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Heusler alloys have been intensively investigated to develop functional materials as half-metals, shape memory alloys, and thermoelectric conversion materials. Heusler alloy Co&lt;sub&gt;2&lt;/sub&gt;Ti&lt;i&gt;Z&lt;/i&gt; (&lt;i&gt;Z&lt;/i&gt; = Si, Ge, Sn) was expected to be a half-metal with characteristics of Weyl fermions by first-principles band calculations [1]. The Weyl semimetals are of great interest materials, due to their unusual magnetoelectronic and magnetothermal properties. In the case of magnetic materials, the spatial and temporal correlations of the magnetization &lt;i&gt;M&lt;/i&gt;(&lt;i&gt;r&lt;/i&gt;,&lt;i&gt;t&lt;/i&gt;) show a tendency to diverge at the critical temperature. The phenomenon in which magnetic properties show peculiar temperature and magnetic field dependence at the critical temperature is called a critical phenomenon. The critical exponent &lt;i&gt;δ&lt;/i&gt; is defined at &lt;i&gt;T&lt;/i&gt; = &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; by&lt;br/&gt;&lt;i&gt;H&lt;/i&gt; = &lt;i&gt;DM&lt;/i&gt;(&lt;i&gt;T&lt;/i&gt;,&lt;i&gt;H&lt;/i&gt;)&lt;sup&gt;δ &lt;/sup&gt;. (1)&lt;br/&gt;In later work, to find the critical exponent &lt;i&gt;δ&lt;/i&gt;, the temperature at which the plot, taking logarithms on both sides of equation (1), is linear in log(&lt;i&gt;M&lt;/i&gt;)-log(&lt;i&gt;H&lt;/i&gt;) scale is defined as the Curie temperature&lt;i&gt; T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; [2]. Theoretically, the molecular field theory predicts &lt;i&gt;δ&lt;/i&gt; = 3.0, the three-dimensional Heisenberg model &lt;i&gt;δ&lt;/i&gt; = 4.80 [2], the three-dimensional Ising model &lt;i&gt;δ&lt;/i&gt; = 4.82 [2], and the spin fluctuation theory by Takahashi &lt;i&gt;δ&lt;/i&gt; = 5.0 [3].&lt;br/&gt;For half-metals with characteristics of Weyl fermions, there are few reports of systematic analyses of the critical exponents. Therefore, we focus on the element substitution effect between Co&lt;sub&gt;2&lt;/sub&gt;TiSn and Co&lt;sub&gt;2&lt;/sub&gt;TiGa. Co&lt;sub&gt;2&lt;/sub&gt;TiSn possesses characteristics of both half-metal and Weyl fermions, and Co&lt;sub&gt;2&lt;/sub&gt;TiGa is the itinerant electron ferromagnet with the high spin polarization. We measured the magnetization in the mixed crystal compound Co&lt;sub&gt;2&lt;/sub&gt;TiGa&lt;sub&gt;0.8&lt;/sub&gt;Sn&lt;sub&gt;0.2&lt;/sub&gt; and investigated the critical exponent &lt;i&gt;δ&lt;/i&gt; near &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;.&lt;br/&gt;Polycrystalline Co&lt;sub&gt;2&lt;/sub&gt;TiGa&lt;sub&gt;0.8&lt;/sub&gt;Sn&lt;sub&gt;0.2&lt;/sub&gt; samples were synthesized by arc-melting high-purity constituent elements under high purity Ar atmosphere. To homogenize the synthesized sample, it was annealed at 1100°C for 3 days and then quenched in water. The magnetization of Co&lt;sub&gt;2&lt;/sub&gt;TiGa&lt;sub&gt;0.8&lt;/sub&gt;Sn&lt;sub&gt;0.2&lt;/sub&gt; was measured using a superconducting quantum interference device (SQUID) (Quantum Design MPMS-XL).&lt;br/&gt;From the magnetization measurements of Co&lt;sub&gt;2&lt;/sub&gt;TiGa&lt;sub&gt;0.8&lt;/sub&gt;Sn&lt;sub&gt;0.2&lt;/sub&gt;, the spontaneous magnetization &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; was estimated to be &lt;i&gt;M&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; = 0.907 &lt;i&gt;μ&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt;/f.u. The critical exponent &lt;i&gt;δ&lt;/i&gt; was analyzed from the magnetic field dependence of the magnetization near &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; using equation (1). The magnetization curves obtained at each temperature were plotted for log(&lt;i&gt;M&lt;/i&gt;/&lt;i&gt;M&lt;/i&gt;&lt;sub&gt;max&lt;/sub&gt;) against log(&lt;i&gt;H&lt;/i&gt;/&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;max&lt;/sub&gt;) in Fig.1. The values of &lt;i&gt;δ&lt;/i&gt; and its fitting error, obtained from the analysis of the magnetization curves in Fig.1, are shown in Fig.2. Since the temperature at which the fitting error is minimized agrees best with equation (1), that temperature can be considered as the Curie temperature &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;. From Fig.2, &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; = 105 K and &lt;i&gt;δ&lt;/i&gt; = 4.45 were obtained. The &lt;i&gt;δ&lt;/i&gt; value obtained in this study was different from the value 3 by the molecular field theory, but was close to the value 5 predicted by the spin fluctuation theory for a weakly ferromagnetic itinerant electron system. Therefore, we also reanalyzed the magnetization below 10 kOe, where the magnitude of the applied magnetic field is 1/5 of 50 kOe, because the strong magnetic field may suppress the spin fluctuations. From the analysis of the data below 10 kOe, &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt; = 104 K and &lt;i&gt;δ &lt;/i&gt;= 4.82 were obtained. Thus, a change of &lt;i&gt;δ&lt;/i&gt; due to the suppression of the critical fluctuation by the strong applied magnetic field seems to be likely at least in this case. The discrepancy between our results and the theoretical models seem to arise from a distribution of the Curie temperatures in the samples since the &lt;i&gt;δ&lt;/i&gt; value changes even at 1 K.

**References:**

[1] G. Chang &lt;i&gt;et al&lt;/i&gt;., Sci. Rep. 6, 38839 (2016).&lt;br/&gt;[2] M. Seeger &lt;i&gt;et al&lt;/i&gt;., Phys. Rev. B 51, 12585 (1995) and References: cited therein.&lt;br/&gt;[3] K. Shimizu &lt;i&gt;et al&lt;/i&gt;., J. Phys. Soc. Jpn. 59, 305 (1990).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bc2f95d7cb6fc566aa6579d1bb42e012.jpg)
Fig.1. The log(&lt;i&gt;M&lt;/i&gt;/&lt;i&gt;M&lt;/i&gt;&lt;sub&gt;max&lt;/sub&gt;)-log(&lt;i&gt;H&lt;/i&gt;/&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;max&lt;/sub&gt;) plots of Co&lt;sub&gt;2&lt;/sub&gt;TiGa&lt;sub&gt;0.8&lt;/sub&gt;Sn&lt;sub&gt;0.2&lt;/sub&gt; near &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;C&lt;/sub&gt;.

![](https://assets.underline.io/uploads/markdown_image/1/image/829df8173ea5fbd2b9218fdb9ac04f21.jpg)
Fig.2. The critical exponent &lt;i&gt;δ&lt;/i&gt; and its fitting error of Co&lt;sub&gt;2&lt;/sub&gt;TiGa&lt;sub&gt;0.8&lt;/sub&gt;Sn&lt;sub&gt;0.2&lt;/sub&gt;.

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 Critical behavior of the magnetization in Heusler alloy Co2TiGa0.8Sn0.2

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Heusler alloys have been intensively investigated to develop functional materials as half-metals, shape memory alloys, and thermoelectric conversion materials. Heusler alloy Co2TiZ (Z = Si, Ge, Sn) was expected to be a half-metal with characteristics of Weyl fermions by first-principles band calculations [1]. The Weyl semimetals are of great interest materials, due to their unusual magnetoelectronic and magnetothermal properties. In the case of magnetic materials, the spatial and temporal correlations of the magnetization M(r,t) show a tendency to diverge at the critical temperature. The phenomenon in which magnetic properties show peculiar temperature and magnetic field dependence at the critical temperature is called a critical phenomenon. The critical exponent δ is defined at T = TC by H = DM(T,H)δ . (1) In later work, to find the critical exponent δ, the temperature at which the plot, taking logarithms on both sides of equation (1), is linear in log(M)-log(H) scale is defined as the Curie temperature TC [2]. Theoretically, the molecular field theory predicts δ = 3.0, the three-dimensional Heisenberg model δ = 4.80 [2], the three-dimensional Ising model δ = 4.82 [2], and the spin fluctuation theory by Takahashi δ = 5.0 [3]. For half-metals with characteristics of Weyl fermions, there are few reports of systematic analyses of the critical exponents. Therefore, we focus on the element substitution effect between Co2TiSn and Co2TiGa. Co2TiSn possesses characteristics of both half-metal and Weyl fermions, and Co2TiGa is the itinerant electron ferromagnet with the high spin polarization. We measured the magnetization in the mixed crystal compound Co2TiGa0.8Sn0.2 and investigated the critical exponent δ near TC. Polycrystalline Co2TiGa0.8Sn0.2 samples were synthesized by arc-melting high-purity constituent elements under high purity Ar atmosphere. To homogenize the synthesized sample, it was annealed at 1100°C for 3 days and then quenched in water. The magnetization of Co2TiGa0.8Sn0.2 was measured using a superconducting quantum interference device (SQUID) (Quantum Design MPMS-XL). From the magnetization measurements of Co2TiGa0.8Sn0.2, the spontaneous magnetization Ms was estimated to be Ms = 0.907 μB/f.u. The critical exponent δ was analyzed from the magnetic field dependence of the magnetization near TC using equation (1). The magnetization curves obtained at each temperature were plotted for log(M/Mmax) against log(H/Hmax) in Fig.1. The values of δ and its fitting error, obtained from the analysis of the magnetization curves in Fig.1, are shown in Fig.2. Since the temperature at which the fitting error is minimized agrees best with equation (1), that temperature can be considered as the Curie temperature TC. From Fig.2, TC = 105 K and δ = 4.45 were obtained. The δ value obtained in this study was different from the value 3 by the molecular field theory, but was close to the value 5 predicted by the spin fluctuation theory for a weakly ferromagnetic itinerant electron system. Therefore, we also reanalyzed the magnetization below 10 kOe, where the magnitude of the applied magnetic field is 1/5 of 50 kOe, because the strong magnetic field may suppress the spin fluctuations. From the analysis of the data below 10 kOe, TC = 104 K and δ = 4.82 were obtained. Thus, a change of δ due to the suppression of the critical fluctuation by the strong applied magnetic field seems to be likely at least in this case. The discrepancy between our results and the theoretical models seem to arise from a distribution of the Curie temperatures in the samples since the δ value changes even at 1 K.

**References:**

[1] G. Chang et al., Sci. Rep. 6, 38839 (2016). [2] M. Seeger et al., Phys. Rev. B 51, 12585 (1995) and References: cited therein. [3] K. Shimizu et al., J. Phys. Soc. Jpn. 59, 305 (1990).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bc2f95d7cb6fc566aa6579d1bb42e012.jpg)
Fig.1. The log(M/Mmax)-log(H/Hmax) plots of Co2TiGa0.8Sn0.2 near TC.

![](https://assets.underline.io/uploads/markdown_image/1/image/829df8173ea5fbd2b9218fdb9ac04f21.jpg)
Fig.2. The critical exponent δ and its fitting error of Co2TiGa0.8Sn0.2.

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Permanent magnets are a key component of a wide range of everyday devices, including motors, actuators, transducers and sensors. Depending on the application needs, magnets are based on high performance rare-earth transition metal phases or on more moderate performance hard ferrite phases, and they may be sintered or polymer bonded. While the remanence of bonded magnets is necessarily limited by dilution of the magnetic material in a non-magnetic matrix, they are cheaper in both material and fabrication costs. What is more, the mechanical properties of the magnets can be tuned according to the choice of matrix. Traditional fabrication routes for polymer bonded magnets include calendering, injection moulding, extrusion, and compression bonding [1] and there has been much recent activity concerning 3D printing of polymer bonded magnets [2,3,4]. Down-sizing magnets opens new opportunities for their use in micro-scaled devices with applications in fields as diverse as telecommunications, energy management and bio-medicine. Sputtering combined with micro-patterning has been used to make fully dense magnets which are a micro-scale equivalent to sintered magnets while various techniques including casting and screen printing combined with photo-lithography have been used to make polymer bonded micro-magnets [5]. Sputtered films may be isotropic or textured, depending on the deposition temperature, whereas micro-scaled polymer bonded magnets reported to date are isotropic. Here we present a process developed to fabricate arrays of anisotropic, flexible bonded micro-magnets. The study focuses on micro-magnets prepared using commercial single crystalline hard ferrite (Br: 195 mT, Hc: 123 kA/m) or Sm-Fe-N (Br: 1.31 T, Hc: 889 kA/m) powders mixed with polydimethylsiloxane (PDMS). This binder was chosen so as to have flexible micro-magnets that can be used to study the influence of mechanical forces on cell development [6]. The innovative aspect of this process, schematized in Fig. 1, consists in the possibility to transfer a specific pattern from a silicon mould, made by deep reactive ion etching (DRIE), to a magnetically aligned powder-polymer composite. The composite is maintained within the mould during the alignment step by coverage with a glass slide. A first soft curing step is performed with the cover-slide in place, then a final curing is performed to attach the micro-magnets to a PDMS base. The procedure has been used to fabricate arrays of micro-magnets of thickness ranging from 50 µm to 300 µm and width in the range from 20 µm to 4000 µm. As a magnetic field source, bulk magnets, a superconductive coil and pulsed magnetic field systems were tested. The degree of alignment was assessed by measuring the hysteresis loops of fully cured micro-magnet arrays with the measuring field applied parallel or perpendicular to the direction of the alignment field. Note that these measurements were made prior to removal of the arrays from the Si mould, to prevent distortion of the flexible micro-magnets under the torque induced by the measuring field. As an example, easy and hard axes hysteresis loops made on an array of SmFeN-bonded square micro-pillars with in-plane dimensions of 200x200 µm2 and a height of 300 µm, aligned in a magnetic field of 800 mT, are compared in Fig. 2 a. As can be expected, higher intensity fields were needed to align the SmFeN particles compared to the ferrite particles. The stray fields produced by aligned and non-aligned micro-magnet arrays were measured using an in-house developed Scanning Hall Probe Microscope [7]. In Fig. 2 b we present the z-component of the stray field produced at a height of 50 µm above the SmFeN micro-magnet array featured in Fig. 2 a. In this presentation, we will give details of structural and magnetic characterisation as well as simulations of arrays of ferrite and SmFeN bonded micro-magnets. We will also report on the actuation of these micro-magnets under the influence of a 3D magnetic field. Finally, we will present prospects for the further development and use of such micro-magnet arrays.

**References:**

[1] J. Ormerod and S. Constantinides, Journal of Applied Physics, Vol. 81, p.4816 (1997) [2] C. Huber, C. Abert and F. Bruckner, Appl. Phys. Lett. , Vol. 109, p.162401 (2016) [3] L. Li, A. Tirado and I. C. Nlebedim, Scientific Reports, Vol. 6, p.36212 (2016) [4] K. Sonnleitner, C. Huber and I. Teliban, Appl. Phys. Lett., Vol. 116, p.092403 (2020) [5] N.M. Dempsey, "Nanoscale Magnetic Materials and Applications", J.P. Liu et al.(eds), p.661, (Springer 2009) [6] N.M. Dempsey, " Handbook of Magnetic Materials", J.M.D. Coey et al. (eds), Springer, (in-press) [7] G. Shaw, R.B.G. Kramer and N. M. Dempsey, Rev Sci Inst, Vol.87, p.113702 (2016)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3a78eeb2c7e66ef3542f55dd6887a55f.jpg)
Fig. 1 Schematic of the process developed for the fabrication of arrays of flexible, anisotropic bonded micro-magnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/a01987af8c35d1a195ab777fd1bb4d16.jpg)
Fig. 2 (a) Hysteresis loops of an array of SmFeN (30 vol %) - PDMS (70 vol %) bonded micro- magnet pillars with in-plane dimensions of 200x200 µm2 and a height of 300 µm. (b) Z-component of the stray magnetic field produced by this array, measured using a micro-Hall probe scanned at a height of 50 µm above the magnet array.

 Fabrication and characterisation of polymer-bonded flexible anisotropic micro-magnet arrays

The CoPt and FePt alloys, when chemically ordered in the L10 phase [1], are among the magnetic materials displaying the highest magnetic anisotropy constant. Therefore, they are perfect candidates for ultra-high density magnetic storage applications, provided nanoparticles can be prepared in such a high anisotropy phase. In the bulk L10 phase both alloys exhibit close magnetic and structural properties. Indeed, the tetragonalization of the unit cell, measured by the c/a ratio is almost the same and equal to 0.97 for both alloys while their anisotropy constant is equal to 5 and 7 MJ.m-3 respectively for CoPt and FePt [1]. The first part of this work is then to determine and compare the intrinsic magnetic anisotropy constant of CoPt and FePt L10 nanoparticles. For this purpose, we dilute, as far as possible, mass-selected nanoparticles (around 3 nm diameter) in an inert carbon matrix to avoid coalescence and to make magnetic interactions negligible. To promote the chemically L10 ordered phase the samples have to be annealed at 600°C during two hours. The magnetic properties are then determined using SQUID magnetometer and a global fitting procedure of the entire set of magnetic measurements [2,3] (see Fig. 1). In a second part we try to explain their significant differences using extended X-ray absorption fine structure measurements and atomic relaxation calculations (see Fig. 2). We conclude that the very high magnetic anisotropy measured in FePt nanoparticles [4] is related to the weak atomic relaxation in this alloy, while for chemically ordered CoPt nanoparticles the strong atomic relaxation in the Co plans [5] seems to reduce drastically the magnetic anisotropy.

**References:**

[1] P. Andreazza et al., Surf. Sci. Rep. 70, 188 (2015) [2] A. Tamion et al., Phys. Rev. B 85, 134430 (2012) [3] A. Hillion et al., Phys. Rev. B 88, 094419 (2013) [4] P. Capiod et al., Phys. Rev. Lett. 122, 106802 (2019) [5] N. Blanc et al., Phys. Rev. B 87, 155412 (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bd365171dd94e366a992d84cc0f1e80e.jpg)
Fig. 1: Low temperature hysteresis loop measured for a diluted assembly of CoPt nanoparticles (left) and FePt nanoparticles (right), after annealing. The dots correspond to measurements while the line is obtained with a global fit taking into account the particle size and magnetic anisotropy distributions. Note that despite the particles are similar (around 3.5 nm diameter), the coercivity is much larger for FePt nanoparticles.

![](https://assets.underline.io/uploads/markdown_image/1/image/3e51fbabcc3e62496eafd8c27717286a.jpg)
Fig. 2: Comparison between the mean c/a ratio (computed from interatomic distances: homoatomic and heteroatomic bonds) around transition metal atoms and Pt atoms, from density functional calculations of relaxed CoPt or FePt clusters. N represents the number of atoms used to build perfect truncated octahedrons. The lines are guide to the eye, while the dashed line indicates the c/a ratio in the bulk L10 phase.

 Magnetic anisotropy of chemically ordered CoPt and FePt nanoparticles, why is it so different?

In the 1980s ferrous materials were the first subject of extensive investigation on magnetic field annealing (MFA). Hereby, the potential of using high external magnetic fields as an additional degree of freedom for materials synthesis and tailoring of microstructures in solid state was demonstrated. Since then, due to the progression in magnetic materials and superconducting magnets, processing in magnetic field has become both less costly and more viable. Hence, MFA is achieving renewed attention nowadays. The processing technique might even evolve into a valuable tool on broad industrial level, since it provides the opportunity to save energy by lowering heat treatment temperatures and shortening processing times. Furthermore, the application of an external high magnetic field as an additional independent processing parameter allows for stabilization of metastable phases and creation of texturized microstructures that are not accessible on zero-field conditions. Nevertheless, a lot of experimental work and modeling is still required to entirely unveil the mechanisms of MFA for gaining control on such material manipulation. Mn3Ga is a very interesting and highly suitable candidate for exploring MFA. The intermetallic compound occurs in three different crystal structures, all of them possessing rich magnetic properties attractive for different kinds of application. Regarded as a rare-earth-free permanent magnet in potential application, especially the tetragonal phase meets the particular requirements of being exceptionally prone to manipulation by MFA. Due to the ferrimagnetic ordering it exhibits a much higher magnetic moment compared to the other Mn3Ga polymorphs. Therefore, it is supposed to be thermodynamically favored in its formation under influence of an external magnetic field. Additionally, the tetragonal structure shows high anisotropy in susceptibility, which is conditional to establish a texture upon MFA. As already reported by Ener et al., the phase transition from hexagonal to tetragonal Mn70Ga30 can be accelerated remarkably by combining severe plastic deformation and MFA [1]. In contrast, the study at hand adds the investigation of the influence of different degrees of deformation plus the impact of MFA on the phase transformation starting from a predominantly cubic structure of the parent material Mn3Ga. For this purpose annealing was performed at 400°C, lasting for at least 0.5 hours and up to 14 days. In the case of MFA samples, a magnetic flux density of 7 T was applied. By X-ray diffraction the different stages of phase transformation were observed. Further characterization regarding microstructure and magnetic properties was achieved using light and electron microscopy as well as SQUID magnetometry. The results indicate that the properties after long-term annealing are very similar, independent of previous state of deformation and use of magnetic field. More specifically, after 14 days of annealing samples attained a phase-pure tetragonal structure and show equal remanence. Nevertheless, within the first 24 hours of annealing the differences are enormous with respect to phase formation, microstructure and magnetic properties. In case of zero-field annealing of highly deformed samples or MFA of undeformed samples, reaching the tetragonal structure is postponed by a pronounced intermediate formation of the hexagonal phase. Apart from that, combining previous deformation and MFA accelerates the phase transformation effectively. Furthermore, with increasing degree of deformation the coercivity can be increased stepwise. However, the development of coercivity over annealing time is complex for both zero-field annealing and MFA. An attempt to solve this complex behavior by relating microstructure and coercivity is presented. Finally, the phase transformation behavior of Mn3Ga under influence of an external magnetic field is correlated to changes in defect mobility and development of local deviations in composition (see Fig. 1).

**References:**

[1] S. Ener, K.P Skokov, D.Y. Karpenkov, M.D. Kuz’min and O. Gutfleisch, Journal of Magnetism and Magnetic Materials, 382, 265-270 (2015)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5271fcdca9ea6f7afc41d135535331f.jpg)
Fig. 1: EDS line scan of highly deformed sample after 1 h of MFA 
A) SEM picture showing local course of scan (bright areas in hexagonal, grey areas in tetragonal structure) 
B) compositional mismatch along line scan

 Manipulation of Phase Transformation and Microstructure in Mn3Ga Using Magnetic Field Annealing

Recently, the topic of rare-earth-free permanent magnets has received considerable attraction for the alternative to rare-earth magnets due to the resource crisis and the high cost of rare-earth metals. Among rare-earth-free permanent magnetic materials, the low-temperature phase (LTP) of MnBi has been considered as a potential alternative because it exhibits an unusual positive temperature coefficient of coercivity in the temperature range 153-550 K. Because of the above magnetic property, the MnBi-LTP has a higher coercivity compared to Nd2Fe14B permanent magnetic material at elevated temperature, and it was recently reported that the coercivity of MnBi-LTP reached up to 28.3 kOe at 530K. According to previous researches, this excellent coercivity characteristic of the MnBi-LTP is attributed to its high magneto-crystalline anisotropy (K1≈1.6 x 106 J/m-3 at 300 K)[1]. In spite of such excellent intrinsic magnetic properties, the MnBi-LTP bulk magnets practically fabricated have a significantly lower energy product compared to its theoretical value (BHmax ≈ 16 MGOe at 300 K) due to engineering issues that occur during the mechanical milling process such as decomposition of the magnetic phase, manganese oxidation, and agglomeration. At present, several approaches including high or low energy ball-milling (HEBM or LEBM), surfactant-assisted ball-milling (SABM) have been reported to avoid those issues. However, those approaches based on a ball milling process at room temperature have inevitably a restriction in reducing the powder size as well as agglomerating the powder by cold welding phenomenon. Consequently, this leads to the degradation of the energy product by lowering the total anisotropic characteristics of the MnBi-LTP bulk magnets. Therefore, it is essential to synthesize the particle size of the MnBi-LTP to be close to that of its single magnetic domain (≈ 500 nm) in order to achieve the MnBi-LTP bulk magnets with improved anisotropic characteristics. In this regard, it has been proposed that the cryo-milling method is able to be one of the approaches to synthesize the MnBi-LTP particle satisfying the above-required size. It is well known that the cryo-milling method is able effectively to reduce the particle size as well as to avoid cold welding and agglomeration of the power because it carried out at a temperature lower than 123 K, where materials become brittle and friable[2]. It has been reported that the cryo-milling method is successfully synthesized nanocrystalline structures in ductile materials such as Fe, Ni, Al, Zn, etc. However, researches into the cry-milling of MnBi alloys have been rarely conducted. In this study, the Mn54Bi46-LTP powders were synthesized by the cryo-milled method combined with the addition of a surfactant (stearic acid) as well as calcium, and a schematic illustration of the process is shown in figure 1. As shown in the figure, a stainless-steel vial containing a mixture of powder, balls, surfactant, and calcium was vibrated with a certain frequency, and the temperature was maintained at 77 K during the milling process by the flow of liquid nitrogen. In addition, surfactant (stearic acid) and calcium were added in order to suppress the particle agglomeration and manganese oxidation, respectively. Figure 2 shows the Hysteresis loops for the cryo-milled Mn54Bi46 powder according to the addition of surfactant and calcium. All of the milling conditions have an identical ball-to-powder ratio of 18:1, and stearic acid and calcium were added 0.225g and 0.01g to Mn54B46 powder of 0.9 g, respectively. As shown in the figure, the cry-milled Mn54B46 powder without any addition has a Hc of 14.1 kOe with a remanence (Mr) of 40.7 emu/g and a magnetization (Ms,2.5T) of 40.7 emu/g, while the cry-milled Mn54B46 powders with the addition of stearic acid have a higher both Mr of 51.0 emu/g and Ms,2.5T of 53.2 emu/g. These results, especially the increase of Mr/Ms,2.5T ratio, indicate that the powders were effectively separated by the addition of stearic acid during the milling process. In addition, the result of improved Ms,2.5T means that the decomposition rate of the magnetic phase decreases as the impact energy received by the powder is alleviated by the stearic acid on the powder surface. Furthermore, from the result of magnetic properties under the calcium addition conditions, it is found that calcium addition plays an important role in the purification of Mn54Bi46-LTP powder by suppressing manganese oxidation. Based on these results, further investigation on the optimization of the cryo-milling process and the magnetic properties of bulk magnets manufactured with cryo-milled powders will be discussed.

**References:**

[1] V. N. Antonov and V. P. Antropov, Low Temperature Physics, vol. 46, no. 1, p.1 (2020) [2] N. K. Katiyar, K. Biswas, and C. S. Tiwary, International Materials Reviews, p.1 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f2a8abc3721902719bd228a4fc2e173e.jpg)
Fig. 1. A schematic illustration of the cryo-milling process used in this study.

![](https://assets.underline.io/uploads/markdown_image/1/image/ad03f42558598a49f705daf6a85b3f5b.jpg)
Fig. 2. Hysteresis loops for the cryo-milled Mn54Bi46 powder measured parallel to the alignment direction.

 Magnetic properties of bulk magnets manufactured by the cryo-milled Mn54Bi46 powder

Introduction The metastable α”-Fe16N2 is considered as a candidate for rare earth free semi-hard magnetic materials [1]. It is necessary to improve magnetocrystalline anisotropy of α”-Fe16N2 to obtain higher coercivity Hc [2]. Many theoretical calculations and thin film experiments substituting Fe with some elements such as Co, Ni, Mn, Al, etc. have been done. For example, Co is suggested to increase in magnetocrystalline anisotropy [3]. As one of the synthesis methods of α”-Fe16N2 nanoparticles, it is well known that the nitridation of α-Fe nanoparticles produced by reduction of iron hydroxide such as α-FeOOH. Previously, we have reported that the influence of substituting Co, Al for Fe by synthesizing α”-(Fe, Co)16N2 or α”-(Fe, Al)16N2 nanoparticles [5] and revealed that Co substitution results in the temperature regimes for reduction and nitridation were confirmed to very narrow limits, on the other hand Al substitution brings the wider temperature regimes. In this paper, in order to investigate the complex substitution effect of Fe by Co and Al, we challenged to the synthesis of α”-(Fe0.95Co0.02Al0.03)16N2 nanoparticles by hydrogen reduction of α-(Fe0.95Co0.02Al0.03)OOH as a starting material and subsequent nitridation. Experimental We used commercially available α-(Fe1-xMx)OOH (M= Co, Al, x= 0, 0.02, 0.05) and α-(Fe0.95Co0.02Al0.03)OOH nanoparticles as a starting material. The conditions for reduction and nitridation were systematically examined to obtain higher yield of α”-(Fe1-xMx)16N2 or α”-(Fe0.95Co0.02Al0.03)16N2 according to the following procedure. The α-(Fe1-xMx)OOH nanoparticles were first reduced at 300 - 500 °C for 4 hours in a H2 gas flow. Nitridation was subsequently performed at 150 - 180 °C for 5 hours in an NH3 gas flow. Crystallite diameter Dc of reduced α-Fe1-xMx nanoparticles was measured as average diameter of nanoparticles using Scherrer’s formula based on X-ray diffraction (XRD) with Co Kα radiation. Morphological changes were observed using transmission electron microscopy (TEM). For magnetic properties measurements, these nanoparticles were packed into a disk shape (6 mm diameter, 1 mm thick) with resin. Magnetization M15k and coercivity Hc were measured using vibrating sample magnetometer (VSM) with a maximum applied magnetic field of 15k Oe. Results Fig. 1 (a) shows the regions in the nitridation temperature versus reduction temperature diagrams corresponding to where the α”-phase was produced. M15k and Hc values of the assembled nanoparticles are also indicated. α”-phase was produced under the limited conditions of reduction temperature of 340 °C and nitridation temperature of 170 °C for starting from α-(Fe0.98Co0.02)OOH. On the contrary, α”-phase was produced under broad conditions of reduction temperatures of 400 - 500 °C and nitridation temperatures of 155 - 170 °C for starting from α-(Fe0.98Al0.02)OOH. In the case of starting from α-(Fe0.95Co0.02Al0.03)OOH, α”-phase was produced under the conditions of reduction temperatures of 400 - 500 °C and nitridation temperature of 160 °C. The conditions of α”-phase production were broadened by Al addition to Co. Fig. 1 (b) shows TEM images for the nanoparticles after nitridation starting from α-(Fe0.98Co0.02)OOH, α-(Fe0.95Al0.05)OOH and α-(Fe0.95Co0.02Al0.03)OOH. These nanoparticles are synthesized with hydrogen reduction at 340 °C for 4 hours and subsequent nitridation at 170 °C for 5 hours for α-(Fe0.98Co0.02)OOH, and with hydrogen reduction at 400 °C for 4 hours and subsequent nitridation at 160 °C for 5 hours for α-(Fe0.98Co0.02)OOH and α-(Fe0.95Co0.02Al0.03)OOH, respectively. The particle size of nanoparticles after nitridation starting from α-(Fe0.98Co0.02Al0.03)OOH are between the ones of starting from (Fe0.98Co0.02)OOH and α-(Fe0.95Al0.05)OOH. This result suggested that Al was effective to avoid sintering during reduction. Fig. 2 (a) shows the relationship between M15k and Hc for the nanoparticles after nitridation starting from α-(Fe0.98Co0.02)OOH, α-(Fe0.95Al0.05)OOH and α-(Fe0.95Co0.02Al0.03)OOH. In the case of starting from α-FeOOH was also shown. Higher Hc were obtained by the complex of Co and Al compared to Co or Al alone. Fig. 2 (b) shows Hc change as a function of Dc of those nanoparticles. This result indicates that there is a good relationship between Hc and Dc regardless additive composition. Hc increases with decrease in Dc. In the case of nanoparticles after nitridation starting from α-(Fe0.95Co0.02Al0.03)OOH gives the smallest Dc of 22 nm and highest Hc of 1800 Oe. It is assumed that Al addition to Co is effective to prevent crystalline growth which leads to high Hc of α”-phase. To clarify the reason of increase in Hc, further precise investigation of the distribution of Al and the relationship between anisotropy field of nanoparticles after nitridation will be presented in this conference.

**References:**

[1] R. Skomski et al., Scr. Mater., 112 (2016) 3 [2] M. Tobise et al., J. Magn. Soc. Jpn, 41 (2017) 58 [3] Y. Jiang et al., AIP Adv., 6 (2016) 056007 [4] L. Ke et al., Phys. Rev. B, 88 (2013) 024404 [5] M. Tobise et al., AIP Adv., 9 (2019) 035233

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/af71dcf495e025c51610d79bc24cb5e1.jpg)
Fig. 1. (a) The regions in the nitridation temperature versus reduction temperature diagrams corresponding to where the α”-phase was produced and M15k and Hc values of the nanoparticles are also indicated. (b) TEM images for the nanoparticles after nitridation starting from the material α-(Fe0.98Co0.02)OOH, α-(Fe0.95Al0.05)OOH and α-(Fe0.98Co0.02Al0.03)OOH.

![](https://assets.underline.io/uploads/markdown_image/1/image/b01b30df78a588a568b32b8156ed275d.jpg)
Fig. 2. (a) The relationship between M15k and Hc for the nanoparticles after nitridation starting from the material α-(Fe0.98Co0.02)OOH, α-(Fe0.95Al0.05)OOH and α-(Fe0.98Co0.02Al0.03)OOH. (b) Hc change as a function of crystalline diameter Dc of those nanoparticles.

 Synthesis of α”-(Fe, M)16N2 nanoparticles obtained by hydrogen reduction and subsequent nitridation starting from α-(Fe, M)OOH (M= Co, Al)

— In this paper, a toolbox baptized “PM-Demag” taking into account the permanent magnet (PM) demagnetization phenomenon has been developed. It is based on a nonlinear demagnetization model which considers the thermal state of the PM and reproduces the knee rounded shape of the B(H) curve. Validations against experimental measurements performed on commercial NdFeB PM are presented. Index Terms— Demagnetization, electrical machines, finite element method, permanent magnet. Nowadays, permanent magnets (PM) are widely used in industry, especially in electrical machines. Their use is expected to grow especially in the context of the energy transition of the 21st century. Like soft magnetic materials, they exhibit nonlinear behavior and hysteresis. The part of the curve situated in the second quadrant of the hysteresis cycle, commonly called the demagnetization curve is of interest because it defines the PM properties and operation. It mainly depends on the temperature and on the applied external field. These two parameters strongly influence the magnetic properties of the PM and can cause reversible or irreversible demagnetization [1]. In the special case of a PM electrical machine, an overheating or a short circuit could lead to partial or total demagnetization of the magnets [2]. In this framework, considering the demagnetization phenomena is necessary to precisely predict the change in the PM characteristics and then the machine performances. The knee in the PM demagnetization curve is crucial for a good knowledge of the magnet state. This state depends on the position of the system operating point (intersection between the load line and the demagnetization curve) with respect to the position of the knee. When the operating point is located in the linear zone, above the knee point (reversible part), the PM keeps its initial performances. However, if the operating point is situated below the knee point (irreversible part), the PM must be considered to be partially demagnetized, the remanent flux density decreases and the PM will operate along a minor hysteresis loop which is often approximated by a recoil line [3]. This phenomenon often occurs in electrical machines (especially on the PM surfaces and edges) and could degrade their performances. The degradation degree depends on the temperatures that the machine could reach and on the PM quality. In this work, a toolbox baptized “PM-Demag” based on a non-linear exponential demagnetization model is developed. The model considers the thermal state and it is expressed as a function of the remanent flux density Br, the coercive field Hc, the relative permeability µr as well as an adjustable coefficient K. All these parameters are themselves expressed as functions of the temperature T. The model parameters are identified from the measurements carried out on a dedicated PM hysteresis meter (HyMpulse of Metis®) for different NdFeB magnets. For example, Fig. 1.a shows the measured B(H) and J(H) demagnetization curves for the N35 NdFeB PM and for different temperatures ranging from room temperature (RT) to 140°C. Figure 1.b shows the simulated B(H) demagnetization curves. The developed “PM-Demag” toolbox will be implemented in code_Carmel, which is a home-made finite element method (FEM) software. Application to an electrical machine is envisaged for the extended paper.

**References:**

[1] &lt;!--[endif]--&gt;Furlani, E.P. (2001) Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications. Academic Press, Waltham. &lt;!--[if !supportLists]--&gt;[2] &lt;!--[endif]--&gt;P. Zhou, D. Lin, Y. Xiao, N. Lambert and M. A. Rahman, "Temperature-Dependent Demagnetization Model of Permanent Magnets for Finite Element Analysis," in IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 1031-1034, Feb. 2012, doi: 10.1109/TMAG.2011.2172395. [3] S. Hamidizadeh, N. Alatawneh, R. R. Chromik and D. A. Lowther, "Comparison of Different Demagnetization Models of Permanent Magnet in Machines for Electric Vehicle Application," in IEEE Transactions on Magnetics, vol. 52, no. 5, pp. 1-4, May 2016, Art no. 2100304, doi: 10.1109/TMAG.2015.2513067.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dcae2862acc82b67848b462f70ff229a.jpg)
Experimental results [B(H) in solid line].

![](https://assets.underline.io/uploads/markdown_image/1/image/b146435ffa1d737ffdbeeac7ad9eb82f.jpg)
Simulated B(H) demagnetization curves.

 Permanent Magnet Non-linear Demagnetization Model for FEM Simulation Environment

The influence of Ce3+ ions substitution for Fe3+ ions in Ni0.42Zn0.58CexFe2-xO4 (x = 0, 0.02, 0.04, 0.06, 0.08, 0.10) compounds on the selected magnetic properties and structure were investigated. The samples were synthesized by means of wet glycine-nitrate technology annealed at the temperature 1200°C for 6 hours. The wide spectrum of characterization methods were used for the study of relevant properties of synthetized materials. X-ray diffraction patterns were recorded by a diffractometer using conventional X-ray tube (CuKα radiation, λ = 1.5418 Å). EDAX were performed by the SEM JEOL 7600-F equipped with both EDX and WDX system. Temperature dependences of magnetic susceptibility was measured using bridge method. The hysteresis loops were recorded using computer controlled digital hysteresisgraph at the same amplitude of applied field Hmax = 1500 A/m, measured at the frequency f = 50 Hz and at room temperature. The determination of real µ' and imaginary µ'' parts of complex (relative) permeability have been performed by means of an impedance analysis procedure using a vector network analyser Keysight E5063A in the frequency range from 1 MHz to 3 GHz. Results and Discussion XRD results indicate a presence of multi-phase structure. The major is found to be spinel phase and secondary, increasing with the addition of Ce3+ ions, corresponds to CeO2. The final number of possible substitution of Ce3+ ions for Fe3+ ions in the B sites, and the difference in their ionic radii, is the cause of the formation of aggregates on the grain boundary as secondary phase [1]. The distribution of elements and their amounts in weight percentages for NiZnCe samples were studied by means of EDAX analysis. The real content of Ni2+, Zn2+, Ce3+, Fe3+ and O2- shown in Tab. I confirmed the substitution of Fe3+ ions by Ce3+ ions, since the increase of Ce3+ content decreases the amount of Fe3+. Temperature dependences of magnetic susceptibility were recorded within the range from room temperature up to 450°C at rise of 4°C/min. Ferrite powder specimens of amount approximately 50 mg were measured; susceptibility values were related to the same weight (1 mg) for all cases. These dependences are decreasing monotonously and they exhibit one strong drop to paramagnetic state. From that, we can conclude that no unwilled phase is present in the ferrite to a significant extent. Curie temperature TC was determined from the point of inflexion at strong decrease of temperature dependence. Even the paramagnetic substituent (Ce3+) ions occupy B-sites dominantly at expense of Fe3+ ions, it does not change the A-B exchange interactions, because TC remains almost constant [2]. The hysteresis loops exhibit quite complicated behavior. By adding larger amount of Ce3+ ions, the maximum flux density Bmax at given maximum applied field sometimes raises and sometimes decreases comparing to the non-substituted ferrite. Note that the value of Bmax at given maximum applied field Hmax = 1500 A/m approaches the largest value for x = 0.08 (only slightly larger than for x = 0.04). The differences can be explained by the fact that the saturation magnetization is an intrinsic parameter (thus, structurally independent) meanwhile the Bmax corresponds to structurally sensitive behavior of material when magnetizing and approaching the saturation. In addition, coercive field is nearly linearly increasing with increment of x. This behavior is similar to that observed in case of Cu-substituted ferrites with the similar chemical formula (except for Cu instead of Ce), [3]. This may be justified by the complexity of the spinel structure, presence of other crystalline phases, etc. In Fig. 1 the frequency dependences of real µ' and imaginary µ'' parts of complex (relative) permeability µ = µ' - jµ'' are presented for prepared spinel ferrites. The obtained frequency dispersion of complex permeability is caused by the domain wall and ferrimagnetic (or spin precession) resonance [4], [5]. The achieved results may be explained as follows. Magnetic properties of nickel-zinc ferrites as representatives of spinel-like ferrites are affected not only by the method of preparation and chemical structure (and composition), but also by properties such as porosity, crystallite size (or grain size), lattice impurities (or defects), concentration of cations, etc. Also the super exchange interactions may strongly change the resultant properties: in spinel ferrite system AA and BB interactions are poorer than AB interaction. In the prepared ferrites, the shrinkage of lattice is present because of the larger ionic radius of cations such as Ce3+ (1.143Å), Zn2+ (0.74Å) and Ni2+ (0.69Å) in comparison with Fe3+ (0.65Å). The magnetic moments of these cations are as follows (in Bohr magnetons): 2.5µB, 0µB, 2.3µB and 5µB. Values of magnetic moments relates the cation distribution of Ni0.42Zn0.58CexFe2-xO4 ferrite system (Ce3+ ions have preference on B sites): (Zn0.582+Fe1-x3+)A[Ni0.422+Cex3+Fe1+x3+]BO42-. Due to the values of ionic radius and magnetic moment, Ce3+ ions replace more Fe3+ ions in the crystal lattice and this leads to the raise of coercive field which in turns changes the value of permeability [5], [6]. Conclusion From the above experimental results, it can be seen that adding even a small amount of cerium element has evident influence on selected properties. Consequently, by adding defined amount of Ce3+ ions, the desired parameters can be easily controlled by a straightforward way and thus tailored for any particular application required in industrial practice.

**References:**

[1] R. S. Yadav, J. Havlica, J. Masilko, J. Magn. Magn. Mater., Vol. 399, pp. 109-117 (2016) [2] M. A. Ahmed, S. F. Mansour, S. I. El-Dek, Solid State Ionics, Vol. 181, pp. 1149-1155 (2010) [3] J. Sláma, A. Grusková, M. Ušáková, J. Magn. Magn. Mater., Vol. 321, pp. 3346-3351 (2009) [4] M. Šoka, R. Dosoudil, M. Ušáková, Acta Phys. Pol. A, Vol. 131, pp. 690-692 (2017) [5] R. Dosoudil, M. Ušáková, A. Grusková, IEEE Trans. Magn., Vol. 50, no. 4 (2014) [6] M. N. Akhtar, M. A. Khan, J. Magn. Magn. Mater., Vol. 460, pp. 268-277 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/eccf1c3546b0486f5775ad28c48f37bb.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/2358bea70a2a67441e24abb7319de58f.jpg)

 Magnetic and Structural Properties Analysis of Cerium Substituted Nickel Zinc Ferrites

Rare heart substituted iron garnets (REIG) are characterized by a high magnetic susceptibility that results in a large magnetization in the presence of small magnetic fields [1]. The magnetic microstructures are influenced by natural or artificial defects; in particular, domain walls (DWs) undergo to nucleation, segmentation and pinning in correspondence to them. In REIG with in-plane spontaneous magnetization, the Néel spike domain structure is one of the most common magnetic microstructure nucleated at microdefects and its charged DWs can produce not negligible stray fields above the REIG. These DWs are interesting both for fundamental studies and for innovative applications such as micro positioning by contactless actuators [2]. To make the most out of this, performing a quantitative analysis is crucial. The experimental characterization by means of quantitative magneto-optical imaging with an indicator film [3] showed that stray fields are detectable above the surface of (Lu, Bi) substituted iron garnets, characterized by a spontaneous in-plane magnetization around 150 kA/m, in correspondence of DWs delimiting a Néel spike that is generated by a micro-crack [4]. In order to understand how the externally detected stray fields are correlated to the pattern of the internal magnetization, here we propose 2D and 3D models based on FEM developed through the COMSOL Multiphysics© software. These models take into account the magnetic microstructure of the Néel spike, i.e., either single DWs that run parallel into the bulk of the domain and a couple of DWs at the Néel spike tip (2D) or DWs that merge in a single point (3D). This approach allows us to describe the magnetic microstructure by means of CAD defined patterns, whose complex structure can be implemented easily in the FEM simulation. It turns out that the results are in agreement both with experiments and with previous numerical calculations performed with a simplified model in MATLAB© [4]. The comparison with experiments allowed us also to determine the distance of measurement between the indicator film of MOI experiments and the REIG under investigation. Figure 1 shows linear profiles across the DWs, along with experimental data. The distance of measurement is about 7 μm and the magnetic induction at the tip of the Néel spike is twice the value found for the single charged DW at the domain boundary. The simplicity of the 2D model limits the computational cost required; on the other hand, the 3D simulation can be useful for reproducing in detail the stray field distribution generated by the complex structure of the Néel spike domain, as shown in Figure 2. In summary, we validated these models for reproducing the stray field distribution above charged DWs, opening the way for the design of artificial structures in order to obtain controlled magnetic patterns, thanks to the powerful 3D engine of the COMSOL Multiphysics© software.

**References:**

[1] L. E. Helseth, M. Kurniawan, R. W. Hansen, and T. H. Johansen, PHYSICAL REVIEW B77, 064433 (2008) [2] L. E. Helseth, R. W. Hansen, T. H. Johansen, and T. M. Fischer, Appl. Phys. Lett.85, 2556 (2004) [3] F. Laviano, D. Botta, A. Chiodoni, R. Gerbaldo, G. Ghigo, L. Gozzelino, S. Zannella and E. Mezzetti, 16, (2003) 71; Physica B 403 (2008) 293 [4] A. Napolitano, C. Ragusa, S. Guastella, S. Musumeci, P. Rivolo, F. Laviano, JMMM, Vol 504, 2020, 166556 [5] O. Khan, C. Ragusa, and F. Khan, IEEE transactions on magnetics, vol. 50, no. 11, November 2014

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7f0da98d3c563c66b54b53692a817a42.jpg)
Figure 1. Cross sectional profiles of the stray field, simulated and experimental values, for a single DW (a) and the tip of the Nèel spike (b).

![](https://assets.underline.io/uploads/markdown_image/1/image/2928dd60fc86135c15716d29f81cc2da.jpg)
Figure 2. Magnetic field distribution of the stray field above a Néel spike: 3D plot of the magnetic induction intensity that clearly shows the stray field peak in correspondence to the tip of the Nèel spike. The distance of measurement was chosen on the basis of the previous comparison between experimental data and 2D simulations.

 Modeling stray-field distribution generated by domain-walls in rare-earth substituted iron garnets

Intensive research on soft magnetic nanoparticles has been attracted by biomedical applications such as MRI markers and cancer therapy by magnetic hyperthermia. These nanoparticles can also be used in additive manufacturing processes, such as inkjet printing, to elaborate magnetic coatings to meet emerging needs such as RFID antenna shielding or wireless power transfer. The nanoparticles are synthesized by thermal decomposition with organic solvents. Two different ways of heating are employed: the conventional one using a heating mantle and the other one using a microwave oven[1]. A good control of the particle size of Fe3O4 through the addition of ethylene glycol has been reported2. Other groups have used this technique to synthesize core-shell Fe3O4 nanoparticles. We have synthetized nanoparticles of mixed oxides ZnxFe3-xO4, where the magnetic and dielectric properties can be tuned by the Zn/Fe ratio[2]. The two processing methods were compared in order to determine the most appropriate way to control the size and morphology spread of the obtained nanoparticles. The influence of the microstructure on the magnetic properties of Zn0.4Fe2.6O4 and Zn0.2Fe2.8O4 (theoretical compositions) nanoparticles was studied by X-ray diffraction analysis and 57Fe Mössbauer spectrometry, under zero field and in-field. Experimental details: The conventional way in a heating mantle allows obtaining various morphologies: cubes, octahedra... However, it induces heterogeneity in terms of size and shape in a batch, due to insufficient monitoring of the temperature during the reaction. The microwave-assisted thermal decomposition enables a fast and more uniform heating, leading reproducibly to nanoparticles with homogeneous size and shape. The difference lies in the choice of solvents and surfactants: respectively benzyl ether and oleic acid for the conventional thermal decomposition, and octadecene for the solvent with a combination of oleic acid and oleylamine for the surfactant for the microwave reactor. These surfactants have two complementary functions in the synthesis. Oleic acid stimulates the growth of nanoparticles along a preferential axis while oleylamine, in addition to redox possibilities, slows down the nanoparticle growth[3]. Tuning their compositional ratio yields a good control of the nanoparticle morphology. Results: The morphology and the size were observed by scanning electron microscopy and transmission electron microscopy. Two different morphologies are highlighted. While 5 nm-nanoparticles (written SP(F)M) are quite spherical, the 35 nm-particles (FM) have a “raspberry” morphology (Fig. 1). These observations are consistent with those of Y-J. Liang’s1 on 50 nm particles. It should be assimilated to a binding between crystallites and the continuity of the crystal planes in a raspberry structure is noticed, as observed by S. Begin-Colin’s group[4] with structures of about 250 nm. The phase purity was probed by X-ray diffraction (XRD). The size of the coherent diffraction domains was calculated with two different methods: using Scherrer’s formula, and through a Rietveld refinement. The results are compared and correlated to TEM observations. The saturation magnetization was determined through the hysteresis cycles measured with a vibrating sample magnetometer (VSM) at room temperature. The superparamagnetism is observed for the 5 nm particles. The magnetization curve has been fitted with a Langevin function[5] which allows recovering the intrinsic saturation magnetization and an apparent size of 5 nm, close to that observed by TEM. The intrinsic saturation magnetization (85.6 emu/g) from the model is in good agreement with that determined at 2 K with a VSM/SQUID (85 emu/g). The saturation magnetization of the two types of nanoparticles is lower (85.6 emu/g for the 5 nm and 80.6 emu/g for the 35 nm) than that of the bulk ferrite Zn0.4Fe2.6O4 which is about 98.8 emu/g. Several contributions have to be taken into account to explain this discrepancy: - A surface spin-canting effect[6] could impact the magnetic moment of particles, especially for the smallest ones. The thickness of the surface spin-canting was estimated and the magnetic moments were thus corrected (Fig. 2). - A cationic disorder with a fraction of Zn2+ ions at the octahedral sites of the spinel structure, and not only at the tetrahedral (A) ones, can be deduced from a Rietveld analysis of X-ray patterns, and in-field Mössbauer spectra. Indeed, these techniques have made it possible to quantify the distribution of cations at the tetrahedral (A) and octahedral (B) sites of the spinel, and thus to calculate the magnetization according to a molecular field model[7] (Fig. 2). - Oxidation of the nanoparticles with conversion of Fe2+ into Fe3+ could lead to the reduction of the saturation magnetization[8]. The analysis of Mössbauer spectra enables to recover values close to the measured magnetic moments, which makes the cations distribution reliable. It therefore makes it possible to predict a magnetic moment close to the experimental one, keeping a spinel-type chemical formula with presence of vacancies to take into account the oxidation of the theoretical composition. The understanding of the effect of the microstructure on the magnetic moment opens up possibilities by tuning magnetic properties of iron oxide nanoparticles.

**References:**

[1] Y-J. Liang, F. Fan and M. Ma, Colloids and Surfaces A., Vol. 530, p.191-199 (2017) [2] A. Fujiwara, M. Tada and T. Nakagawa, J. Magn. Magn. Mater., Vol. 320, p.L67-L69 (2008) [3] S. Mourdikoudis and L. M. Liz-Marzán, Chem. Mater., Vol. 25, no. 9, p.1465–1476 (2013) [4] O. Gerber, B. Pichon, and C. Ulhaq, J. Phys. Chem. C., Vol. 119, p.24665-24673 (2015) [5] J.L. Dormann, D. Fiorani and E. Tronc, Adv. Chem. Phys., Vol. 98, p.283-494 (1997) [6] E. Tronc, P. Prené, J.P. Jolivet, J.L. Dormann and J-M. Greneche, Hyper. Inter., Vol. 112, p.97-100 (1997) [7] P. G. Bercoff and H. R. Bertorello, J. Magn. Magn. Mater., Vol. 169, p.314–322 (1997) [8] A. Demortiere, P. Panissod and B.P. Pichon, Nanoscale., Vol. 3, p.225-232 (2011)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d0fab6a72fe682a60b495b03c6b78453.jpg)
Fig. 1. TEM picture of raspberry-like nanoparticles

![](https://assets.underline.io/uploads/markdown_image/1/image/3f6da719018112feef39b97921fb4966.jpg)
Fig. 2. Magnetic moments predicted from microstructural characterizations for SP(F)M and FM particles with different Zn contents (0.2 and 0.4).

 Quantitative retrieving of the magnetic moment of iron oxide nanoparticles through structural characterizations

A new intermetallic ternary compound La6Pd2.28Sb15 was synthesized from the reaction of lanthanum and palladium metals in a molten antimony flux. The compound crystallizes in the orthorhombic space group Immm with a= 4.3082(9) Å, b=15.399(3) Å, and c=19.689(4) Å. The crystal structure contains a three-dimensional framework of Sb squares and ribbons that extend along the a axis, including complex Sb–Sb bonding. Magnetization measurements indicate that the intrinsic magnetic behavior of La6Pd2+xSb15 (x = 0.28) is diamagnetic, which we associate with Landau diamagnetism slightly larger than Pauli paramagnetism in this compound. The resistivity (ρ) decreases when lowering the temperature, indicating metallic behavior, and at low temperatures r depends quadratically on T. Interestingly, both the Hall resistivity and magnetoresistance present a nonlinear dependence on the applied magnetic field, suggesting a multiband behavior. This is supported by density-functional electronic structure calculations which show a complex Fermi surface originated in the antimonide substructures and containing both electron and hole pockets as well as open sheets.

**References:**

M. I. Sturza, M. L. Amigó, J. I. Facio et al., Journal of Solid State Chemistry, Vol. 291, pp. 121578 (2020),

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/809fee0358e093416661fd556c5c2f76.jpg)
Fig 1. Ball-and-stick representations of three-dimensional structure of La6Pd2+xSb15 (x = 0.28) viewed down the crystallographic a-axis. The red dashed lines outline the La6 trigonal prisms.

![](https://assets.underline.io/uploads/markdown_image/1/image/0a2b239811e304dece46ec3eebd0d4db.jpg)
Fig 2. Temperature dependence of the susceptibility for zero field cooling (ZFC) and field cooling (FC) procedures. Inset: Field dependence of the magnetization for several temperatures. In all cases, the background of the glue and the sample holder was subtracted, as well as, the core diamagnetic contribution.

Critical behavior of the magnetization in Heusler alloy Co2TiGa0.8Sn0.2

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