France



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/m&lt;sup&gt;3&lt;/sup&gt;, which is twice as large as the one of best Nd&lt;sub&gt;2&lt;/sub&gt;Fe&lt;sub&gt;14&lt;/sub&gt;B 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.&lt;br/&gt;&lt;br/&gt;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 L1&lt;sub&gt;0&lt;/sub&gt; 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.&lt;br/&gt;&lt;br/&gt;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).&lt;br/&gt;&lt;br/&gt;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 L1&lt;sub&gt;0&lt;/sub&gt; 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.&lt;br/&gt;&lt;br/&gt;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.&lt;br/&gt;&lt;br/&gt;This work is supported by the ANR collaborative project &quot;SHAMAN&quot;: Soft in Hard MAgnetic Nanocomposites (2017-2020).

**References:**

1. Skomski R. and Coey J. M. D. Phys. Rev. B 48, 15812 (1993).&lt;br/&gt;2. Balasubramanian B. et al, Scientific reports 4, 6265 (2014)&lt;br/&gt;3. Tournus F. et al, Journal of Magnetism and Magnetic Materials, vol. 323, p. 1868 (2011)&lt;br/&gt;4. Liu Y. et al, Appl. Phys. Lett. 99, 172504 (2011)&lt;br/&gt;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 Si&lt;sub&gt;3&lt;/sub&gt;N&lt;sub&gt;4&lt;/sub&gt; 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 L1&lt;sub&gt;0&lt;/sub&gt;-FePt sample without Co. The NC sample has higher saturation magnetization than the bare L1&lt;sub&gt;0&lt;/sub&gt;-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 μ&lt;sub&gt;0&lt;/sub&gt;Hc on the Co content for the NF and NC.

INTERMAG 2021

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

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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.

technical paper

I. INTRODUCTION A phase with extraordinarily high room-temperature coercivity in the Sm-Fe-Ti system was first observed in thin films crystallized from an amorphous precursor where μ0Hc reached 3.85 T for a Sm2Fe7Ti1 composition [1]. Giant room-temperature coercivities up to 5.03 T were reported later [2] in a ‘new and possibly metastable phase’ with Sm2Fe7Ti1 composition prepared by mechanical alloying. The reason for the maximum in coercivity at the Sm2Fe7Ti1 composition has been a subject of debate. The observed unit cell expansion is smaller than expected when replacing the respective Fe atoms with Ti, which led to the conclusion that the amount of Ti in the Sm5Fe17 phase has to be smaller than weighted and thus the remaining Ti must form a secondary phase [3]. The interesting question arises then, whether the high coercivity is caused solely by the intrinsic magnetic properties of the Sm5Fe17 phase or is a result of a multi-phase microstructure. To answer this, in this work we have performed a detailed microstructural investigation of samples with varying Ti contents and correlated our findings with the observed magnetic properties. II. EXPERIMENTAL Mechanical alloying of Sm-Fe-Ti samples was carried out by high energy ball milling (SPEX 8000D) under argon atmosphere from elemental Fe (74 -149 μm, 99.9%, Alfa Aesar), Ti (-74 μm, 99%, Alfa Aesar) powders and Sm pieces (3-4 mm, 99.9%, ChemPUR). The resultant powders were subsequently compacted, and heat treated in a horizontal tube furnace at different temperatures. The samples were handled in an Ar filled glovebox (p(O2) &lt; 0.1 ppm, MBraun) to avoid oxidation. Magnetic measurements were performed using a Quantum Design Physical Property Measurement System (PPMS) vibrating sample magnetometer (VSM). The magnetization measurements were extended up to 43 T using a non-destructive pulsed-field coil at the Dresden High Magnetic Field Laboratory. A single 1.44 MJ capacitor bank was used. When fully charged, it could produce a maximum magnetic field of 60 T with a rise time of about 7 ms and a total pulse duration of 25 ms. In our experiments, the capacitor module was charged to about two thirds. The magnetization was detected by the induction method using a coaxial pick-up coil system surrounding the sample. All pulsed-field data were calibrated against the magnetization recorded in steady fields. III. RESULTS AND DISCUSSION As shown in Fig. 1a, ultrahigh coercivities, 7.18 T at room temperature (8.86 T at 10 K), were achieved for the Sm20Fe70Ti10 alloy. The coercivity as high as 2.18 T is maintained even at 500 K. Anisotropy field μ0Ha of 20.7±0.8 T determined from high-field pulse measurements demonstrates that Hc reaches 35% of the Ha at room temperature. Large switching field of around 7 T is visible in the initial magnetization curve. This behavior is similar to fine-grained (below the critical single-domain grain size) Nd-Fe-B alloys. The Curie temperature TC of Sm20Fe70Ti10 is 577 K and calculated exchange stiffness parameter A is 7.72 pJ/m. Because of high rare earth content as well as presence of a nonmagnetic secondary phase, the magnetization was only 60 A m2 kg-1, which is roughly 0.58 T. Detailed transmission electron microscopy investigations presented in Fig. 1b show two-phase microstructure consisting of the Sm5Fe17-based hard magnetic matrix phase with size below 200 nm and fine, &lt;100 nm, Fe2Ti grains. Majority of the Fe2Ti secondary phase grains are located at the grain boundaries as well as inside of the 5:17 grains. No distinct segregation of any element at the grain boundaries can be seen. Despite high areal fraction of the Fe2Ti grains, near single-phase demagnetization loops are observed. Aiming at enhancing Ms by realizing Sm5Fe17/α-Fe composite magnets, the effect of Ti content on the phase constitution, magnetic properties and microstructure was investigated in detail for Sm20Fe70Tix with 4≤x≤10. The fraction of Fe2Ti phase decreases with x and for x=4 Sm2Fe17 phase appears. Ms increases and Hc decreases for the Ti-lean compositions. Based on the microstructural investigations, it is concluded that the reduced coercivities are the consequence of both intrinsic and extrinsic factors, such as the lower anisotropy field, larger grain size and smaller volume fraction of the Fe2Ti precipitates. ACKNOWLEDGEMENTS We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project ID No. 405553726-TRR 270, and Elements Strategy Initiative Center for Magnetic Materials (ESICMM), Grant Number JPMXP0112101004, through the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. We also acknowledge the support of the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL).

**References:**

1. N. Kamprath, N.C. Liu, H. Hegde, F.J. Cadieu, J. Appl. Phys. 64 (1988) 5720–5722. 2. L. Schultz, K. Schnitzke, J. Wecker, J. Magn. Magn. Mater. 83 (1990) 254–256. 3. H. Stadelmaier, G. Schneider, E.T. Henig, M. Ellner, Mater. Lett. 10 (1991) 303–309.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8e90a5cf8fd14c1e53d388b8def552ce.jpg)
Fig. 1 (a) Room temperature hysteresis loop and (b) the corresponding microstructure of the Sm20Fe70Ti10 sample. Two-phase microstructure consisting of the Sm5Fe17-based hard magnetic matrix phase with fine Fe2Ti grains is visible.

 Magnetic properties and microstructure of Sm5Fe17-based two-phase magnets

Demand for rare earths or cobalt is set to soar the next decade boosted especially by demand for valuable NdPr or SmCo magnets used in electric motors (electric vehicles, wind turbines, consumer electronics, military & aerospace applications). The global permanent magnet market size is expected to reach €30 billion by 2030 from the current €20 billion. It is predicted that by 2030 a) Market for rare-earth oxides will increase 5-fold, b) annual NdFeB shortages of 48,000 tonnes expected by 2030, c) annual Dy oxide Shortages of 1850 tonnes is expected by 2030. Extending the forecasting Dr. M.Sagawa had predicted that by 2050 every one on earth will be served by at least 2 robots each one having at least 10 magnets, a market that has to be served by novel groundbreaking approaches [1]. In Fig. 1. the opportunities that exist for novel permanent magnets are shown. For centuries the design concepts of alloys has been based on only one or two principle elements, while minor fraction of other elements are added for property enhancement. This classical approach was broken in 2004 by Yeh et.al, [2] who suggested of a new alloy design concept, which he called high entropy alloys. The original definition was “multiprincipal elements alloys composed of five or more elements in equal or near-atomic percentages” .. Most of the current dominant (PMs) are intermetallic compounds containing rare earth elements e.g. NdPr or Sm and Co, both expensive and originating mainly from either China or Congo. These natural elements from the periodic table have a fixed atomic radii, fixed valence electron configuration and specific electronegativity, parameters that are crucial for the formation of intermetallic compounds. By creating artificial elements of the type of HEAs based on multicomponent rare-earth elements (RE-HEAs) and HEAs based on multicomponent transition metal elements (TM-HEAs), we have created a library of elements with tunable atomic radii, valence electron configuration and electronegativity. This approach enhances the opportunities for discovering novel permanent magnets [3]. The concept of using artificial elements based on either rare-earths or transition metals is depicted in Fig. 2. for the case of SmCo5-type alloys, an approach that we followed for the stabilization of the SmFe3CoNi magnetic phase [4,5]. We have extended this substitutional approach to the class of RFe12-xTx a and R2Fe14B alloys and the results so far are very promising. For example: Sample Ms (emu/g) HA (T) Tc (K) (BH)maxTheory (MGOe) (RE-HEAs)-Co5 75-90 &gt;10 &gt;800 8-18 Sm(TM-HEAs)5 65-80 &gt;8 &gt;800 8-15 (RE-HEAs)-Fe11T 120-135 &gt;5 570-600 8-18 (RE-HEAs)2-Fe14B 125-145 4-6 550-600 10-25 We will present a general approach by unlocking the new possibilities of using artificial elements to create new magnetic alloys that can be processed towards (PMs) to address the opportunities that are shown in Figure 1. This approach also works not only with metallic alloying but with oxides, pnictides, nitrides etc. We can also use the configurational entropy to stabilize metastable phases, since entropy is increased and competes with enthalpy towards negative Gibbs energy.

**References:**

1. J.M.D.Coey, Engineering 6 (2020) 119–131. 2. Yeh, J. W et al, Adv. Eng. Mater. 6, 299-303 (2004) 3. PCT/EP2019/074449 , approved June 2020, Rare Earth Based High Entropy Alloys (RE_HEAs) as building blocks for novel materials:Rare-Earth-HEAS permanent Magnets 4. P. Soderlind, et al. Phys. Rev. B 96, 100404(R) – Published 14 September 2017 5. Landa et al. Journal of Alloys and Compounds 765 (2018) 659-663.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ecf9f0013e053c9c7c2683178359ac0f.jpg)
Figure 1. Opportunities for novel magnet alloys, suitable for permanent magnets, as a function of (BH)max vs cost (Arnold Engineering)

![](https://assets.underline.io/uploads/markdown_image/1/image/81de3429a852f73a7faab3f1e4932d1b.jpg)
Figure 2. Three steps towards HEA-Magnetic Alloys. Step1 is the fabrication of the artificial elements RE-HEAs and TM-HEAs with variable atomic radii and valence electron concentration, Step2 use these artificial elements to synthesize model structures as counter-alloys of existing structures e.g. SmCo5 and in Step3 with proper heat treatment stabilize through entropy optimization a phase e.g. SmFe3CoNi, that otherwise is not possible because the formation energy is just slightly positive.

 “Αrtificial Elements” Based on High Entropy Alloys as “Building Blocks” for Novel Magnetic Alloys Suitable for Permanent Magnets: Special Case SmFe3CoNi

Nd-Fe-B bonded magnets have been widely applied in data storage and consumer electronic devices [1-3]. Theoretically, the maximum energy product of anisotropic magnets is four times as that of isotropic magnets, hence making anisotropic bonded magnets attractive. To produce bonded magnets, magnetic powders are mixed with thermoset- or thermoplastic- polymers for compression or injection molding methods, respectively. In addition to the specific performance of the magnetic powder used, a higher remanent magnetization, hence high energy product, can be achieved with a higher loading fraction of magnetic powder. For anisotropic bonded magnets, a high degree of magnetic alignment (DOA) of the powders in polymer matrix is important. However, the desire for higher loading fraction needs to be balanced with the requirement for good mechanical properties which decreases with loading fraction. As part of our endeavor to develop high-performance Nd-Fe-B bonded magnets, we studied different processing parameters that contribute to the resultant magnetic alignment and hence magnetic properties of anisotropic Nd-Fe-B bonded magnets. We select Nylon12 as binder and Magfine Nd-Fe-B powder to fabricate bonded magnets. Magfine powder is a commercial Nd-Fe-B anisotropic magnetic powder produced by hydrogenation, disproportionation, desorption, and recombination (HDDR). Different loading fractions of Nd-Fe-B powder were mixed with binder and warm-compacted (450 K) into bonded magnets with a diameter of 8mm and a length of 5mm. To magnetically align Nd-Fe-B powder in the as-prepared bonded magnets, a post-compaction magnetic field alignment was performed with an applied external magnetic field of up to 30 kOe. Samples were heated in magnetic fields from 300 to 530 K (Nylon-12) with a dwell time of 15 min at 530 K, and then cooled down to 300 K. After each alignment process, the magnetic hysteresis loops were measured again at 300 K using a Quantum Design Versalab VSM magnetometer. For Nd-Fe-B bonded magnet with 70% loading fraction of magnetic powder, the magnetic remanence increases from 4.8 kGs to 7.2 kGs, while the intrinsic coercivity remains almost unchanged (12 kOe) upon magnetic alignment (Fig. 1). The enhancement of remanence is due to the magnetic alignment of magnetic powder in bonded magnets. Thermomagnetic measurement data shown in Fig. 2 reveal a jump of magnetization at 480-490 K during post-compaction annealing under external applied fields. This temperature is slightly higher than the melting point of Nylon-12 (450 K), which means the binder (Nylon-12) is melted and at a low viscous state. The low viscosity of binder reduces friction between binder and particle and facilitates the magnetic powder alignment under magnetic field. This is a necessary condition for achieving alignment of magnetic particles in Nd-Fe-B bonded magnets during post-compaction magnetic alignment process. We performed magneto-static calculations which show that the DOA are determined mainly by the interplay between the Zeeman energy (Eapp.) and the inter-particle magnetic-static energy (Estat.) at the chosen alignment temperature and the applied magnetic fields. The good alignment can be achieved by an alignment magnetic field which is twice as its coercivity in anisotropic Nd-Fe-B bonded magnet.

**References:**

1. J. M. D. Coey and K. O’Donnell, J. Appl. Phys., vol. 81, no. 8 PART 2B, pp. 4810–4815, 1997. 2. J. Ormerod and S. Constantinides, J. Appl. Phys., vol. 81, no. 8 PART 2B, pp. 4818–4820, 1997. 3. M. P. Paranthaman et al., Jom, vol. 68, no. 7, pp. 1978–1982, 2016.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/aa6cc50624b84ea940e8b8226900b19a.jpg)
Fig. 1. Magnetic hysteresis of J-H of nonaligned- and aligned samples for 75 vol% Magfine Nd-Fe-B Nylon bonded magnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/a31262fd5b839b2fb205f3d5100df188.jpg)
Fig. 2. Thermomagnetic curve of J-T for 75 vol% Magfine Nd-Fe-B Nylon bonded magnets

 Magnetic alignment in anisotropic Nd-Fe-B bonded magnets

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

I. INTRODUCTION With the increasing risk of global rare earth supply and the growing environmental cost of recycling Nd2Fe14B waste by conventional hydrometallurgical technology, development of green and efficient recycling technology has become particularly important [1]. Recently, the reduction diffusion (RD) technology has been developed as an eco-friendly method for recycling Nd2Fe14B sludge waste [2]. At present, researchers mainly use granular calcium or CaH2 as reducing agent, and the amount of reducing agent will affect the phase, morphology, and magnetic properties of recycled powders [3]. Owing to the differences in physical and chemical properties of different reducing agents, the phase, morphology, and magnetic properties of the powders are substantially different in the recovery process. However, the influence of different reducing agents to the recovery of Nd2Fe14B sludge waste by RD method is rarely reported. In this paper, we respectively used granular calcium and CaH2 as reducing agents to recycled Nd2Fe14B sludge waste by RD method. The effect of different reducing agents on the phase, microstructure, and magnetic properties of the recycled powder were investigated. II. EXPERIMENTAL The multi-wire cutting sludge waste was collected from Anhui Earth-Panda Advance Magnetic Material Co. Ltd. The sludge was purified and then mixed with appropriate amount of Ca or CaH2. The mixtures compacted and heated to 1073 K, 1123 K, 1173 K, and 1323 K under high purity argon atmosphere for 2 h. Finally, deionized water was used to wash the powder for removing CaO and then vacuum dried at room temperature to obtain the recycled powders. The phase and orientation were characterized by X-ray diffraction meter (XRD). Microscopic morphology was observed by scanning electron microscopy (SEM). The magnetic properties of the samples at room temperature were measured by a vibrating sample magnetometer (VSM) with a maximum magnetic field of 3T. III. RESULTS AND DISCUSSIONS The XRD patterns of the recycled powders at different reaction temperatures are shown in Fig. 1. The results show that single phase Nd2Fe14B powder can be obtained with granular calcium as the reducing agent at 1323 K. However, when CaH2 is used as the reducing agent, single phase Nd2Fe14B powder can be obtained at 1123 K. This indicates that the latter can carry out the RD reaction at lower reaction temperature. In addition, Fig.1(a) shows that the diffraction peak of Nd2O3 is detected at 1073 K, which indicates that the Ca has not completely reacted with Nd2O3, but the diffraction peak of Nd2O3 is not detected at 1073 K with CaH2 as reducing agents. This proves that CaH2 is more prone to reduction reactions since the melting point of CaH2 (948 K) is lower than that of Ca (1115 K), so the former can be liquefied at lower temperature and thus liquid-solid RD reactions can occur more easily. In addition, since the size of CaH2 powder is smaller than that of granular calcium, it can be better mixed with sludge waste, which is beneficial to promote the RD reaction. On the other hand, the magnetic properties of the recovered powder of the latter (M3T=141.55 emu/g) are higher than that of the former (M3T=137.00 emu/g). And the M3T is increased by 12.9% compared with the purified sludge raw material (M3T=125.38 emu/g). To explore the reason, we observed the morphology of the cross section and powder of the products, and the results are shown in Fig. 2. Since CaH2 releases hydrogen during the RD process, there are many pores in the cross section as shown in Fig.2(c), instead of the dense and smooth cross section shown in Fig. 2(a). From Fig.2(b), it can be seen that the powder has severe sintering and agglomeration, but the dispersion of the powder is better and the powder particle size is more uniform in Fig. 2(d). Owing to the better dispersibility, it is easier to remove CaO during the washing process, so the non-magnetic phase and oxygen content in the corresponding washed magnetic powder are lower, which is also the reason for the better magnetic performance. IV. CONCLUSIONS In summary, using CaH2 as a reducing agent can obtain a single-phase Nd2Fe14B powder at 1123 K by RD method, which is lower than the 1323 K with Ca as the reducing agent. Besides, the dispersion of the powder is better and the powder particle size is more uniform. The magnetic properties of the recovered powder of the former (M3T=141.55 emu/g) are higher than that of the latter (M3T=137.00 emu/g). And the M3T is increased by 12.9% compared with the purified sludge. ACKNOWLEDGEMENT This work was supported by the National key R & D project (2018YFC1903405, No. 2016YFB0700902), and by State Key Laboratory of Rare Earth Permanent Magnetic Materials Opening Foundation (No. SKLREPM17OF02).

**References:**

[1] O. Takeda, T.H. Okabe. Metall. Mater. Trans. E. 1 (2014) 160-173. [2] S.K. Haider, J.Y. Lee, D. Kim, Y.S. Kang. ACS Sustainable Chem. Eng. 8 (2020) 8156-8163. [3] C.Q. Chen, D. Kim, C. Choi. J. Magn. Magn. Mater. 355 (2014) 180-183.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/cfe0e3b8c51ae6e7f90d40fc0c30d0d5.jpg)
Fig. 1 XRD patterns of recycled powder obtained at different temperatures with Ca (a) or CaH2(b) as reducing agent, and recycled powder after washing (c) and the hysteresis loop of recycled powder (d)

![](https://assets.underline.io/uploads/markdown_image/1/image/173ce736e80abaa2509bfd3607afee06.jpg)
Fig.2. SEM micrograph of the cross section and recycled powder of the reaction products with Ca (a and b) or CaH2 (c and d) as reducing agent

 Influence of reducing agent to recovery of Nd2Fe14B sludge waste by Calcium reduction diffusion method

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

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

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