France



Submicron and nanosized cylindrical amorphous Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; and (Co&lt;sub&gt;0.94&lt;/sub&gt;Fe&lt;sub&gt;0.06&lt;/sub&gt;)&lt;sub&gt;72.5&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; wires with diameters between 100 and 900 nm have been successfully cast by means of an upgraded variant of the glass-coated melt spinning technique [1]. Amorphous samples with both compositions show a magnetically bistable behavior, i.e., a single step axial magnetization reversal with a characteristic rectangular hysteresis loop. This reversal consists in the displacement of a 180-degree domain wall along the wire axis when the applied field is equal to or larger than the switching field. The values of the switching field are significantly different, with the positive magnetostrictive amorphous submicron wires (Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt;) displaying one to two orders of magnitude larger values than the nearly zero magnetostrictive (Co&lt;sub&gt;0.94&lt;/sub&gt;Fe&lt;sub&gt;0.06&lt;/sub&gt;)&lt;sub&gt;72.5&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; ones. This emphasizes the importance of the types and magnitudes of the intrinsic magnetic anisotropies.&lt;br/&gt;Here we report on the study of structural relaxation within the amorphous submicron wires using measurements of the 180-degree domain wall velocity, in order to gain deeper insights into the roles played by the various types of magnetic anisotropy in amorphous submicron wires with different magnetostriction, such as Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; with the magnetostriction constant of 25 × 10&lt;sup&gt;-6&lt;/sup&gt;&lt;sub&gt; &lt;/sub&gt;and (Co&lt;sub&gt;0.94&lt;/sub&gt;Fe&lt;sub&gt;0.06&lt;/sub&gt;)&lt;sub&gt;72.5&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; with the magnetostriction constant of -1 × 10&lt;sup&gt;-7&lt;/sup&gt;, respectively. The samples have been furnace annealed in vacuum at 200°C and 350°C for 1h, in order to induce structural relaxation phenomena in the amorphous phase without crystallization. Domain wall velocity measurements have been performed on as-cast and annealed samples with both compositions and different diameters, using a method developed specifically for such ultrathin cylindrical wires [2].&lt;br/&gt;Fig. 1 shows the dependence of the domain wall velocity on the annealing temperature for highly magnetostrictive amorphous Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; samples with diameters between 230 and 850 nm. Fig. 2 illustrates the same dependence in the case of nearly zero magnetostrictive (Co&lt;sub&gt;0.94&lt;/sub&gt;Fe&lt;sub&gt;0.06&lt;/sub&gt;)&lt;sub&gt;72.5&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15 &lt;/sub&gt;samples with 300 and 770 nm in diameter, respectively.&lt;br/&gt;The domain wall velocity increases monotonically with the annealing temperature for all the highly magnetostrictive samples. The slope of the curves decreases with the increase in the wire diameter. This behavior originates in the stress relief that accompanies the structural relaxation and shows the important role played by the magnetoelastic anisotropy in the Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; samples. The effect is more pronounced in the thinner samples, due to their stronger intrinsic magnetoelastic interaction.&lt;br/&gt;A completely different behavior has been observed in the nearly zero (Co&lt;sub&gt;0.94&lt;/sub&gt;Fe&lt;sub&gt;0.06&lt;/sub&gt;)&lt;sub&gt;72.5&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; samples. For a wire with 770 nm in diameter, a monotonic decrease of the domain wall velocity with the annealing temperature was observed. For a thinner one, with 300 nm in diameter, a change of slope was observed: the wall velocity slightly increases after annealing at 200°C, and then drops below the value of as-cast sample after annealing at 350°C. This behavior is consistent with a diminished role of the magnetoelastic anisotropy and a more prevalent role of the shape anisotropy. Only the latter is important in the thicker sample. In the thinner one, the magnetoelastic anisotropy contributes to the magnetic behavior until a sufficiently large annealing temperature is used, so that the residual stresses are decreased.&lt;br/&gt;The results show that measuring the domain wall velocity of amorphous submicron wires with different magnetostriction constants can provide essential information on the structural relaxation effects by means of the dominant magnetic anisotropy type and its changes triggered by the low temperature annealing process. This analysis is important for the future application of cylindrical amorphous submicron wires.&lt;br/&gt;&lt;br/&gt;Acknowledgements - Work supported by the Romanian Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI) under contract no. 511PED/2020 (project PN-III-P2-2.1-PED-2019-0586/NanoCyliCon).

**References:**

[1] T.-A. Óvári, N. Lupu, and H. Chiriac, Recent trends in magnetic nanowires and submicron wires prepared by the quenching and drawing technique, in Magnetic Nano- and Microwires (Second Edition), edited by M. Vázquez (Woodhead Publishing, Cambridge, 2020), pp. 221-253.&lt;br/&gt;[2] S. Corodeanu, H. Chiriac, and T.-A. Óvári, Accurate measurement of domain wall velocity in amorphous microwires, submicron wires and nanowires, Rev. Sci. Instrum. 82 (2011) 094701.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d460a15c063e392de7c341532897f628.jpg)
Fig. 1. Domain wall velocity vs. annealing temperature for highly magnetostrictive amorphous Fe&lt;sub&gt;77.5&lt;/sub&gt;Si&lt;sub&gt;7.5&lt;/sub&gt;B&lt;sub&gt;15&lt;/sub&gt; glass-coated submicron wires.

![](https://assets.underline.io/uploads/markdown_image/1/image/2b1a79db360ef8ca5113605e7160f667.jpg)
Fig. 2. Domain wall velocity vs. annealing temperature for nearly zero magnetostrictive amorphous (Co&lt;sub&gt;0.94&lt;/sub&gt;Fe&lt;sub&gt;0.06&lt;/sub&gt;)&lt;sub&gt;72.5&lt;/sub&gt;Si&lt;sub&gt;12.5&lt;/sub&gt;B&lt;sub&gt;15 &lt;/sub&gt;glass-coated submicron wires.

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 Correlation between Structural Relaxation and Magnetic Behavior in Amorphous Submicron Magnetic Wires

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Submicron and nanosized cylindrical amorphous Fe77.5Si7.5B15 and (Co0.94Fe0.06)72.5Si12.5B15 wires with diameters between 100 and 900 nm have been successfully cast by means of an upgraded variant of the glass-coated melt spinning technique [1]. Amorphous samples with both compositions show a magnetically bistable behavior, i.e., a single step axial magnetization reversal with a characteristic rectangular hysteresis loop. This reversal consists in the displacement of a 180-degree domain wall along the wire axis when the applied field is equal to or larger than the switching field. The values of the switching field are significantly different, with the positive magnetostrictive amorphous submicron wires (Fe77.5Si7.5B15) displaying one to two orders of magnitude larger values than the nearly zero magnetostrictive (Co0.94Fe0.06)72.5Si12.5B15 ones. This emphasizes the importance of the types and magnitudes of the intrinsic magnetic anisotropies. Here we report on the study of structural relaxation within the amorphous submicron wires using measurements of the 180-degree domain wall velocity, in order to gain deeper insights into the roles played by the various types of magnetic anisotropy in amorphous submicron wires with different magnetostriction, such as Fe77.5Si7.5B15 with the magnetostriction constant of 25 × 10-6 and (Co0.94Fe0.06)72.5Si12.5B15 with the magnetostriction constant of -1 × 10-7, respectively. The samples have been furnace annealed in vacuum at 200°C and 350°C for 1h, in order to induce structural relaxation phenomena in the amorphous phase without crystallization. Domain wall velocity measurements have been performed on as-cast and annealed samples with both compositions and different diameters, using a method developed specifically for such ultrathin cylindrical wires [2]. Fig. 1 shows the dependence of the domain wall velocity on the annealing temperature for highly magnetostrictive amorphous Fe77.5Si7.5B15 samples with diameters between 230 and 850 nm. Fig. 2 illustrates the same dependence in the case of nearly zero magnetostrictive (Co0.94Fe0.06)72.5Si12.5B15 samples with 300 and 770 nm in diameter, respectively. The domain wall velocity increases monotonically with the annealing temperature for all the highly magnetostrictive samples. The slope of the curves decreases with the increase in the wire diameter. This behavior originates in the stress relief that accompanies the structural relaxation and shows the important role played by the magnetoelastic anisotropy in the Fe77.5Si7.5B15 samples. The effect is more pronounced in the thinner samples, due to their stronger intrinsic magnetoelastic interaction. A completely different behavior has been observed in the nearly zero (Co0.94Fe0.06)72.5Si12.5B15 samples. For a wire with 770 nm in diameter, a monotonic decrease of the domain wall velocity with the annealing temperature was observed. For a thinner one, with 300 nm in diameter, a change of slope was observed: the wall velocity slightly increases after annealing at 200°C, and then drops below the value of as-cast sample after annealing at 350°C. This behavior is consistent with a diminished role of the magnetoelastic anisotropy and a more prevalent role of the shape anisotropy. Only the latter is important in the thicker sample. In the thinner one, the magnetoelastic anisotropy contributes to the magnetic behavior until a sufficiently large annealing temperature is used, so that the residual stresses are decreased. The results show that measuring the domain wall velocity of amorphous submicron wires with different magnetostriction constants can provide essential information on the structural relaxation effects by means of the dominant magnetic anisotropy type and its changes triggered by the low temperature annealing process. This analysis is important for the future application of cylindrical amorphous submicron wires. Acknowledgements - Work supported by the Romanian Executive Agency for Higher Education, Research, Development and Innovation Funding (UEFISCDI) under contract no. 511PED/2020 (project PN-III-P2-2.1-PED-2019-0586/NanoCyliCon).

**References:**

[1] T.-A. Óvári, N. Lupu, and H. Chiriac, Recent trends in magnetic nanowires and submicron wires prepared by the quenching and drawing technique, in Magnetic Nano- and Microwires (Second Edition), edited by M. Vázquez (Woodhead Publishing, Cambridge, 2020), pp. 221-253. [2] S. Corodeanu, H. Chiriac, and T.-A. Óvári, Accurate measurement of domain wall velocity in amorphous microwires, submicron wires and nanowires, Rev. Sci. Instrum. 82 (2011) 094701.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d460a15c063e392de7c341532897f628.jpg)
Fig. 1. Domain wall velocity vs. annealing temperature for highly magnetostrictive amorphous Fe77.5Si7.5B15 glass-coated submicron wires.

![](https://assets.underline.io/uploads/markdown_image/1/image/2b1a79db360ef8ca5113605e7160f667.jpg)
Fig. 2. Domain wall velocity vs. annealing temperature for nearly zero magnetostrictive amorphous (Co0.94Fe0.06)72.5Si12.5B15 glass-coated submicron wires.

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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.

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

Mn2YZ based inverse Heusler alloys with cubic or tetragonal structures and high Curie temperature (TC) display exceptional tunability of their properties either by controlling the degree and the type of atomic ordering [1] or by controlling the total valence electron concentration (VEC) of the alloy [2]. Here the Mn atoms occupy both the (0,0,0) or (½, ½, ½) and (¼, ¼, ¼) or (¾, ¾, ¾) sites in the Heusler structure with antiparallel spins of different magnitude resulting in a ferrimagnetic order. Several theoretical and experimental studies on Mn2YZ alloys have predicted interesting properties like half-metallicity, spin gapless semiconductor with a high magnetic ordering temperature, anomalous hall effect and even zero field exchange bias, spin valve behaviour [3,4] etc. Mn2NiSn is one such cubic ferrimagnetic Heusler alloy with a moderately high magnetic moment of ~2.5 mB [5]. Density functional calculations as well as neutron diffraction studies have shown that the magnetic moment of Mn2NiSn can be tuned by controlling antisite disorder [5,6]. There are also reports suggesting a strong relation between the magnetic moment and the VEC controlled essentially by the Z element in Mn2NiZ alloys [7]. In the present work we aim to understand the role of antisite disorder on the magnetic properties of Mn2NiSn. We have employed two routes to introduce the antisite disorder. Firstly, we have systematically replaced Ni by Mn at the X site in Ni2MnSn by preparing alloys of the type Ni2-xMn1+xSn (where x = 0, 0.25, 0.5, 0.75 and 1) Secondly, the two alloy compositions, Ni1.25Mn1.75Sn (x = 0.75) and Mn2NiSn (x = 1) were subjected to an additional thermal treatment. The alloys were prepared by arc melting constituent elements in argon atmosphere and subsequently annealed at 800 oC for 72 hours in evacuated quartz tubes and quenched in ice cold water (referred to as rapid quenched (RQ)). The arc melted Ni1.25Mn1.75Sn and Mn2NiSn were cut into two halves and were sealed in four different quartz tubes. While two of these tubes containing the respective alloys were quenched from 800oC in ice water, the temperature of the other two tubes with the same compositions as that of the RQ alloys was lowered from 800oC to 427oC after 72 hours of annealing and were annealed at this lower temperature for the next 28 hours and cooled in furnace (referred as FC). All the alloys were characterized by x-ray diffraction (XRD) and SEM-EDX for the determination of their structure and composition. SEM-EDX indicated the compositions to be within 1% of their starting values. Rietveld refinement of the XRD patterns for the RQ alloys showed them to be largely single phase with a cubic L21 Heusler structure (SG: Fm-3m). Small percentage (~ 1 – 2 %) of the MnO impurity phase was noticed in a few compositions. In the case of FC alloys, while Ni1.25Mn1.75Sn alloy was cubic, Mn2NiSn was biphasic with major L21 phase (~93%) and minor (~7%) Mn3Sn type hexagonal phase (SG: P63/mmc) (Fig 1) . Magnetization measurements as a function of temperature (3 K to 390 K) were carried out in 100 Oe applied magnetic field employing zero-field cooling and field cooling protocols. TC increased from 340 K in x = 0 to above the highest measured temperature for all alloys with x =0.5 and above . Isothermal magnetization at 5 K was measured in the field interval of ± 7 T to determine the saturation magnetic moment. All the compositions showed ferromagnetic like M(H) loop with very low coercivity. The saturation magnetization in Ni2MnSn gave an effective moment of 4.06 mB/f.u. good agreement with reported values [8]. In the RQ alloys, with increase in Mn content, the magnetic moment decreases steadily from 4.06 mB/f.u. to 1.93 mB/f.u. in Ni1.25Mn1.75Sn and then increased to 2.80 mB/f.u. in NiMn2Sn. The FC Ni1.25 Mn1.75Sn showed a significant increase in its magnetic moment to 3.31 mB/f.u. This increase is surprising considering its structure to be the same as that of its RQ counterpart. In the phase separated Mn2NiSn the magnetic moment showed a marginal increase to 2.83 mB/f.u. To understand the above magnetic properties, local structures of Ni, Mn and Sn in all the alloys were studies by employing extended x-ray absorption fine structure (EXAFS) spectroscopy. In all the alloys EXAFS data were analysed together using a model based on their respective crystal structure. Excellent fits were obtained for RQ alloys with x = 0, 0.25 and 0.5. In case of Ni1.25Mn1.75Sn, only Ni EXAFS could be well described with the crystal structure model. Both Mn and Sn EXAFS could not be fitted and relaxation of structural constraints indicated a much lower value for the Mn – Sn bond distance than the predicted 3.025 Å from its crystal structure. Introduction of additional Mn – Sn and Mn – Mn correlations derived from hexagonal Mn3Sn resulted in a good fit to the EXAFS data of x = 0.75 and 1 RQ and FC alloys. Mn3Sn like environment can exist in Mn2NiSn type alloys if, in addition to the A2 type disorder, there is also an antisite disorder between Mn and Sn atoms (Fig 2). EXAFS analysis indicated a defect concentration ~ 20 ± 7 % in RQ and FC Mn2NiSn and much less in Ni1.25Mn1.75Sn. Such a segregation of defect within the overall Heusler structure due to antisite disorder seems to be the reason for the increased magnetic moment in Mn2YZ alloys.

**References:**

[1] T. Graf, C. Felser, S. Parkin, Prog. Solid State Chem. 39, 1 (2011). [2] C. Felser, L. Wollmann, S. Chadov, Chem Int Ed. 46:668-99, (2007). [3] S. Ouardi, G. Fecher, C. Felser, Phys. Rev. Lett. 110, 100401 (2013). [4] A. K. Nayak, M. Nicklas, S. Chadov et al, Phys. Rev. Lett. 110, 127204 (2013). [5] R. B. Helmholdt and K. H. J. Buschow, J. Less-Common Met. 128, 167 (1987). [6] S. Paul, A. Kundu, B. Sanyal, J. Appl. Phys. 116, 133903 (2014). [7] H. Luo, G. Liu, F. Meng, J. of Magn. Magn. Mater. 321, 4063–4066 (2009). [8] M. Nazmunnahar, T. Ryba, J. J. delVal, J. of Magn. Magn. Mater. 386, 98–101 (2015).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/caad83c069f8c7210cc235e36301d783.jpg)
X-ray diffraction patterns for Ni2-xMn1+xSn series of RQ alloys where (x = 0, 0.25, 0.5, 0.75, 1) and Ni1.25Mn1.75Sn, NiMn2Sn FC alloys.

![](https://assets.underline.io/uploads/markdown_image/1/image/147e5a0f09a0160a24d74cfbbc2a0169.jpg)
Schematic diagram of the ab plane of Mn2NiSn showing the segregation of Mn3Sn- type Hexagonal defect phase.

 Antisite disorder and defect phase segregation and its role in magnetic properties of Mn2NiSn

The search for new functional magnetic materials has led to the exploration into multi-component alloys (MCAs), which contain four or more elements with percentages between 12.5 % and 33 %. These include the sub-class of high entropy alloys (HEAs) which often exhibit single phases, thought to be stabilised by the high entropy of mixing of these compounds amongst other competing thermodynamic contributions. The resulting alloys often have interesting functional properties, which are linked to their structure. This work has explored a number of different compositions (CoFeNi0.5Cr0.5Alx, CoFeNi0.5CrxAl CoFeNiCryCux) in both bulk form, to understand how the phases present in the alloys influence the magnetic properties. The work has also used semi-empirical models to predict the different phases within the compositions and machine learning has been used to predict the saturation magnetisation. For example, in bulk CoFeNi0.5Cr0.5Al it was found that Fe-Cr nanoparticles formed in a weakly magnetic CoNiAl matrix [1]. This formation of round nanoparticles increased the magnetisation of the CoFeNi0.5Cr0.5Al alloy by a factor 4 at room temperature. For all the CoFeNi0.5Cr0.5Alx samples, the coercive field was small and the saturation magnetisation comparable with NiFe. While for the bulk CoFeNi0.5CrxAl samples, nanoparticles formed in all the samples containing Cr, with the CoFeNi0.5Cr1.0Al sample having square nanoparticles. Thus the amount of Cr in CoFeNi0.5Al dominates the geometry of the FeCr nanoparticles that form. Plus encapsulating the Cr in Fe-Cr nanoparticles meant that the Curie Temperatures for all the alloys containing Cr and Al were above 300 K (Fig. 1a). While for bulk CoFeNiCryCux (x = 0.0 - 1.5 and y = 0.0 - 1.0) samples, it was found that the addition of Cu could be used to tune the Curie Temperature over a 100 K range, with less than a 30 % reduction in the saturation magnetisation at 10 K, while the addition of Cr changed the Curie Temperature by 700 K and reduced the saturation magnetisation by 60 % at 10 K. By tuning the Cu to Cr ratio it is possible to achieve a Curie temperature around room temperature. The magnetocaloric effect (MCE) was studied in these materials, as the compositions tend to involve cheaper, more widely available elements, plus careful tuning of the composition will allow for the Curie Temperature to be around 300 K. It was found that the refrigeration capacity for the CoFeNiCryCux alloys was ~ 70 J/kg and for the CoFeNi0.5Cr0.5Alx alloys was ~ 75 J/kg at 2 T (Fig. 1b) [2]. Although these are smaller than existing materials such as LaFeSi, these HEAs still have advantages due to the presence of second order transitions, and having a wider operational temperature range for the MCE. In conclusion, the MCAs studied have promising functional magnetic properties, with small coercive fields, and reasonable saturation magnetisations. The phases present can be tuned via the composition, allowing for two-magnetic phase systems to be fabricated, that improve the magnetic properties compared to a single solid solution. The research carried out is only the tip of the iceberg, but these alloys are showing encouraging results.

**References:**

[1] N. A. Morley, C. R. B. Lim, J. Xi, A. Quintana-Nedelcos, and Z. Leong, Scientific Reports, 10, 14506, (2020) [2] A. Quintana-Nedelcos, Z. Leong, and N.A. Morley, Materials Today Energy, (accepted 2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/279780d9001aefe47b6797a2a7923640.jpg)
Figure 1a. Curie Temperature for CoFeNi0.5Cr0.5Alx, CoFeNi0.5CrxAl and CoFeNiCryCux alloys. 1b. Refrigeration capacity at 2 T for CoFeNi0.5Cr0.5Alx, CoFeNi0.5CrxAl and CoFeNiCryCux alloys. Shaded area useful temperature range.

 High Entropy Alloys: The next big thing in functional magnetic alloys

Fe-Co alloys have been ideal materials for various applications where high saturation magnetization (Ms), high permeability (µ) and low coercivity (Hc) are needed, especially for the applications where the minimization of mass and volume is a design parameter, such as aerospace industries [1-6]. In addition, their high Curie temperature makes them competitive candidates for high temperature applications [4]. In this study, in order to fully understand the compositional effect of Fe-Co alloys on their magnetic behaviour, Fe25Co75, Fe50Co50 and Fe75Co25 alloys were produced by using arc melting technique and characterized with the help of X-ray diffraction (XRD) analysis and superconducting quantum interference magnetometer (SQUID). XRD analysis indicated that all the samples were single phase (BCC), proving that oxidation did not occur during the manufacturing process. Furthermore, from their hysteresis loops, their magnetic saturations, remnant magnetizations and coercivities were found in the ranges 253-280 emu/gr, 2.06-6.15 emu/gr and 8.67-40.24 Oe, [4] respectively (Fig. 1). It was observed that as the % Co (wt.) content increases, saturation and remnant magnetization decreases, thus the Fe-rich alloys have higher magnetic properties. Also, after arc melting, stress-relief annealing was employed at 1073 K for 1 hr, resulting in reduction of the magnetic saturation (220-272 emu/gr), remnant magnetization (1.08-3.8 emu/gr) and coercivity (4.73-13.28 Oe) [5] due to the microstructural refinement, as it can be seen clearly in Fig.1. This study confirms that arc melting helps to improve the magnetic properties of Fe-Co alloys, because their magnetic properties is higher than the magnetic properties of those fabricated by mechanical alloying (Ms: 150-225 emu/gr, Hc: 25-70 Oe) [4] and cold rolling (Ms: 217.8 emu/gr, Hc: 87.7 Oe) [3]. Curie temperatures of the as-cast samples (1097-1181 K), are slightly lower than the values in the literature [5], also decreased slightly to the value range of 1071-1107 K after the heat treatment. By looking at Fig. 2, for the high temperature magnetic performances of as cast and annealed specimens, it can be seen that the annealed samples have a higher saturation magnetisation as a function of temperature. Further study has been undertaken to design and develop a new Fe-based amorphous alloy, with similar properties to Fe-Co alloys. The alloy of Fe45Co15B28Al10B2 was arc-melted followed by stress-relief annealing at 573 K for 1 hr to achieve the desired magnetic properties and amorphous morphology. Using DCS and temperature dependence magnetisation measurements up to 1000 K, the temperature dependence structural and magnetic behaviour was studied. DSC analysis indicates that the sample has glassy phase with the melting point of 1200 K and glass transition temperature of 800 K. Moreover, its Curie temperature was found as 940 K. Thus, this composition has promising results as a new soft magnetic material for high temperature applications.

**References:**

[1] S. Bergheul, A. Haddad, H. Tafat and M. Azzaz, “Magnetic , Microwave and Absorbing Properties Fe-Co of Alloy Synthesized by Mechnanical Alloying Process,” in Application of Contemporary Non-Destructive Testing in Engineering, Portoroz, Slovenia, 2005. [2] R. Fingers and G. Kozlowski, “Microstructure and magnetic properties of Fe–Co alloys,” Journal of Applied Physics, vol. 81, no. 8, pp. 4110-4111, 1997. [3] S. Honjo, S. Kikuchi, A. Sakuma, S. Ishio and J. Balachandran, “Preparation of magnetic Fe-Co alloy using texture controlled technique,” Journal of Magnetism and Magnetic Materials, vol. 465, pp. 64-69, 2018. [4] F. Sanchez-De Jesus, A. Bolarin-Miro, C. Cortes Escobedo, G. Torres-Villasenor and P. Vera-Serna, “Structural Analysis and Magnetic Properties of FeCo Alloys Obtained by Mechanical Alloying,” Journal of Metallurgy, vol. 2016, p. 8347063, 2016. [5] R. Sundar and S. Deevi, “Soft magnetic FeCo alloys: alloy development, processing, and properties,” International Materials Reviews, vol. 50, no. 3, pp. 157-192, 2005. [6] Y. Zhang, R. Ma, S. Feng, L. Cheng, P. Davies and P. Yu, “Microstructures and magnetic properties of Fe-35%Co alloy fabricated bymetal injection molding,” Journal of Magnetism and Magnetic Materials, vol. 497, p. 165982, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b10699c413116d6f4d080b35248523dd.jpg)

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 Heat treatment investigations of Fe-based alloys

Permanent Magnet Synchronous Machines (PMSM) have gradually become the mainstream solution for drive motors. One main trend for advanced PMSM optimization is focused on new material application. Conventional PMSM iron core is fabricated by Non Grain-Oriented (NGO) silicon steel sheet lamination, based on traditional technic, the high-strength NGO silicon steel uses solid solution strengthening and precipitation strengthening methods to enhance mechanical strength [1]. As mentioned in [2-3], due to the increase in mechanical strength of high-strength NGO steel, a narrower magnetic bridge design can be applied in the rotor design. Thereby reducing the leakage flux to increase the output torque and the overall efficiency. Even though the high-strength NGO had higher iron loss, counting the reduction in the rotor bridge width, the overall performance can be significantly enhanced. The maximum speed of advanced PMSM is mostly greater than 12000rpm, thus the rotor sustains significant tensile stress due to centrifugal force. It’s easier to form the striped 180° domain with higher permeability under tensile stress [4]. While the frequency influence and thermal condition has not been discussed in [4]. In this paper, we designed an equivalent sample to simulate the condition of an iron core, similarly in [5], with different excitation and manufacture parameter such as laminated number and thermal condition. Three types of high-strength NGO (SW35YS600\SW35YS900\B35AHS500) and a controlled group (conventional NGO B35A270) has been tested. Magnetic performance of equivalent sample is measured by ring sample method. Two narrow sides of the sample are subjected to large tensile stress concentration, the lamination number is 5, 10, and 20. At high excitation frequencies, the level of iron loss improvement caused by tensile stress is significant. Four materials have also been annealed respectively at 720°C for 10 hours under argon atmosphere. After annealing, the tensile stress has lower effect on the magnetic properties for B35AHS500 and B35A270, but is significant for SW35YS600 and SW35YS900. Therefore, it is speculated that a large proportion of heat treatment process has been adopted during SW35YS600 and SW35YS900. In addition, we also conduct metallographic experimental observations on the material of the sample and the tensile fracture, and analyze the reasons for this result at the grain level. And in the subsequent experiment process, we further explored the influence of different environmental temperatures and different tensile stresses on the magnetic properties of these four NGO materials.

**References:**

[1] GONG, Jian, and Hai-wen LUO. "Progress on the research of high-strength non-oriented silicon steel sheets in traction motors of hybrid/electrical vehicles." Journal of Materials Engineering 43.6 (2015): 102-112. [2] Tietz, Marco, et al. "Effects and advantages of high-strength non grain oriented (NGO) electrical steel for traction drives." 2013 3rd International Electric Drives Production Conference (EDPC). IEEE, 2013. [3] Tanaka, Ichiro, et al. "Application of high-strength nonoriented electrical steel to interior permanent magnet synchronous motor." IEEE transactions on magnetics 49.6 (2012): 2997-3001. [4] Senda, Kunihiro, et al. "Magnetic properties and domain structure of non-oriented electrical steel under stress." IJTFM 131.10 (2011): 884-890. [5] Gao, Lingyu, et al. "Application of grain-oriented electrical steel used in super-high speed electric machines." AIP Advances 10.1 (2020): 015127.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ccde1a3a9953b57d9bd60bd246980599.jpg)
metallographic experimental observations

![](https://assets.underline.io/uploads/markdown_image/1/image/793eec53db2c5ec9c61420c606acc711.jpg)
sample of the tensile experiment and result of the magnetic test

 Magnetic Performance Improvement caused by Tensile Stress in Equivalent Iron Core fabricated by High-Strength Non-Oriented Electrical Steel

Grain-oriented (GO) electrical steel sheets, as a core material used in power transformers broadly, often holed at particular and suitable regions to make the stacking of the sheet easier. The magnetic properties around the hole will be deteriorated, and the local magnetic domain structure will be impacted [1]. These phenomena will significantly influence the performance of the transformer [2]. It is necessary to accurately measure and study the influence of hole on local vector magnetic properties to optimize the core structure. Some studies use the search coils wound by drilling through the sample to analyze the flux orientations [3]-[4]. Yet the distributions of local magnetic properties around the hole have not been clarified. To obtain a more comprehensive and accurate distribution of local vector magnetic properties, and avoid damaging the sample to wind the search coils, the needle probes and double H-coils, which were discussed in [5] and [6], are adopted and developed. In this paper, a novel local magnetic property testing system using an accurately-movable B-H sensor is designed and constructed to study the local vector magnetic properties around the hole in a transformer type core made of grain-oriented electric steel sheets. The influence of sizes and positions of the holes on the properties is compared and analyzed at 50-400 Hz. In addition, the changes of the magnetic domain are observed and analyzed. Fig. 1 shows the local testing system with an accurately-movable B-H sensor and sample with 300 mm × 300 mm studied in this paper. The distance between the needles of B sensor is 3.5 mm, and H-sensor coil is 2 mm × 2 mm assembled using wire with 0.01 mm diameter. The number of turns is 600. The sensor is mounted to a XYZ-precise-positioning device, hence, the magnetic flux density, B, magnetic field strength, H, and core loss, P, of each point in the local area can be measured. Eight holes with diameter of D and interval of 100 mm are punched in the transformer sheets. W is the distance of the center of hole to the inner edge. Different D and W are studied in the paper. Single layer grain-oriented steel sheet (namely, B30P120) is tested. To study the vector magnetic properties around the hole, the square area (47 × 47 mm2) centered at the hole is measured and studied. The H = H (x, y), B = B (x, y) and P = P (x, y) are measured when the sensor is moved 1 mm in interval along the x-, or y-directions and the total number of measured points are 2000. As a criterion of measurements, the peak flux density is measured and controlled with a search coil, which wound uniformly around the sample. Fig. 2 shows P distributions around the hole with D = 4 mm and W = 25 mm when B is controlled to be 50 Hz sinusoidal waveform with 1.5 T amplitude. The domain structures at particular areas A1 and A2 are also shown in Fig. 2. The results show that the core loss P around the hole is much larger than that around points far to the hole. It could be attributed to the non-uniform flux density distributions, in particular, increasing flux density close to the hole. It is consistent with the observation of domain structure around the hole. The domain structure is disordered close to the hole due to strain introduced by hole punching while it is uniform at the point far to the hole. In addition, the distribution of the flux density B, field strength H, and core loss P around the hole with different diameters (D = 4, 6, 8, 10 mm) and different positions (W = 20, 25, 30 mm) are measured and analyzed in the flux density ranges of 0.1 – 1.5 T at 50 – 400 Hz. The experiment results show that the local B and H distributions are altered by the hole. The domain pattern is also restructured due to strain introduced by hole punching. As a result, the local losses are increased. In addition, the losses around the hole increase to 150 – 300 % compared with the losses at the far point depending on D value of 4 – 10 mm. However, the location of hole has minor influence on the losses, in particular, when the hole is located at the symmetrical position (W = 25 mm). In conclusion, small size of the hole and symmetrical position of the hole during stacking of the core can minimize the deterioration of local magnetic properties and improve the performance of the stacked electrical steel sheets ultimately.

**References:**

[1] T.Gunes, R. Schäfer and N.Derebasi, IEEE Transactions on Magnetics., Vol. 54, p.1-8 (2018) [2] G. teNyenhuis, S. Girgis and F. Mechler, IEEE Transactions on Power Delivery., Vol. 16, p.648-653 (2001) [3] T.Gunes, N.Derebasi and C.Erdonmez, IEEE Transactions on Magnetics., Vol. 51, p.1-4 (2015) [4] N Derebasi. C Erdonmez, Journal of Superconductivity and Novel Magnetism., Vol. 30, p.3309-3313 (2017) [5] S. Imamori, S. Aihara and H. Shimoji, Journal of Magnetism and Magnetic Materials., Vol. 500 (2020) [6] S Aihara, H Shimoji and T TodakaM, IEEE Transactions on Magnetics., Vol. 48, p.4499-4502 (2012)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/dd07283974bbc51d0a8991dc1207b2ad.jpg)
Fig. 1.Novel local measurement system and measurement sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/cf2651f0e011db64b56bc65193d42edc.jpg)
Fig. 2. Distributions of the core loss around the hole and magnetic domain structure at area A1, A2.

 Influence of Size and Position of Stacking-Hole on Local Vector Magnetic Properties of Grain-Oriented Steel Sheet

Introduction: Non-oriented silicon steel is widely used in the manufacture of motors and other equipments due to its excellent magnetic properties. In the production process, non-oriented electrical steel often needs to be punched to form the required shape. During the punching process the magnetic properties of silicon steel sheets will be deteriorated due to the mechanical stress [1-4]. As a result, the plastic deformation and residual stress emerge around the area of cutting edge, which have a significant impact on the magnetic properties and magnetic domain structure of electrical steel sheets. In this paper the effects of punching on the magnetic properties and magnetic domain structure of non-oriented electrical steel are studied. And the deterioration degree of the magnetic properties caused by different punching load are analyzed quantitatively. Ι Test samples and methods The test samples of cold-rolled non-oriented electrical steel B35A270 are punched on the precision punching machine by the 25-ton and 80-ton punching load, respectively. Then, two kinds of samples with a size of 49.5*49.5*0.35mm are obtained. The sample processed by 25 tons of punching load is denoted as sample A, and the one processed by 80 tons of punching load is denoted as sample B. The 2D magnetic properties measurement apparatus consists of two single C-shaped yokes, excitation windings and silicon steel sheet samples. An AC magnetic field with a frequency of 50 ~ 200Hz is applied along the rolling direction of the sample The samples supported by the sample holder are placed in the gap between the two yokes, and the yoke air gap matches the size of the sample. The sensing system is specially designed to measure the local magnetic properties in different position of the sample. In the sensing system, the micro-size H coil is wound on a 0.05mm thick PCB substrate with a length of 3mm to measure the H signal in the rolling direction of the sample. Two retractable B probes are fixed on a 1.5mm thick PCB with a spacing of 3.5mm to measure the B signal in the rolling direction of the sample. Taking the midline of the sample along the tangential direction as the measurement characteristic sampling line, the micro-size composite B-H sensor can be moved smoothly along the characteristic sampling line with a 2 mm distance step. ΙΙ Experimental results and analysis The core loss curves of the two samples measured at 50Hz sinusoidal signals are depicted in Fig.1 (a) and (b). The loss of the sample A increases by 0.9% ~ 15.25% in the range of 8 mm from the edge, especially in the range of 6 mm. The loss of the sample B increases by 6.8 % ~ 29.55%, while the deteriorated area expands to 14 mm. According to the Bertotti loss separation, the hysteresis, eddy current and excess loss coffficient are identified by the experimental results. It is concluded that the punching process cause an increase of the hysteresis loss. It can be attributed to plastic deformation and residual stress around the punching edge. The moving of magnetic domains can be hindered with the increase of the width of plastic deformation area. During the magnetization process, the movement resistance of the edge domain increases, so the hysteresis loss increases, which increases the iron loss of the sample. At the edge of the sample A, the magnatic coercivity increases by 5.5%, the magnetic remanence and permeability decreases by 11.7% and 29.2%. The magnatic coercivity increases by 24.3%, the remanence and the permeability decreases by 35.9% and 47.9% at the edge of the sample B. ΙΙΙ Observation of magnetic domain structure In order to investigate the mesoscopic properties of punching effect, the 8*8mm sample need to be prepared for Kerr microscope, which is cut by wire electrical discharge machining from the above sample A and B in the edge and center area of the samples.After sanding, mechanical polishing and other steps, shiny mirror-like samples are obtained. Using a Kerr microscope to observe the magnetic domains of the sample, as shown in Fig. 2(a), the center of the sample A is dominated by sheet-like magnetic domains, while there are a large number of labyrinth domains near the punching edge as shown in Fig. 2 (b). The size and shape of the domains also change. In addition, the magnetic domain in the center is parallel to the rolling direction, while the direction of the magnetic domain at the edge changes, which makes it difficult to magnetize. This leads to the increase of iron loss and the deterioration of magnetic properties. IV Conclusion Based on the local 2D magnetic measurement and magnetic domain observation, the magnetic properties of non-oriented electrical steel deteriorate by the punching processing. Furthermore, the deterioration degree of the magnetic properties become more significant by larger punching load.

**References:**

[1] Campos M F D , Sablik M J, and Landgraf F J G . Journal of Magnetism & Magnetic Materials., Vol.320, p.e377-e380(2008) [2] René Siebert, Wetzig A, and Beyer E. IEEE Electric Drives Production Conference., (2013) [3] Nakata T. IEEE Translation Journal on Magnetics in Japan., (2008) [4] Senda K , Ishida M, and Nakasu Y. Journal of Magnetism and Magnetic Materials., Vol.304, p.e513-e515, (2006)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2e1b0ece638ad406cd008f90715dcef9.jpg)
Fig.1 Core loss curves of sample A and B

![](https://assets.underline.io/uploads/markdown_image/1/image/b2c57ff57baf50342830843dfc45b66b.jpg)
Fig.2 Magnetic domain structure of sample A

 Effect of Punching on Magnetic Properties of Non-Oriented Electrical Steel

Thin magnetic cylindrical wires attract considerable attention due to interesting features of a domain wall motion like absence of the Walker breakdown that prevents fast domain wall dynamics [1]. Amorphous glass-coated microwires are composite material, in which very high domain wall velocities have been observed [2-3]. Owing to the amorphous state of wires, the magnetocrystalline anisotropy vanishes. Recently, it was shown that the axial magnetic anisotropy resulting from rapid quenching has comparable strength, leading to a tilted domain wall orientation [4]. It is an open question of how the tilted domain wall in cylindrical wires moves at high velocities and the origin of the so-called unidirectional effect [5]. An essential prerequisite for understanding the magnetic domain walls dynamics is a detailed knowledge of its spin structure in static. While several experimental techniques allow for well controllable deposition of magnetic structures with complex geometries [6], a reliable determination of a surface magnetization usually meets several obstacles in case of sample with curved surface. In the first part, we extend our analytical model of the Magneto-Optical Kerr Effect (MOKE) contrast [7] for cylinders with reduced diameter. Understanding the underlying mechanisms allows devising a new approach for interpretation of magneto-optical observations of thin magnetic cylinders. It is shown that the cylindrical shape of sample surface gives rise to a spatial distribution of the planes of incidence that are all tilted each to other. Phase diagrams of a magneto-optical contrast are calculated for various angles of incidence, extinction angles between polarizer and analyzer and as a function of thickness of a glass coat. In particular, it is shown that additional layer of a glass coat changes remarkably the circumferential dependence of light intensities. Our framework is used to optimize the LASER MOKE setup for direct visualization of a surface shape of domain wall in thin magnetic cylinders [4]. Stabilization of a domain wall is achieved by two opposite magnetic fields, resulting in effective one-dimensional potential well. Periodic back-and-forth motion of the well is used to synchronize the domain wall position with MOKE imaging and direct time-resolved images of a surface magnetism are performed. In contrary to previous measurements, a small pick-up coil is wounded around a thin glass capillary in order to detect spin dynamics inside the wire (Fig. 1). A direct comparison between surface domain wall position detected by MOKE and a signal from pick-up coils is given. It is shown that the voltage induced in pick-up coil has two sources: a, the voltage from spatially dependant magnetic field controlling the domain wall position and b, the signal from the domain wall. Employing simulations based on finite element method, the shape of a magnetic potential well is calculated. The profile of the magnetic domain wall potential well is then used to calculate the contribution from domain wall. At slow motion of a domain wall potential well, the signal from pick-up coils is well synchronized with a surface domain wall motion. The result implies almost planar structure of a domain wall. At high domain wall velocities, the signal in pick-up coil is induced earlier than surface boundary arrives to the position of a pick-up coil. The findings show that the tilted domain wall in microwires is not planar during the propagation. Our time-resolved observations of a domain wall depinning process show domain wall strongly distorts at pinning centres (Fig. 2). The finding is important for correct interpretation of a domain wall velocities measured by Sixtus-Tonks method. Finally, we propose a single scheme for wireless magneto-optical sensor based on domain wall motion in thin magnetic cylinders.

**References:**

[1] M. Yan, A. Kákay, S. Gliga, et al., Phys. Rev. Lett., Vol 104, p.057201 (2010) [2] P. Klein, R. Varga, M Vázquez, J. Alloy. Compd., Vol 550, p.31 (2013) [3] R. Varga, K. L. Garcia, M. Vazquez, P. Vojtanik, Phys. Rev. Lett., Vol 94, p.017201 (2005) [4] K. Richter, A. Thiaville, R. Varga, J. McCord, J. Appl. Phys., Vol. 127, p.193905 (2020) [5] J. Onufer, J Ziman, M. Kladivova, J. Magn. Magn. Mater., Vol 396, p.313 (2015) [6] A. Fernandez-Paecho, et al., Sci. Rep., Vol 3, p.1492 (2013) [7] K. Richter, A. Thiaville, and R. Varga, Phys. Rev. B, Vol. 96, p.064421 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a9c31b25e237279d8a20cbb60d77e613.jpg)
Fig. 1 Stabilization of a domain wall by potential well. Microwire (M) is places between coils. Pair of driving coils (C1 and C2) generates opposite magnetic fields H1 and H2. The domain wall is moved back-and-fforth by ramping the current in one coil. Surface magnetization is detected by two LASER spots (red lines). Inner magnetization dynamics is sensed by pick-up coil (P).

![](https://assets.underline.io/uploads/markdown_image/1/image/1264f9eaa0f431b2bb7352ea0cd982ce.jpg)
Fig. 2 Time-resolved observation of a domain wall depinning proces in amorphous glass-coated microwire. Images are perfomed by time-rsolved MOKE microscopy.

 Time-resolved observation of a domain wall motion in microwires with positive magnetostriction

—The idea of the present work is devoted to improving the SOLT calibration standard by specially designed microstrip cells as a PCB SOLT standard for VNA calibration and measuring the high-frequency magnetoimpedance (MI) for the development of various high-performance micro-sensor devices. The high-frequency sensitivity of MI was enhanced by the current annealing of partially crystalline wires. In the past few years, soft ferromagnetic amorphous wires have attracted growing attention in research due to their miniature dimensions, excellent soft magnetic properties, and giant-magnetoimpedance (MI) effect [1,2]. The MI effect which is referred to as a large and sensitive change in the complex-valued impedance of a magnetic conductor in the presence of an external magnetic field and/or mechanical stress is of particular interest for the development of various high-performance micro-sensor devices [3]. To optimize sensing operation regimes, it is important to measure the impedance characteristics of the individual wire which may present considerable problems at higher frequencies in the GHz range. This is related to uncertainties occurring due to the calibration of measuring devices (Network Analyzer). In the present work, we suggest an application-specific calibration technique with a specially designed microstrip cell for the impedance measurement for frequencies up to 6 GHz. We also demonstrate that the MI plots change their shape with increasing frequency and high sensitivity range caused by the directional change in the dc magnetization vanishes at frequencies of about 2 GHz for Co-rich wires with a circumferential anisotropy. The frequency range of high MI sensitivity can be enhanced by inducing a surface anisotropy in partially crystallized wires. Coaxial and microstrip transmission lines are widely used as sample holders, however, in the case of the impedance measurements when the sample is subjected to mechanical stress, coaxial lines are not convenient. Here we discuss the calibration procedures for microstrip lines. In the microwave de-embedding methods, the electrical reference planes are shifted to the sample location. This requires the use of dummy sample holders with specific terminations, for example, three reflection standards (open, short, and match load) and two ports connected together (thru). This calibration procedure is known by its name as short-open-load-thru (SOLT) or thru-open-short-match (TOSM). Accurate calibration standards can be fabricated on customized PCB, then, the complex impedance Z is calculated from the S21–parameter using a simple formula without solving any equations. Fig. 1 shows the MI characteristics at different frequencies of amorphous Co66.6Fe4.28B11.51Si14.48Ni14.4Mo1.69 microwires in an as-prepared state (total diameter D=25.8 µm metal core diameter d=25 µm and d=14.2 µm). The wire has a well-defined circular anisotropy with an anisotropy field of about 7.5 Oe. The wires of this composition are of particular interest due to low Curie temperature, so they can be used as embedded temperature sensors. It is seen that the high sensitivity of MI due to the dc magnetization re-orientation is preserved for frequencies below 2 GHz. When the dc magnetization is along the wire and does not change by the field, only the permeability parameter determines the field behavior of the impedance: for high frequencies, it increases with a much lower slope: the sensitivity of the impedance change is about few present per Oe. In the case of wires with partial crystallization, the current annealing establishes a stronger surface anisotropy which improves the MI behavior at higher frequencies. Moreover, it is possible to realize a strong stress dependence of MI at zero fields as demonstrated in Fig. 2. Acknowledgment: This work was supported by the Russian Foundation for Basic Research (RFBR 19-32-90129) and the part from the Ministry of Education and Science of the Russian Federation in the framework of the Increase Competitiveness Program of MISiS.

**References:**

 [1] L. V. Panina, K. Mohri, T. Uchiyama, Giant Magneto-Impedance in Co-Rich Amorphous Wires and Films, IEEE Trans. Magn. Vol. 31, p. 1249-1260 (1995). [2] M. Vázquez, Soft magnetic wires, in: Phys. B Condens. Matter. Vol 299, p. 302-313 (2001). [3] J. Alam, C. Bran, H. Chiriac, et al, Cylindrical micro and nanowires: Fabrication, properties and applications, J. Magn and Magnetic Mater. Vol. 513 (2020) 167074.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0925a8b841221cb3b8ae375e66205925.jpg)
Fig. 1: MI vs magnetic field of amorphous Co66.6Fe4.28B11.51Si14.48Ni14.4Mo1.69 microwires in as-prepared state at GHz frequency range a) 0.1 GHz to 0.9 GHz and b) 1.5 GHz to 2.5 GHz

![](https://assets.underline.io/uploads/markdown_image/1/image/37529af52350f8e5679fc02dc7919582.jpg)
Fig. 2: Effect of tensile stress on the MI vs. magnetic field of Co71Fe5B11Si10Cr3 (total diameter, a metal core diameter, partially crystalline) microwires after DC current annealing at 50 mA for 30 minutes. The frequency is 2.1 GHz.

 Magneto-Impedance Behavior of Soft Ferromagnetic Microwires at Ghz-Frequency for The Application of High-Performance Magnetic Sensory Devices

Thermal treatments of amorphous alloys are known to cause structural relaxation which is followed by an evaluation of the magnetic anisotropy and saturation magnetostriction. In this work we investigated the effect of annealing with a temperature close to the onset of the crystallization on the magnetic hysteresis properties of glass-coated amorphous microwires of Co-rich compositions with a nearly zero magnetostriction. The annealing process was performed on the wires by two methods: dc current annealing and conventional annealing in finance (at 475-490 oC for 30 min). The current intensities were chosen such to ensure similar annealing conditions. The annealing temperatures were higher than the Curie temperature (~360 oC) and slightly lower than the primary crystallization temperature (510 oC). We have demonstrated a sharp change in the shape of the magnetic hysteresis after annealing which is caused by the change in the magnetostriction. Typically, amorphous microwires of Co-rich compositions with negative magnetiostriction are regarded as excellent soft magnetic materials suitable for large and sensitive magnetoimpedance (MI) [1]. A well-defined circumferential anisotropy could be established in these wires by a proper choice of composition, geometry and annealing treatments, which increases the MI ratio up to hundred percent in characteristic fields of few Oersted [2]. The high sensitivity of impedance to low magnetic fields makes amorphous ferromagnetic microwires a promising material for the construction of different sensor systems. In the present work, the transformation of the sign of magnetostriction in amorphous microwires of composition: Co71Fe5B11Si10Cr3 (diameter: D/d = 29/25 µm) and Co66.6Fe4.28B11.51Si14.48Ni1.44Mo1.69 (diameter: D/d = 35/25 µm) was established after annealing in a narrow temperature range near the crystallization onset. This restores soft magnetic properties and ensures high temperature stability of all magnetic parameters. The wires under the study were produced by quenching and drawing technique (also referred to as modified Taylor-Ulitovskiy method). The choice of composition is justified by specific magnetoelastic properties with near zero magnetostriction of the order . It is known that annealing without applied stress can produce short-range order relaxation and consequently releases some frozen-in stresses and improves soft magnetic properties. In the present paper, we propose current and conventional annealing at relatively high temperatures slightly lower than the primary crystallization temperature. This causes nano crystallization and sharp change in the saturation magnetostriction. Therefore, we proposed a method of controllable change in magnetic anisotropy by changing the sign of magnetostriction. In particular, this results in a change in the shape of magnetic hysteresis and enhances the sensitivity of MI at microwave frequencies. The hysteresis loop of samples annealed by dc current and by conventional annealing are shown in Figures 1, 2. The annealing at temperatures higher than the Curie temperature increases the saturation magnetostriction and induces an axial easy anisotropy. A sharp change in the behavior of the hysteresis loops occurs after annealing with temperatures near the crystallization point, which can be explained by a change in the sign of the magnetostriction constant from small positive to large negative. Acknowledgment: This work was supported by the Russian Foundation for Basic Research (RFBR: 19-32-50097; 20-32-90145)

**References:**

[1] M. G. Nematov, I. Baraban, N.A. Yudanov at all, Journal of Alloys and Compounds, 837, 155584 (2020) [2] A. Zhukov and V. Zhukova, Nova Science Publishers, New York (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/2bbc7c20b4da82c458e9605dc6b74369.jpg)
Fig. 1. Hysteresis loops of amorphous Co71Fe5B11Si10Cr3 (diameter: D/d = 29/25 µm)microwires after dc current of which approximately corresponds to 490oC.

![](https://assets.underline.io/uploads/markdown_image/1/image/021e6e0bc8a907964c76b7edc22e8cfa.jpg)
Fig. 2. Hysteresis loops of amorphous Co71Fe5B11Si10Cr3 (diameter: D/d = 29/25 µm) microwires after annealing at furnace (475oC, 485oC, 490oC)

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