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A spin-thermoelectric generator is composed of a thin paramagnetic metal (PM) layer, ferrimagnetic insulator (FMI) and PM/FMI bilayer interface. To raise the spin thermoelectric voltage VSTE, studies for improving the characteristics of each part have been done.1-3 We took notice of the bismuth-substitution for yttrium to increase the spin pumping at the PM/FMI interface,2,4 and tested the Bi-substituted YIG films grown by liquid phase epitaxy (LPE). LPE Bi-substituted YIG films exhibit a large growth-induced magnetic anisotropy perpendicular to the film surface,5 and the in-plane M-H properties vary due to this anisotropy. Figure 1 shows the normalized M-H and VSTE-H curves concerning Y3-xBixFe5O12 films. It is confirmed that the VSTE-H curve agrees well with the M-H curve indicating VSTE strongly depends on the magnetic properties of FMI’s. Figure 2 shows the dependence of the spin Seebeck coefficient SSSE on the Bi-concentration x. SSSE increases very clearly with increasing x, and the SSSE value for x=1.3 is about 1.5 times that of x=0 in our measurements. It has been suggested that the mixing of the 6p orbitals of Bi ions with the O 2p orbitals increases the effective spin-orbit coupling of Fe3+ ions.6 We presume that this physical situation increases the damping constant αBi:YIG and, as a result, the spin mixing conductance gr at the PM/FMI interface becomes large. We have obtained the high VSTE value of 80μV (SSSE=3.2μV/K) with a generator comprising the Y2.35Bi0.65Fe5O12 film in the condition of ld=5mm, tPt=4nm and ΔT=25K. To obtain higher VSTE values, the issue of a heat-flow in the STE generator is important from its structural viewpoint. [The ref. paper #3 (3M. Imamura et al., Electr Eng Japan, Vol. 208, No. 3-4 (Wiley Online Library 2019)) can be referred by putting the paper title “Spin-thermoelectric voltage in longitudinal SSE elements incorporating LPE YIG films and polycrystalline YIG slabs with an ultrathin Pt layer” into Google’s search window.]References: 1K. Uchida, H. Adachi and T. Kikkawa, Proc. IEEE, Vol. 104, p.1946 (2016) 2M. Ishida, JJAP, Vol. 87, p.11 (2018) in Japanese 3M. Imamura, H. Asada and D. Tashima, Electr Eng Japan, Vol. 208, No. 3-4, p.10 (Wiley Online 2019) 4H. Asada, A. Kuwahara and N. Sakata, JAP, Vol. 117, p.17C724 (2015) 5P. Hansen, K. Witter and W. Tolksdorf, Phys. Rev. B, Vol. 27, p.6608 (1983) 6P. Hansen and J. P. Krumme, Thin Solid Films, Vol. 114, p.69 (1984)

MMM 2020

Enhancements of the Spin Seebeck Effect owing to the Bismuth-substitution in Thermoelectric Generators Comprising an LPE Bi-substituted YIG Film

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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poster

Bayesian optimization (BO) is a well-developed machine learning algorithm for black box optimization. In BO a predictive model, here a Gaussian process regression, is implemented to predict the black box function and the uncertainty of the predictive model is evaluated as predicted variance, then an acquisition function defined by the surrogate predictive model decides where to sample next. In this study we applied this technique to known ferroic materials such as ferromagnetic (Fe100−y Gay)1−xBx (x=0–21 & y=9–17) and ferromagnetic (Co0.5Fe0.5)1-xCx (x=0–16) to provide proof of concept of how BO can be used to optimize properties such as magnetostriction and ferromagnetic resonance (FMR) linewidth with fewer samples required than traditional experimental approaches.1,2 Additionally, we applied this technique to optimize thin films of ferromagnetic (Fe100−y Gay)1−xCx (x=1–26 and y=2–18) and ferroelectric (HfO2)1-xYx (x=0–15). For each of these systems, we applied BO through building a predictive model with the GPy library (https://sheffieldml.github.io/GPy/) and evaluating the next experiment to sample with the GPyOpt library (https://github.com/SheffieldML/GPyOpt), both in python.References: [1] J. Lou et al. Appl. Phys. Lett. 91, 182504 (2007). [2] J. Wang et al. Phys. Rev. Applied 12, 034011 (2019)

Application of Bayesian Optimization to Ferroic Materials Development

The BaTiO3 (BTO)/CoFe multiferroic material interface is an example of an interface which displays voltage-controlled magnetic anisotropy (VCMA), a valuable property in the operation of multiferroic tunnel junctions in an STT-MRAM device. Through first principles calculations, it is possible to predict trends in film magnetic anisotropy energy (MAE) and enumerate the individual physical mechanisms contributing to ferroelectric control of MAE in the CoFe film. For CoFe of up to 2 atomic layers on BTO, MAE can be modulated by ferroelectric switching through Fe-O orbital interations in BaO-terminated interfaces, and Ti-Fe orbital interactions in TiO2-terminated interfaces. A difference in interface termination produces a difference of MAE in CoFe films of up to 9 atomic layers. The inclusion of a 5d transition metal capping layer (Hf, Ta, W, Re, Os, Ir, Pt, or Au) on top of the CoFe layer exerts a significant effect on both MAE and the ferroelectric switching effect, in particular inducing a discernible ferroelectric switching control even in thicker CoFe films. This points to the additional, if counterintuitive, contribution of CoFe 3d top interface (or surface) states and their interactions with partially filled 5d orbitals of the capping layer atoms.References: A. P. Chen and Y. P. Feng, ACS Appl. Mater. Interfaces., Vol. 12, p25383-25389 (2020) A. P. Chen, W. Lin, J.-S. Chen, and Y. P. Feng, in preparation.

Free Layer Magnetic Anisotropy Control in the Multiferroic Tunnel Junction: a Computational Study on Materials Interfaces

The coupling between ferroelectric and magnetic orders is an enduring experimental challenge with fundamental importance to elucidate the nature of magnetoelectric (ME) effects in multiferroic materials. In this work, we have studied the response of magnetization to ferroelectric switching in thin-film hexagonal YbFeO3, an improper multiferroic which is a fruitful platform for investigating the ME coupling in single-phase materials. The bulk ME decoupling and potential domain-wall ME coupling were revealed using X-ray magnetic circular dichroism (XMCD) measurements with in-situ ferroelectric polarization switching. Our Landau theory analysis suggests that the bulk ME-coupled ferroelectric switching path has an higher energy barrier than that of the ME-decoupled path; this extra barrier energy is also too high to reduce by the magneto-static energy in the process of breaking single magnetic domains into multi-domains. In addition, the reduction of magnetization around the ferroelectric domain walls predicted by the Landau theory, may induce the domain-wall ME coupling in which he magnetization is correlated with the density of ferroelectric domain walls. These results provide important experimental evidences and theoretical insights to the rich possibilities of ME couplings in hexagonal ferrites.References: 1] J.F. Scott, Room-temperature multiferroic magnetoelectrics, NPG Asia Materials, 5 (2013) e72-e72. [2] S. Fusil, V. Garcia, A. Barthelemy, M. Bibes, Magnetoelectric Devices for Spintronics, Annual Review of Materials Research, 44 (2014) 91-116. [3] P. Mandal, M.J. Pitcher, J. Alaria, H. Niu, P. Borisov, P. Stamenov, J.B. Claridge, M.J. Rosseinsky, Designing switchable polarization and magnetization at room temperature in an oxide, Nature, 525 (2015) 363-366. [4] N.A. Spaldin, R. Ramesh, Advances in magnetoelectric multiferroics, Nat. Mater., 18 (2019) 203-212. [5] S.-W. Cheong, Topological domains/domain walls and broken symmetries in multiferroics, National Science Review, 6 (2015) 624-626. [6] S. Dong, J.M. Liu, S.W. Cheong, Z.F. Ren, Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology, Adv Phys, 64 (2015) 519-626. [7] M. Fiebig, T. Lottermoser, D. Meier, M. Trassin, The evolution of multiferroics, Nature Reviews Materials, 1 (2016). [8] H. Das, A.L. Wysocki, Y. Geng, W. Wu, C.J. Fennie, Bulk magnetoelectricity in the hexagonal manganites and ferrites, Nature communications, 5 (2014) 2998. [9] S. Artyukhin, K.T. Delaney, N.A. Spaldin, M. Mostovoy, Landau theory of topological defects in multiferroic hexagonal manganites, Nat. Mater., 13 (2014) 42-49. [10] W. Wang, J. Zhao, W. Wang, Z. Gai, N. Balke, M. Chi, H.N. Lee, W. Tian, L. Zhu, X. Cheng, D.J. Keavney, J. Yi, T.Z. Ward, P.C. Snijders, H.M. Christen, W. Wu, J. Shen, X. Xu, Room-temperature multiferroic hexagonal LuFeO3 films, Phys Rev Lett, 110 (2013) 237601. [11] X. Xu, W. Wang, Multiferroic hexagonal ferrites (h-RFeO3, R = Y, Dy-Lu): a brief experimental review, Modern Physics Letters B, 28 (2014) 1430008. [12] S. Cao, K. Sinha, X. Zhang, X. Zhang, X. Wang, Y. Yin, A.T. N'Diaye, J. Wang, D.J. Keavney, T.R. Paudel, Y. Liu, X. Cheng, E.Y. Tsymbal, P.A. Dowben, X. Xu, Electronic structure and direct observation of ferrimagnetism in multiferroic hexagonal YbFeO3, Physical Review B, 95 (2017). [13] W. Wang, J.A. Mundy, C.M. Brooks, J.A. Moyer, M.E. Holtz, D.A. Muller, D.G. Schlom, W. Wu, Visualizing weak ferromagnetic domains in multiferroic hexagonal ferrite thin film, Physical Review B, 95 (2017). [14] K. Sinha, H.H. Wang, X. Wang, L.Y. Zhou, Y.W. Yin, W.B. Wang, X.M. Cheng, D.J. Keavney, H.B. Cao, Y.H. Liu, X.F. Wu, X.S. Xu, Tuning the Neel Temperature of Hexagonal Ferrites by Structural Distortion, Phys Rev Lett, 121 (2018). [15] K. Du, B. Gao, Y.Z. Wang, X.H. Xu, J. Kim, R.W. Hu, F.T. Huang, S.W. Cheong, Vortex ferroelectric domains, large-loop weak ferromagnetic domains, and their decoupling in hexagonal (Lu, Sc)FeO3, Npj Quantum Mater, 3 (2018). [16] Y. Geng, N. Lee, Y.J. Choi, S.W. Cheong, W. Wu, Collective magnetism at multiferroic vortex domain walls, Nano Lett, 12 (2012) 6055-6059. [17] J.A. Moyer, R. Misra, J.A. Mundy, C.M. Brooks, J.T. Heron, D.A. Muller, D.G. Schlom, P. Schiffer, Intrinsic magnetic properties of hexagonal LuFeO3 and the effects of nonstoichiometry, APL Materials, 2 (2014) 012106. [18] M.E. Holtz, K. Shayovalov, J.A. Mundy, C.S. Chang, Z.W. Yan, E. Bourret, D.A. Muller, D. Meier, A. Cano, Topological Defects in Hexagonal Manganites: Inner Structure and Emergent Electrostatics, Nano Lett, 17 (2017) 5883-5890. [19] T. Matsumoto, R. Ishikawa, T. Tohei, H. Kimura, Q. Yao, H. Zhao, X. Wang, D. Chen, Z. Cheng, N. Shibata, Y. Ikuhara, Multivariate statistical characterization of charged and uncharged domain walls in multiferroic hexagonal YMnO3 single crystal visualized by a spherical aberration-corrected STEM, Nano Lett, 13 (2013) 4594-4601. [20] Y.K. Jeong, J.H. Lee, S.J. Ahn, S.W. Song, H.M. Jang, H. Choi, J.F. Scott, Structurally tailored hexagonal ferroelectricity and multiferroism in epitaxial YbFeO3 thin-film heterostructures, J Am Chem Soc, 134 (2012) 1450-1453. [21] Y.N. Geng, H. Das, A.L. Wysocki, X.Y. Wang, S.W. Cheong, M. Mostovoy, C.J. Fennie, W.D. Wu, Direct visualization of magnetoelectric domains, Nature materials, 13 (2014) 163-167.

Magnetoelectric coupling and decoupling in multiferroic hexagonal YbFeO3 thin films

Being studied mostly in nonpolar chiral structures, skyrmions in polar crystals are of great interest owing to their interplay with electric polarization, giving rise to fascinating multiferroic properties. Recently, skyrmion lattices have been reported in lacunar spinel GaV4S8 [1], where a complex phase diagram comprising paramagnetic, ferromagnetic, skyrmion, and cycloidal states has been demonstrated, and the spin-driven excess polarization was assigned in each magnetic phase with a total value of ~100 μC/m2 [2]. The existence of multiple ferroelectric phases in GaV4S8 indicates an intricate interplay between charge, spin, and lattice degrees of freedom, making their theoretical description extremely important. In our studies, we present the microscopic theory of spin-driven electric polarization P in GaV4S8 and GaMo4S8 [3,4]. To this end, we extend the theory of superexchange for magnetic interactions to deal with the change of electric polarization depending on the relative direction of spins in each bond. Based on realistic Hubbard-type models derived for the magnetically active molecular orbitals formed in the V4 and Mo4 tetrahedra, we show that (i) although a skyrmion layer in these materials is mainly formed by the in-plane magnetic interactions, the spin-excess polarization perpendicular to the rhombohedral z axis is given by the interlayer electron transfer and originates from strongly competing isotropic and antisymmetric contributions; (ii) P arises from the stacking misalignment of such layers in the perpendicular direction, which is inherent to the lacunar spinel structure; (iii) while the interorbital Hund’s coupling is small, it is one of the key parameter responsible for P in lacunar spinels; (iv) an importnat aspect of multiferroicity in GaMo4S8, which can also potentially host skyrmionic states, is strong exchange anisotropy; and (v) the direction of rhombohedral distortions leads to opposite signs of P in GaV4S8 and GaMo4S8.References: [1] I. Kézsmárki, S. Bordács, P. Milde et. al, Nat. Mater., Vol. 14, 1116 (2015). [2] E. Ruff, S. Widmann, P. Lunkenheimer et. al, Sci. Adv., Vol. 10, e1500916 (2015). [3] S. A. Nikolaev and I. V. Solovyev, Phys. Rev. B, Vol. 99, 100401(R) (2019). [4] S. A. Nikolaev and I. V. Solovyev, Phys. Rev. B 102 014414 (2020).

Microscopic theory of spin driven electric polarization in lacunar spinels GaV4S8 and GaMo4S8

Magnetoelectric materials with exceptional properties emerging from the coupling between the magnetic and electric ferroic orders bring about functionalities that can be exploited in fields such as sensors, energy harvesters, MERAM, antenna, and biomedical 1,2. Multi-phase ME composites that are composed of a ferromagnetic/piezoelectric junction can be fabricated in versatile connectivity configurations with a wide choice of materials and microstructure 3,4. The extrinsic ME effect in these composites occurs due to the generation of magnetostriction in the ferromagnetic phase and its transfer via the interface to the piezoelectric one, which induces a voltage. Cobalt ferrite as a ferrimagnet and barium titanate as a piezoelectric are promising candidates for the preparation of nanostructured ME materials due to their outstanding magnetic and electric properties, respectively 5. We report synthesis, characterization, and optimization of CoFe2O4-BaTiO3 composite using commercial nanoparticle precursors. The dry ball milling followed by high-temperature annealing of pressed powder was used as a low cost and highly reproducible synthesis method. We have investigated the structural, electric, magnetic, and magnetoelectrical properties of CFO-BTO composites prepared and electrically poled with two different types of BTO nanoparticles: 50 nm (cubic) and 200 nm (tetragonal) in conjunction with CFO nanoparticles of about 30 nm. The transformation of non-piezoelectric cubic BTO to piezoelectric tetragonal one after sintering at temperatures higher than Curie point was confirmed utilizing XRD. The maximum obtained ME coefficient (3.7 mV/Oe.cm for 50 nm BTO) is higher than the reported values for core-shell structures 6. The hypothesis is that the smaller BTO nanoparticles can form shell-like structures around CFO nanoparticles and enhance the interface and resistivity of the samples. This enhancement results in a more efficient poling process and an improved ME coupling. The ME analysis has confirmed the dependence of the coupling coefficient on the size and fraction of BTO nanoparticles in the composite.References: 1. Cheng, Y., Peng, B. and Hu, Z., Physics Letters A vol. 382 3018–3025 (2018). 2. Spaldin, N. A., Cheong, S.-W. & Ramesh, R, Physics Today vol. 63 38–43 (2010). 3. Andrew, J. S., Starr, J. D. & Budi, M. A. K, Scripta Materialia vol. 74 38–43 (2014). 4. Ortega, N., Kumar, A., Scott, J. F. & Katiyar, R. S, Journal of Physics: Condensed Matter vol. 27 504002 (2015). 5. Baji, A., Mai, Y.-W., Yimnirun, R. & Unruan, S, RSC Adv. vol. 4 55217–55223 (2014). 6. Duong, G. V., Groessinger, R. & Turtelli, R. S, IEEE Transactions on Magnetics vol. 42 3611–3613 (2006).

Materials characterization and multiferroic properties optimization of magnetoelectric composites based on sintered cobalt ferrite/barium titanate nanoparticles

Complex dielectric and magnetic properties of micro- and nano-size hexagonal ferrites have been studied. Two different measurement techniques as shown in Fig. 1 have been applied to characterize the samples in the broad frequency range from 1.7 GHz to 120 GHz. It was observed that the constitutive material properties, namely permittivity and permeability, as well as the ferromagnetic resonance frequency of the samples vary with the change in particle dimensions. Based on the results of these measurements, a model for calculating the ferromagnetic resonance frequency of ferrite powders has been derived, which takes into account the size and shape of the particles in the sample. Since the properties have been found to be size dependent, it is important that the measurement set-up is accurate enough to detect these differences. In the past, the powder samples have been diluted with conductive materials or epoxy to fabricate a solid sample for measurements. The procedure followed in this study does not use any such additive. Therefore, the properties of the samples can be determined precisely. The results presented in Fig. 2 reveal that the ferromagnetic resonance frequency of the ferrite samples varies with the particle size. Therefore, the material can be tuned to resonate at different frequencies by changing the size of the particles. The resonance observed in the case of nanoparticles is much sharper than that observed for bulk samples or samples containing micro-sized particles. Absolutely no resonance was observed in case of samples that did not contain the proper phase of barium hexaferrite. The techniques developed in this study can be used for non-destructive testing to check if the desired phase has been achieved or not. Accurate characterization would allow scientists to utilize nanomaterials to their full potential and achieve high performance in diverse applications.

Study of Ferromagnetic Resonance of Micro and Nano Size Barium Ferrite Powders

Voltage control of the structure, magnetic and electronic properties of materials enables the realization of new types of nonvolatile magnetoelectric memory devices. Here, we investigate the effect of ionic liquid gating on the magnetic properties of self-assembled heterostructure films consisting of nanoscale CoyFe3-yO4 (CFO) spinel pillars embedded in a SrCo1-xFexO3-δ (SCFO) perovskite (P) or brownmillerite (BM) matrix, over a range of compositions x and y. These self-assembled nanocomposites are grown by pulsed laser deposition on SrTiO3 substrates using SrCoO3-δ-SrFeO3-δ, SrCoO3-δ-Fe3O4, or SrFeO3-δ-Co3O4 pairs of targets. We first describe the growth kinetics of these nanocomposites, focusing on how the oxygen pressure affects the distribution of Co and Fe between the two phases and the formation of P vs. BM structure for the matrix. Unusually, at high oxygen pressures, the two-phase structure can grow from the codeposition of SrCoO3-δ and SrFeO3-δ, attributed to depletion of the Sr in the film. The pillar CFO magnetism depends on y, e.g. ferrimagnetic with room temperature saturation magnetization Ms ~300 kA/m for y=1 and paramagnetic for y=0. The matrix SCFO with the BM phase has antiferromagnetic ordering irrespective of x, while the magnetism of the P phase depends strongly on x and can exhibit a room temperature Ms ~100 kA/m for x=0.5 but almost no moment for x=0 and x=1 [1]. With the gating voltage of -3V/+3V, the lattice parameter of matrix SCFO changes ±3% and induces strain transfer around ±1% to the pillar phase (Fig. 1). In particular, for x=0.5 and y=0 (Fig. 2), the negative gating inserts oxygens into the BM phase and changes it into a P phase showing ferromagnetism. Our study clarifies the manipulation of the magnetism of composite materials through an electrochemical process, expanding the applications of magnetoelectric coupling.References: [1] S. Ning, Q. Zhang and C. A. Ross, ACS Nano, https://dx.doi.org/10.1021/acsnano.0c03750 (2020)

Controlling Magnetic Properties of Epitaxial Nanocomposite Thin Films Through Ionic Liquid Gating

We report large field-like torques with non-negligible damping-like torques in sputtered, amorphous Ru2Sn3 thin films. We confirm the amorphous structure of the films with high resolution tunneling electron microscopy and the 2:3 composition with Rutherford backscattering techniques. Through the second harmonic Hall measurement we can extract and characterize the damping-like (DL) and field-like (FL) SOTs originating in the Ru2Sn3 films. We find room temperature a DL torque efficiency of 0.14 ± 0.008 and 0.07 ± 0.012 and a FL torque efficiency of -0.03 ± 0.006 and -0.20 ± 0.009 for 4 and 10 nm Ru2Sn3 films respectively. By analyzing the resistivity dependence of the spin torque efficiencies, we extracted the contributions from the intrinsic and extrinsic spin Hall effects. The FL torques show dominant contributions from the intrinsic spin Hall effect with intrinsic spin conductivity up to -240 ± 19 (Ωcm)-1 while the DL torques show dominate contributions from the extrinsic spin hall effects with sum of the skew scattering and side jump up to -175 ± 19 μΩcm. We performed macro-spin calculations of the LLGS equation to simulate switching a perpendicular magnetic layer including both the DL and FL torques generated from our Ru2Sn3 SOT channel. We find the inclusion of FL toques three times greater than the DL can reduce the critical current required for switching and the switching time by almost 50% compared to the DL torque only case.

Large field like torque in amorphous Ru2Sn3 originated from intrinsic spin Hall effect

Spin-orbit coupling (SOC) and symmetry breaking, which may be due to the interface between a thin film of a ferromagnet and a heavy metals aid to the development of Dzyaloshinskii-Moriya interaction (DMI) 1,2, favoring the formation of a chiral arrangement of spin configurations. Electrical detection and manipulation are the key requirements for any potential exploitation of these materials and that demands proper understanding of the transport behavior of charge carriers in these materials. Different feature such as topological Hall effect3,4, narrow band noise5 unusual magneto resistance6 in electronic transport measurements are observed owing to interactions between conduction electrons and different magnetic states and their dynamics, revealing intriguing underlying physics. In this work, we have performed electronic transport (Hall, magnetoresistance, noise fluctuation spectroscopy) measurements for CoFe/Pt-based thin film sample. A characteristic peak in Hall resistance is reproducibly observed during up and down sweep of the magnetic field as shown in Fig.1. Temperature dependent Hall effect measurements reveal that such peak shifts towards higher value with decreasing temperature as shown in the inset of Fig.1. The dynamics of charge carriers as measured using noise fluctuation spectroscopy technique at varying field as shown in Fig.2 shows systematic and reproducible variations across Hpeak. Particularly, electronic fluctuations are found to increase at around these fields. The results demonstrate an interesting correlation between the interface induced magnetic states and the carrier dynamics.References: 1 I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). 2 T. Moriya, Phys. Rev. 120, 91 (1960). 3 A. Neubauer, et al., Phys. Rev. Lett. 102, (2009). 4 D. Liang, et al., Nat. Commun. 6, 8217 (2015). 5 T. Sato, et al., Phys. Rev. B 100, (2019). 6 K. Meng, et al., Sci. Rep. 6, 20522 (2016).

Unusual Electronic Transport Properties of Sputter-deposited Co25Fe75 /Pt Based Heterostructured Thin Film Sample

We measured the Hall effect (HE) in a ferromagnetic nanomagnet with a strong perpendicular magnetic anisotropy (PMA), in which the local magnetic moments are very stable and well- aligned along the easy axis of the nanomagnet. The adopted mechanisms of HE predict linear plus a constant dependence on the external field originating from the ordinary and anomalous Hall effects, respectively. Our measurement revealed an extra non- linear contribution indicating an additional contribution to HE, which was suggested to be the Inverse Spin Hall effect (ISHE). The ISHE describes the fact that an electrical current is created perpendicularly to the flow of the spin- polarized current. The ISHE requires existence of the spin-polarized electrons. In a ferromagnetic metal the electron gas is spin- polarized even in equilibrium and any electrical current in a ferromagnetic metal is spin- polarized. As a result, any electrical current in a ferromagnetic metal must always experience the ISHE and there must be a flow of the Hall current perpendicularly to the bias current. There are several methods to change the number of spin- polarized electron in a ferromagnetic metal and therefore the magnitude of the ISHE. E.g. the spin polarization can arise due to the influence of an external magnetic field, the mechanism considered by Landau and Lifshitz a long time ago[1]. The Hall angle αHE can be presented as αHE = αOHE H+ αAHE + αISHE PS(H) where the non-linear dependence of spin polarization PS on magnetic field is calculated as[2] PS(H)=(PS,0+H/HS)/(1+H/HS) where PS,0 is the spin polarization at H=0. HS is the scaling magnetic field. Figure 1 shows that the fit of the experimental data with the above relation is excellent proving the importance of the ISHE contribution to the HE in a ferromagnetic metal.References: [1] L. D. Landau and E. M. Lifshitz, Phys. Z. Sowjetunion. Vol. 8, p.153 (1935). [2] V. Zayets, J. Magn. Magn. Mater. Vol. 356, p. 52 (2014).

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Enhancements of the Spin Seebeck Effect owing to the Bismuth-substitution in Thermoelectric Generators Comprising an LPE Bi-substituted YIG Film

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