Due to the expected increase of the energy consumption related to cooling, finding more energy efficient and environment friendly alternatives is of high interest for researchers. A promising alternative are cooling systems based on the magnetocaloric effect (MCE).1,2 Since the discovery of the giant MCE,3 several material systems, e.g. La-Fe-Si-,4 Fe2P-,5 and Heusler alloys,6 have been studied extensively as their MCE properties are tunable by the elemental composition. However, systematic studies on the effect of microstructure and intrinsic properties, e.g. anisotropy, are limited. We propose a methodology for calculating the MCE in the vicinity of TC in second-order-type materials by combining micromagnetic simulations with the Arrott-Noakes equation (ANE). Firstly, micromagnetic simulations are performed using the Object Oriented MicroMagnetic Framework (OOMMF)7 in which the microstructure and intrinsic properties can be varied. Secondly, the parameters of the ANE are determined from the simulations. Finally, the parameterized ANE is used to calculate the entropy change ΔST around TC according to the Maxwell relations.8 We choose Co2B nanograins as an example system. A simple microstructure of 4x4x4 cube-shaped Co2B nanograins is generated, for which we vary the grain size and boundary thickness. Fig. 1 shows the calculated ΔST in comparison with experimental results on a Co2B single crystal.5 It is found that decreasing the grain size results in increased ΔST, while the influence of the grain boundary thickness is negligible. The proposed methdology allows for investigating the effect of microstructure and intrinsic properties in micromagnetic simulations and extrapolating them to temperatures above TC. This allows for more systematic studies on the relation between microstructural and intrinsic properties and the MCE. The authors acknowledge the support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No 743116, project CoolInnov) and from the CRC/TRR 270 HoMMage (DFG).References: 1. O. Gutfleisch, M. A. Willard, E. Brück, Adv. Mater., 23(7), 821–842, 2011. 2. V. Franco, J.S. S Blázquez, B. Ingale, Annu. Rev. Mater. Res., 42(1), 305–342, 2012. 3. V. K. Pecharsky, K. A. Gschneidner, Phys. Rev. Lett., 78(23):4494–4497, 1997. 4. J. Liu, J. D. Moore, K. P. Skokov, Scr. Mater., 67(6), 584–589, 2012. 5. M. Fries, L. Pfeuffer, E. Bruder, Acta Mater., 132, 222–229, 2017. 6. T. Gottschall, K. P. Skokov, D. Benke, Phys. Rev. B, 93(18), 2–7, 2016. 7. M. J. Donahue, D. G. Porter. OOMMF User Guide. xiii–xxii, 2012. 8. J. C. Maxwell, Phil. Trans. R. Soc., 155, 459–512, 1865.

Calculating the magnetocaloric effect in second-order-type material by micromagnetic simulations

As the energy consumed by cooling systems is expected to increase over the next decades, magnetocaloric cooling systems are of high interest as a promising more energy efficient alternative to conventional vapor compression refrigerators.1–3 Heusler alloys show large magnetocaloric effects (MCE) and are therefore of high interest for possible application in magnetocaloric cooling devices.4,5 They exhibit a magnetostructural transition resulting in larger entropy changes ΔS, thus in larger adiabatic temperature changes ΔTad. We propose a phase field model based on Landau theory to simulate the magnetic domain evolution during the martensite formation, e.g. in Heusler alloys. With our model, we are able to simulate field- and pressure-induced phase transitions, including the martensite and magnetic domain evolution. This is of high interest for a multicaloric cooling cycle as proposed by Gottschall et al.6 In the model, the three order parameters η1, η2, and η3, represent the three martensite variants in a cubic to tetragonal phase transition. The energy of the martensite transformation is described by a Landau-type formulation after Cui et al.7 and is coupled with micromagnetic formulations to take magnetism into account. The 3D finite-element (FE) implementation has been performed within the MOOSE framework.8 The model is capable of reproducing the formation and evolution of domains in magnetic materials under external magnetic field (Fig. 1) or mechanical loading. Modeling field- and pressure-induced tansformation aims at investigating pressures and fields used in a multicaloric cooling cycle. The FE implementation further allows to investigate the influence of microstructure on the MCE. The authors acknowledge the support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No 743116, project CoolInnov).References: 1. C. Zimm, A. Jastrab, A. Sternberg, Adv. Cryog. Eng., 1759–1766. Springer US, Boston, MA, 1998. 2. O. Gutfleisch, M. A. Willard, E. Brück, Adv. Mater., 23(7), 821–842, 2011. 3. V. Franco, J.S. S Blázquez, B. Ingale, Annu. Rev. Mater. Res., 42(1), 305–342, 2012. 4. J. Liu, T. Gottschall, K. Skokov, Nat. Mater., 11(7), 620–626, 2012. 5. T. Gottschall, K. Skokov, D. Benke, Phys. Rev. B, 93(18), 2–7, 2016. 6. T. Gottschall, A. Gràcia-Condal, M. Fries, Nat. Mater., 17(10), 929–934, 2018. 7. S. Cui, J. Wan, X. Zuo, Int. J. Solids Struct., 109, 1–11, 2017. 8. D. R. Gaston, C. J. Permann, J. W. Peterson, Ann. Nucl. Energy, 84, 45–54, 2015.

Phase field model for ferromagnetic domain evolution during martensitic transformation of Heusler alloys

A4: Magneto-Elastic and Magneto-Caloric Materials I

technical paper

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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Dominik Ohmer

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Calculating the magnetocaloric effect in second-order-type material by micromagnetic simulations

Phase field model for ferromagnetic domain evolution during martensitic transformation of Heusler alloys

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