Journal articles: 'Modeling Magnetic Anisotropy'

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Ben, Tong, Yuqi Kong, Long Chen, Fangyuan Chen, and Xian Zhang. "Magnetostriction property modeling of silicon steel considering stress-induced and magnetocrystalline anisotropy." AIP Advances 13, no. 2 (February 1, 2023): 025031. http://dx.doi.org/10.1063/9.0000421.

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This paper proposed an improved magnetostriction model for correlation of anisotropy in non-oriented (NO) silicon steel based on the free energy, which considers stress-induced and magnetocrystalline anisotropy. Firstly, the free energy model, which includes stress-induced anisotropy energy, the energy of magnetic field, and the anisotropic energy of magnetic crystals, is incorporated into the anhysteretic magnetization parameter M an. Then, to obtain the magnetic field and proposed model parameters related to stress-induced and magnetocrystalline anisotropy, the magnetostrictive strain loops at different magnetization directions of NO silicon steel are measured. Finally, based on the parameters obtained from experimental data of the proposed model, magnetostrictive strain loops under varying magnetization directions are simulated. This improved magnetostriction model can be applied to the calculation of the vector magnetostriction of the motor core.

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Yamaguchi, Shinichi, Akihiro Daikoku, and Norio Takahashi. "Cogging torque calculation considering magnetic anisotropy for permanent magnet synchronous motors." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 23, no. 3 (September 1, 2004): 639–46. http://dx.doi.org/10.1108/03321640410540548.

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This paper describes the cogging torque of the permanent magnet synchronous (PM) motors due to the magnetic anisotropy of motor core. The cogging torque due to the magnetic anisotropy is calculated by the finite element method using two kinds of modeling methods: one is the 2D magnetization property method, and the other is the conventional method. As a result, the PM motors with parallel laminated core show different cogging torque waveform from the PM motors with the rotational laminated core due to the influence of the magnetic anisotropy. The amplitudes of the cogging torque are different depending on the modeling methods in the region of high flux density.

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Nowicki, Michał, Roman Szewczyk, and Paweł Nowak. "Experimental Verification of Isotropic and Anisotropic Anhysteretic Magnetization Models." Materials 12, no. 9 (May 11, 2019): 1549. http://dx.doi.org/10.3390/ma12091549.

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The anhysteretic magnetization curve is the key element of modeling magnetic hysteresis loops. Despite the fact that it is intensively exploited, known models of anhysteretic curve have not been verified experimentally. This paper presents the validation of four anhysteretic curve models considering four different materials, including isotropic, such as Mn-Zn soft ferrite, as well as anisotropic amorphous and nanocrystalline alloys. The presented results indicate that only the model that considers anisotropic energy is valid for a wide set of modern magnetic materials. The most suitable of the verified models is the anisotropic extension function-based model, which considers uniaxial anisotropy.

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Akin, Meriem, Autumn Pratt, Jennifer Blackburn, and Andreas Dietzel. "Paper-Based Magneto-Resistive Sensor: Modeling, Fabrication, Characterization, and Application." Sensors 18, no. 12 (December 11, 2018): 4392. http://dx.doi.org/10.3390/s18124392.

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In this work, we developed and fabricated a paper-based anisotropic magneto-resistive sensor using a sputtered permalloy (Ni 81 Fe 19 ) thin film. To interpret the characteristics of the sensor, we proposed a computational model to capture the influence of the stochastic fiber network of the paper surface and to explain the physics behind the empirically observed difference in paper-based anisotropic magneto-resistance (AMR). Using the model, we verified two main empirical observations: (1) The stochastic fiber network of the paper substrate induces a shift of 45 ∘ in the AMR response of the paper-based Ni 81 Fe 19 thin film compared to a Ni 81 Fe 19 film on a smooth surface as long as the fibrous topography has not become buried. (2) The ratio of magnitudes of AMR peaks at different anisotropy angles and the inverted AMR peak at the 90 ∘ -anisotropy angle are explained through the superposition of the responses of Ni 81 Fe 19 inheriting the fibrous topography and smoother Ni 81 Fe 19 on buried fibrous topographies. As for the sensitivity and reproducibility of the sensor signal, we obtained a maximum AMR peak of 0 . 4 % , min-max sensitivity range of [ 0 . 17 , 0 . 26 ] % , average asymmetry of peak location of 2 . 7 kA m within two consecutive magnetic loading cycles, and a deviation of 250–850 A m of peak location across several anisotropy angles at a base resistance of ∼100 Ω . Last, we demonstrated the usability of the sensor in two educational application examples: a textbook clicker and interactive braille flashcards.

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Ježek, J., and F. Hrouda. "Software for modeling the magnetic anisotropy of strained rocks." Computers & Geosciences 28, no. 9 (November 2002): 1061–68. http://dx.doi.org/10.1016/s0098-3004(02)00023-7.

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Rogovoy, Anatoli A., and Olga S. Stolbova. "Microstructural Modeling of the Magnetization Process in Ni2MnGa Alloy Polytwin Crystals." Magnetochemistry 8, no. 8 (July 25, 2022): 78. http://dx.doi.org/10.3390/magnetochemistry8080078.

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In this article, based on the theory of micromagnetism, a microstructural model of the behavior of the Heusler alloy in a magnetic field is constructed. The dynamics of the magnetic process is described by the Landau–Lifshitz–Gilbert equation. Using the Galerkin procedure, variational equations corresponding to the differential relations of the magnetic problem are written out. For numerical simulation, we consider the problem of magnetization of a Ni2MnGa alloy polytwin crystals, each grain of which is a twinned variant of martensite and has pronounced anisotropic properties. First, we consider the process of magnetization of a single grain, when an external magnetic field is applied at different angles to the anisotropy axes of twinned variants, and then, based on the results obtained, we plot magnetization curves for various (isotropic and texture-oriented) polycrystalline samples. This paper does not consider the process of detwinning, which can occur in such a material during the magnetization at a sufficiently high external field strength.

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Xiao, Xiao, Fabian Müller, Martin Marco Nell, and Kay Hameyer. "Modeling anisotropic magnetic hysteresis properties with vector stop model by using finite element method." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 41, no. 2 (December 2, 2021): 752–63. http://dx.doi.org/10.1108/compel-06-2021-0213.

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Purpose This paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field problems in electrical machines. The vector stop hysteresis model is valid for representing the anisotropic magnetization characteristics of electrical steel sheets. Comparisons of the simulated results with measurements show that the model is well appropriate for the simulation of electrical machines with alternating, rotating and harmonic magnetic flux densities. Design/methodology/approach The anisotropy of the permeability of an electrical steel sheet can be represented by integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model. The parameters of the vector stop hysteresis model were identified by minimizing the errors between the simulated results and measurements. In this paper, a damped Newton method is applied to solve the nonlinear problem, which ensures a robust convergence of the finite elements simulation with vector stop hysteresis model. Findings Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows the importance to consider the anisotropic and saturation behavior of the material. Comparing the calculated and measured data corroborates the hypothesis that the presented energy-based vector stop hysteresis model is able to represent these magnetic properties appropriately. To ensure a unique way of hysteresis loops during finite elements simulation, the memory of the vector stop hysteresis model from last time step is kept unchanged during the Newton iterations. Originality/value The results of this work demonstrates that the presented vector hysteresis stop model allows simulation of vector hysteresis effects of electrical steel sheets in electrical machines with a limited amount of measurements. The essential properties of the electrical steel sheets, such as phase shifts, the anisotropy of magnetizations and the magnetization characteristics by alternating, rotating, harmonic magnetization types, can be accurately represented.

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Liu, Yikuo, Anton Ziolkowski, and Paul L. Stoffa. "Time evolution of the electric field using the rapid expansion method with pseudospectral evaluation of spatial derivatives — Part 2: Inclusion of anisotropy and the earth-air interface." GEOPHYSICS 84, no. 5 (September 1, 2019): E323—E335. http://dx.doi.org/10.1190/geo2018-0143.1.

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We have evaluated an extension of the 3D 3C rapid-expansion method for time-domain electromagnetic modeling with pseudospectral evaluation of spatial derivatives that includes anisotropic conductivity and the earth-air interface. We found that transverse isotropic anisotropy can be included in the modeling with the manipulation of the conductivity tensor. We model the response of the earth-air interface by using the upward continuation of the time derivative of the magnetic induction. All three electric field components are collocated with the electric conductivities and are modeled independently and simultaneously with spectral accuracy in space and time. Numerical tests against the analytical solution for a half-space and spectral methods for 1D anisotropic layered earth models demonstrate the excellent accuracy of this approach.

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Zhao, Yang, and H. Neal Bertram. "Micromagnetic modeling of magnetic anisotropy in textured thin‐film media." Journal of Applied Physics 77, no. 12 (June 15, 1995): 6411–15. http://dx.doi.org/10.1063/1.359114.

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10

Zhang, Yue, Weisheng Zhao, Yahya Lakys, Jacques-Olivier Klein, Joo-Von Kim, Dafiné Ravelosona, and Claude Chappert. "Compact Modeling of Perpendicular-Anisotropy CoFeB/MgO Magnetic Tunnel Junctions." IEEE Transactions on Electron Devices 59, no. 3 (March 2012): 819–26. http://dx.doi.org/10.1109/ted.2011.2178416.

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Bottauscio, Oriano, Fausto Fiorillo, Cinzia Beatrice, Ambra Caprile, and Alessandro Magni. "Modeling High-Frequency Magnetic Losses in Transverse Anisotropy Amorphous Ribbons." IEEE Transactions on Magnetics 51, no. 3 (March 2015): 1–4. http://dx.doi.org/10.1109/tmag.2014.2361534.

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Lee, Hochul, Albert Lee, Shaodi Wang, Farbod Ebrahimi, Puneet Gupta, Pedram Khalili Amiri, and Kang L. Wang. "Analysis and Compact Modeling of Magnetic Tunnel Junctions Utilizing Voltage-Controlled Magnetic Anisotropy." IEEE Transactions on Magnetics 54, no. 4 (April 2018): 1–9. http://dx.doi.org/10.1109/tmag.2017.2788010.

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Smolin, Sergei V. "Modeling of Anisotropy Dynamics of the Proton Pitch Angle Distribution in the Earth’s Magnetosphere." Journal of Siberian Federal University. Mathematics & Physics 14, no. 5 (October 2021): 632–37. http://dx.doi.org/10.17516/1997-1397-2021-14-5-632-637.

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Last years the attention to research of anisotropy of the charged particle pitch angle distribution has considerably increased. Therefore for research of anisotropy dynamics of the proton pitch angle distribution is used the two-dimensional Phenomenological Model of the Ring Current (PheMRC 2-D), which includes the radial and pitch angle diffusions with consideration of losses due to wave-particle interactions. Experimental data are collected on the Polar/MICS satellite during the magnetic storm on October 21–22, 1999. Solving the non-stationary two-dimensional equation of pitch angle and radial diffusions, numerically was determined the proton pitch angle distribution anisotropy index (or parameter of the proton pitch angle distribution) for the pitch angle of 90 degrees during the magnetic storm, when the geomagnetic activity Kp-index changed from 2 in the beginning of a storm up to 7+ in the end of a storm. Dependence of the perpendicular proton pitch angle distribution anisotropy index with energy E = 90 keV during the different moments of time from the McIlwain parameter L (2.26 < L < 6.6) is received. It is certain at a quantitative level for the magnetic storm on October 21–22, 1999, when and where on the nightside of the Earth’s magnetosphere (MLT = 2300) to increase in the geomagnetic activity Kp-index there is a transition from normal (pancake) proton pitch angle distributions to butterfly proton pitch angle distributions. That has allowed to determine unequivocally and precisely the anisotropy dynamics of the proton pitch angle distribution in the given concrete case. It is shown, that with increase of the geomagnetic activity Kp-index the boundary of isotropic proton pitch angle distribution comes nearer to the Earth, reaching L ≈ 3.6 at Kp = 7+

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Fuliang, Xiao, and Feng Xueshang. "Modeling Density and Anisotropy of Energetic Electrons Along Magnetic Field Lines." Plasma Science and Technology 8, no. 3 (May 2006): 279–84. http://dx.doi.org/10.1088/1009-0630/8/3/07.

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Ježek, J., and F. Hrouda. "A technique for numerical modeling of magnetic anisotropy to strain relationship." Physics and Chemistry of the Earth, Parts A/B/C 27, no. 25-31 (January 2002): 1247–52. http://dx.doi.org/10.1016/s1474-7065(02)00118-3.

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Carcione, José M., and Michael A. Schoenberg. "3-D ground‐penetrating radar simulation and plane‐wave theory in anisotropic media." GEOPHYSICS 65, no. 5 (September 2000): 1527–41. http://dx.doi.org/10.1190/1.1444841.

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Modeling ground‐penetrating radar (GPR) waves requires simulation of the 3-D full wavefield and the correct description of the electromagnetic (EM) properties. Magnetic and dielectric relaxations are described by relaxation functions associated with each principal component of the respective tensorial property. Anisotropy is modeled up to orthorhombic symmetry, i.e., the principal coordinate systems of the three EM material tensors coincide, and each property is described by three different principal components. The algorithm uses the pseudospectral method for computing the spatial derivatives and a second‐order finite difference in time. A complete plane‐wave analysis, including energy balance, gives the expressions of measurable quantities such as the EM-wave velocity and the quality factor as a function of frequency and propagation direction. The algorithm reproduces the wavefront shape and attenuation predicted by the plane‐wave analysis. In addition, the results are in excellent agreement with an analytical 3-D transient solution. The modeling is applied to evaluation of the EM response of two pipes buried in an anisotropic sand overlying a clay layer. The results demonstrate that anisotropy and loss mechanisms cause significant amplitude and phase distortions.

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Han, Bo, Yuguo Li, and Gang Li. "3D forward modeling of magnetotelluric fields in general anisotropic media and its numerical implementation in Julia." GEOPHYSICS 83, no. 4 (July 1, 2018): F29—F40. http://dx.doi.org/10.1190/geo2017-0515.1.

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We have developed a finite volume (FV) algorithm for magnetotelluric (MT) forward modeling in 3D conductivity structures with general anisotropy. The electric and magnetic fields are discretized on a conventional staggered grid, which cannot directly address the full-tensor conductivity. To overcome this difficulty, an interpolation scheme is used to average different components of the electric field to the same position. We formulate the algorithm in pure matrix form and implement it in a new language, Julia, making the programming process highly efficient and leading to a code with excellent readability, maintainability, and extendability. The validity of the FV Julia code is demonstrated using a layered 1D anisotropic model. For this model, the FV code provides accurate results, and the computational cost is reasonable. Being preconditioned with the electromagnetic potential ([Formula: see text]) system, the iterative solvers including quasi-minimal residual and biconjugate gradient stabilized exhibit a good convergence rate for a wide range of periods. The direct solvers MUMPS and PARDISO are highly efficient for small model sizes. For a relatively large model size with 2.18 millions unknowns, the linear system of one period can be solved by MUMPS within 360 s with multiple threads involved in the computation, and the memory usage is only 11.6 GB in the “out-of-core” mode. We further calculated MT responses of a 3D model with dipping and horizontal anisotropy, respectively. The results suggest that the electrical anisotropy can have significant influence on the MT response.

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Chekanova, L. A., E. A. Denisova, Roman N. Yaroslavtsev, S. V. Komogortsev, D. A. Velikanov, A. M. Zhizhaev, and R. S. Iskhakov. "Micro Grid Frame of Electroless Deposited Co-P Magnetic Tubes." Solid State Phenomena 233-234 (July 2015): 64–67. http://dx.doi.org/10.4028/www.scientific.net/ssp.233-234.64.

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The morphology and magnetic characterization results of electroless deposited CoP coating on the copper microgrid with the mesh size of 50 microns are presented and discussed. The deposited coating is found to be well uniform by the thickness. Magnetic anisotropy in the plane of the grid has been studied by the hysteresis loops and the FMR spectra and discussed with the modeling of the grid as the frame grid system of magnetic tubes.

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Fahmy, Mohamed Abdelsabour. "A Nonlinear Fractional BEM Model for Magneto-Thermo-Visco-Elastic Ultrasound Waves in Temperature-Dependent FGA Rotating Granular Plates." Fractal and Fractional 7, no. 3 (February 24, 2023): 214. http://dx.doi.org/10.3390/fractalfract7030214.

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The primary goal of this study is to create a nonlinear fractional boundary element method (BEM) model for magneto-thermo-visco-elastic ultrasound wave problems in temperature-dependent functionally graded anisotropic (FGA) rotating granular plates in a constant primary magnetic field. Classical analytical methods are frequently insufficient to solve the governing equation system of such problems due to nonlinearity, fractional order heat conduction, and strong anisotropy of mechanical properties. To address this challenge, a BEM-based coupling scheme that is both reliable and efficient was proposed, with the Cartesian transformation method (CTM) used to compute domain integrals and the generalized modified shift-splitting (GMSS) method was used to solve the BEM-derived linear systems. The calculation results are graphed to show the effects of temperature dependence, anisotropy, graded parameter, and fractional parameter on nonlinear thermal stress in the investigated plates. The numerical results validate the consistency and effectiveness of the developed modeling methodology.

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Зверев, В. В., Е. Ж. Байкенов, and И. М. Изможеров. "Динамические перестройки трехмерной топологической структуры движущейся доменной границы в магнитной пленке при наличии случайных возмущений." Физика твердого тела 61, no. 11 (2019): 2070. http://dx.doi.org/10.21883/ftt.2019.11.48410.226.

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Dynamic processes in a domain wall (DW) moving under a constant magnetic field in a soft-magnetic uniaxial film with in-plane anisotropy were studied using three-dimensional micromagnetic modeling. It was shown that the nature of the dynamics of topological transformations occurring in the DW can vary significantly due to disturbing factors depending randomly on coordinates or on time (spatially inhomogeneous anisotropy; magnetic field fluctuating in time). At the same time, typical configurations of the magnetization field in the vicinity of intrafilm vortex cores and singular (Bloch) points retain their appearance. The dependences of the energies and displacements of the DWs on time are found for a wide range of film thicknesses, temperatures, and magnetic fields. When analyzing the magnetization configurations, visualization methods based on the calculation of two types of topological charges were used.

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Ovcharenko, Sergei, Mikhail Gaponov, Alexey Klimov, Nicolas Tiercelin, Philippe Pernod, Elena Mishina, Alexander Sigov, and Vladimir Preobrazhensky. "Ultrafast manipulation of magnetic anisotropy in a uniaxial intermetallic heterostructure TbCo₂/FeCo." Journal of Physics D: Applied Physics 55, no. 17 (February 1, 2022): 175001. http://dx.doi.org/10.1088/1361-6463/ac4a9a.

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Abstract We study experimentally and theoretically the dynamics of spin relaxation motion excited by a femtosecond pulse in the TbCo2/FeCo multilayer structures with different ratios of TbCo2 to FeCo thicknesses r d = d T b C o 2 / d F e C o . The main attribute of the structure is in-plane magnetic anisotropy that is artificially induced during sputtering under a DC magnetic field. The optical pump-probe method revealed strongly damped high-frequency oscillations of the dynamical Kerr rotation angle, followed by its slow relaxation to the initial state. Modeling experimental results using the Landau–Lifshitz-Gilbert (LLG) equation showed that the observed entire dynamics is due to destruction and restoration of magnetic anisotropy rather than to demagnetization. For the pumping fluence of 7 mJ cm−2, the maximal photo-induced disruption of the anisotropy field is about 14% for the sample with r d = 1 and decreases when r d increases. The anisotropy relaxation is a three-stage process: the ultrafast one occurs within several picoseconds, and the slow one occurs on a nanosecond time scale. The Gilbert damping in the multilayers is found to be one order of magnitude higher than that in the constituent monolayers.

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Popov, V. V., and N. A. Buznikov. "Modeling the Giant Magnetoimpedance Effect in Amorphous Microwires with Induced Magnetic Anisotropy." Physics of Metals and Metallography 121, no. 11 (November 2020): 1033–38. http://dx.doi.org/10.1134/s0031918x20110071.

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Dobák, Samuel, Cinzia Beatrice, Vasiliki Tsakaloudi, and Fausto Fiorillo. "Magnetic Losses in Soft Ferrites." Magnetochemistry 8, no. 6 (June 2, 2022): 60. http://dx.doi.org/10.3390/magnetochemistry8060060.

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We review the basic phenomenology of magnetic losses from DC to 1 GHz in commercial and laboratory-prepared soft ferrites considering recent concepts regarding their physical interpretation. This is based, on the one hand, on the identification of the contributions to the magnetization process provided by spin rotations and domain walls and, on the other hand, the concept of loss separation. It additionally contemplates a distinction between the involved microscopic dissipation mechanisms: spin damping and eddy currents. Selected experimental results on the broadband behavior of complex permeability and losses in Mn-Zn ferrites provide significant examples of their dependence on sintering methods, solute elements, and working temperature. We also highlight the peculiar frequency and temperature response of Ni-Zn ferrites, which can be heavily affected by magnetic aftereffects. The physical modeling of the losses brings to light the role of the magnetic anisotropy and the way its magnitude distribution, affected by the internal demagnetizing fields, acts upon the magnetization process and its dependence on temperature and frequency. It is shown that the effective anisotropy governs the interplay of domain wall and rotational processes and their distinctive dissipation mechanisms, whose contributions are recognized in terms of different loss components.

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Morreeuw, J. P., A. Sangam, B. Dubroca, P. Charrier, and V. T. Tikhonchuk. "Electron temperature anisotropy modeling and its effect on anisotropy-magnetic field coupling in an underdense laser heated plasma." Journal de Physique IV (Proceedings) 133 (June 2006): 295–300. http://dx.doi.org/10.1051/jp4:2006133058.

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Beljakov, Igor, Velimir Meded, Franz Symalla, Karin Fink, Sam Shallcross, and Wolfgang Wenzel. "Magnetic anisotropy of graphene quantum dots decorated with a ruthenium adatom." Beilstein Journal of Nanotechnology 4 (July 10, 2013): 441–45. http://dx.doi.org/10.3762/bjnano.4.51.

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The creation of magnetic storage devices by decoration of a graphene sheet by magnetic transition-metal adatoms, utilizing the high in-plane versus out-of-plane magnetic anisotropy energy (MAE), has recently been proposed. This concept is extended in our density-functional-based modeling study by incorporating the influence of the graphene edge on the MAE. We consider triangular graphene flakes with both armchair and zigzag edges in which a single ruthenium adatom is placed at symmetrically inequivalent positions. Depending on the edge-type, the graphene edge was found to influence the MAE in opposite ways: for the armchair flake the MAE increases close to the edge, while the opposite is true for the zigzag edge. Additionally, in-plane pinning of the magnetization direction perpendicular to the edge itself is observed for the first time.

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Chérif, S. M., Y. Roussigné, M. Belmeguenai, C. R. Chang, Y. C. Lee, J. C. Wu, C. M. Lee, T. H. Wu, A. A. Stashkevich, and F. Zighem. "Dynamic and Magnetotransport Properties of Perpendicularly Magnetized CoFeB Magnetic Tunnel Junctions." SPIN 06, no. 04 (December 2016): 1640010. http://dx.doi.org/10.1142/s2010324716400105.

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We present the study of the dynamic properties of CoFeB (CFB) based magnetic tunnel junctions (MTJ) by Brillouin light scattering spectroscopy and micro-strip ferromagnetic resonance technique as well as magnetoresistance measurements. Two different MTJs: single and double barrier systems have been investigated. The dynamic studies revealed mostly similar perpendicular anisotropy field for both CoFeB layers for the single barrier MTJ with the thickest CFB layers, while two sensibly different perpendicular anisotropy fields were revealed in the case of the double barrier MTJ with the thickest CFB soft and hard layers. Modeling the spin wave frequencies behavior allows us the analysis of the experimental data and the derivation of the pertinent magnetic parameters. Our results suggest an interfacial origin of the anisotropy. Therefore, by changing the thickness of the perpendicularly magnetized CFB layers, it is possible to obtain a free and pinned layer usually ensured by the use of synthetic antiferromagnetic material. The tunnel magnetoresistance has been measured in elliptical elements of double barrier MTJ of different sizes. Strong size-dependent switching fields and antiparallel state being more unstable in the smallest device are observed. Patterning effect, lowering the anisotropies around the edge areas and increasing the dipolar coupling that favors the parallel state in the case of stacked layers, are probably the origin.

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Manière, Charles, Gabriel Kerbart, Christelle Harnois, and Sylvain Marinel. "Modeling sintering anisotropy in ceramic stereolithography of silica." Acta Materialia 182 (January 2020): 163–71. http://dx.doi.org/10.1016/j.actamat.2019.10.032.

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Xu, Bin, Ming-Jay Chow, and Yanhang Zhang. "Experimental and Modeling Study of Collagen Scaffolds with the Effects of Crosslinking and Fiber Alignment." International Journal of Biomaterials 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/172389.

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Collagen type I scaffolds are commonly used due to its abundance, biocompatibility, and ubiquity. Most applications require the scaffolds to operate under mechanical stresses. Therefore understanding and being able to control the structural-functional integrity of collagen scaffolds becomes crucial. Using a combined experimental and modeling approach, we studied the structure and function of Type I collagen gel with the effects of spatial fiber alignment and crosslinking. Aligned collagen scaffolds were created through the flow of magnetic particles enmeshed in collagen fibrils to mimic the anisotropy seen in native tissue. Inter- and intra- molecular crosslinking was modified chemically with Genipin to further improve the stiffness of collagen scaffolds. The anisotropic mechanical properties of collagen scaffolds were characterized using a planar biaxial tensile tester and parallel plate rheometer. The tangent stiffness from biaxial tensile test is two to three orders of magnitude higher than the storage moduli from rheological measurements. The biphasic nature of collagen gel was discussed and used to explain the mechanical behavior of collagen scaffolds under different types of mechanical tests. An anisotropic hyperelastic constitutive model was used to capture the characteristics of the stress-strain behavior exhibited by collagen scaffolds.

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Wang, Guanda, Yue Zhang, Jinkai Wang, Zhizhong Zhang, Kun Zhang, Zhenyi Zheng, Jacques-Olivier Klein, Dafine Ravelosona, Youguang Zhang, and Weisheng Zhao. "Compact Modeling of Perpendicular-Magnetic-Anisotropy Double-Barrier Magnetic Tunnel Junction With Enhanced Thermal Stability Recording Structure." IEEE Transactions on Electron Devices 66, no. 5 (May 2019): 2431–36. http://dx.doi.org/10.1109/ted.2019.2906932.

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Liu, Shuang, Xiangyun Hu, Maurizio Fedi, and Rixiang Zhu. "Forward and inverse modeling of magnetic data under complex magnetism effects: Remanence, self‐demagnetization and magnetic anisotropy." Acta Geologica Sinica - English Edition 93, S1 (May 2019): 325. http://dx.doi.org/10.1111/1755-6724.14115.

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Landa, Alexander, Per Söderlind, Emily E. Moore, and Aurelien Perron. "Thermodynamics and Magnetism of YCo5 Compound Doped with Fe and Ni: An Ab Initio Study." Applied Sciences 10, no. 17 (August 31, 2020): 6037. http://dx.doi.org/10.3390/app10176037.

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YCo5 permanent magnet exhibits high uniaxial magnetocrystalline anisotropy energy and has a high Curie temperature. These are good properties for a permanent magnet, but YCo5 has a low energy product, which is notably insufficient for a permanent magnet. In order to improve the energy product in YCo5, we suggest replacing cobalt with iron, which has a much bigger magnetic moment. With a combination of density-functional-theory calculations and thermodynamic CALculation of PHAse Diagrams (CALPHAD) modeling, we show that a new magnet, YFe3(Ni1-xCox)2, is thermodynamically stable and exhibits an improved energy product without significant detrimental effects on the magnetocrystalline anisotropy energy or the Curie temperature.

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One, Roxana-Alina, Sever Mican, Angela-Georgiana Cimpoeșu, Marius Joldos, Romulus Tetean, and Coriolan Viorel Tiușan. "Micromagnetic Design of Skyrmionic Materials and Chiral Magnetic Configurations in Patterned Nanostructures for Neuromorphic and Qubit Applications." Nanomaterials 12, no. 24 (December 10, 2022): 4411. http://dx.doi.org/10.3390/nano12244411.

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Our study addresses the problematics of magnetic skyrmions, nanometer-size vortex-like swirling topological defects, broadly studied today for applications in classic, neuromorphic and quantum information technologies. We tackle some challenging issues of material properties versus skyrmion stability and manipulation within a multiple-scale modeling framework, involving complementary ab-initio and micromagnetic frameworks. Ab-initio calculations provide insight into the anatomy of the magnetic anisotropy, the Dzyaloshinskii–Moriya asymmetric exchange interaction (DMI) and their response to a gating electric field. Various multi-layered heterostructures were specially designed to provide electric field tunable perpendicular magnetization and sizeable DMI, which are required for skyrmion occurrence. Landau–Lifshitz–Gilbert micromagnetic calculations in nanometric disks allowed the extraction of material parameter phase diagrams in which magnetic textures were classified according to their topological charge. We identified suitable ranges of magnetic anisotropy, DMI and saturation magnetization for stabilizing skyrmionic ground states or writing/manipulating them using either a spin-transfer torque of a perpendicular current or the electric field. From analyzing the different contributions to the total magnetic free energy, we point out some critical properties influencing the skyrmions’ stability. Finally, we discuss some experimental issues related to the choice of materials or the design of novel magnetic materials compatible with skyrmionic applications.

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Bang, Jon, Arne Solstad, and Svein Mjaaland. "Formation Electrical Anisotropy Derived From Induction-Log Measurements in a Horizontal Well." SPE Reservoir Evaluation & Engineering 4, no. 06 (December 1, 2001): 483–88. http://dx.doi.org/10.2118/75115-pa.

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Summary An existing theory describes how electrical anisotropy in the formationaffects the response of resistivity logging tools. We have related this theory to the processing of logging while drilling (LWD) induction logs and are thus able to calculate the anisotropic resistivities directly from the logs. The method has been demonstrated by application to logs from a horizontal well section. Anisotropy ratios of 2 to 5, and occasionally higher values, were obtained for this formation. We also addressed the accuracy of these numbers by using independent sets of input logs. The results indicate that the logs are influenced by factors like invasion, in addition to the anisotropy. Our approach provides a fast and efficient computer algorithm. The output is calculated at the depths of the input logs; hence, the resulting anisotropy becomes a depth-dependent formation property. Introduction Electrical anisotropy has gained considerable attention in recent years. If present in the formation, neglection of this property when interpreting resistivity logs may lead to erroneous saturation estimates and may thus have great consequences upon development and production strategies and the overall economic situation. Electrical anisotropy denotes that the resistivity shows directional dependence. In sedimentary formations, it is commonly assumed that the anisotropy is caused by the deposition process, which yields different small-scale (grain and pore-size scale) structural properties in the vertical and horizontal directions. Anisotropy may also occur on a lithology scale[i.e., as a result of thin layers (compared to the extension of the electricfield) having individual isotropic properties]. Because the effect is determined by the sedimentary structure, a formation can be expected to show anisotropy in several properties, such as electric, acoustic, and fluid-flow resistance (permeability) properties, simultaneously. A common way of describing anisotropy is to distinguish between the vertical direction and directions in the horizontal plane. In this paper, we shall denote the resistivities in these directions by RV andRH, respectively. However, the terms "vertical" and"horizontal" refer to the original deposition process and may no longer correspond to the actual orientation of the formation owing to small- or large-scale geological activity. For dipping beds, it is common practice to assume one resistivity (R H) in the bedding plane and one (RV) in the direction normal to the bed, unless evidence of intrabed disturbances suggests other orientations of the anisotropy. Numerous publications have addressed the influence of electrical anisotropy on resistivity logs. Among the effects that have been studied are anisotropy in dipping and thinly laminated formations1–3 and in crossbedded formations.4 Effort has been put on theoretical tool response modeling and simulation 5–7 and on anisotropy corrections to logs.8,9 From field cases, anisotropy ratios(RV/R H) up to the order of 5 to 10 have been reported.7,8,10 In this paper, we demonstrate a method for calculating the electrical anisotropy directly from well logs, based on the theory developed by Hagiwara.6 The method has been implemented and applied to log data from a horizontal North Sea well. Theory Hagiwara6 has analyzed the resistivity log's response in anisotropic formations. According to this reference, two different measurements are sufficient to determine the anisotropy unambiguously, as long as the anisotropy orientation is known. The measurements may differ with respect to one or more of the following:antenna spacing (which is a prerequisite for phase- and attenuation-derived resistivity),frequency, ordeviation angle between tool axis and anisotropy orientation. In our work, we consider the LWD induction response. For this instrument class, Hagiwara shows that the complex voltage V recorded by one transmitter-receiver pair of electrodes isEquation 1 where i=the imaginary unit (i=-11/2) and L=the antenna spacing. Further,Equation 2 where a2= RH/RV is the anisotropy ratio between horizontal and vertical resistivitiesRH and RV, and ?=the deviation of tool direction from the R V direction. Notice the interpretation of the terms "vertical" and "horizontal," as discussed in the introduction. The wave number k is defined byEquation 3 where ?=the measurement angular frequency, µ=the magnetic permeability, andeH=the horizontal dielectric constant. In this study, we used the free space magnetic permeability µ=µ0=4p×10–7 N/A, and approximated eH from the logged resistivity through an empirical relation. Both these approximations are considered to have negligible influence on the results.

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UESHIMA, Nobufumi, Masato YOSHIYA, and Hideyuki YASUDA. "Elucidation of Mechanism of Emergence of Magnetic Anisotropy in FePd by Phase-Field Modeling." Journal of the Japan Society for Precision Engineering 83, no. 5 (2017): 415–19. http://dx.doi.org/10.2493/jjspe.83.415.

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Elbidweihy, Hatem, Anthony S. Arrott, and Virgil Provenzano. "Modeling the Role of the Buildup of Magnetic Charges in Low Anisotropy Polycrystalline Materials." IEEE Transactions on Magnetics 54, no. 11 (November 2018): 1–5. http://dx.doi.org/10.1109/tmag.2018.2832294.

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Pirgazi, Hadi, Roumen H. Petrov, and Leo Kestens. "Modeling the Magnetic Properties of Non-Oriented Electrical Steels Based on Microstructural Parameters." Materials Science Forum 702-703 (December 2011): 734–37. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.734.

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Magnetic properties of electrical steels such as magnetization behavior and electrical losses are mainly related to chemical composition, crystallographic orientation and microstructure. By now, several models have been proposed to empirically correlate magnetic properties and affecting parameters. A quantitative model based on physical understanding of the interaction between the magnetic field variables (e.g. domain structure) and local microstructural variables (e.g. grain orientation and misorientation, grain boundary plane inclination) is still missing. To obtain a better understanding of the interaction between grain boundaries and domain walls, the magnitude of free pole density at grain boundaries was taken into account. Experimental results from 3-dimentional EBSD experiments were employed to measure the grain boundary orientation for several samples with different chemical composition and grain size. The free pole density was calculated using the relative misorientation between adjacent grains, and was included in a model together with grain size, magnetocrystalline anisotropy energy and silicon equivalent. By comparison with the experimental results of the magnetic induction measured at low, medium and high magnetic fields, is shown that the magnetization behavior can be more accurately predicted when the above mentioned phenomena are taken into account.

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van der Laan, G., K. Chesnel, M. Belakhovsky, A. Marty, F. Livet, S. P. Collins, E. Dudzik, A. Haznar, and J. P. Attané. "Magnetic anisotropy of aligned magnetic stripe domains in FePd studied by soft x-ray resonant magnetic scattering, magnetic force microscopy and micromagnetic modeling." Superlattices and Microstructures 34, no. 1-2 (July 2003): 107–26. http://dx.doi.org/10.1016/j.spmi.2004.01.005.

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Starodubtsev, Evgenii. "Effect of small anisotropy and absorption on metamaterial applications: “non-ideal” features of propagation and tunneling of electromagnetic waves." EPJ Applied Metamaterials 5 (2018): 1. http://dx.doi.org/10.1051/epjam/2017014.

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For cases of isotropic, uniaxial, and biaxial electromagnetic metamaterials (MM), a comparative analysis of the effect of small deviations of local material parameters from “ideal” values on the realization of MM applications (“zero” media, the Veselago-Pendry superlens) has been carried out. On the basis of the detailed investigation of the solutions of dispersion equations, it is established that even a very small dielectric and (or) magnetic anisotropy of a general form is the universal “non-ideal” factor determining (to a much greater extent than small losses) the operability of those MM applications where the wave misphasing in the effective medium is undesirable. The characteristics of wave attenuation in the absorbing isotropic and weakly anisotropic MM are mainly comparable for the applications. Limitations of the traditional approaches using the second-order curves (or surfaces) for analytic modeling of the absorbing MM dispersion equations are shown.

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Lim, Young Soo, Bae Gun Park, and Gil-Geun Lee. "Synthesis of N-type Bi2Te2.7Se0.3 Compounds through Oxide-Reduction Process and Related Thermoelectric Transport Properties." Korean Journal of Metals and Materials 60, no. 6 (June 5, 2022): 463–70. http://dx.doi.org/10.3365/kjmm.2022.60.6.463.

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We present a study on the synthesis of Bi2Te2.7Se0.3 powders through an oxide reduction process and also on the effect of the oxide reduction process on the thermoelectric transport properties of the resulting Bi2Te2.7Se0.3 compounds. Starting materials of Bi2O3, TeO2 and SeO2 were mechanical milled for homogeneous mixing, and then oxidized to prepare complex oxide powders. The complex oxide powders were reduced at different reduction temperatures under hydrogen atmosphere, and a single phase of Bi2Te2.7Se0.3 could be achieved in the reduced powder, with shorter reduction times as the reduction temperature was increased. The shape of the synthesized powder particles changed from granules to flakes with increasing reduction temperature and longer reduction time. Bi2Te2.7Se0.3 powders with different shapes were consolidated by spark plasma sintering (SPS). The SPSed Bi2Te2.7Se0.3 compounds exhibited anisotropic n-type thermoelectric transport properties along the vertical and parallel planes with respect to the pressing direction of the SPS. The degree of anisotropy in the thermoelectric properties was quite consistent with the degree of anisotropy in the microstructure, which originated from the anisotropic shapes in the Bi2Te2.7Se0.3 powders depending on the reduction conditions. Detailed thermoelectric transport properties of the n-type Bi2Te2.7Se0.3 compounds were interpreted in terms of anti-site defect formation and their structural anisotropy.

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Ahmed, Tanjina N., Christopher Selsor, Jitendra S. Tate, and Wilhelmus J. Geerts. "Magnetic behavior and chaining of strontium ferrite-nylon composite above the melting temperature." AIP Advances 13, no. 2 (February 1, 2023): 025024. http://dx.doi.org/10.1063/9.0000596.

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To better understand Magnetic Field Assisted Additive Manufacturing (MFAAM) the effect of a magnetic field on the orientation and distribution of magnetic particles in a molten magnetic composite was studied. Vibrating Sample Magnetometer (VSM) measurements were made on Sr-ferrite/PA12 fused deposition modeling filaments of different packing fraction (5 and 40 wt. %). The rotation of the sample’s magnetic moment upon application of a field perpendicular to the easy axis was monitored with a biaxial VSM above the PA12’s softening temperature. The observed magnetic moment transients depend on the temperature, the applied alignment field, the packing fraction, and the initial field-anneal procedure. Longer field-anneals result in larger time constants and seem to induce a hurdle that prevents complete alignment at low temperatures and/or for small fields. Results indicate the molten composite is a non-Newtonian fluid that can support a yielding stress. Scanning Electron microscopy (SEM) images taken on field-annealed samples at 230 °C show strong chaining with little PA-12 left between individual Sr-ferrite particles suggesting that direct particle to particle interaction is the reason for the observed non-zero yielding stress. The melt viscosity of the composite increases with the number of thermal cycles above the melting temperature (Tm). Room temperature (RT) torque magnetometry measurements show that magnetic anisotropy depends on the field annealing process through induced shape anisotropy contributions originating from magnetic particle agglomerates.

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Lim, Hyein, Seungjun Lee, and Hyungsoon Shin. "A Survey on the Modeling of Magnetic Tunnel Junctions for Circuit Simulation." Active and Passive Electronic Components 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/3858621.

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Spin-transfer torque-based magnetoresistive random access memory (STT-MRAM) is a promising candidate for universal memory that may replace traditional memory forms. It is expected to provide high-speed operation, scalability, low-power dissipation, and high endurance. MRAM switching technology has evolved from the field-induced magnetic switching (FIMS) technique to the spin-transfer torque (STT) switching technique. Additionally, material technology that induces perpendicular magnetic anisotropy (PMA) facilitates low-power operation through the reduction of the switching current density. In this paper, the modeling of magnetic tunnel junctions (MTJs) is reviewed. Modeling methods and models of MTJ characteristics are classified into two groups, macromodels and behavioral models, and the most important characteristics of MTJs, the voltage-dependent MTJ resistance and the switching behavior, are compared. To represent the voltage dependency of MTJ resistance, some models are based on physical mechanisms, such as Landau-Lifshitz-Gilbert (LLG) equation or voltage-dependent conductance. Some behavioral models are constructed by adding fitting parameters or introducing new physical parameters to represent the complex switching behavior of an MTJ over a wide range of input current conditions. Other models that are not based on physical mechanisms are implemented by simply fitting to experimental data.

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Luca, Delia, and Simona Miclăuş. "Two Dimensions Simulation of a Magnetotactic Bacteria Cell Exposed to an Electromagnetic Field at 3 GHz." International conference KNOWLEDGE-BASED ORGANIZATION 27, no. 3 (June 1, 2021): 48–54. http://dx.doi.org/10.2478/kbo-2021-0088.

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Abstract The effect of the presence of magnetite nanoparticles inside biological objects when they are exposed to microwaves has not yet been investigated completely. Microwaves magnetic hyperthermia is a field under development, and the use of biogenic magnetite is a relatively new vista. In this regard, the present approach presents a first step in a modeling-simulation process focused on the computation of the absorbed power distribution in bacteria cells containing native magnetite nanoparticles in the form of chains (magnetosomes). The presented simulations’ results refer to the simplest case of two-dimensional computation, which doesn’t take into consideration the geometric and magnetic anisotropy characteristics of the real magnetosomes.

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Klokishner, Sophia I., Serghei M. Ostrovsky, Oleg S. Reu, Andrei V. Palii, Philip L. W. Tregenna-Piggott, Theis Brock-Nannestad, Jesper Bendix, and Hannu Mutka. "Magnetic Anisotropy in the [CuIILTbIII(hfac)2]2Single Molecule Magnet: Experimental Study and Theoretical Modeling." Journal of Physical Chemistry C 113, no. 20 (May 21, 2009): 8573–82. http://dx.doi.org/10.1021/jp8090842.

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Gaponov, Mikhail, Sergey Ovcharenko, Nikita Ilyin, and Elena Mishina. "Laser-Induced Magnetization Dynamics in Si-Doped Yttrium-Iron Garnet Film." Condensed Matter 7, no. 4 (October 8, 2022): 55. http://dx.doi.org/10.3390/condmat7040055.

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We experimentally demonstrate that the excitation of a silicon-doped yttrium-iron garnet film by femtosecond laser pulses triggers a magnetization precession with an amplitude determined by the external magnetization direction. The maximum efficiency is achieved at the pump wavelength corresponding to the absorption maximum due to doping with silicon ions. Based on the azimuthal dependences of the precession amplitude and frequency, it is shown that the magnetization dynamics is induced by a thermal disruption of the magnetocrystalline anisotropy. By modeling hysteresis loops, it was found that the silicon doping leads to a decrease in the value of the exchange interaction in the film and an increase in the anisotropy field.

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Raposo, Víctor, and Eduardo Martínez. "All optical writing and current-driven shifting of bits in ferrimagnetic strips: A micromagnetic study." AIP Advances 13, no. 1 (January 1, 2023): 015120. http://dx.doi.org/10.1063/9.0000516.

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Nucleation of domains and domain walls by means of ultrashort laser pulses, and their current-driven shifting along a ferrimagnetic strip with high perpendicular magnetic anisotropy on top of a heavy metal, are both explored here by means of advanced micromagnetic modeling. Our results indicate that these systems are ideal candidates to develop high-density and high-efficient domain wall-based memory devices where the information is coded in series of bits in the form of perpendicular up and down domains flanked by chiral domain walls.

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Raposo, Victor, Rodrigo Guedas, Felipe García-Sánchez, M. Auxiliadora Hernández, Marcelino Zazo, and Eduardo Martínez. "Micromagnetic Modeling of All Optical Switching of Ferromagnetic Thin Films: The Role of Inverse Faraday Effect and Magnetic Circular Dichroism." Applied Sciences 10, no. 4 (February 14, 2020): 1307. http://dx.doi.org/10.3390/app10041307.

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There is a lot of experimental evidence of All Optical Switching (AOS) by applying ultrashort laser pulses on ferromagnetic thin films with perpendicular magnetic anisotropy. However, the physical origin behind these processes remains under debate. In addition to the heating caused by the laser pulses, the Inverse Faraday Effect (IFE) and Magnetic Circular Dichroism (MCD) have been proposed as the most probable phenomena responsible for the observations of helicity-dependent AOS. Here, we review the influence of both phenomena by means of realistic micromagnetic simulations based on the Landau–Lifshitz–Bloch equation coupled to the heat transport caused by the laser heating. The analysis allows us to reveal the similarities and differences between both effects. While both mechanisms may lead to the local inversion of the initial magnetic state of a ferromagnetic sample submitted to a train of circularly polarized laser pulses, the Inverse Faraday Effect proves to be more efficient for nucleation and domain wall movement and it reproduces more accurately the different magnetic configurations that the experiments report for different values of the fluence of the laser beam.

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Bentley, J., J. E. Wittig, and T. P. Nolan. "Segregation In Cocrptta/Cr Magnetic Recording Media Measured By Eftem." Microscopy and Microanalysis 5, S2 (August 1999): 136–37. http://dx.doi.org/10.1017/s1431927600014008.

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Development of high-density longitudinal magnetic recording media (used for computer hard disks) with good noise performance and high thermal stability requires optimization of both alloy composition and processing methods. In CoCr(PtTa) thin films, intergranular Cr segregation is responsible for decoupling the magnetic exchange between the small ferromagnetic grains. The corresponding Cr depletion within the grains affects the “bulk” magnetic anisotropy. However, the nanoscale structural and chemical details that are needed for modeling and for guiding material development are not well understood. Energy-filtered transmission electron microscopy (EFTEM) has been used to characterize a series of CoCrTa/Cr, CoCrPt/Cr, and CoCrPtTa/Cr media sputtered under various processing conditions, in order to understand their structure-property-processing relationships.Processing typical for hard-disk media was used: 30 or 60-nm films of a Cr underlayer followed by a Co alloy were d.c. magnetron sputtered onto a NiP-plated Al substrate pre-heated to 250°C.

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Kools, Thomas J., Marnix C. van Gurp, Bert Koopmans, and Reinoud Lavrijsen. "Magnetostatics of room temperature compensated Co/Gd/Co/Gd-based synthetic ferrimagnets." Applied Physics Letters 121, no. 24 (December 12, 2022): 242405. http://dx.doi.org/10.1063/5.0127694.

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Flexibility for interface engineering and access to all-optical switching of the magnetization make synthetic ferrimagnets an interesting candidate for advanced optospintronic devices. Moreover, due to their layered structure and disordered interfaces, they also bear promise for the emerging field of graded magnetic materials. The fastest and most efficient spin–orbit torque driven manipulation of the magnetic order in this material system generally takes place at compensation. Here, we present a systematic experimental and modeling study of the conditions for magnetization compensation and perpendicular magnetic anisotropy in the synthetic ferrimagnetic Co/Gd/Co/Gd system. A model based on partial intermixing at the Co/Gd interfaces of this system has been developed which explains the experiments well and provides a tool to understand its magnetic characteristics. More specifically, this work provides further insight into the decay of the Co proximity-induced magnetization in the Gd, and the role the capping layer plays in the Gd magnetization.

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Śniadecki, Z. "The Influence of 3d and 4d Transition Metals on the Glass Forming Ability of Ternary FeCo-Based Alloys." Metallurgical and Materials Transactions A 52, no. 5 (March 11, 2021): 1861–68. http://dx.doi.org/10.1007/s11661-021-06196-7.

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AbstractThermodynamic modeling was used to determine enthalpies of formation and other thermodynamic parameters describing glass forming ability of Fe-Co-TM (TM = V, Nb, Cr, Mo) alloys. FeCo-based alloys are considered as candidates for applications as high magnetic flux density materials due to their high magnetic saturation and low magnetic anisotropy. Nevertheless, mechanical properties, especially the lack of ductility, are their main weakness. Therefore, further optimization by vitrification, further heat treatment and alloying should be considered. As the most crucial step is the synthesis of amorphous precursors, discussion is concentrated on the effect of transition metal substitution on the glass forming ability. The highest glass forming ability was reported for Fe-Co-Nb alloys. It can be also noted that the driving force for vitrification can be improved by substitution of Fe by other transition elements, as glass forming ability parameter ∆PHS reaches the lowest values for Fe-less compositions.

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Wang, Fengmao, Xiangli Zhang, Zongzhi Zhang, and Yaowen Liu. "Deterministic magnetization switching by spin–orbit torque in a ferromagnet with tilted magnetic anisotropy: A macrospin modeling." Journal of Magnetism and Magnetic Materials 527 (June 2021): 167757. http://dx.doi.org/10.1016/j.jmmm.2021.167757.

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Journal articles on the topic 'Modeling Magnetic Anisotropy'

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