ae9088.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/477a15e1897832130a1c615bcab204cb.jpg)

 Effects of Composition on the Ordered Phase Formation in Mn-Al and Mn-Ge Alloy Thin Films Grown on Cr(001) Single-Crystal Underlayers

The L10 structured τ-phase of the Mn-Al-C system gained interest for the potential use as a rare earth free hard magnetic material [1]. It has been reported that the formation of a small fraction of Mn3AlC precipitates leads to an increase in coercivity of the τ-phase [2]. Mn3AlC is also of interest because it is ferromagnetic, has a wide phase field in the Mn-Al-C equilibrium diagram and shares a two-phase region with the ε-phase of MnAl, which is the origin of τ-MnAl-C. Despite its broad homogeneity range, the Curie temperature (TC) of Mn3AlC is often reported to be at around 290 K [3,4]. There are only few reports of the influence of composition on the TC [5,6,7] and one has demonstrated a dramatic increase in TC up to 880 K with increasing Mn-content [5]. Furthermore, it has been reported that a full substitution of Al with Mn is possible, while retaining the ferromagnetic properties, resulting in Mn4C with a TC of 870 K [8]. The aim of the current work is to carry out a systematic investigation of the intrinsic magnetic properties of Mn3AlC in order to confirm the dramatic results presented in the literature and to assess the possible influence of Mn3AlC precipitates on the properties of MnAl-C permanent magnets. Two series of Mn-Al-C alloys have been prepared: in one series the Mn-content was constant while Al was substituted with C (compositions: Mn58Al34-xC8+x x = 0, 5, 10) and in the other series the C-content was constant, while Al was substituted with Mn (compositions: Mn60+xAl21-xC19 x = 0,5 ,10). The alloys were arc-melted in 10 g ingots, followed by a homogenisation at 1100°C in Ar-atmosphere for 5 days and were finally quenched into water. The chemical composition of the homogenised materials was determined using Inductively Coupled Plasma Optical Emission Spectroscopy for Mn- and Al-contents and by carrier-gas hot-extraction for C-content. In Fig. 1 and Fig. 2 the measured values of Mn-content were used for alloys produced in this study. Structural information about the phases in the alloys was gathered from XRD measurements, using a Bruker diffractometer with a Co-Kα radiation. Analysis of the XRD patterns was done using FullProf Suite software. Local chemical analysis of the microstructure was done by EDX-measurements using a Gemini Leo 1530 SEM. The magnetic properties of the alloys were measured using the VSM-mode of a Quantum Design PPMS. M(T)-curves were measured at an applied field of 0.1 T in a temperature range from 10 K to 900 K with a heating and cooling rate of 5Kmin-1. Furthermore, hysteresis loops up to an applied field of 14 T were measured at room temperature and at 100 K. In Fig.1 the TC of Mn3AlC is plotted against the Mn content of the phase from various sources. The Mn-content is related to the Mn3AlC formula unit containing 5 atoms. The curves represent the work of different groups that investigated the influence of composition on the TC. The results of the current work are shown in separate branches, since the two different series of alloys focus on different changes of the composition. The substitution of Al with C in the current work (solid black squares) shows a nearly constant TC at around 290 K, despite the change of the overall Mn-content. The same kind of substitution was done by Tong et al. [7], who reported a somewhat larger influence on TC: a change of 60 K was found in going from a composition of 2.75 to 3.0 Mn atoms per formula unit. Contrary to that, the substitution of Al with Mn in the current work (unfilled black squares) shows a drastic increase of the TC from around 355 K to 765 K. This behaviour of the TC is similar to the increase of the TC shown by the work of Wang et al. [5] and Butters et al. [6], who substituted Al with Mn as well. The work of Si et al. [8] focused on the properties of Mn4C, which shows a similar crystal structure to Mn3AlC. The TC of the Mn4C phase seems to fit well to the dependence of TC of Mn3AlC, which could confirm that a full substitution of Al with Mn is possible. Fig. 2 shows the magnetisation (M) as a function of Mn-content measured in the current work and data taken from Wang et al. [5]. The data for M was taken at 1.5 T, for which the samples are close to saturation. The Mn-content is related to the Mn3AlC formula unit. The M values are taken at 100 K. The curves represent the work of our group and the work of Wang et al. Compared to Fig. 1 we do not consider alloys of the first series, since they do not contain Mn3AlC only which means a change of M is connected to the phase fraction of Mn3AlC and not only connected to a change of composition. The alloy series in which Al was replaced by Mn shows a maximum of 92 Am2kg-1 at 3.4 Mn atoms per unit formula. Compared to the work of Wang et al. [5], who found a maximum for M of 90 Am2kg-1 for a stoichiometric composition the maximum of magnetisation is shifted to higher values of Mn atoms per unit cell. In the current work two different alloy series were used to study the effect of composition on the TC and M of Mn3AlC. The results confirm the dramatic increase in TC on substituting Al with Mn reported in the literature [5] and the decrease in M of Mn3AlC on increasing Mn content. The ferromagnetic nature of the Mn3AlC phase may influence the magnetic properties of τ-MnAl-C magnets, particularly for low temperature applications. To investigate this in more detail, further studies are needed.

**References:**

[1] Feng, L. et al. Acta Materialia 199, 155-168 (2020) [2] Ohtani, T. et al. IEEE Transactions on Magnetics 13, 1328–1330 (1977) [3] Dierkes, H. et al. Inorganic Chemistry 56, 1045-1048 (2017) [4] Wang, B. et al. Journal of Applied Physics 108, 093925 (2010) [5] Wang, X. et al. Journal of Magnetics 24 123-127(2019) [6] Butters, R. P.; Myers H.P. CI. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 46, 895-902 (1955) [7] Tong, P. et al. Solid State Communications 138, 64-67 (2006) [8] Si, P. et al. Applied Physcis Letter 112 192407 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/87556979e163a2e8decd39c3937fb997.jpg)
Fig. 1: Curie temperature of Mn3AlC depending on the Mn content per formula unit.

![](https://assets.underline.io/uploads/markdown_image/1/image/91b633b019279b6a999f1d50417249b0.jpg)
Fig. 2: Measured magnetisation at an applied field of 1.5 T at 100 K for different MnAlC-alloys.

 The Dependence of the Intrinsic Magnetic Properties of Mn3AlC on its Chemical Composition

Nowadays the use of permanent magnets (PMs) plays a key role in different applications such as energy and electromobility. In order to obtain a high magnetic performance, the most extended choice is PMs containing rare-earths (REs). Alternative RE-free PM materials are investigated to plug the gap between ferrites and NdFeB magnets [1]. MnAlC alloy is a promising RE-free PM candidate, but further optimization is required in order to achieve a proper combination of saturation magnetization (provided by the only ferromagnetic phase of the system: L10 or τ-MnAl) and coercivity. Studies on MnAl alloys typically focus on obtaining a maximum content of τ-phase, which results in an optimized saturation magnetization [2]. We have recently shown the possibility of developing coercivity in gas-atomized MnAl powder by applying milling times as short as 30-270 s via the self-developed “flash milling” method [3]. A successful combination of nanostructuring and a controlled phase transformation process is behind the observed increase in coercivity [3]. In this study we have used ε-phase MnAlC powder produced by gas-atomization and flash-milling (60 s) to fabricate MnAlC bulk magnets, with no need to transform previously the ε into τ phase. Under the optimal combination of pressure (300 MPa) and temperature (600 °C), hot-pressing applied to ε-phase MnAlC alloy has been able to manage simultaneously the ε-to-τ transformation and the powder compaction to end with a high-density (93%) MnAlC magnet [4]. Figure 1(a) shows the X-ray diffraction pattern of the precursor ε-phase loose powder and the successful transformation into τ-phase after the hot-pressing process. The room temperature hysteresis loops measured for the hot-pressed magnet showed an enhancement of the coercivity of up to 25 % and a slightly superior magnetization at remanence by comparison with the annealed gas-atomized loose powder (Fig. 1 (b)). The large coercivity obtained for the magnet may be explained based on the formation of both β-Mn and Mn3AlC phases together with a reduced mean crystallite size (27 nm) and the induced strain during compaction [4]. On this basis, we have demonstrated that coercivity of the compacted magnet can be further increased in about 15% by starting from flash-milled gas-atomized powder, due to a larger content of β-Mn and Mn3AlC phases. We have obtained comparable magnetization and coercivity values when compacting the starting material with a crystallographic structure based on τ-phase (i.e., involving two steps: annealing for managing ε into τ phase transformation followed by hot-pressing), thus validating our single-step process. This is a promising cost-efficient route which opens the path to new possibilities for the fabrication of MnAlC-based magnets. Acknowledgements IMDEA acknowledges financial support from EU M-ERA.NET and MINECO through the projects "NEXMAG" (Project Success Case at H2020 M-era.Net Programme, Ref. PCIN-2015-126) and "3D-MAGNETOH" (Ref. MAT2017-89960-R); Regional Government of Madrid through "NANOMAGCOST" project (Ref. P2018/NMT-4321); and Höganäs AB through the industrial collaboration "ECNanoManga".

**References:**

[1] J.M.D. Coey, IEEE Trans. Magn., 47, 4671 (2011) [2] V. Øygarden et al., J. Alloys Compd., 779, 776 (2019) [3] J. Rial et al., Acta Mater., 157, 42 (2018); Engineering, 6 (2), 173 (2020) [4] C. Muñoz-Rodríguez et al., J. Alloys Compd., 847, 156361 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ee90b2b1fd40d0e1617728e809b5f480.jpg)
Fig. 1. (a) X-ray diffraction pattern of the ε-phase gas-atomized loose powder and hot-pressed powder. (b) Room temperature hysteresis loops (second quadrant) of the loose annealed powder (ε transformed into τ-phase) and the magnet obtained by hot-pressing the ε-phase powder. Inset shows an image of the resulting compacted MnAlC magnet.

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