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Magnetic elastomers are one of the most important types of magnetoresponsive materials. They are characterized by large changes in their shape and rehological properties as a response to external magnetic fields [1]. Similarly to magnetic fluids and gels, these are hybrid materials that consist of magnetic nano- or microparticles embedded in a magnetically passive carrier material. Magnetic elastomers are candidate materials for many technological applications, like adaptive damping devices, vibrational absorbers, stiffness tunable mounts, soft actuators and micromanipulators, force sensors or artificial muscles, see [2] and references therein. Here, we study theoretically a novel microstructural design for a hybrid magnetic elastomer material that has been synthesized for the first time very recently [3-5]. This design is based on the embedding within the polymer matrix of two types of magnetic particles in different amounts: a low volume fraction of magnetically hard (MH) colloidal particles---typically, ferromagnetic particles of 5-100μm of diameter---and a high volume fraction of smaller, magnetically soft (MS) particles---paramagnetic particles with a diameter typically smaller than 5μm. We study the response of this hybrid magnetic material to external magnetic fields by means of two theoretical approaches. First, we perform extensive computer simulations with a bead-spring model of the system that takes into account the magnetic influence of the MH particles on the MS ones, as well as the mechanical coupling imposed by the polymer matrix on the rearrangements of the particles [6]. Finally, we compare the results obtained from this approach with the ones provided by a continuous magnetomechanical model. In both approaches we focus on a minimal representative volume of the material, consisting of a single MH particle surrounded by a cloud of MS ones and the mechanical coupling between all of them. We analyze the deformations of this elementary volume as a response to the external fields.References: [1] S. Odenbach. Arch. Appl. Mech., 86:269–279, (2016). [2] P. Sánchez et al., Soft Matter, 15, 175-189 (2018). [3] J.M. Linke, D.Y. Borin, S. Odenbach, RSC Adv., 6, 100407 (2016). [4] M.V. Vaganov, J. Linke, S. Odenbach, Yu.L. Raikher, J. Mag. Mag. Mat. 431, 130-133 (2017). [5] P. Sánchez et al., Soft Matter, 14, 2170-2183 (2018). [6] P. Sánchez et al., Soft Matter, 15, 7145--7158 (2019).

MMM 2020

Theoretical Modelling of Hybrid Magnetic Elastomers

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Heuser alloys present a rich phase diagram to engineer new materials and alter tunability of the desired material properties for potential technological applications in spintronic devices. We investigate the structural, static, and dynamic properties of Co1.5Ti0.5FeAl Heusler alloy thin films, with variable thickness (t = 5 nm, 10 nm, 20 nm, 35 nm, 50 nm, and 70 nm) grown by sputter beam epitaxy on cubic MgO (100), MAO (100) (Fig. 1), and hexagonal Al2O3 (110) substrates. By partial substitution of Ti for Co in parent alloy Co2FeAl i.e Co1.5Ti0.5FeAl, we demonstrate a very low total damping parameter of 0.00156 ± 0.00003 and a low linewidth term 17 ±1 Oe (Fig. 2) for 20 nm film grown on MAO (100) substrate using ferromagnetic resonance spectroscopy comparable to elemental Fe1,2. A pronounced fourfold anisotropy is consistent with the fourfold crystalline symmetry in the epitaxial thin films grown on cubic substrates. A saturation magnetization of ~ 5.0 μB/f.u. (where f.u. represents formula unit) was obtained at room temperature, nearly double the value based on the Slater-Pauling rule. Co1.5Ti0.5FeAl films simultaneously exhibit a very low damping and approximately 40 % lower moment than that of elemental Fe3. Taken together, the smaller value of damping, saturation moment, and linewidth for Co1.5Ti0.5FeAl films can significantly improve the efficiency of STT-switching and makes it a promising metallic ferromagnet to engineer low-loss spintronic devices.References: 1) B. Khodadadi, A. Rai, A. Sapkota, A. Srivastava, B. Nepal, Y. Lim, D.A. Smith, C. Mewes, S. 16 Budhathoki, A.J. Hauser, M. Gao, J.-F. Li, D.D. Viehland, Z. Jiang, J.J. Heremans, P. V Balachandran, T. Mewes, and S. Emori, Phys. Rev. Lett. 124, (2020). 2) M. Oogane, T. Wakitani, S. Yakata, R. Yilgin, Y. Ando, A. Sakuma, and T. Miyazaki, Jpn. J. Appl. Phys. 45, 3889 (2006) 3) J. M. D. Coey, Magnetism and magnetic materials. Cambridge, UK: Cambridge University Press, 2012.

Structural and magnetic properties of Co1.5Ti0.5FeAl Heusler alloy epitaxial thin films

Tailoring the electromagnetic properties of synthetic magnetic structures is advantageous for high frequency applications, such as engineering shielding materials in magnetic recording where control of properties such as permeability is essential. Design of suitable components requires the characterisation of materials in the gigahertz frequency range to determine the parameters necessary for simulations. We present a systematic study of the dependence of the ferromagnetic resonance (FMR) and spin wave properties of NixFe100-x alloy thin films with varied Ni composition and deposition conditions using a vector network analyser (VNA) and coplanar waveguide [1][2][3][4]. The quality of the FMR response and the effective permeability in single layer films is particularly affected by the NiFe crystal structure, most notably over the fcc-bcc boundary at x=40, Figure 1. The FMR was also improved by proper choice of seed layer and lowering deposition pressure. Increasing substrate temperature was observed to have an actively detrimental effect on ferromagnetic resonance. The effect on FMR of modulating the composition in NiFe thin films was also studied using repeated bilayer structures with a constant total thickness of the form n[NixFe100-x/NiyFe100-y], where n is the number of bilayers and determines the period of modulation. Compared to single layers, the compositionally modulated structures were generally seen to enhance the FMR signal and increase the frequency of resonance, Figure 2.References: [1] Y. Ding et al. J. Appl. Phys. 96, 2969 (2004) [2] C. Kittel, Phys Rev 73, 2 (1948) [3] Y.V. Khivintsev. J. Appl. Phys. 108, 023907 (2010) [4] Kalarickal et al. J. Appl. Phys. 99, 093909 (2006)

A Systematic Ferromagnetic Resonance Study of Deposition Conditions in NiFe Thin Films for Shielding Applications.

Two-magnon scattering (TMS) is a well-known extrinsic scattering process in ferromagnets, which is usually observed through its broadening effect on ferromagnetic resonance (FMR) lineshapes for in-plane magnetic field [1]. A lesser known effect is frequency pulling on FMR as a result of the hybridization between interacting magnon modes. The frequency pulling is not independent of the linewidth broadening effect and can be calculated if the two-magnon linewidth is known. We present broadband ferromagnetic resonance measurements for in-plane (IP) and perpendicular-to-plane (PP) directions of applied field in order to demonstrate the two-magnon frequency pulling effect in Fe0.7Ga0.3 thin films. We first show that a satisfactory fit of the resonance frequencies cannot be obtained when the magnetization is IP, and further, that the fit parameters which are obtained differ greatly from the fit parameters obtained for PP magnetization. We address these problems by first fitting the linewidths (where the two-magnon effect is very pronounced) to a combined two-magnon scattering and Gilbert damping model, and with those fit parameters calculate the corresponding two-magnon resonance line shifts (see figure). The fit to the two-magnon model yields a defect correlation length which we corroborate with structural characterization. We then show that this leads to a much better fit of the IP field-dependent dispersion. In addition, the effective demagnetizing field can be fixed to the value obtained for PP magnetization, and a good fit is still obtained. Thus the inconsistencies between IP and PP dispersions are eliminated by accounting for the frequency pulling effect of two-magnon scattering, and we emphasize the importance of this effect when using FMR to characterize static magnetic properties of thin films. This work was supported by SMART, a center funded by nCORE, a Semiconductor Research Corporation program sponsored by NIST.References: [1] R. D. McMichael and P. Krivosik, IEEE Trans. Mag. 40, 2 (2004).

Two-Magnon Frequency Pulling Effect in Ferromagnetic Resonance

Current magnetocaloric materials exhibit large adiabatic changes in temperature (ΔTad~10 °K) in applied magnetic fields (H) with the strength in several tens of kilo-oersted (kOe). To achieve an appreciable magnetocaloric effect (MCE) with moderate H, new magnetic materials with tailored magnetocaloric properties must be synthesized [1]. We explore the MCE in a layered system composed of a ferromagnet, NixCu1-x (x~0.7), with a relatively low Curie temperature (TC~300 °K), which is sandwiched by stronger ferromagnets, Ni80Fe20 and Co90Fe10, and exchange coupled to them across the interfaces. Switching of magnetization in the softer ferromagnetic surrounding, Ni80Fe20, exposed to H~0.1 kOe provides the isothermal magnetic entropy change (magnetocaloric potential) in the system because of magnetization redistribution in the spacer. In the limit, in which the NixCu1-x spacer can be magnetized at the interfaces up to its saturation magnetization of 4πms≈2.5 kG, the magnetocaloric potential is [2] Δs=ms2/C≈105 erg/cm3/°K (1) with C=0.4 °K being the Curie constant, whereas a separate NixCu1-x film with the same composition x exhibits such an MCE at H~100 kOe only. In real stacks with the spacer thickness ranging between 5 nm and 20 nm, we have found a significant (up to a factor of ~20) enhancement of MCE by comparison to a separate NixCu1-x film [3, 4]. However, the MCE obtained experimentally is still much lower than that expected in accordance with Eq. (1). To understand a reason for this inconsistency, we have performed simulations of the magnetization distributon across the spacer upon the basis of the phenomenological Landau theory for second-order phase transitions [4]. We find that the results of these simulations are compatible with the experimental data at realistic values of the interfacial exchange coupling constant.To further enhance the MCE in such systems, one should choose a material for the spacer, which would have a higher ms but still a low TC not far from room temperatures. This work was supported by the Russian Foundation for Basic Research (Grant No. 20-02-00356) and by the Ministry of Education and Science of Russian Federation (Grant No. 0035-2019-0022-C-01).References: [1] T. Mukherjee, et al., Magnetocaloric properties of Co/Cr superlattices, Phys. Rev. B, Vol. 79, 144406 (2009) [2] A. A. Fraerman, I. A. Shereshevskii, Magnetocaloric effect in ferromagnet/ paramagnet multilayer structures, JETP Lett., Vol. 101, p.618 (2015) [3] S.N. Vdovichev, et al., High magnetocaloric efficiency of a NiFe/NiCu/CoFe/MnIr multilayer in a small magnetic field, Phys. Rev. B, Vol. 98, 014428 (2018) [4] M.A. Kuznetsov, et al., Magnetocaloric effect in exchange-coupled strong/weak/ strong ferromagnet stacks, J. Appl. Phys., Vol. 127, 183904 (2020)

Effect of magnetic proximity on magnetocaloric properties of Ni80Fe20/NixCu1-x/Co90Fe10 stacks

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

First Order Reversal Curve (FORC) distributions of magnetic hysteresis is a well-recognized tool to extract information about magnetic interactions or to fingerprint magnetic materials [1, 2]. Their success is based on the extensive modeling that allows to correlate features of the distribution with characteristics of the transition. Recently, magnetocaloric materials are starting to be studied with Temperature-FORC (TFORC) distributions, extending the technique to the analysis of their thermal hysteresis [3,4]. However, the theory supporting the interpretation of the diagrams is still lacking, limiting TFORC to a fingerprinting technique so far. This work is a first approach to correlate the modeling of first-order phase transitions, using the Bean-Rodbell model combined with a phenomenological transformation mechanism, with the features observed in TFORC distributions. The different characteristics of the transformations e.g. transition temperatures, symmetry, temperature range, etc. can be correlated to distinct features of the distributions. Fig. 1 shows some illustrative examples of situations typically found in magnetocaloric materials (magnetization curves plotted in panel (a)): 1) symmetric cooling and heating transformations with the same temperature range produce circular distributions; 2) different temperature ranges for heating and cooling transformations give rise to ellipsoidal distributions; 3) asymmetry in the transformations makes the distribution triangular. This work systematically shows how the different model parameters affect the distributions and prove that the catalogue of figures is be able to explain the experimentally observed distributions. Work supported by AEI/FEDER-UE (grants MAT-2016-77265-R and 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] I. Mayergoyz, IEEE Transactions on Magnetics., Vol 22(5), p. 603-608 (1986). [2] C. R Pike, A. P. Roberts and K L. Verosub, Journal of Applied Physics., Vol. 85(9) p. 6660-6667 (1999). [3] V. Franco, T. Gottschall, K. P. Skokov et al., IEEE Magnetics Letters., Vol. 7 p. 6602904 (2016). [4] V. Franco, Journal of Applied Physics., Vol. 127 p. 133902 (2020).

Setting the Basis for the Interpretation of Temperature First Order Reversal Curve (TFORC) Distributions of Magnetocaloric Materials

Magnetic refrigeration based on magnetocaloric effect (MCE) has attracted great attention due to its environmentally friendly nature and potential to improve energy efficiency. In this work, we explore the rare earth chromites (RCrO3) to understand the effect of R-site ionic radii (R= Tb and Er) on their structural and magnetic properties. Bulk powders of TbCrO3 and ErCrO3 were prepared by citrate route and characterized by x-ray diffraction (XRD) and Raman spectroscopy that revealed that both samples crystallized in the orthorhombically distorted perovskite structure (Pbnm space group). The structure was found to be more distorted for ErCrO3 (rEr= 1.062Å) as compared to TbCrO3 (rTb=1.095Å). The dc magnetization measurements revealed that the temperature decreased from 156 K to 131 K with decreasing ionic radii. Interestingly, the maximum MCE was also found to reduce with decreasing ionic radii. The maximum entropy change for TbCrO3 was calculated to be 13.4 J /kg K as compared to 10.7 J/kg K for ErCrO3. The results indicate that the structural distortions induced by the decreasing ionic radii at R-site could be a promising strategy to tune the magnetic and MCE properties in rare earth chromites.References: Gschneidner Jr, K. A., and Vitalij K. Pecharsky. Annual Review of Materials Science 30, no. 1 (2000): 387-429.

The Effect of Ionic Radii of the Rare-earth Ion on the Magnetocaloric Effect of Rare-earth Chromites

In this work, we report on an investigation of the effect of the permeability of magnetic particles on the effective macroscopic behavior of magnetorheological elastomers (MREs). MREs are a class of soft active materials known for their tunable deformation [1], [2]. Dispersed with magnetically permeable particles, these polymer-based composites deform under the action of a magnetic field. Such deformational changes in the mechanical properties of these materials are often attributed to the magnetic interaction among the filler particles [3]. Generally, for a maximum possible magnetorheological (MR) effect, particles of high relative permeability µr are required [4]. In this study, we determine the effect of the µr of the particles on the macroscopic behavior of MREs. Using a finite element simulation method based on continuum field theory, the constitutive and geometric properties on the microscale are considered in order to predict the composite’s macroscopic behavior as a function of µr by means of a computational homogenization [5]. Additionally, a magnetic flux density B ≤ 0.5T was used, below the saturation magnetization of the filler particles, hence linear constitutive relationships can be utilized. The simulations were performed for isotropic microstructures for different particle permeabilities (µr =1, 100, 10000 and 50000) and volume fractions (φ= ~10, 20 and 27%). The effective magnetic and mechanical properties are calculated as shown in Fig. 1 and Fig. 2. Fig. 1 shows the magnetic flux density distribution for isotropic MRE while Fig.2 shows the average magnetostrictive strain parallel to the direction of the magnetic field as a function of average magnetic flux density for varying permeability of the particles. The results confirmed assumptions stated in the literature whereby higher permeability of the particles caused larger deformation of the MRE (Fig.2). However, for very large permeability values (µr = 10,000 and 50,000), only negligible change in effective MRE deformation is observed.References: [1] Y. Han, A. Mohla, and L. E. Faidley Int. J. Appl. Mech., vol. 7, no. 1, pp. 1–16, 2015. [2] K. A. Kalina et al., Smart Mater. Struct., vol. 26, no. 10, 2017. [3] B. Marvalova, “Modelling of Magnetosensitive Elastomers,” Model. Simul., 2008. [4] R. Ahamed and S. Choi, “A state of art on magneto-rheological materials and their potential applications,” 2018. [5] C. Spieler, M. Kästner, and V. Ulbricht, Acta Mech., vol. 224, no. 11, pp. 2453–2469, 2013.

Effect of Particle Permeability on Macroscopic Behavior of Magnetorheological Elastomers

The demand of flexibility in the existing rigid devices has introduced a new field of research ‘Flexible Spintronics’, which has enormous significance from application viewpoint [1-2]. Flexible device requires all the components of rigid spintronics in a flexible i.e. bendable, foldable, twistable and stretchable mode [3]. The ideal next generation device need to be power efficient as well as flexible. To meet such device requirement stress/strain has proven to be a potential candidate [4-5]. As magnetic thin films are prime component of every spintronic device hence the flexible counterpart of those are prerequisite. Cobalt/Platinum (Co/Pt) thin films with perpendicular magnetic anisotropy (PMA) are well studied as it has increased magnetic storage density, thermal stability etc. [6]. In our work we have prepared a PMA Co/Pt film on a flexible polyimide substrate by magnetron sputtering. Strain has been generated on the film by fixing it on semi-circular shaped molds of different radius. Here systematically we have measured the effect of both tensile and compressive stresses on the PMA, domain dynamics and relaxation mechanism by MOKE based microscopy. A minimal in-plane tensile strain has increased the coercivity of the film by 34% of its initial value, while a very small change of coercivity has been found under compressive strain (fig. 1) [7]. The size of ferromagnetic domains also decreases under tensile strain, while no change is observed under compressive stress (fig. 2). Due to stress induced anisotropy, Bloch wall formation energy has increased which hindered the domain wall motion and size of bubble domains reduced. Further, magnetization relaxation measured at sub-coercive field values yields a longer relaxation time in the tensile strained state.References: 1. P. Sheng et al., J. Semicond. 39, 011006 (2018) 2. Z. Bao et al., Adv. Mater. 28, 4177 (2016) 3. K. Harris et al., J. Mater. Sci. 51, 2771–2805 (2016) 4. A. Bukharaev et al., Phys. Uspekhi 61, 1175 (2018) 5. A. K. Biswas et al., Nano letters 17, 3478–3484 (2017) 6. B. Tudu et al., Vacuum 146, 329 (2017) 7. E. Pandey et al., Nano Express 1, 010037 (2020)

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