DFT calculation and experimental investigation of Mn doping effect in Fe₁₆N₂

Advanced permanent magnet materials provide high efficiency and reliability, low cost, and low maintenance solutions for renewable energy technologies. α″-Fe₁₆N₂ is considered as a potential candidate for rare-earth-free magnets with a high energy product because of its giant saturation magnetization and large magnetocrystalline anisotropy.^1–3 

The α″-Fe₁₆N₂ phase was first discovered by Jack,⁴ but its magnetic properties remained unexplored until 1972 when Kim and Takahashi⁵ reported its high magnetization in films obtained by evaporating iron onto a glass substrate in low-pressure nitrogen. This discovery has inspired many groups all over the world to explore the material by using different synthesis techniques.^3,6–17

Encouraged by the promising magnetic properties demonstrated by thin films, researchers have been interested in preparing bulk samples with a larger volume fraction of Fe₁₆N₂ phase while exhibiting the same promising magnetic properties.^9,12,15 These experiments have essentially followed Jack’s early approach⁴ via γ and $α ́$⁠. A novel approach has been developed by Wang’s group in University of Minnesota to prepare bulk Fe₁₆N₂ by a strained wire method with the cold-crucible system,¹⁸ which shows promising results as rare-earth free permanent magnet and is very close to practical application.

To reach the application requirement the thermal stability of the Fe₁₆N₂ magnet needs to be improved. α″-Fe₁₆N₂ is a kind of metastable phase due to the incorporation of nitrogen atoms at the interstitial sites, resulting in expansion of bcc-Fe units into distorted bct units. Based on its phase diagram,¹⁹ its phase will decompose at temperatures above 214 °C. In fact, it has been observed that Fe and N atoms tend to diffuse out at temperatures as low as 400 K.^20,21 This imposes an intrinsic limitation for iron nitrides in succeeding as good permanent magnets. A good permanent magnet should have good thermal stability at temperatures of 150-250 °C.² The Nd-Dy-Fe-B magnet used in hybrid vehicles is required to be stable above 180 °C.² It is therefore critical to find an effective method to improve the thermal stability of the Fe₁₆N₂ permanent magnet.

Previous research shows that adding a tiny amount of a third element to form ternary Fe-M-N films (M = Ta, Zr, Hf, Nb, Cr, Al, Mn or Ti) can improve the thermal stability.^22–24 However these works are mainly based on thin film samples for recording applications. Moreover, the choice of element is rather arbitrary and lacks any supporting theory.

In this work, a first principle DFT calculation is conducted beforehand to determine the magnetization of each atom in the α″-Fe₁₆N₂ matrix. Guidelines for the selection of doping elements are proposed, including the preferred position and magnetic coupling way with other Fe atoms in the Fe₁₆N₂ matrix. Based on the DFT calculation, it is found that manganese can be considered as a candidate doping element in Fe₁₆N₂ bulk sample. Furthermore, characterizations of thermal stability and magnetic property are conducted on the resultant doped Fe₁₆N₂ samples to show the influence of manganese doping on Fe₁₆N₂ magnet.

The poor thermal stability of a prepared Fe₁₆N₂ bulk magnet lies in the fact that the affinity between iron and nitrogen is rather weak. So the main mechanism of the α″-Fe₁₆N₂ phase decomposition is nitrogen diffusion at an elevated temperature. To keep nitrogen from moving and escaping, a third element which has more affinity to N than Fe is required to trap the nitrogen and prevent nitrogen diffusion. In this way, the binding energy of the system can be increased and thus improve the thermal stability of the sample. At the same time, the atomic size should be similar to iron and can be substitutionally dissolved into α″-Fe₁₆N₂ unit cell.

Based on the above analysis, the key point to improve thermal stability is to identify a suitable dopant. The requirements for the third element include the following three aspects: similar atomic size, more affinity to N than Fe and ferromagnetic coupling in the α″-Fe₁₆N₂ matrix. The aspects of atomic size and affinity to N are always considered in other published works.^22–24 The ferromagnetic coupling situation with dopant has not yet been considered in terms of thermal stability. Here, the DFT calculation is used to include the coupling situation.

All calculations were performed with the Quantum Espresso package (www.quantumespresso.org). A super-cell of bulk bcc Fe containing 16 atoms is initially constructed and 2 nitrogen atoms are inserted in octahedral positions, which is the crystal structure generally associated with the α″-Fe₁₆N₂ phase. Through a structural optimization on the vertical cell parameter and the atomic positions through the minimization of forces and internal stresses, the equilibrium lattice parameters and atomic positions were obtained, as shown in Fig. 1(a).

Once the crystal structure was clarified, the electronic properties of the resulting crystal were calculated using both “standard” exchange-correlation functions (generalized gradient approximation, GGA) and Hubbard-corrected energy models (GGA+U) with Hubbard parameters accurately computed from the first-principles linear response.

The crystal structure of the α″-Fe₁₆N₂ phase, as shown in Fig. 1(a), indicates the different crystallographic sites occupied by Fe ions around N. The computed magnetization for each Fe site, is reported in Table I for both the “standard” DFT (GGA) and the Hubbard-corrected functions (GGA+U). Non collinear spin calculations were also performed on the material to evaluate the strength of the magnetic interactions between Fe atoms and to assess the role of possible magnetocrystalline anisotropies.

As can be observed in this table, the atomic moments of the Fe ions depend on their position with respect to N: Fe closer to N (Fe1 and Fe2) have their d states more hybridized with the p states of N and show a lower magnetic moment than Fe3, which is at larger distance from N. This is true both for GGA and GGA+U although the numerical values are different. The orbital-projected density of states, shown in Fig. 1(b), 1(c) and 1(d), confirm these results. Fig. 1(d) shows that Fe3 is characterized by narrower d bands due to a smaller interaction and hybridization with the N p states, typically characterized by higher dispersion. The enhanced localization of electrons on d states obtained with the Hubbard correction leads to higher magnetic moments. Calculations were made to investigate possible hybridization between the p states of N and those of Fe and of the redistribution of electrons between d and p states. The role of the break of cubic crystal symmetry, due to the presence of N, on differentiating the d states of Fe ions and on promoting a different role, was also studied. Both these aspects, together with the possible change in the Fermi surface topology, could contribute to the observed giant magnetization.

The doping effect on the electronic structure of Fe₁₆N₂ was investigated based on the extracted crystalline structure in Fig. 1(a). Here Mn and Co impurities were chosen because these species are the most similar to Fe from the periodic table and the most likely to show affinity with the host structure and to possibly contribute to its magnetization.²⁵ The impurities were inserted into the tetragonal unit cell by replacing one of the Fe atoms. The atomic positions were optimized and the cell dimensions were fixed. In order to identify the most favorable position of the impurities in the crystal, the total energies of the system with the dopant atoms in each of the three different crystallographic positions of Fe were computed and compared. Results are also compared with those obtained from doping bulk Fe with the same impurities to assess the role of N atoms in determining the position and the magnetization of the dopants and to evaluate the thermodynamic stability of the doped crystal.

It is well known that Mn impurities couple anti-ferromagnetically, while Co impurities couple ferromagnetically in bulk Fe.²⁶ Firstly Mn/Co impurities are inserted in a 16 atom supercell of bulk Fe and the structure was optimized. The resulting densities of states, shown in Fig. 2, confirmed the trends predicted in literature.²⁶ 

Using the optimized structure of α″-Fe₁₆N₂ in Fig. 1(a), the densities of states of Mn- and Co-doped Fe₁₆N₂ are shown in Fig. 3. It is important to note that Mn impurities are not anti-ferromagnetically coupled to the rest of the Fe atoms, unlike in bulk Fe, suggesting a non-trivial effect of N on the inter-site magnetic couplings.

The relative energies of the possible impurity positions in Fe₁₆N₂were calculated and are shown in Table II.

As can be seen, Co impurities prefer the Fe3 site, while Mn impurities prefer the Fe1 site. The goal of dopant introduction in α″-Fe₁₆N₂ is to enhance the binding energy and increase the thermal stability. In this sense, Mn would be preferred over Co because the Fe1 site is nearer to nitrogen than Fe3. The Mn impurities on the Fe1 site will interact with nitrogen in a tighter manner than the Co on the Fe3 site. Also, there will be some unavoidable sacrifice of saturation magnetization with the dopant introduction. As seen in Table I, Fe1 contributes the lowest magnetization value while Fe3 corresponds to the highest. Replacement of the dopant on Fe1 would have the smallest influence on the saturation magnetization. Actual calculations demonstrate this point. The Mn doping decreases the saturation magnetization of Fe₁₆N₂ from 2.28 T to 2.23 T, while Co doping decreases it to 2.21 T.

Based on the above calculation, manganese is a good candidate dopant in α″-Fe₁₆N₂ to increase the thermal stability since manganese prefers the Fe1 site with enhanced affinity to nitrogen. Experiments were conducted to demonstrate the calculation, as shown in next section.

The α″-Fe₁₆N₂ bulk permanent magnet was prepared from commercially available bulk iron of high purity (99.99 %) in the cold crucible system (Crystalox Bridgman Stockbarger System), as previously described.¹⁸ The surface of the rod was shiny and no surface treatment was applied during the following course, with a 9 at.% nitrogen concentration measured by Auger Electron Spectroscopy (AES). To be comparable, undoped and doped samples were prepared according to the same recipe. Structural and morphological characterizations were measured using X-Ray Diffraction (XRD) (Siemens D5005, with Cu Kα radiation source). Magnetic measurements were taken using a Vibrating Sample Magnetometer (μV SM, Princeton Measurements Corporation), calibrated by a standard Ni sample at room temperature.

The thermal stability was investigated at elevated temperatures by observing the crystalline structure. Figure 4 shows the XRD results for the undoped sample and the 10 % Mn doped sample exposed to different temperatures for 4 hrs. As shown in Fig. 4(a), the Fe₁₆N₂ phase in the pure Fe₁₆N₂ bulk sample is stable at 160 °C. However, when the temperature increases to 180 °C, it is partially decomposed. At 200 °C, the α″-Fe₁₆N₂ phase has completely vanished. This observation confirms other published results.^3,19,22

However, the 10% Mn sample, with the help of the impurities in the sample, is stable even at 200 °C for 4 hrs in atmosphere, as shown in Fig. 4(b). Further incremental increases in temperature, up to 220°C, can lead to completely decomposition of the Fe₁₆N₂ phase. In this way, it is demonstrated experimentally that the Mn impurity increases the thermal stability of Fe₁₆N₂.

A series of samples were prepared in the cold-crucible system with an Mn concentration of 5 wt.% , 8 wt.% , 10 wt.% and 15 wt.%, separately. Their hysteresis loops are shown in Fig. 5. A tendency for the saturation magnetization to drop as the concentration of the impurity increases can be observed. On the other hand, the coercivity rises at higher doping concentrations. This shows that the Mn impurity in Fe₁₆N₂ can also help to increase the coercivity. The value of Hc for samples with C_Mn = 5-15 % is larger than that of sample without impurities. This is attributed to the contribution of impurities in sample with the sacrifice of Ms value.

In this paper, a method to evaluate whether an element is an effective dopant in α″-Fe₁₆N₂ is proposed, based on a DFT calculation, and later verified by experiment. It shows that Mn prefer to replace Fe1 and is not anti-ferromagnetically coupled in the Fe₁₆N₂ bulk sample. It can be used as an impurity to improve the magnetic property and thermal stability of the Fe₁₆N₂ magnet. Based on experimental observations of the crystalline structure, the thermal stability is demonstrated to be improved with the help of Mn impurities in the Fe₁₆N₂ bulk sample. In terms of experimental magnetic properties, the values of coercivity rise obviously with the increment of Mn doping concentration while the Ms values drop in a balance manner accordingly.

This work was supported in part by ARPA-E (Advanced Research Projects Agency-Energy) BCT Fe₁₆N₂ Magnet project under contract No.0472-1595. Parts of this work were carried out in using the Characterization Facility, which receives partial support from NSF through the NSF Minnesota MRSEC program under Award Number DMR-0819885.Dr. Jian-Ping Wang has equity and royalty interests in, and serves on the Board of Directors and the Scientific Advisory Board for, Niron Magnetics LLC, a company involved in the commercialization of FeN magnets. The University of Minnesota also has equity and royalty interests in Niron Magnetics LLC. These interests have been reviewed and managed by the University of Minnesota in accordance with its Conflict of Interest policies.