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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.

MMM 2020

Effect of Particle Permeability on Macroscopic Behavior of Magnetorheological Elastomers

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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technical paper

Insulator / 3d ferromagnet / 5d metal trilayers with broken inversion symmetry along the film normal direction is of great interest, since the broken symmetry is known to contribute to the perpendicular magnetic anisotropy (PMA) and the conversion of in-plane charge current to perpendicular spin current through the Rashba spin-orbit coupling [1, 2]. Here, we report on the PMA and magnetization dynamics of the MgO/Fe/Au trilayer with the Fe layer thickness from 0.4 nm to 1.2 nm, and compare the results with the Au/Fe/Au system with a symmetric structure along the film normal. These trilayers were grown on MgO(001) substrate by molecular beam epitaxy method. The PMA and dynamics were investigated by the time-resolved magneto-optical Kerr effect (TRMOKE) measurements. Figure 1 shows Fe thickness dependence of (a) effective anisotropy field Hkeff, (b) g-factor, (c) anisotropy distribution ΔHkeff, and (d) damping constant α of MgO/Fe/Au and Au/Fe/Au trilayers. Both MgO/Fe/Au and Au/Fe/Au showed an increase of Hkeff with decreasing the Fe thickness, and MgO/Fe/Au was confirmed to exhibit slightly larger Hkeff than Au/Fe/Au due to the Rashba effect. The g-factor of both trilayers decreased from the bulk value with decreasing the Fe thickness. ΔHkeff increased at Fe thickness of 0.8 nm for both trilayers which is considered to be due to the relaxation of lattice mismatch around the Fe thickness of 1 nm. The damping constant α of both trilayers increased with decreasing the Fe thickness from 0.8 nm to 0.4 nm due to the effect of spin pumping. The reduction of α at Fe thickness of 0.8 nm is explained by the effect of two-magnon scattering which is enhanced by the increase of ΔHkeff. Interestingly, MgO/Fe/Au trilayers show larger damping constant than Au/Fe/Au with the same Fe thickness, which may reflect the Rashba spin-orbit coupling and/or the variation in the density of states at the Fermi level.References: [1] S. E. Barnes et. al., Sci. Rep. 4, 4105 (2014). [2] I. M. Miron et al., Nat. Mater. 9, 230 (2010).

Perpendicular anisotropy and damping of MgO/Fe/Au trilayers with broken inversion symmetry

Recently, antiferromagnetic spintronics have attracted great attention, with extensive research devoted to spin transport between ferromagnetic (FM) and antiferromagnetic (AFM) materials in FM/AFM heterostructures [1-6]. In order to enable a deeper understanding of the mechanisms behind this effect, it would be invaluable to perform time resolved studies of GHz spin dynamics in systems with antiferromagnetic order with sensitivity to each absorber site individually, however, to date experimental techniques that offer these capabilities are lacking. Here, we present the first experimental observation of dynamic X-ray magnetic linear dichroism (XMLD) from GHz spin precessions driven by ferromagnetic resonance (FMR). We explore the capabilities of this new technique in two model systems, a ferromagnetic metal, i.e., Ni80Fe20 (Py), and a ferrimagnetic insulator, i.e., Ni0.65Zn0.35Al0.8Fe1.2O4 (NZAFO). Both systems yield dynamic XMLD signals consistent with our models. Under experimental geometries with oblique x-ray polarization (i.e., when the angle between static magnetization and x-ray polarization is near 45°) the dynamic XMLD response occurs primarily at the fundamental frequency of the driving RF excitation (see Fig. 1). This effect is well suited for in-plane magnetic anisotropy studies conducted in normal incidence geometry. For studies that require complementary geometries (e.g., vertical or horizontal polarization), the dynamic signal can be extracted from the 2nd harmonic response. This also works for grazing incidence measurements that are sensitive to in- vs. out-of-plane magnetic anisotropy. The presented results are a breakthrough achievement in detecting dynamic manifestations of the XMLD effect at technologically relevant, GHz frequencies. By utilizing the sensitivity of XMLD to the spin axis rather than the spin direction, one can expand conventional x-ray detected FMR towards the direct dynamic study of antiferromagnetic order.References: [1] C. Hahn et al., EPL 108, 57005 (2014) [2] H. Wang et al., Phys. Rev. Lett. 113, 097202 (2014) [3] W. Lin et al., Phys. Rev. Lett. 116, 186601 (2016) [4] Z. Qiu et al., Nat. Commun. 7, 12670 (2016) [5] Q. Li et al., Nat. Commun. 10, 5265 (2019) [6] M. Dabrowski et al., Phys. Rev. Lett. 124, 217201 (2020)

Experimental realization of linearly polarized x-ray detected ferromagnetic resonance

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.

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Effect of Particle Permeability on Macroscopic Behavior of Magnetorheological Elastomers

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Perpendicular anisotropy and damping of MgO/Fe/Au trilayers with broken inversion symmetry

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