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The giant magnetostrictive material TbDyFe alloy is considered to be an ideal material for making the core drive components of high-power, high-frequency magnetostrictive transducers. It has the characteristics of fast output response and large output displacement. Under high-frequency excitation conditions, the accurate calculation of TbDyFe alloy magnetic energy loss is a major and difficult point, and it is also an important step in the design of high-power magnetostrictive devices. Reference [1] improves the traditional loss separation formula based on high-frequency loss test data of TbDyFe alloy. Reference [2] analyzed the dynamic magnetic characteristic parameters of the TbDyFe alloy laminations, and conducted an in-depth study on the loss mechanism in the high frequency range. The above studies all assume that the temperature of the sample remains unchanged, but in actual work, the magnetostrictive transducer will produce serious hysteresis loss, eddy current loss and coil copper loss under high-frequency excitation, which will change the temperature distribute of the device. Considering the temperature-sensitive characteristics of TbDyFe alloy&lt;sup&gt; [3]&lt;/sup&gt;, the novelty of this article is mainly to study the change trend of the magnetic properties and loss characteristics of TbDyFe alloy at different temperatures. On the basis of the existing research, a temperature-controllable high-frequency magnetic characteristic test platform is built with AMH-1M-S dynamic magnetic characteristic tester and temperature box, so as to obtain the dynamic magnetic characteristic curve and loss of TbDyFe alloy at different temperatures.&lt;br/&gt;&lt;br/&gt;When the magnetic density amplitude and frequency are constant, the dynamic hysteresis loop of the sample at different temperatures is shown in Figure 1. As the temperature increases, the dynamic hysteresis loop narrows laterally, the required magnetic field strength decreases, and the coercive force gradually decreases. When the magnetic density amplitude is constant, the magnetic loss of the sample at different temperatures at different frequencies is shown in Figure 2.&lt;br/&gt;&lt;br/&gt;In the classic Bertotti loss separation model, the loss is a binary function of the magnetization frequency &lt;i&gt;f&lt;/i&gt; and the magnetic density amplitude &lt;i&gt;B&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;. The formula assumes that under a fixed magnetization condition, no matter what the temperature of the sample is, the calculation results of the loss model will not change, which is obviously inconsistent with the experimental results. At the same time, because the TbDyFe alloy is significantly affected by the eddy current skin effect and dynamic hysteresis under high frequency conditions, the loss coefficient is no longer constant. Hence, the traditional calculation method is no longer accurate and must be improved.&lt;br/&gt;&lt;br/&gt;In order to solve the above problems, a high-frequency loss calculation model of magnetostrictive materials under variable temperature conditions is proposed. The model corrects the loss coefficient by introducing temperature-related terms. In addition, considering the effects of high-frequency hysteresis characteristics and skin effect, a loss-added magnetic flux density term and loss-added frequency term are introduced. The hysteresis, eddy current and residual loss coefficients &lt;i&gt;k&lt;/i&gt;&lt;sub&gt;h&lt;/sub&gt;, &lt;i&gt;k&lt;/i&gt;&lt;sub&gt;e&lt;/sub&gt; and &lt;i&gt;k&lt;/i&gt;&lt;sub&gt;a&lt;/sub&gt; are all regarded as ternary functions of Δ&lt;i&gt;T&lt;/i&gt;, &lt;i&gt;f&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;. Combining the experimental test data, analyze the influence weights of the three free variables of temperature, frequency and magnetic density amplitude on the loss coefficient through curve fitting, and obtain the changes of hysteresis loss, eddy current loss and residual loss with Δ&lt;i&gt;T&lt;/i&gt;, &lt;i&gt;f&lt;/i&gt;, &lt;i&gt;B&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;. Thus an improved loss calculation model that can effectively consider the temperature effect is established. The results show that the calculation method can accurately calculate the high-frequency magnetic energy loss of magnetostrictive materials under variable temperature conditions. The average error between the calculated value and the measured value is 2.29%.

**References:**

[1] W. M. Huang, C.Y. Gao, et al. Experimental and Calculating Analysis of High Frequency Magnetic Energy Losses for Terfenol-D Magnetostrictive Material. IEEE Trans. Magn, 99 (2018): 1-4.&lt;br/&gt;[2] W. M. Huang, X.Q. Wu, et al. Analysis of high frequency dynamic magnetic characteristics and loss characteristics of TbDyFe alloy[J]. Chinese Journal of Scientific Instrument, 2020, 41(01): 215-222.&lt;br/&gt;[3] Jin K , Kou Y , et al. A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys[J]. Journal of Magnetism &amp; Magnetic Materials, 2012, 324(12):1954-1961.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0329a17f3fa659f6ad808c5272f42a5f.jpg)
Fig.1. Dynamic hysteresis loop at different temperatures&lt;br /&gt;
(&lt;i&gt;f&lt;/i&gt;=10kHz, &lt;i&gt;B&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; =0.06T)

![](https://assets.underline.io/uploads/markdown_image/1/image/c6ac98b1f9107a7725f4cae4a60d7fa2.jpg)
Fig.2. Variation of loss with frequency at different temperatures（&lt;i&gt;B&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;=0.05T）

INTERMAG 2021

 High Frequency Characteristic Test and Loss Calculation of TbDyFe Alloy under Variable Temperature

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The giant magnetostrictive material TbDyFe alloy is considered to be an ideal material for making the core drive components of high-power, high-frequency magnetostrictive transducers. It has the characteristics of fast output response and large output displacement. Under high-frequency excitation conditions, the accurate calculation of TbDyFe alloy magnetic energy loss is a major and difficult point, and it is also an important step in the design of high-power magnetostrictive devices. Reference [1] improves the traditional loss separation formula based on high-frequency loss test data of TbDyFe alloy. Reference [2] analyzed the dynamic magnetic characteristic parameters of the TbDyFe alloy laminations, and conducted an in-depth study on the loss mechanism in the high frequency range. The above studies all assume that the temperature of the sample remains unchanged, but in actual work, the magnetostrictive transducer will produce serious hysteresis loss, eddy current loss and coil copper loss under high-frequency excitation, which will change the temperature distribute of the device. Considering the temperature-sensitive characteristics of TbDyFe alloy [3], the novelty of this article is mainly to study the change trend of the magnetic properties and loss characteristics of TbDyFe alloy at different temperatures. On the basis of the existing research, a temperature-controllable high-frequency magnetic characteristic test platform is built with AMH-1M-S dynamic magnetic characteristic tester and temperature box, so as to obtain the dynamic magnetic characteristic curve and loss of TbDyFe alloy at different temperatures. When the magnetic density amplitude and frequency are constant, the dynamic hysteresis loop of the sample at different temperatures is shown in Figure 1. As the temperature increases, the dynamic hysteresis loop narrows laterally, the required magnetic field strength decreases, and the coercive force gradually decreases. When the magnetic density amplitude is constant, the magnetic loss of the sample at different temperatures at different frequencies is shown in Figure 2. In the classic Bertotti loss separation model, the loss is a binary function of the magnetization frequency f and the magnetic density amplitude Bm. The formula assumes that under a fixed magnetization condition, no matter what the temperature of the sample is, the calculation results of the loss model will not change, which is obviously inconsistent with the experimental results. At the same time, because the TbDyFe alloy is significantly affected by the eddy current skin effect and dynamic hysteresis under high frequency conditions, the loss coefficient is no longer constant. Hence, the traditional calculation method is no longer accurate and must be improved. In order to solve the above problems, a high-frequency loss calculation model of magnetostrictive materials under variable temperature conditions is proposed. The model corrects the loss coefficient by introducing temperature-related terms. In addition, considering the effects of high-frequency hysteresis characteristics and skin effect, a loss-added magnetic flux density term and loss-added frequency term are introduced. The hysteresis, eddy current and residual loss coefficients kh, ke and ka are all regarded as ternary functions of ΔT, f, Bm. Combining the experimental test data, analyze the influence weights of the three free variables of temperature, frequency and magnetic density amplitude on the loss coefficient through curve fitting, and obtain the changes of hysteresis loss, eddy current loss and residual loss with ΔT, f, Bm. Thus an improved loss calculation model that can effectively consider the temperature effect is established. The results show that the calculation method can accurately calculate the high-frequency magnetic energy loss of magnetostrictive materials under variable temperature conditions. The average error between the calculated value and the measured value is 2.29%.

**References:**

[1] W. M. Huang, C.Y. Gao, et al. Experimental and Calculating Analysis of High Frequency Magnetic Energy Losses for Terfenol-D Magnetostrictive Material. IEEE Trans. Magn, 99 (2018): 1-4. [2] W. M. Huang, X.Q. Wu, et al. Analysis of high frequency dynamic magnetic characteristics and loss characteristics of TbDyFe alloy[J]. Chinese Journal of Scientific Instrument, 2020, 41(01): 215-222. [3] Jin K , Kou Y , et al. A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys[J]. Journal of Magnetism & Magnetic Materials, 2012, 324(12):1954-1961.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0329a17f3fa659f6ad808c5272f42a5f.jpg)
Fig.1. Dynamic hysteresis loop at different temperatures 
(f=10kHz, Bm =0.06T)

![](https://assets.underline.io/uploads/markdown_image/1/image/c6ac98b1f9107a7725f4cae4a60d7fa2.jpg)
Fig.2. Variation of loss with frequency at different temperatures（Bm=0.05T）

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HoFeO3 is one of the most interesting representatives of the rare-earth orthoferrites RFeO3 with orthorhombic structure possessing different useful for potential applications physical properties. Dzyaloshinskii-Moriya interaction (DMI) which leads to a weak ferromagnetic (WF) moment in the Fe sublattice, might play an essential role in their occurrence. A spontaneous electric polarization occurs in HoFeO3 at ~ 210 K [1]. At lower temperatures, strong magneto-caloric effect makes the compound to a promising candidate for the magnetic cooling in the cryogenic gases liquefying technology. Three peaks in the entropy-change occur for field variation 0-7 T: ΔSM=9 J/Kg K at 53 K, ΔSM=15 J/Kg K at 10 K and ΔSM=18 J/Kg K at 3 K [2]. The first peak is associated with a spin reorientation in the Fe subsystems. Below 53 K the Fe sublattice starts to polarize the Ho. Thus, the second and third peaks should be associated with some processes related also to the Ho subsystem. The crystal structure of HoFeO3 is described by space group Pbnm. Below 637 K, the Fe sublattice orders antiferromagnetic (AFM) along the a-axis, and WF moment along c-axis (magnetic phase Gm4). At zero field, the compound has two spin reorientation transitions: at 53 K where the Fe moments rotate from a to b-axis (magnetic phase Gm1) and at 35 K where the magnetic moments align almost along c-axis (magnetic phase Gm2). Ho orders at a temperature of 4 K [3]. Polarized Neutron diffraction (PND) experiments were performed at the Heinz Maier-Leibnitz Zentrum (Garching, Germany) on the diffractometer POLI [4]. The used instrumental setup with a 2.2 T cryogen-free, compact high-Tc superconducting magnet is presented in Ref. [5]. The evolution of the magnetic structure in HoFeO3 with temperature and magnetic field in the range of 300-47 K and 0.15-2.2 T was investigated. In particular, the effect of the magnetic field on the reorientation transition from Gm4 to Gm1 symmetry, which takes place in zero field at 53 K, has been studied in detail. Originating from the mmm Laue class of HoFeO3, the Bragg reflections to which the Fe sublattice contributes can be separated in four sets: F: (h + k even, l even), A: (h + k even, l odd), C: (h + k odd, l even) and G: (h + k odd, l odd). The asymmetry values A=(I+-I-)/( I++I-) for 275 Bragg reflections were measured at 65 K. Here, I± is the measured intensity for the two antiparallel spin orientations of the incoming neutron beam. Using these values, we could refine the precise orientation of the AFM moments in HoFeO3 in the Gm4 phase (Fig. 1). Our results are in good agreement with the previously published structure at 70 K [6] but superior in details. To follow the magnetic phase transition explicitly, the asymmetries of 70 selected peaks (mostly of G-type) were measured in 2 K steps between 67-47 K. Below 53 K in the lowest field (0.15 T), the magnitude of the x-component of the Fe moment decreases abruptly whilst that of the y-component increases. This behavior is consistent with the reorientation transition to the Gm1 structure observed in zero field. Further increasing the applied field lowers the temperature of the transition, until it does not occur within the scanned temperature range for 2.2 T. However, an attempt to fit the intermediate phase ( Fig. 1-2) as a linear combination of different volume fractions of Gm1 and Gm4 phases did not lead to a converging solution. In particular, the observed presence of significant asymmetry values for G type reflections below 53 K suggests, that the applied field may introduce some distortion of the purely AFM Gm1 structure. This is confirmed by the occurrence of a G-type z-component in the intermediate phase, which is forbidden in both Gm1 and Gm4. Taking also into account the occurrence of magnetic moments on the Ho positions, we can finally conclude that the observed intermediate state is a correlated phase with monoclinic symmetry. Additionally, in the Gm4 phase the magnetic field aligns the WF moment along its direction. This lifts the degeneracy between 180 degrees AFM domains, since the orientation of the AFM structure to the WF moment is fixed by the DMI. Conversely, the sign of the DMI can be determined by the refined precise orientations of the AFM moments in the Gm4 phase from PND data (Fig. 2). By performing a proper averaging over the four Fe sublattices of the Gm4 structure, we could reduce the DMI interaction to two independent parameters D12 and D14, pointing in y-direction. Dnm denotes the interaction of the Fe sublattice n to m, with sublattice notations from Ref. [6]. With this clear convention, positive signs for D12 and D14 could be deduced. Corresponding DMI and exchange interactions magnitudes were determined in our previous work by inelastic neutron scattering [7]. One may conclude that the competition between the external magnetic field, the DMI and the exchange interactions between different magnetic sublattices leads to a complex picture of phase transitions in rare-earth orthoferrites causes also their useful functionality.

**References:**

1. K. Dey, A. Indra, S. Mukherjee, S. Majumdar, J. Strempfer, O. Fabelo, E. Mossou, T. Chatterji, and S. Giri. Phys. Rev. B 100, 214432 (2019) 2. M. Shao et al. / Solid State Communications 152 (2012) 3. T. Chatterji, M. Meven, P. J. Brown, AIP ADVANCES 7, 045106 (2017) 4. V. Hutanu, M. Meven, S. Masalovich, G. Heger, and G. Roth, J. Phys.: Conf. Ser. 294 12012 (2011) 5. H. Thoma,W. Luberstetter, J. Peters, and V. Hutanu, J. Appl. Cryst. 51 17-26 (2018) 6. T Chatterji et al, J. Phys.: Condens. Matter 29 385802 (2017) 7. A.K.Ovsianikov, I.A.Zobkalo, W.Schmidt, S.N.Barilo, S.A.Guretskii, V.Hutanu, JMMM, Volume 507, 166855 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8a7a1f6a643a1d20fc4e008a7653ed53.jpg)
Fig.1: Magnetic structure evolution by the reorientation phase transition in HoFeO3 near 50 K with magnetic field along [001]. An intermediate phase braking orthorombic simmetry occurs between the magnetic phases Gm4 and Gm1. Here: blue balls - Fe ions, green - Ho, red - O, colored arrows denote ordered magnetic moments.

![](https://assets.underline.io/uploads/markdown_image/1/image/6f114888b1245ad04fa87bafc996b68a.jpg)
Fig. 2: Temperature/field map for the measured asymmetry of G-type peak (3 0 -1). Redish area denotes magnetic phase Gm4, blue - Gm1, celestial-greenish - intermediate monoclinic phase.

 Breaking the magnetic symmetry by reorientation transition near 50 K in multiferroic, magnetocaloric HoFeO3.

Magnetic refrigeration based on magnetocaloric effect (MCE) is attractive cooling technology because of its high energy efficiency and environmental friendliness. MCE is defined as the changes in temperature and entropy by changing a magnetic field. Magnetic refrigeration for near room temperature needs the magnetocaloric materials with large magnetic entropy change (ΔSm) near room temperature. Hf1-xTaxFe2 crystallizes the hexagonal structure. The magnetism of Hf1-xTaxFe2 changes by Ta substitution. For example, Hf1-xTaxFe2 for 0.1&lt;x&lt;0.3 shows the successive transitions from ferromagnetic order to antiferromagnetic order on cooling [1]. For x=0.17, large ΔSm at 225 K is reported [2]. The magnetic transition temperature (TM) decreases with applying pressure [3]. On the contrary, the volume expands by inserting the interstitial atom, TM would be decrease. In this work, we study the B doping effect on the magnetic properties of Hf1-xTaxFe2. The Hf0.83Ta0.17Fe2Bz (z=0, 0.1, and 0.5) alloys were synthesized by arc-melting under Ar atmosphere. The crystal structure was confirmed by the powder X-ray diffraction (XRD) technique. Magnetic properties were measured in the range of 150≤T≤270 K up to 5 T. The XRD pattern of Hf0.83Ta0.17Fe2 indicates a single phase as the hexagonal structure. For z=0.1, the minor phases as HfO2 and HfB2 were observed. For z=0.5, the intensity of the peak of HfB2 phase increased and is comparable to those of Hf0.83Ta0.17Fe2 phase. The scattering angles of Hf0.83Ta0.17Fe2 shifted higher, indicating the volume shrinking. These results suggest that the unit cell volume decreased due to deficiency of Hf by forming HfB2 in B-doped Hf0.83Ta0.17Fe2. Figure 1 shows the temperature dependence of magnetization (M) of Hf0.83Ta0.17Fe2Bz (z=0 and 0.1) in a magnetic field of 0.1 T. For z=0, M increased suddenly at 215 K with decreasing temperature. The values of M for z=0.1 increased at 200 K. The obtained data indicate that the TM decreased by B-doping. The result is consistent with the volume reduction. The maximum values of ΔSm for z=0 and 0.1 are both 5 J/K kg, which is approximately one-third of the previously reported data [2]. In summary, introducing B into Hf1-xTaxFe2, B elements reacted Hf atoms to form HfB2. The volume and TM decreased due to the deficiency of Hf.

**References:**

[1] Y. Nishihara and Y. Yamaguchi, J. Phys. Soc. Jpn. Vol. 51, p.1333 (1982). [2] J. F. Herbst, C. D. Fuerst and R. D. McMichael, J. Appl. Phys. Vol. 79, p.5998 (1996). [3] K. Hoshi, J. Phys. Soc. Jpn. Vol. 57-9, p.3112 (1988).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/20e9a98a4f97b628bf140ad7928bd159.jpg)
Fig. 1. Magnetization versus temperature of Hf0.83Ta0.17Fe2Bz (z=0 and 0.1) in a magnetic field of 0.1 T.

 Magnetocaloric effect in Hf1-xTaxFe2By

One of the possible practical applications of magnetocaloric effect (MCE) is eco-friendly magnetic refrigeration [1]. A condition for the successful operation of a magnetic refrigerator is a high efficiency of heat transfer between the working body and the surroundings. This is facilitated by an increase in the surface to the volume ratio for the working body. The material in the form of powder meets this requirement [2]. Therefore, the features of MCE in powder samples are the subject of active research [3-5]. Ball milling is a well-established technique for producing different materials in powder shape. This process contributes to the reduction of the crystal size down to nanometric scales and the accumulation of defects in grain boundaries [6]. For magnetic materials, this causes a decrease in magnetization and slow change in magnetization near the phase transition temperature. This lowers the MCE [3]. On the other hand, nanostructuring causes the effect of a Curie temperature distribution. In turn it leads to a broadening of the peak of the temperature change of the magnetic entropy (ΔSM) and an increase in a refrigeration capacity (RC) value, which can be defined as the product of the maximum value of the peak of magnetic entropy change and the width of ΔSM peak at its half-height [1]. In addition, nanostructuring can enhance the field dependence of the magnetocaloric effect [5-7]. Appropriate annealing of polycrystalline materials can to some extent restore the perfection of their crystal structure and magnetization behavior, thereby establishing an advantageous balance between the height and width of ΔSM peak, which determine the RC value [8]. In this work, we present the result of detailed study of influence of thermal treatment on structure, magnetic and magnetocaloric properties of Gd powder obtained by ball milling. Ball milling was performed with a mixer/mill using hardened-steel vials in acetone. Gd powder samples were annealed in vacuum at different temperatures up to 600 K. The structure of the samples was studied by X-ray diffraction technique using automatic PHILIPS X’PERT PRO diffractometer operating with Cu-Ka radiation. The magnetic entropy change was calculated using the Maxwell relation follow the standard procedure [1]. The temperature dependence of the magnetic entropy change measured for Gd powder samples annealed at different temperature shows that ΔSM peak is constricted in each case (Fig. 1). The value of the ΔSM peak height and the RC values are decreased with the increase of the temperature (Fig. 2). Observed MCE behavior was understood taking into account the changes in the crystal structure including strain values and contribution of the partial surface oxidation as a result of the heat treatment. At the same time, heat treatment at the temperature of 500 K results in the shift of MCE peak exactly for the room temperature point that might be very useful for applications. This study was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. FEUZ -2020-0051) and Elkartek AVANSITE grant of the Basque Government.

**References:**

[1] V. Franco, J.S. Blázquez, J.J. Ipus, at al. Prog. Mater Sci. 93 (2018) 112. [2] Q. Gao, B.F. Yu, C.F. Wang, at al. Int. J. Refrig. 29 (2006) 1274. [3] J.S. Blázquez, J.J. Ipus, L.M. Moreno-Ramírez, at al. Metall. Mater. Trans. E 2 (2015) 131. [4] S. Wolf, T.M. Riedemann, J. Barclay, at al. Powder Technol. 359 (2020) 331. [5] A.V. Svalov, A.V. Arkhipov, S.V. Andreev, at al. Mater. Lett. 284 (2021) 128921. [6] J.S. Blázquez, J.J. Ipus, L.M. Moreno-Ramírez, at al. J. Mater. Sci. 52 (2017) 11834. [7] D. Doblas, L.M. Moreno-Ramírez, V. Franco, at al. Mater. Design 114 (2017) 214. [8] S.V. Taskaev, V.D. Buchelnikov, A.P. Pellenen, at al. J. Appl. Phys. 113, (2013) 17A933.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a2f6aa8431127d60a2c6250253cd8552.jpg)
Fig 1. The magnetic entropy changes versus the temperature for Gd powder samples in initial state (curve I) and after annealing at different temperatures (curves II, III, IV, V and VI for 350 K, 450 K, 500 K, 550 K and 600 K, respectively). Magnetic field changes from 0 to 7 T.

![](https://assets.underline.io/uploads/markdown_image/1/image/d536f7c3aa1aa8bf5e20e19fa17c0027.jpg)
Fig 2. RC versus the magnetic field for Gd powder samples in initial state (curve I) and after annealing at different temperatures (curves II, III, IV and V for 350 K, 450 K, 500 K and 550 K, respectively).

 Magnetocaloric properties of ball milled Gd powder subjected to heat treatments

Recent studies on multicomponent systems and high entropy alloys offer enormous motivation and scope to study the magnetic and magnetocaloric properties of a multicomponent Laves phase intermetallic compound, RAl2, where R site is occupied by five equiatomic heavy rare earth elements [1]. Polycrystalline intermetallic compound Gd0.2Tb0.2Dy0.2Ho0.2Er0.2Al2 has been prepared by arc-melting under argon atmosphere and the single phase nature was confirmed by powder X-ray diffraction (XRD) study carried out at room temperature. DC magnetization has been measured in the temperature range of 2 K to 300 K in applied magnetic fields up to 70 kOe. Electrical resistivity, heat capacity and thermoelectric power have been measured as a function of temperature from 300 K to about 4 K. Magnetization data reveal that Gd0.2Tb0.2Dy0.2Ho0.2Er0.2Al2 compound orders ferromagnetically at ~80 K (TC) [Fig. 1]. This ordering temperature is approximately equal to the mean value of the ferromagnetic ordering temperatures of the single rare earth component compounds GdAl2, TbAl2, DyAl2, HoAl2 and ErAl2 respectively. The Arrot plots and the nature of the temperature variation of magnetization suggest second order nature for this transition at 80 K. In the present work, electrical resistivity, thermopower and specific heat of the title compound are studied. Electrical resistivity shows metallic behaviour and one does see an anomaly around TC. Electrical resistance vs field is measured at a few selected temperatures in fields up to 50 kOe. A weak, negative magnetoresistance is observed below TC. The heat capacity vs temperature plot shows a weak second order transition around 80 K. However, thermoelectric power did not register the magnetic anomaly strongly. The isothermal magnetic entropy change calculated using the magnetization-field data near TC reveal a broad magnetocaloric effect around TC, as one would expect for ferromagnetic material showing a second order transition. These results are compared with that of the individual heavy rare earth Laves phase dialuminides in order to understand the collective behavior of magnetic rare earth moments in such a multicomponent system. This along with the studies on high entropy alloys should pave a new way in the materials design for magnetics and magnetocalorics.

**References:**

P. K. Jesla, J. Arout Chelvane, A. K. Nigam and R. Nirmala, AIP conference proceedings 2265 (2020) 030565

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a9d5598e21fb3da4e0e8f55d874357e8.jpg)
Fig. 1 Zero-field-cooled (ZFC) and field-cooled cooling and warming (FCC and FCW) Magnetization vs temperature data of Gd0.2Tb0.2Dy0.2Ho0.2Er0.2Al2 measured in 100 Oe field [Inset dM/dT vs T plot]

 Magnetic and Transport properties of Multicomponent Laves Phase Intermetallic Compound Gd0.2Tb0.2Dy0.2Ho0.2Er0.2Al2

A new type of rare-earth giant magnetostrictive transducer, working in ultrasonic frequencies, is designed by the structural dynamic model and the dynamic coupling model. Based on the vibration, wave and frequency equations, the structural dynamic model of the transducer is established. By using COMSOL Multiphysics software parametric design method, considering the influence of materials, shapes and dimensions on the output characteristics of the transducer, the optimum mechanical structure of the ultrasonic transducer is determined. The magnetic circuit structure is analyzed by the dynamic coupling model based on the Jiles-Atherton model, Maxwell’s equations and magneto-mechanical coupling effect. The prototype of the ultrasonic transducer is fabricated. The relationship between the output characteristics and the frequency is studied. The results demonstrate that the ultrasonic transducer can work in the range of 18-22 kHz, and exhibits higher magneto-mechanical conversion efficiency at the frequency of 19.5 kHz. I. Introduction The rare-earth giant magnetostrictive transducer has the advantages of high power, large amplitude and high response speed and it can be used in the fields of accurate actuation and ultrasonic machining [1]. At present, the transducers used in ultrasonic applications are mainly piezoelectric ceramic transducer [2]. Compared with piezoelectric materials, rare-earth giant magnetostrictive material, Terfenol-D (Tb0.7Dy0.3Fe2), has greater strain, smaller hysteresis, and lower saturation magnetic field. Wang designed a giant magnetostrictive transducer (GMT) with a resonant frequency of 2 kHz [3]. Karunanidhi designed a GMT. The resonant frequency was 3 kHz. The transducer with mechanical amplifier and permanent magnet biasing was designed and realized [4]. Sheykholeslami proposed an approach to design a GMT. The resonant frequency was 8.25 kHz. This approach can make the transducer have high mechanical quality factor [5]. Fang introduced a design and finite element analysis method of a GMT. The working frequency of the transducer is 15.2 kHz [6]. Karafi designed a new hybrid longitudinal–torsional GMT with a resonant frequency of 20.6 kHz. The output displacement of the transducer was 0.6 µm [7]. References [3]-[5] studied the design method and output characteristics at relatively lower frequency magnetostrictive transducers. Reference [7] designed the giant magnetostrictive ultrasonic transducers, but the output displacement is small. So, how to design and manufacture a rare-earth giant magnetostrictive transducer with large output displacement, working in ultrasonic frequencies, is still a crucial problem for the development of transducers. II. The magnetic circuit and mechanical structure design of the ultrasonic transducer The magnetic circuit design needs to improve the magnetic flux density of magnetostrictive rod and reduce losses of the magnetic circuit. Based on the Jiles-Atherton model, Maxwell’s equations and magneto-mechanical coupling effect, the magnetostrictive rod, magnetic yoke and magnetic circuit structure of the ultrasonic transducer are designed. It is found that the magnetic circuit structure of two Terfenol-D rods with coils in series connection is more suitable for the ultrasonic transducer. The radius of the Terfenol-D rod is 7.5 mm, and the length is 102 mm. To reduce the effect of dynamic losses, the Terfenol-D rod is machined into 2 mm slices and glued together by epoxy resin. The width of the magnetic yoke is 16 mm and the length is 60 mm. Based on the vibration, wave and frequency equations, the structural dynamic model of the ultrasonic transducer is established. By using COMSOL Multiphysics software parametric design method, considering the influence of materials, shapes and dimensions on the output characteristics of the ultrasonic transducer, the optimum mechanical structure of the ultrasonic transducer is determined. The whole mechanical structure of the transducer is analyzed, and the resonant frequency of the transducer is obtained. A detailed and complete design scheme is given and the main body of the ultrasonic transducer consists of two Terfenol-D rods, driving coils, disc spring, adjusting nut, vibrating horn, magnetic yoke and shell, as shown in Fig.1. III. Experimental results The prototype of the ultrasonic transducer was fabricated. The relationship between the output characteristics and the frequency is experimentally studied by using laser displacement sensor (LK-H008, KEYENCE). Output displacement amplitude versus frequency is shown in Fig.2. The amplitudes of exciting current are 1A and 2A. The frequencies are 16.5 kHz-22.5 kHz. The experimental results have obvious resonance peaks, and their changing tendencies are consistent. When f&lt;19.5 kHz, the amplitudes of vibration increase with increasing frequencies; When f=19.5 kHz, the output amplitude reaches the maximum value, the amplitude reaches 6.07 μm at 1A and 9.46 μm at 2A exciting current respectively; When f&gt;19.5 kHz, the amplitudes of vibration decrease with frequency increasing. It can be seen that the measured resonant frequency is 19.5 kHz, and the resonant frequency almost does not change at the different applied magnetic field.

**References:**

[1] J. J. Scheidler and V. M. Asnani, Smart Materials and Structures, vol. 26, p. 035057 (2017) [2] X. Wei, Y. Yang and W. Yao, Sensors, vol. 17, p. 2253, (2017) [3] W. Wang and P. J. Thomas, Sensors and Actuators A: Physical, vol. 263. p. 113, (2017) [4] S. Karunanidhi and M. Singaperumal, Sensors and Actuators A: Physical, vol. 157, p. 185, (2010) [5] M. R. Sheykholeslami, Y. Hojjat and S. Cinquemani, Smart Structures & Systems, vol. 17, p. 313, (2016) [6] S. Fang, Q. Zhang and H. Zhao, Micromachines, vol. 9. p. 98, (2018) [7] M. R. Karafi, Y. Hojjat and F. Sassani, Smart Materials & Structures, vol. 22, p. 065013, (2013)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f023af9851d401207c90b3e5c84b22a2.jpg)
Fig.1 (a) Structure of the ultrasonic transducer (b) Prototype of the ultrasonic transducer

![](https://assets.underline.io/uploads/markdown_image/1/image/01445a34938883b4dcd818b6e049f4f1.jpg)
Fig.2 Output displacement amplitude versus frequency at different exciting current

 The Design and Output Characteristics of Ultrasonic Transducer Based on Rare-earth Giant Magnetostrictive Material

Magneto-elastic beams in a cantilever configuration represents a quite common layout for a vibration energy harvester and its design is aimed to increase performances in terms of geometrical characteristic and power conversion [1-4]. Cantilever-like harvesters are employed when a quite constant vibration source is available, dealing to periodic steady state conditions. But the analysis of such a system is still a multiphysics problem, involving the mechanical deformation of the elastic body coupled with the electromagnetic problem through the magneto-elastic characteristics of the active material. In [1] and [4] the importance of cantilever’s geometry has been outlined, showing the importance of the neutral axis location for the output power optimization, also providing [4] a qualitative analysis describing the phenomenon. In the same contribution, the focus was on the design and development of the harvester through an experimental analysis of several layouts. The effort was so addressed on the identification of the converted electrical source supplying the output electrical circuit by the standard tools of circuit’s theory (Thevenin’s theorem), which was designed to optimize load resistance and efficiency for the whole device. The modeling of the harvester as a magneto-mechanical converter requires more effort, e.g. coupling the beam’s dynamics through the Euler-Bernoulli equation and the magneto-elastic characteristics of the beam. Despite interesting contributions exploiting 3-D FEM algorithms to describe the beam dynamics [3],[5],[6], in the present contribution attention is focused on the definition of a semi-coupled model where the mechanical behavior (in periodic steady state conditions) is taken into account through a model, described synthetically in Fig. 1b, and referred to the cantilever beam, described in Fig. 1a, supplied by a vertical sinusoidal acceleration on the left tip, in ACsinusoidal steady state, with amplitude a. The well-known solution (not provided for brevity) describes the behavior of the beam deformation w(z,t) which provides the moment bending and therefore the longitudinal stress and the strain along the cantilever, [7] and, through the assumed linear magneto-elastic coupling of the magnetostrictive alloy, the flux linkage and the emf at the coil terminals, the as shown in Fig. 2. The detailed derivation of eqns. requires some algebra and will be detailed in the paper. The emf measured at coil’s ends is related to the beam’s deformation dynamics and to the cantilever’s geometry. In particular, when the neutral axis is exactly in the middle of the magnetostrictive sheet (x1 = - x2) the total emf is zero. This result seems to fit with the experimental evidence of. In Fig. 2b where the output power on a 5.6Ω resistive load is plotted vs frequency, with a = 1g, 2g, 3g, 4g, for three different cantilever layouts. In the first one a magnetostrictive (Fe-Ga) lamination is “sandwiched” by two Al sheets (C2) and realizes a configuration with neutral axis at almost the middle of the active alloy. The second is conversely realized by an Al sheet “sandwiched” by two Fe-Ga laminations (C1), while in the last a single Al sheet is sticked to a Fe-Ga lamina (C3). In both C1 and C3 cases, the neutral axis lays outside the magnetostrictive laminas. All configurations share the same two bias magnets on the upper side of the cantilever. In linear assumptions, the RMS power in the plot is proportional to ε2 and according to the model shows a much lower converted power of C2 case with respect to other configurations. An accurate analysis on the influence of geometric and physical parameters of the cantilever by the proposed modeling will be discussed in the paper. Such plot confirms that a simplified magnetostrictive cantilever’s modeling could provide information on the parameters that impact the harvester design and represents a simple but effective generalization of [4]. Further, without significative effort, a natural introduction of a nonlinear magneto-elastic behavior could be plugged in.

**References:**

[1] T. Ueno, S. Yamada, Performance of energy harvester using iron–gallium alloy in free vibration, IEEE Trans. Magn. 47 (10) (2011) 2407–2409. [2] J.-H. Yoo, A.B. Flatau, A bending-mode Galfenol electric power harvester, J. Intell. Mater. Syst. Struct. 23 (6) (2012) 647–654. [3] Z. Deng, M.J. Dapino, Modeling and design of Galfenol unimorph energy harvesters, Smart Mater. Struct. 24 (12) (2015) 125019. [4] V. Apicella, C. S. Clemente, D. Davino, D. Leone, C. Visone, Magneto-mechanical optimization and analysis of a magnetostrictive cantilever beam for energy harvesting, J. of Magnetism and Magnetic Materials, 475, (2019), 401-407. [5] Mojtaba Ghodsi, Hamidreza Ziaiefar, Morteza Mohammadzaheri, Amur Al-Yahmedi, Modeling and characterization of permendur cantilever beam for energy harvesting, Energy, 176 (2019), 561-569. [6] M. Borowiec, A. Syta, G. Litak, Energy Harvesting Optimizing with a Magnetostrictive Cantilever Beam System, International Journal of Structural Stability and Dynamics Vol. 19, No. 05, 1941002 (2019). [7] S. H. Crandall, Mechanics of Solids, McGraw-Hill, Third Edition.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7cfc0d5eff81b7d787608d9a833e4c02.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/6787b6aca4d66b15409c7c97beb82ee6.png)

 Effects of geometrical and physical parameters on a cantilever beam energy harvester in periodic steady state conditions.

As a single solid element, the magnetoelectric (ME) gyrator has verified Tellegen's conjecture about the gyrator. In recent years, a number of attempts have been made to reduce losses in the energy conversion process. It is well known that the properties of spinel ferrites are dependent on such as composition, cation substitutions. A small contents of rare earth doping can modify the magnetic and magnetostrictive properties by replacing the tetrahedral (A) or octahedral (B) sites, which is beneficent to ME coupling1. It has been reported that Dy elements possess high magnetocrystalline anisotropy due to the strong anisotropy of the 4f electron clound, thus inducing strong magnetostriction2. However, due to the high loss in the energy conversion process of the pure spinel ferrite ME gyrator, it is necessary to improve the ability of energy capture by means of the change of magnetic properties caused by Dy3+ doping. Therefore, the research on the improvement of gyration properties caused by high magnetostriction induced by Dy3+ doped ferrite has been initiated. Here, a variety of ME gyrators composed of nickel zinc ferrite and piezoelectric ceramic under various Dy3+ concentration were fabricated with coil around it and systematically characterized of magnetic properties,dynamic piezomagnetic coefficient, resonance ME response, V/I-I/V conversion ratio and power conversion efficiency, and each stage involved in the magneto-mechanical-electric energy conversion process under influences of Dy3+ concentration was clarified. Fig.1 shows the V/I conversion ratio spectra of the ME gyrators with frequency, applied flied and Dy3+ concentration, respectively. It can be clearly seen that under the resonant frequency and optimal bias, the maximum V/I of 1610 V/A occurring at sample with x=0.04 while the minimum of 998 V/A occurring at the one with x=0. Compared with pure spinel ferrite, the conversion effect of the ME gyrators is improved by 161% by Dy3+ doping. The experimental results attributed to the strong ME coupling is caused by the high magnetocrystalline anisotropy of Dy3+. Therefore, it can be concluded that Dy3+ doping reduces the loss in the energy conversion process of ME gyrator and promotes the improvement of gyration properties. Consequently, the high gyration properties of ME gyrator has important potential application for miniaturized V/I converters for power electronics.

**References:**

1 A. Anwar, S. Zulfiqar, and M. A. Yousuf, Journal of Materials Research and Technology-Jmr&T. Vol. 9, p.5313-5325 (2020) 2 T. Y. Jin, W. Wu, and C. B. Jiang, Scripta Materialia. Vol. 74, p.100-103 (2014)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/606efb870463e67f36a0cefd9acfefa5.jpg)
Fig.1 V/I conversion of the ME gyrators with different Dy3+ concentrations under optimal bias in the frequency range of 54kHz-66kHz. The insets are the V/I as a function of the Dy3+ concentration and Applied Flied respectively.

 Improvement of gyration effects by dysprosium doping in spinel ferrite/piezoelectric magnetoeletric gyrators

In recent years, energy harvester around power lines have received widely attention due to the convenient power supply for monitoring devices around power lines such as vibration and conductor temperature sensors, fault diagnosis and prediction devices, intelligent sensor monitoring devices etc. Generally, energy harvested from near power lines includes solar energy, wind energy, sound energy, vibration and magnetic field, and so on. In terms of reliability and stability, energy harvesting using magnetic fields has been reported as optimum mode to provide energy to monitoring devices around power lines. Compared to solar and wind energy sources, magnetic field energy is almost unaffected by the environment or weather conditions. Traditional magnetic energy harvesters are the best represented by electromagnetic induction energy harvesters. While featuring low cost and wide applicability, these electromagnetic induction energy harvesters are generally limited by large volume, heavy weight and low output power density[1]. The recent development of magnetoelectric (ME) materials enables novel electromagnetic devices. The ME energy harvester are composed of ME composites that show many excellent advantages, such as low cost, small volume perfect and high output power density[2]. These advantages offer the potential of ME energy harvesters to be a new generation of magnetic energy harvesters. Over the past decade, considerable reports have been published using ME materials to realize magnetic energy harvest. Previous investigations have focused on ME laminates whose piezoelectric/magnetostrictive layers are some simple configurations of disk, square, or rectangular shapes. However, for harvesting the magnetic energy around power lines, these geometries cannot make full use of the magnetic energy. In this case, the ME sample best geometry is the toroidal configuration. It is thus desirable to develop ME energy harvester with toroidal configuration, along with high output power density. This paper is on a high power density, dual-output ME energy harvester. It consisted of strictly concentric ferrites/piezoelectric rings with toroidal solenoid wound around that was operated in C-C mode. The electrode lead of the piezoelectric ring is port 1 and the coil lead is port 2 forming dual port. The ferrite in the collector senses the alternating magnetic field and transforms it into circumferential dynamic strain, which is transferred to the piezoelectric ring and finally output in the form of voltage from port 1. At the same time, according to the principle of electromagnetic induction, due to the existence of closed loop alternating magnetic field, the coil will produce induced electromotive force and output in the form of voltage from part 2. This dual-output ME energy harvester can ample harvest of the magnetic field energy produced by power lines and offer unique possibilities for possible use of ME energy harvester.

**References:**

[1] J. Ryu, J. Kang, and Y. Zhou, Energy & Environmental Science. Vol. 7, P.2402-2408 (2015) [2] D. Zhao, N. Han, Energy Convers Manage. Vol. 178, p.311–21 (2018)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c899e3e5797e3392284061b4210fbcbe.jpg)
Fig.1. Schematic diagram of the presented dual-output magnetoelectric energy harvester

 A dual-output magnetoelectric energy harvester in ferrite/piezoelectric toroidal magnetoelectric composites

Magnetostrictive materials possess the potential to be used in wide variety applications such as sensing, straintronic, spintronic devices etc due to the coupling between the strain and the magnetization. In this context, FeGa which has a very high magnetostrictive constant, high tensile strength and low coercivity proves to be an efficient material for current research. Commercial producibility of FeGa is cheaper and easier compared to the rare earth alloy families since it does not include any rare earth elements. Fe100-xGax with x = 19% has the highest magnetostriction constant with a value of around 3/2 × λ100= 400 ppm [1]. A thin film with this composition is attributed to the formation of next-nearest-neighbours (NNN) Ga-Ga pairs along [100] directions which leads to the formation of ordered D03 lattice structure [2]. In our report, we characterized the magnetic properties of Fe70Ga30 deposited on Si/SiO2 substrate (rigid material) and Kapton substrate (flexible material) by measuring room-temperature hysteresis loops by AGFM and MFM characterisation as a function of magnetic field. The magnetic hysteresis behaviour is quite different for Fe70Ga30 sputtered Si/SiO2 and Kapton as shown in Fig. 1(a, b). The coercive field obtained for Fe70Ga30/Kapton is approximately 20 times higher than that of Fe70Ga30/SiO2/Si. This can be referred to the interface induced strain which results in higher anisotropy for Fe70Ga30/Kapton. MFM results reveal linear stripe domains for the both Fe70Ga30/SiO2/Si and Fe70Ga30/Kapton shown in Fig. 1(c, d). The periodicity of domains is higher for the samples on Kapton due to high anisotropy. The substrate induced effect largely changes the properties of FeGa. We further try to measure the properties of Fe81Ga19 deposited on both Si/SiO2 and Kapton for comparison. The dependence of strain percentage with magnetic anisotropy will be studied for Fe81Ga19/Kapton.

**References:**

[1] A. E. Clark et al. Journal of Applied Physics 93, 8621 (2003). [2] H. Yangkun et al. Adv. Funct. Mater. 28 (20) 1800858 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/fe11bced4390bcf46677e66807dd5c28.jpg)
Fig. 1 Hysteresis loops and MFM domain patterns of Fe70Ga30/SiO2/Si (a, c) and Fe70Ga30/Kapton (b, d), respectively.

 Magnetic Properties of FeGa on Rigid and Flexible Substrates

Under high-frequency excitation, the large magnetic energy losses of magnetostrictive materials have limited the output characteristic of the magnetostrictive transducer [1]. Many magnetostrictive transducers are usually operated under DC bias to eliminate the frequency doubling effect and optimize the output performance. Based on the Steinmetz losses model, Ref. [2] proposed an improved total iron losses model considering DC bias, however, the separated losses compositions were not explored. Ref. [3] established a separated core losses model with the DC pre-magnetization, however, the model is more suitable for rectangular excitation and it was not about the giant magnetostrictive materials. Ref. [4] measured the magnetic energy losses on Terfenol-D material at different frequency f and peak flux magnetic density Bm, variable coefficients separated losses model without biased magnetic field had been shown. However, the effect of DC bias on magnetic energy losses of Terfenol-D cannot be ignored due to the max losses deviation will reach 27.6％when f=10 kHz and Bm＝0.06T by losses measuring. Therefore, it is not suitable to use the losses model of an unbiased magnetic field to predict the operation condition with a bias magnetic field. On this basis, an improved magnetic energy losses separation model on giant magnetostrictive materials considering DC bias excitation at high-frequency is emphatically studied here. In this paper, according to the actual operation conditions, a kind of high-frequency losses testing system for magnetostrictive materials under DC bias is built. The dynamic hysteresis loops of Terfenol-D samples at different magnetic frequencies and exciting magnetic densities are studied experimentally under the condition of variable DC bias excitation. The total magnetic energy losses are obtained from these dynamic hysteresis loops aimed to provide the data basis for the establishment of a high-frequency magnetic energy losses model. The three-variables magnetic energy loss matrix is established by these measured data. Based on the Bertotti losses separation theory, the high-frequency losses calculating model of magnetostrictive materials considering variable DC bias excitation is established by using the algorithm of Levebverg-Marquard and the method of matrix transformation. In this model, according to the multivariate parametric regression, the losses coefficients are modified by introducing DC bias-related terms. The comparison of computed and experimental data of losses at different operating conditions are compared and analyzed. By comparing the experimental data, it is proved that the computed results in this proposed model are in good agreement with the experimental results. Based on the built dynamic magnetic characteristic testing system, the dynamic hysteresis loops of Terfenol-D samples at different f (1 kHz~20 kHz), Bm (0.01 T~0.06 T), and Hdc (0 A/m~5000 A/m) can be measured. And the trend of hysteresis loops varying with different DC bias excitation can be shown in Fig.1. It can be seen that the dynamic hysteresis loops will be seriously distorted and asymmetric when the different DC bias applied. This phenomenon is caused by the increase of the magnetization working point and the change of the relative permeability of the material. And the losses can be computed based on the measured hysteresis loops. Using the proposed variable coefficients losses model, the losses could be separated into magnetic hysteresis, eddy-current, and anomalous losses. In fig.2, the bar graphs of the losses changing with DC bias frequency are obtained. The magnetic energy losses decrease with the DC bias. When the f=15 kHz and Bm=0.05T, the measured losses change from 513.74 W/kg to 409.022 W/kg with the DC bias changing from 0 to 5000 A/m. Based measured losses matrix and the method of multivariate parametric regression, an improved losses separation model is proposed to calculate the losses components when the Terfenol-D samples under DC bias excitation. The computed losses in this proposed model have high accuracy over the measured results (average percentage error&lt;5.6%). It shows that the suitable DC bias can decrease the losses for the magnetostrictive materials. This research could provide significant theoretical guidance and experimental data support for the giant magnetostrictive device structure optimization and thermal analysis at high-frequency excitation.

**References:**

[1] Rudd, Jonathan, Myers, et al. Experimental fabrication and nondestructive testing of carbon fiber beams for delaminations using embedded Terfenol-D particles. Journal of intelligent material systems and structures,29(4):600-609 (2018). [2] W. Chen, X. Huang, S. Cao, et al. Predicting Iron Losses in Soft Magnetic Materials Under DC Bias Conditions Based on Steinmetz Premagnetization Graph. IEEE Transactions on Magnetics, 52, (7):1-4 (2016) [3] Y. Zhou and Q. Chen, Predicting core losses under the DC bias based on the separation model, IEEE Journal of Emerging and Selected Topics in Power Electronics 5, 833 (2017). [4] W. M. Huang, X. Q. Wu, and P. P. Guo, Variable Coefficient Magnetic Energy Losses Calculation Model for Giant Magnetostrictive Materials, IEEE Transactions on Magnetics, Aug.2020. DOI: 10.1109/TMAG.2020.3013393, 2020.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e716e9343e523cfb8b7a2e376dc67e90.jpg)
Fig.1.Measured dynamic hysteresis loops at different DC bias excitation)

![](https://assets.underline.io/uploads/markdown_image/1/image/f3b3a5fe58667b168d8946a6c05f0e6c.jpg)
Fig.2 Calculated loss components and measured values with different DC bias (f=15 kHz, Bm=0.05T)

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