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We present analysis of microscopic origin of magneto-optical spectra from the electronic structure of bcc Fe. The magneto-optical (MO) permittivity spectra are obtained by the WIEN2k code [1] and compared to the corresponding experimental MO Kerr effect spectra. The ab-initio spectra are given by the Kubo formula, i.e., as a result of summation over all pairs of electronic bands and integration over the Brillouin zone that all sum up to the single MO spectrum. We investigate what features of electronic structure contribute to the outgoing total MO spectrum. We have also developed several novel ways of visualizing MO-related phenomena in the Brillouin zone.&lt;br/&gt;&lt;br/&gt;It turns out that strong MO signal comes from several isolated k-points in the Brillouin zone, where the band degeneracy is avoided by the spin-orbit interaction (Fig.1). There are two major types of MO contributions determined by the nature of the avoided degeneracy (given by topology of the approaching bands), that contribute differently to the total MO spectrum. Both types are visualized and their contributions to the total spectrum are demonstrated in the form of local MO spectra.&lt;br/&gt;&lt;br/&gt;K-points, where the strong MO signal is originated, also give rise to strong Berry curvature. We show the flow of the Berry curvature in the vicinity of those k-points (Fig.2) and in the full Brillouin zone.

**References:**

[1] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka and J. Luitz, WIEN2k

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/89049a3a7102cf0d095032f0f6b7b2d8.jpg)
(a) Band structure of bcc Fe with colors corresponding to the &lt;i&gt;d&lt;/i&gt;-character of bands with spin-up being positive and spin-dwon negative. (b) Joint band structure with colors representing the strength of the magneto-optical response. Strong magneto-optical transitions are marked by arrows and labelled by the corresponding band indices.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc6681d80eadbec89b015c676343ea08.jpg)
Flow of the Berry curvature in the vicinity of k-point with strong magneto-optical response.

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 Magneto-Optical Effect in bcc Fe: Microscopic Origin and Topological Aspects

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We present analysis of microscopic origin of magneto-optical spectra from the electronic structure of bcc Fe. The magneto-optical (MO) permittivity spectra are obtained by the WIEN2k code [1] and compared to the corresponding experimental MO Kerr effect spectra. The ab-initio spectra are given by the Kubo formula, i.e., as a result of summation over all pairs of electronic bands and integration over the Brillouin zone that all sum up to the single MO spectrum. We investigate what features of electronic structure contribute to the outgoing total MO spectrum. We have also developed several novel ways of visualizing MO-related phenomena in the Brillouin zone. It turns out that strong MO signal comes from several isolated k-points in the Brillouin zone, where the band degeneracy is avoided by the spin-orbit interaction (Fig.1). There are two major types of MO contributions determined by the nature of the avoided degeneracy (given by topology of the approaching bands), that contribute differently to the total MO spectrum. Both types are visualized and their contributions to the total spectrum are demonstrated in the form of local MO spectra. K-points, where the strong MO signal is originated, also give rise to strong Berry curvature. We show the flow of the Berry curvature in the vicinity of those k-points (Fig.2) and in the full Brillouin zone.

**References:**

[1] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka and J. Luitz, WIEN2k

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/89049a3a7102cf0d095032f0f6b7b2d8.jpg)
(a) Band structure of bcc Fe with colors corresponding to the d-character of bands with spin-up being positive and spin-dwon negative. (b) Joint band structure with colors representing the strength of the magneto-optical response. Strong magneto-optical transitions are marked by arrows and labelled by the corresponding band indices.

![](https://assets.underline.io/uploads/markdown_image/1/image/dc6681d80eadbec89b015c676343ea08.jpg)
Flow of the Berry curvature in the vicinity of k-point with strong magneto-optical response.

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In the age of climate change and the global goal of reducing CO2 emissions, the increase of energy efficiency becomes an important aspect of material and device development in many industrial sectors. The energy spent for cooling and air conditioning in industry and households represents a significant part of the global energy consumption. Furthermore, it is predicted that the amount of energy needed for cooling will rise drastically within this century [1]. Magnetocaloric (MC) refrigeration attracts a lot of attention since it can be more energy efficient and environmentally friendly than current vapor compression technology [2]. It uses a solid-state magnetic material that heats up and cools down cyclically when exposed to a changing magnetic field. Many efforts are guided towards a reduction of the thermal hysteresis to enhance the cyclic magnetocaloric effect (MCE) in first-order materials [3]. An alternative solution has been proposed, which benefits from the thermal hysteresis by using two stimuli to trigger the phase transition in a multicaloric material [4]. In a first step, the application of a magnetic field induces the high-magnetization state which leads to a negative adiabatic temperature change for the case of an inverse MC material. The large thermal hysteresis prevents the back transformation and locks the material in its high-magnetization phase, which allows an efficient heat exchange in zero field. In order to transform the material back, an external stress is applied as a second stimulus leading to a conventional elastocaloric effect (ECE). The use of two stimuli enables a complete first-order transformation under cyclic conditions. Therefore, the drawback of the thermal hysteresis which limits the cyclic performance in a MC cycle can be overcome by using a second stimulus. Furthermore, the amount of permanent magnets to generate the magnetic field can be significantly reduced in a multi-stimuli cycle because the material needs to be magnetized only for a short time and in a small volume. The caloric material for the new multi-stimuli cycle requires a large sensitivity of the phase transition towards both stimuli as well as a good mechanical stability. In this work, we present the concept of the new multi-stimuli cooling concept including potential material systems and methods to tailor their functional and mechanical properties. The main objective is adapting the properties for a classical MC cycle towards the extended needs of the multi-stimuli cycle and tailoring the desired properties by intrinsic and extrinsic means. The most promising materials are Ni-(Co)-Mn-based Heusler alloy due to their adjustable transition temperature and large MCE [5]. We studied these alloy systems with respect to their MC response in low and high magnetic fields as well as for varying field-sweep rates. For the second applied stimulus, the behavior under uniaxial stress application has been investigated for arc-molten and suction-cast alloys. The influence of microstructural modifications, such as grain refinement and precipitates, were studied regarding mechanical stability and caloric performance. Especially the microstructure has an influence on the thermal hysteresis and caloric functionality. Thus, we studied the possibility of tailoring the thermal hysteresis as well as improving the mechanical stability by the addition of secondary phases. We could show that the doping with Gd introduces Gd-rich precipitates into a Ni-(Co)-Mn-In matrix. The alloy shows a magnetic entropy change of 9 Jkg-1K-1 and an adiabatic temperature change of 4 K in 2 T, comparable with values for phase-pure Ni-Mn-In alloys. Compression tests show that the strength is increased significantly for samples with Gd-rich precipitates. In parallel, the development of new Heusler systems opened up broad perspectives since the realization of all-d-Heusler alloys [6]. Recently, the system of Ni-Co-Mn-Ti is investigated intensively because of large MCE and good mechanical properties for a single-phase microstructure. In addition, a large volume change during the martensitic phase transition leads to a large ECE. By optimizing the heat treatment, we could enhance the sharpness of the phase transition and reach large isothermal entropy changes of up to 40 Jkg-1K-1 in 2 T [7]. A systematic study of different Co- and Ti-contents results in a phase diagram, from which the transition temperature can be estimated by the e/a ratio. In addition, the magnetic-field-sensitivity as well as the stress-sensitivity of the phase transition and the thermal hysteresis can be designed precisely by tuning the stoichiometry. The mechanical stability required for a cyclic application of stress can be tailored by the microstructure, e.g. by variation of the processing route. In order to evaluate general design rules for magnetocaloric compounds, the novel all-d Heusler system is compared to the well-characterized Ni-Mn-X alloys with X being a main group element. Significant differences could be attributed to the preferred state of atomic order, which has been analysed by combining the experimental results with theoretical calculations. This work was supported by the ERC Advanced Grant "CoolInnov" (No 743116), and the CRC/TRR 270 “HoMMage” (DFG).

**References:**

[1] M. Isaac, D. P. van Vuuren, Energy Policy 37, 507 (2009) [2] O. Gutfleisch et al., Adv. Mater. 23, 821-842 (2011) [3] F. Scheibel et al., Energy Technol. 6, 1397-1428 (2018) [4] T. Gottschall et al., Nature Mat. 17, 929-934 (2018) [5] A. Taubel et al., Phys. Status Solidi B 255, 1700331 (2018) [5] Z. Y. Wei et al., Appl. Phys. Lett. 107, 022406 (2015) [6] A. Taubel et al., Acta Mater. 201, 425-434 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7435144c2cb405ced22b83f1c2045ae1.jpg)
Schematic of the six-step multi-stimuli cycle, which makes use of a large thermal hysteresis [4].

![](https://assets.underline.io/uploads/markdown_image/1/image/67235d93137d710950d00008a4b37bf2.jpg)
Tailoring the functional properties of Ni-Co-Mn-Ti by varying the stoichiometry (a) and tuning mechanical properties of Ni-Mn-In by introducing secondary phases (b).

 Designing multicaloric materials for using thermal hysteresis in a novel multi-stimuli cooling cycle

To get more insight into fundamental physical properties and their application relevance, the studies on Rare-earth intermetallic compounds are always remarkable. One of such systems that vastly studied is R2TX3 series (R- Rare-earth element, T- Transition element, and X-p-block element), which shows magnetic properties like spin glass, Kondo interaction, Heavy fermion, skyrmions, etc1,2. Also, the good magnetocaloric properties of the series make them relevant for magnetic cooling applications as well3. In this work, Tb2Ni0.94Si3.2 alloy from the same series has been prepared using the arc melting technique followed by annealing at 1073 K for one week. And magnetic, magnetocaloric, and magnetoresistance properties of the alloy have been investigated. Tb2Ni0.94Si3.2 alloy crystallizes in AlB2-type structure (space group = P6/mmm) with lattice parameters, a = b = 3.9210(3) Å, and c = 4.0044(5) Å, respectively, which are determined from the Rietveld refinement of room temperature powder XRD studies. The magnetic state of the alloy consists of spin-glass behavior around Tf =5.2 K and an antiferromagnetic transition at TN = 12.7 K (See Fig.1). Anomalies corresponding to these magnetic transitions are clearly observed in the variation of DC magnetization with temperature in an applied magnetic field of 0.01 T. Further, the appearance of small thermomagnetic irreversibility at higher temperature ( TN &lt; T &lt; 55 K) denotes the presence of short-range ferromagnetic correlation in the alloy. It is concordant with the positive Curie Weiss temperature (θP = 3.13 K) and slight higher effective magnetic moment of Tb atom (µeff = 9.78 µB/ Tb atom) from the Curie-Weiss fit (@ B=1T). The spin-glass behavior around Tf can be confirmed from the variation of AC magnetic susceptibility with temperature for different frequencies (f =10, 100, and 1000 Hz). As shown in inset of Fig.1.a, the peak corresponding to Tf shows a frequency dependence and shifted to higher temperatures as the AC frequency increases, confirms spin-glass behavior. Along with the reentrant spin glass behavior of the alloy, the magnetic state is marked with successive metamagnetic transitions around BC1 = 1 T and BC2 = 2.5 T in isothermal magnetization data. Studies on magnetocaloric properties of the alloy are done by calculating isothermal entropy change (-ΔSM) and Relative Cooling Power (RCP) from the isothermal magnetization studies. As demonstrated in Fig.2, -ΔSM has reached peak values of 12 J/kg K and 8 J/kg K for a magnetic field change of 9T and 5T, respectively, which is comparable with the other magnetocaloric material in the R2TX3 series like Pr2CuSi3 and Gd2CuSi3 compounds4. Calculated RCP values of the alloy are 504 J/kg and 330 J/kg for ΔB = 9T and 5T, respectively, which are higher than the other compounds5 having the same -ΔSM. Enhanced magnetocaloric effect (MCE) of the alloy is the result of the presence of the short-range correlation, which increases the working temperature span of the material. As an extension to the analysis, the magnetoresistance properties of the alloy were studied. Alloy is noted with a magnetoresistance(MR) of -22% for T = 4 K in B = 9 T. Also, the influence of metamagnetic transition and short-range correlation is reflected in the variation of MR with the applied magnetic field. It denotes the strong correlation between the magnetic and lattice state of the alloy. In conclusion, magnetic, magnetocaloric, and magnetoresistance properties of Tb2Ni0.94Si3.2 alloy shows reentrant spin glass behavior with good MR and enhanced MCE property. Acknowledgment: This research work was supported partially by VEGA 1/0611/18, 1/0705/20 and APVV-16-0079, and project No. 001PU-2-1/2018.

**References:**

1 P. Zhi-Yan, C. Chong-De, B. Xiao-Jun, S. Rui-Bo, Z. Jian-Bang, and D. Li-Bing, Chinese Phys. B 22, 056102 (2012). 2 R. Kumar, K.K. Iyer, P.L. Paulose, and E. V. Sampathkumaran, Phys. Rev. B 101, 144440 (2020). 3 V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, and A. Conde, Prog. Mater. Sci. 93, 112 (2018). 4 F. Wang, F. Yuan, J. Wang, T. Feng, and G. Hu, J. Alloys Compd. 592, 63 (2014). 5 L. Li, D. Huo, Z. Qian, and K. Nishimura, J. Phys. Conf. Ser. 263, 2 (2011).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/81a75c94ad45a9b5801f82776076af93.jpg)
Fig.1.Variation of DC magnetic susceptibility (M/B) as a function of temperature in applied magnetic field B = 0.01 T. Inset shows AC magnetic susceptibility for frequencies 10,100 and 1000 Hz.

![](https://assets.underline.io/uploads/markdown_image/1/image/1e209a16d7d503cbccef602dcd3d78f3.jpg)
Fig.2. Variation of isothermal entropy as a function of temperature

 Influence of Short-Ranged Correlation on Magnetocaloric Properties of Tb2Ni0.94Si3.2 Alloy

1. Entropy change of successive martensitic transformations in Ni-Mn-Ga Heusler alloys can be utilized to realize enhanced magnetocaloric properties. A detailed study of phase transformations of Ni2.15Mn0.85Ga, (ΔQ = 4900 J/kg at 343 K and 140 kOe) is reported here. Upon cooling, paramagnetic austenite (L21) transforms into a ferromagnetic 7M monoclinic martensitic phase. This phase is stable in a narrow temperature range and, upon further cooling, transforms into a non-modulated ferromagnetic tetragonal (L10) phase. The separation between the equilibrium temperatures of the L21 and the L10 phases is only ~50 K. The alloy undergoes reversible temperature-induced martensitic and inter-martensitic phase transformations with thermal hysteresis about 25 K. The conclusions from the detailed study of the phase transformations lead to new possibilities to enhance the magnetocaloric effect by utilizing the entropy associated with multi-structural transformations. 2. Introduction Magnetic cooling based on the giant magnetocaloric effect (GMCE) is a proposed solution to the low-efficiency and eco-adverse refrigerant of current technologies [1]. Developing a material that produces a GMCE near room temperature is key to the more efficient and economical cooling technology. Ni-Mn-X alloys are under the spotlight because they are inexpensive and non-toxic. The isothermal entropy changes exhibited by some Ni-Mn-Ga alloys are in close range or even higher than those reported in Gd and La-based compounds [2]. Several techniques are available to enhance the GMCE demonstrated by Ni-Mn-X alloys. Combining magnetocaloric and elastocaloric effects by applying stress to the refrigerants is one technique [3]. The latest trend is to utilize the two consecutive structural transformations of these alloys [4]. Here we report a study of the inter-martensitic phase transformations of such an alloy. The analysis of the structures, phase transformation temperatures, and the thermal hysteresis will support the search for new avenues to enhance the magnetocaloric effect by utilizing the entropy associated with multi-structural transformations [5]. 3. Experimental A polycrystalline sample was prepared by arc-melting in an argon atmosphere and then annealed at 1073 K for 50 hours [6]. The chemical composition, Ni2.15Mn0.85Ga, was determined by energy dispersive spectroscopy. In-situ synchrotron diffraction data were collected at beamline 11-ID-C of the Advanced Photon Source at Argonne National Laboratory (λ = 0.010804 nm). Diffraction data were analyzed using the General Structure Analysis System EXPGUI [7]. Magnetization measurements were done using a SQUID magnetometer. 4. Results and Discussion The diffraction data (Fig. 1) at selected temperatures (400-100 K) shows that the alloy undergoes martensitic and inter-martensitic transformations and mixtures of phases in different temperature intervals. The austenitic structure is cubic L21 (Fm-3m space group). Upon cooling, the alloy transforms into a 7M monoclinic (P 1 2/m 1 space group). Upon further cooling, it transforms into a non-modulated tetragonal L10 structure (I 4/m m m space group). The thermograms (Fig. 2) were constructed by the calculated phase fractions obtained from Rietveld refinements. The alloy undergoes martensitic transformation around 310 K from austenite to 7M modulated martensite. Upon further cooling (~ 260 K), the inter-martensitic phase transformation [8] occurs from monoclinic to tetragonal phase. The reverse-phase transformations occur while heating (see fig. 2). The characteristic temperatures of the austenitic (TMH), martensitic (TMC), and inter-martensitic transformations (TIMH and TIMC) were defined at 50% phase fraction of the respective phases upon cooling and then heating, respectively. Thermal hystereses of the transformations, calculated by the differences between TMH & TMC and between TIMH & TIMC, respectively, are very close (~25 K). Because of the similar hysteresis, the separation between the martensitic and inter-martensitic transformation temperatures, while heating and cooling, are the same and is ~50 K. The austenitic phase is paramagnetic, and the martensitic phases are ferromagnetic. The austenitic phase transformation temperature (332 K) and Curie temperature (337 K) are very close. Under a suitable field, these two transformations could coincide to give a much higher MCE. 5. Conclusions and Future work The alloy undergoes two successive phase transformations with narrow separation between them (~50 K). The hystereses are less than 25 K. These conditions suggest that utilizing two successive phase transformations may result in higher GMCE. To optimize the GMCE, extensive knowledge of two transformations is required. The magnetic phase transformation temperature increases with increasing magnetic field [6]. However, the behavior of the crystalline phase transformation temperatures under magnetic fields is unknown and essential to study. Also, isothermal magnetization measurements could reveal the possible magnetic phase transformations.

**References:**

1. D. R. Brown, N. Fernandez, J. A. Dirks, U.S. Department of Energy, (2010) 2. J. Liu, T. Gottschall, K. P. Skokov, nature materials, Vol. 11.7, p.620-626 (2012) 3. Y. Hu1, Z. Li, B. Yang, APL Materials Vol.5, p.046103 (2017) 4. Z. Li, K. Xu, Y. Zhang, Scientific Reports, Vol. 5, p.15143 (2015) 5. Z. Li, Y. Zhang, C. F. Sanchez-Valdes, Appl. Phys. Lett., Vol.104, p.044101 (2014) 6. A. Kamantsev, V. Koledov, A. Mashirov, J. Appl. Phys., Vol. 117, p.163903 (2015) 7. B. H. Toby, J. Appl. Cryst., Vol. 34, p.210-213 (2001) 8. S.M. Konoplyuk, V.V. Kokorin, Ukr. Phys. J. Vol.43, p.1275 (1998)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f4d4617604cc887d5b8421a9c3cb488f.jpg)
Diffraction patterns collected while cooling from 395 to 100 K. At 395 K, the alloy is austenitic, and upon cooling, it transforms into a 7M monoclinic phase. Upon further cooling, it transforms into a tetragonal L10 structure.

![](https://assets.underline.io/uploads/markdown_image/1/image/952feea6b45327a2d71ceb6d345b754d.jpg)
Variation of the three phases' phase fractions upon heating (red) and cooling (blue). Characteristic temperatures of the martensitic and inter-martensitic phase transformations were determined by the intersections as shown.

 Temperature-induced successive martensitic and inter-martensitic phase transformations of Ni2.15Mn0.85Ga Heusler alloy

Introduction: Magnetocaloric refrigeration is an emerging technology that shows significant potential to reduce the dependence on traditional vapor compression systems that support most of the cooling and refrigeration needs. Unlike significant body of work on the development of magnetocaloric materials, only a limited number of reports address their functional and chemical stability. This study focuses on a known refrigerant – intermetallic compound of lanthanum, iron, and silicon with minor amounts of cobalt, La(Fe0.84Co0.07Si0.08)13, and its stability in a standard heat exchange fluid, that is, water [1]–[3]. Experimental Details: An alloy with a nominal composition of La(Fe0.84Co0.07Si0.08)13 weighing 20 g was prepared by arc-melting of the elements under argon atmosphere on a water-cooled Cu-hearth. The ingot was re-melted four times, being turned over each time to achieve homogeneity. The total measured weight loss was less than 0.5 wt. %. The as-cast ingot was broken into smaller pieces, which were wrapped in a tantalum-foil, sealed inside a fused-silica tube under vacuum, and annealed at 1050°C for one week, followed by quenching in ice-cold water. Powders from the annealed pieces were prepared by crushing and grinding in an agate mortar with an agate pestle inside an argon-filled glove box and screened to particle sizes of 100 µm and below. Thus, prepared powder was divided into two samples. One sample was stored in deionized water and another in air, both for 14 days. Magnetic measurements were carried out using the Physical Property Measurement System (PPMS) VersaLab and PPMS Dynacool, whereas heat capacity was measured using PPMS Dynacool [4], [5]. Results and Discussions: Figure 1 presents ΔS vs. T calculated from magnetization isotherms and Fig. 2 shows the same calculated from heat capacity data after ground powders were stored in water and air. Both sets of data are in good agreement. The powders stored in water exhibit larger magnetocaloric effects by ~40% when compared to the same after stored in air. The most likely reason is nearly complete dissolution of the smallest particles in water, leaving behind only the largest particles with relatively low concentration of surface reaction products. Storing in air, on the other hand, likely leads to severe oxidation of the smallest particles but does not remove them from the material, thus effectively reducing the measured magnetocaloric effect. Further analysis of the powders to confirm this hypothesis is underway and the results will be reported in due time. Acknowledgment: Ames Laboratory is operated for the U.S. Department of Energy (DOE) by Iowa State University of Science and Technology under contract No. DE-AC02-07CH11358. Work at Ames Laboratory was supported by the U.S. DOE, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.

**References:**

[1] F. Hu, B. Shen, J. Sun, Z. Cheng, G. Rao, and X. Zhang, “Influence of negative lattice expansion and metamagnetic transition on magnetic entropy change in the compound LaFe11.4Si1.6,” Appl. Phys. Lett., vol. 78, no. 23, pp. 3675–3677, Jun. 2001, doi: 10.1063/1.1375836. [2] F. X. Hu et al., “Magnetocaloric effect in itinerant electron metamagnetic systems La(Fe1−xCox)11.9Si1.1,” J. Appl. Phys., vol. 97, no. 10, p. 10M303, May 2005, doi: 10.1063/1.1847071. [3] L. Mañosa et al., “Inverse barocaloric effect in the giant magnetocaloric La-Fe-Si-Co compound.,” Nat. Commun., vol. 2, p. 595, Jan. 2011, doi: 10.1038/ncomms1606. [4] K. Javed, S. Gupta, V. K. Pecharsky, and R. L. Hadimani, “Stability of magnetocaloric La(FexCoy Si1-x-y )13 in water and air,” AIP Adv., vol. 9, no. 3, p. 035239, Mar. 2019, doi: 10.1063/1.5080108. [5] D. Clifford, V. Sharma, K. Deepak, R. V. Ramanujan, and R. Barua, “Multicaloric Effects in (MnNiSi)1-x (Fe2Ge)x Alloys,” IEEE Trans. Magn., pp. 1–1, 2020, doi: 10.1109/TMAG.2020.3025002.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7b87e1a7d4cdbd8c05245787b4a63d1.jpg)
Fig.1: Comparison of ΔS vs T calculated using Maxwell's equation for samples stored in air and water for ΔH = 3T.

![](https://assets.underline.io/uploads/markdown_image/1/image/a6b1b75cb35af4ff1e22c0837bdc6f80.jpg)
Fig. 2 Comparison of ΔS vs T calculated using heat capacity measurements for samples stored in air and water for ΔH = 3 T.

 Chemical stability of magnetocaloric La(FexCoySi1-x-y)13 particles

Power law to express the field dependence of the isothermal entropy change (ΔsT ∝ ΔHn) has been widely employed for obtaining information of the thermomagnetic second-order phase transitions (e.g. critical exponents [1] or Curie temperatures [2]). Recently, the analysis of this field dependence has been extended to materials undergoing thermomagnetic first-order phase transitions, the most promising magnetocaloric materials up to the moment. It has been shown that the value of the exponent n overshoots above 2 for first-order phase transitions, while it does not overshoot for the second-order case, allowing to establish a quantitative criterion for determining the order of the phase transitions [3]. This is in excellent agreement with previous phenomenological observations, supporting the validity of the proposed criterion. For direct magnetocaloric effect (MCE), the overshoot feature for fingerprinting first-order transitions can be validated in the frame of the Bean-Rodbell model [4], obtaining an excellent agreement between experiments (e.g., for La(Fe,Si)13 which undergoes a ferromagnetic (FM) to paramagnetic (PM) magnetoelastic transition [5]) and the model. However, for inverse MCE, the validity of the proposed criterion and the characteristics of the field dependence have only been studied experimentally. In this work, the magnetic field dependence of the inverse MCE is analyzed using a mean field approach for describing antiferromagnetic (AF) to FM magnetoelastic transitions. The model is able to describe both second- and first-order phase transitions through the introduction of a magnetovolume energy term according to the Callen-Callen theory [6] (having a Gibbs energy term of the form -βωM2/4 , being ω the relative volume change, M the magnetization and β an introduced magnetoelastic coupling parameter). Using this model, we are able to reproduce the experimentally observed features for the exponent n, showing the existence of the characteristic overshoot for first-order transitions (which corresponds to β&gt;0) and its absence for second-order ones (β=0), as shown in Fig. 1. We explore the influence of different parameters of the model on exponent n, such as the transition temperature and Curie temperature separation or the exchange constant between the moments of the different sublattices. The existence of the overshoot feature is corroborated for all the different cases. This supports the extension of the quantitative criterion to AF-FM phase transitions and set the basis for the analysis of exponent n in these materials. A main difference with respect to direct MCE is that negative values of the exponent n are obtained at temperatures close to the transition. This is ascribed to the reduction of the inverse MC response due to the influence of the unavoidable FM to PM transition at higher temperatures. The obtained features for exponent n (field dependence and temperature dependence) are qualitatively compared to those of GdBaCo2O6 [7] (AF to FM magnetoelastic transition), showing a good agreement between both the experiment and the model. The obtained results are extrapolated to understand the behavior of the exponent n for a Ni49Mn36In15 sample [8] (low magnetization to high magnetization magnetostructural transition). Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212 and Sevilla University under VI PPIT-US program.

**References:**

[1] V. Franco, A. Conde, Int. J. Refrig. Vol. 33 pp. 465–473 (2010) [2] L.M. Moreno-Ramírez, J.S. Blázquez, V. Franco et al., IEEE Magn. Lett. Vol. 7 Art no. 6102004 (2016) [3] J.Y. Law, V. Franco, L.M. Moreno-Ramírez et al., Nat. Commun. Vol. 9 Art no. 2680 (2018) [4] C.P. Bean, D.S. Rodbell, Phys. Rev. Vol. 126 pp. 104–115 (1962) [5] L.M. Moreno-Ramírez, C. Romero-Muñiz, J.Y. Law et al., Acta Mater. Vol. 175 pp. 406–414 (2019) [6] E. Callen, H.B. Callen, Phys. Rev. Vol. 139 p. A455–A471 (1965) [7] J.Y. Law, V. Franco, A. Conde et al., J. Alloys Compd. Vol. 777 pp. 1080–1086 (2019) [8] J.Y. Law, Á. Díaz-García, L.M. Moreno-Ramírez et al., Acta Mater. Vol. 166 pp. 459–465 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3c9078ab03a39d089b10c5aa280ea645.jpg)
Fig. 1. Temperature dependence of exponent n for different magnetovolume coupling parameter β. Inset: maximum value of the overshoot above 2 as a function of β.

 Analysis of the Magnetic Field Dependence of the Isothermal Entropy Change of Inverse Magnetocaloric Materials

Magnetocaloric effect (MCE) receives an increasing interest for its promising applicability in energy efficient refrigerators. Among the different magnetocaloric materials having potential applications for cooling devices that operate near room temperature, those exhibiting a first-order phase transition (FOPT) usually show larger responses than those exhibiting a second-order phase transition (SOPT), but the intrinsic hysteresis could be deleterious for cyclic operations [1]. Some FOPT materials such as Heusler alloys can also exhibit the Curie transition of their magnetic phases, thus leading to alloys exhibiting both direct (positive isothermal entropy change, ΔSiso) and inverse MCE (negative ΔSiso). However, the close proximity of the two types of transitions can produce a convoluted and compensated global response due to the different nature, direct and inverse, of their MCEs [2]. In order to evaluate the potential of the FOPT for magnetocaloric applications and, therefore, ascertain the usefulness of tuning the Curie temperature of the alloy by compositional modifications, it is necessary to be able to deconvolute its responses. It has previously been shown that concurrent SOPTs can be deconvoluted by applying the scaling laws of the MCE [3]. In this work, we propose an extension of the methodology to deconvolute concurrent FOPT and SOPT. For this purpose, a Heusler alloy with stoichiometry Ni48.1Mn36.5In15.4 has been used as a model case. Upon heating, this sample exhibits a FOPT from a low magnetization martensite to an austenite with higher magnetization. This magneto-structural transition produces an inverse MCE that is immediately followed by the Curie transition of the austenite, with its corresponding conventional MCE. With increasing the magnetic field, two different behaviors are observed: 1) the onset of the FOPT shifts to lower temperatures, with a peak ΔSiso value that increases abruptly at the beginning, reaches a maximum for ~5 T and subsequently decreases, and 2) a Curie transition whose response increases gradually in height and width, with a peak position that remains almost field independent. Due to the proximity of these two competing transitions, the overlapping of their responses increases with increasing field. The application of the scaling laws for the SOPT magnetocaloric response allows us to deconvolute the contributions of the two transitions. Top panel of Fig. 1 shows the experimental ΔSiso of the sample together with its reconstructed response. The separated contributions of the two phase transitions are presented in the bottom panel of Fig. 1. The good agreement between experimental and reconstructed curves allows us to reach the following conclusions: - Universal scaling can be used to deconvolute overlapping first and second order phase transitions. - The broadening of the SOPT with increasing field causes a larger overlap between transitions despite the shift of the FOPT to lower temperatures. - The experimental decrease of the inverse MCE peak above ~5T is due to the competing contribution of the SOPT and is not intrinsic to the FOPT. This deconvolution methodology allows to extract the information of the different phase transitions in the material without having to experimentally synthesize new alloys with different compositions. Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), and Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212.

**References:**

[1] V. Franco, J.S. Blázquez, J.J. Ipus, J.Y. Law, L.M. Moreno-Ramírez, A. Conde, Prog. Mater. Sci. 93 (2018) 112–232. [2] J. Y. Law, Á. Díaz-García, L. M. Moreno-Ramírez, V. Franco, A. Conde, A. K. Giri, Acta Mater. 166 (2019) 459. [3] Á. Díaz-García, J. Y. Law, P. Gebara, V. Franco, JOM 72 (2020) 2845–2852.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/181f71a01791952162fe6704a962d0ff.jpg)
Fig. 1 (Top panel) Experimental temperature dependence of ΔSiso of Ni48.1Mn36.5In15.4 Heusler alloy for different magnetic fields (open symbols) and its reconstructed ΔSiso response (stars symbols). (Bottom panel) Temperature dependence of ΔSiso for different fields of the deconvoluted responses of the SOPT (open symbols) and the FOPT (solid symbols).

 Deconvolution of First and Second Order Phase Transitions using the Scaling Laws of the Magnetocaloric Effect

Magnetocaloric materials with a first order phase transition exhibit thermal hysteresis, which is one of the key limiting factors that prevent their efficient implementation in magnetic refrigerators. This problem has to be tackled in a twofold way: a) understanding the different sources of thermal hysteresis of technologically relevant materials in order to minimize them, and b) predicting the response of the materials upon an arbitrary sequence of excitations, so that the trajectories of the minor loops in the M(T,H) space is known and their behavior in a magnetic refrigerator can be suitably modeled. To achieve those, in the recent years, the temperature variant of the first order reversal curves technique (T-FORC) has been proposed as a fingerprinting method for the characterization of thermal hysteresis in magnetocaloric materials [1]. This initial approach has been expanded in two complementary directions: the implementation of a faster characterization technique that makes use of an effective temperature approach (T*FORC) [2], and the development of models of the phase transformation that provide a physical meaning to the distinct features observed in experimental T-FORC distributions [3]. In this presentation we will show an overview of the T-FORC technique and highlight its potential for the characterization of hysteretic thermomagnetic phase transitions by applying it to two different Heusler alloys of the Ni50Mn34In16 family, with similar Curie temperatures but different temperatures of the martensitic transition (see figure). Experiments have been performed upon cooling and heating for different fixed values of magnetic field. The different relative distance between transitions leads to different features in their T-FORC distributions. The comparison of the experimental distributions with those obtained from the model of the magneto-structural transitions allows us to associate the distinct T-FORC features to different characteristics of the transformations. The existence of different rates during the transition is what mainly defines the features of the T-FORC distributions. The model also allows us to separate the effects of the structural transformation and the temperature dependence of magnetization of the martensitic and austenitic phases, making us conclude that T-FORC distributions mainly reveal the characteristics of the structural component of the hysteretic transition. The appearance of a negative elongation in the cooling mode T-FORC (and positive in the heating one) is associated to the significant temperature dependence of the magnetization of both pure phases. Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212, Sevilla University under VI PPIT-US program, and by the FRIMAG project, funded by Emilia Romagna region within the 2014-20 POR-FESR program (CUP E32F16000190007). The authors thank Dr. Cecilia Bennati for her contributions on the synthesis of the samples.

**References:**

[1] V. Franco, T. Gottschall, K.P. Skokov, O. Gutfleisch, IEEE Magn. Lett. 7 (2016) 6602904. [2] L.M. Moreno-Ramírez, V. Franco, Metals 10 (2020) 1039. [3] V. Franco, J. Appl. Phys. 127 (2020) 133902.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6ed8091fdfb1e863af4f3a30dd0be729.png)
Magnetothermal hysteresis loops for (a) Ni49.65Mn34.19In16.17 and (c) Ni49.42Mn34.35In16.23 alloys with their corresponding T-FORC distributions, (b) and (d) respectively, where white dashed lines indicate schematically the most relevant features: (1) main peak distorted downwards; (2) elongation along the +45o direction that forms a ridge; (3) sinking to negative values.

 T-FORC as a tool for the characterization of magnetocaloric materials: from experiments to models

Since the discovery of the Giant Magnetocaloric Effect (MCE) on Gd5Si2Ge2 by Pecharsky and Gschneidner [1], the Gd5(Si1-xGex)4 family compounds have been intensively studied for applications in magnetic refrigeration (MR) at room temperature. The vast investigation at the macroscale on these alloys up to this time revealed many other important properties, such as giant magnetoresistance and colossal magnetostriction (CMS) [2]. Such behaviors arise from a strong magneto-volume coupling extreme sensitivity to variation of external (e.g., temperature, magnetic field, and pressure) and internal (e. g., stoichiometry, dimensionality, and doping) parameters. For this reason, this family compound presents a rich phase diagram that, for example, gives a wide range of temperatures for device operations. However, the low mechanical stability and oxidations issues are some drawbacks for long periods of appliance operation. Reducing it to the micro and nanoscales can improve the alloys' properties and also find novel properties. In the last years, some experimental approaches have been used to produce micro/nanostructures of Gd5(Si,Ge)4 [3]. It is possible to mention high-energy ball milling, RF magnetron sputtering, and laser ablation techniques, being the most promising. Using a femtosecond pulsed laser deposition, our group successfully obtained Gd5Si1.3Ge2.7 nanogranular film composed of 80 nm particles presenting a magnetostructural transition [4] and a negative thermal expansion [5]. Although this evidence revealed the great potential of ultrashort laser ablation, a more conventional and low-cost technique should be pursued aiming practical applications of these compounds. For example, Tarasenka et al. were able to produce colloidal suspensions of Gd-Si-Ge nanoparticles in liquid with a more accessible Nd:YaG nanosecond pulsed laser [6]. Although the NPs presented fine crystalline features, the formation of silicon carbide and particle segregation after an additional laser ablation occurs. Given this, in addition to finding the most appropriate experimental technique, reasonable control of the intrinsic structures is essential to optimize the material production on a large scale. Here, we demonstrate that a more simple gas-phase synthesis using a Nd:YaG and KrF Excimer nanosecond pulsed lasers can be used to produce Gd5(Si1-xGex)4 nanostructures with x = 0, 0.45 and 0.60. The stoichiometries were selected to cover all the possible structures adopted by this family: orthorhombic-II [O(II)] for x = 0; monoclinic (M) of x = 0.45; and orthorhombic-I [O(I)] for x = 0.60. It is worth mentioning that x = 0.45 and 0.60 are in the vicinity of the phase-mixed region to show the feasibility of this method along with the family phase-diagram. In particular, the KrF Excimer was chosen due to the laser wavelength that presents higher penetration depth and reduced reflectance in metals. The nanostructures were obtained by ablating the polished surface of ingots produced by tri-arc melting with 10 Hz of frequency and maximum energy of 550 mJ and 200 mJ, for Nd:YaG and KrF Excimer lasers, respectively. The chamber was pumped several times down to a base pressure of 10-6 Torr to prevent oxidation. During the deposition, Argon inert gas was used in a continuous flux in constant pressure of 1 Torr inside the chamber. From this process, Gd5(Si,Ge)4 grains with an average particle size between 10-30 nm were achieved with good crystalline features, as can be seen in Fig.1(a). Synchrotron X-ray Diffraction confirmed the great level of the structures crystallinity and revealed a change in symmetry for x = 0 and 0.45 respectively from O(II) and M to O(I). The structural shrinkage was found to be around 2% for the Si-rich compositions and less than 1% for Gd5Ge4 (x=0). Given the lower unit cell volume for the O(I) structure, a shortening between the Si(Ge)-Si(Ge) distances is responsible for a change in the transition order from a first to a second one for x = 0.45. Also, the magnetic transition occurs at 290 K for this 0.45 composition nanostructure, see Fig.1(b), confirming the XRD analysis. Distinctly, for x = 0, the reduction to the nanometric scale leads to a superparamagnetic-like behavior that leads to a maximum of 8 J/kgK at 5 K that drastically reduces to null values as the temperature increases. Furthermore, the reduction of the unit cell volume was found to be directly related to the bulk target volumetric compressibility that is due to intrinsic surface tension (st) rising from the nanostructuring process. Thereby, we can conclude that the nanosecond PLD successfully produces dispersed crystalline nanoparticles of Gd5(Si1-xGex)4 family compounds. This technique allows the formation of NPs with particles size under 30 nm without loss on the stoichiometry of the targets, as observed through Synchrotron XRD [7]. Notwithstanding, the direct relation between bulk compressibility and nanoparticle size due to an intrinsic surface pressure might be the path to understand the particles' growth from pulsed laser deposition techniques under inert gas in the chamber.

**References:**

[1] V. K. Pecharsky and K. A: Gschneidner Jr., Phys. Rev. Lett., vol. 78, p. 4494 (1997); [2] L. Morellon, et al., Phys. Rev. B, vol. 58, p. R14721(R) (1998); [3] J. H. Belo, et al., J. of Mater. Res., vol. 34, p. 134 (2019); [4] R. L. Hadimani, et. al., Appl. Phys. Lett., v. 106, p. 032402 (2015); [5] J. H. Belo, et al., PRB, vol. 100, p. 134303 (2019); [6] N. Tarasenka, et al., J. Nanosci. Nanotechnol., vol. 16, p. 7451 (2016); [7] V. M. Andrade, et al., J. Alloys Compd., vol. 849, p. 156384 (2020[AP1] ).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/afe5422997f395a3795a6766687f1f04.jpg)
Figure 1: (a) TEM images for x = 0.45 nanoparticles with 27 nm of the mean size where the SAED reveals the good crystalline features of the structures. (b) Magnetic entropy change curves for all produced samples for an applied field of 5 T.

 Unit cell volume reduction of Gd5(Si,Ge)4 nanoparticles controlled by bulk compressibility

Faraday effect was a first demonstration of magnet influence on the light. Since then many generations of scientists tried to strengthen it. A decade ago, a breakthrough based on plasmonics was proposed for a significant enhancement of the magneto-optical interaction. However, all metals, even noble ones, introduce rather notable absorption which worsen quality factor of the optical resonances and constrains their role in the magneto-optical enhancement. Here we demonstrate that low lossy all-dielectric magnetic structures are more advantageous in this respect. We propose a specially designed all-dielectric magnetic meta-surface allowing a novel mechanism of the magneto-optical intensity effect [1]. It consists of a 2D array of iron-garnet nanopillars on an ultrathin iron-garnet slab. The nanostructure exhibits high transparency and superior quality-factor resonances followed by multifold increase of the magnetooptical intensity modulation. Unlike the magneto-optical intensity effects in smooth films and plasmonic gratings the photonic crystal metasurface provides the magnetically induced modulation of light intensity not only in a single light polarization, e.g. p-polarization, but also in the orthogonal one (s-polarization). It is due the wide variety of the excited mode types in the all-dielectric nanostructure. It is very promising for sensing, magnetometry and light modulation applications. This work was financially supported by the Russian Ministry of Education and Science, Megagrant project N 075-15-2019-1934.

**References:**

[1] D.O. Ignatyeva et al., Nature Communications 11, 5487 (2020).

**Images:**

 All-dielectric magnetophotonics INVITED

In the last decade, a huge amount of work has been devoted to constructing a composite thin film where magnetic anisotropy becomes tunable by coupling ferromagnetic layer to a functionalized layer. Electrical control of interfacial anisotropy with an insulator and interfacial strain transferred from an electrically controlled piezoelectric or ferroelectric material are still heavily pursued. In 2016, Feng et al. [1] proposed a novel approach to manipulate magnetic anisotropy by interfacial strain transferred from a thermally controlled NiTiNb shape memory alloy (SMA). They obtained pioneering results in showing small variation of interfacial anisotropy in NiTiNb (0.5mm)/FePt (10–20 nm) with in-plane anisotropy. This innovative architecture benefits from the shape memory effect, in particular, from the two-way shape memory effect (TWSME). The TWSME consists in a reproducible hysteretic transformation of shape memory alloys from a strained B19’ structure (at low temperature) to a differently strained B2 structure (at high temperature) during the thermal cycle. NiTi-based alloys are among the most used shape memory alloys within a wide range of applications in industry, military technologies, health care, etc. [2]. They are metallic and may be grown by regular microelectronics industry deposition techniques. NiTi-based SMAs can produce as much as 4% of TWSME strain and recover up to 10% of the initial deformation [3]. The transformation temperatures can be easily tuned from 250 K to 1000 K [2]. In our talk, we demonstrate that the NiTi alloy can be used to reproducibly switch by 90° the in-plane uniaxial anisotropy of a 20 nm thick Ni thin film during a thermal cycle between room temperature and 100°C (as shown in Figure 1) [4]. We first properly quantify NiTi sample longitudinal strain and transverse strain produced by an external uniaxial tensile stress followed by a thermal cycle, required to setup the TWSME. We demonstrate that NiTi is a Pauli paramagnetic material and explain temperature variations of its magnetic susceptibility by comparing experimental data with ab-initio calculations [5]. We show that both martensitic transition temperature and magnetic susceptibility depend on NiTi lattice structure, which we tuned through strain and characterized by TEM and XRD techniques. Secondly, we characterize magnetic anisotropy of the Ni layer, deposited by PVD on top of NiTi after tensile deformation. As shown in Fig. 1, when NiTi is in its martensite (respectively, austenite) phase, Ni anisotropy points along (respectively, perpendicular to) the initial tensile axis. Variation of Ni anisotropy up to 1.105 J.m-3 was achieved. It is a promising result since the strain transfer at NiTi/Ni interface is not yet optimized. Indeed during the TWSME strain in NiTi varies from 0% to 2.7% whereas Ni strain varies only from 0% to 1.3. We performed transmission electron microscopy and reveal that a thin oxidized interface layer is the main origin of strain loss at the NiTi/Ni interface.

**References:**

[1] C. Feng et al., Appl. Phys. Lett. 109, 212401 (2016) [2] J. Mohd Jani, et al., Mater. Des. (1980–2015) 56, 1078 (2014) [3] O. Benafan, et al., J. Appl. Phys. 112, 093510 (2012) [4] A. Kyianytsia et al., Appl. Phys. Lett. 115, 222402 (2019) [5] A. Kyianytsia et al., Appl. Phys. Lett. 117, 122411 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c19037b2f749a5e8b58c235308b7d528.jpg)
(a–b) Magnetization vs magnetic field when the field is applied along the x-axis (0°), and y-axis (90°), when NiTi is in martensite state (E state) and austenite state (F state). (c) Remanent magnetization of NiTi/Ni as a function of magnetic field angle for E and F state.

Magneto-Optical Effect in bcc Fe: Microscopic Origin and Topological Aspects

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