Literature on micromagnetism

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  • Including effects of microstructure and anisotropy in theoretical models describing hysteresis of ferromagnetic materials, H. Hauser et al. (2007)
    TitleIncluding effects of microstructure and anisotropy in theoretical models describing hysteresis of ferromagnetic materials
    AuthorsH. Hauser, Y. Melikhov, D. C. Jiles
    PublicationApplied Physics Letters
    DateOctober 22, 2007
  • Solid-state physics: Response with a twist, Karin M. Rabe (2007)
    TitleSolid-state physics: Response with a twist
    AuthorKarin M. Rabe
    DateOctober 11, 2007
  • Observation of ferrotoroidic domains, Bas B. Van Aken et al. (2007)
    TitleObservation of ferrotoroidic domains
    AuthorsBas B. Van Aken, Jean-Pierre Rivera, Hans Schmid, Manfred Fiebig
    DateOctober 11, 2007
  • Magnetism & Magnetic Materials; 3S100 course syllabus 2007-2008, H.M. Swagten (2007)
    TitleMagnetism & Magnetic Materials; 3S100 course syllabus 2007-2008
    AuthorH.M. Swagten
    PublisherEindhoven University of Technology
  • Electrical switching of the vortex core in a magnetic disk, Keisuke Yamada et al. (2007)
    TitleElectrical switching of the vortex core in a magnetic disk
    AuthorsKeisuke Yamada, Shinya Kasai, Yoshinobu Nakatani, Kensuke Kobayashi, Hiroshi Kohno, Andre Thiaville, Teruo Ono
    PublicationNat Mater
    DateApril 2007
  • The role of nucleation field of media in heat-assisted magnetic probe recording, Li Zhang (2007)
    TitleThe role of nucleation field of media in heat-assisted magnetic probe recording
    AuthorLi Zhang
    PublicationPhysica B: Condensed Matter
    DateMarch 1, 2007
    AbstractWe characterize a method of heat-assisted magnetic probe recording on perpendicular media. Heating source is field emission current from a scanning tunneling microscope (STM) tip. Recording media are three kinds of magnetic films, Co/Pt, CoNi/Pt, and Co/Pd multilayers with different nucleation fields. Pulses with amplitude of 5�V were applied between the STM tip and the recording medium. Experiments show that magnetic marks with an average size of 180�nm were formed on both Co/Pt and CoNi/Pt films whose nucleation fields are greater than their saturation magnetization. No marks were observed on the Co/Pd film whose nucleation field is smaller than its saturation magnetization. A model is built to simulate the dynamic process of domain formation in probe-based magnetic recording system. Simulation results agree with experiments and it explains the effect of the nucleation field of medium in perpendicular recording.
  • Current-induced magnetic vortex core switching in a Permalloy nanodisk, Y. Liu et al. (2007)
    TitleCurrent-induced magnetic vortex core switching in a Permalloy nanodisk
    AuthorsY. Liu, S. Gliga, R. Hertel, C. M. Schneider
    PublicationApplied Physics Letters
    AbstractThe authors report on the switching of a magnetic vortex core in a submicron Permalloy disk, induced by a short current pulse applied in the film plane. Micromagnetic simulations including the adiabatic and nonadiabatic spin-torque terms are used to investigate the current-driven magnetization dynamics. They predict that a core reversal can be triggered by current bursts a tenth of a nanosecond long. The vortex core reversal process is found to be the same as when an external field pulse is applied. The control of a vortex core's orientation using current pulses introduces the technologically relevant possibility to address individual nanomagnets within dense arrays.
  • Current induced switching of vortex polarity in magnetic nanodisks, Denis D. Sheka et al. (2007)
    TitleCurrent induced switching of vortex polarity in magnetic nanodisks
    AuthorsDenis D. Sheka, Yuri Gaididei, Franz G. Mertens
    PublicationApplied Physics Letters
    AbstractIt is shown that the vortex polarity can be irreversibly switched by injecting a spin-polarized direct electrical current, which flows perpendicular to the disk plane. Intensive numerical spin-lattice simulations demonstrate that the switching process involves a vortex-antivortex pair creation. This differs from magnets with no dipolar interaction, where the spin dc acts similar to a static magnetic field.
  • The breakdown of the fingerprinting of vortices by hysteresis loops in circular multilayer ring arrays, V. Rose et al. (2007)
    TitleThe breakdown of the fingerprinting of vortices by hysteresis loops in circular multilayer ring arrays
    AuthorsV. Rose, X. M. Cheng, D. J. Keavney, J. W. Freeland, K. S. Buchanan, B. Ilic, V. Metlushko
    PublicationApplied Physics Letters
  • Supermagnetism in magnetic nanoparticle systems, S. Bedanta (2006)
    TitleSupermagnetism in magnetic nanoparticle systems
    AuthorS. Bedanta
    Date11 Dec, 2006
  • Micromagnetic energy barriers, R. Skomski et al. (2006)
    TitleMicromagnetic energy barriers
    AuthorsR. Skomski, J. Zhou, R. D. Kirby, D. J. Sellmyer
    DateApril 15, 2006
    Proceedings Title50th Annual Conference on Magnetism and Magnetic Materials
    Conference Name50th Annual Conference on Magnetism and Magnetic Materials
    PlaceSan Jose, California (USA)
    AbstractThe structure of micromagnetic energy barriers responsible for slow magnetization processes is investigated. Thermally activated slow magnetization processes proceed over energy barriers whose structure is determined by the micromagnetic free energy. This restricts the range of physically meaningful energy barriers. An analysis of the underlying micromagnetic free energy yields power-law dependences with exponents of 3/2 or 2 for physically reasonable models. This must be contrasted to other power laws, such as linear laws, and to 1/H-type dependences. In the limit of small energy barriers, corrections to the Arrhenius law become important. In this regime, there is no simple expression for the relaxation behavior, but two requirements help to judge models and approximations. First, at low temperatures, the Arrhenius-type power laws must be reproduced. Second, as in the Arrhenius limit, the approaches must correspond to well-defined energy landscapes.
  • Small Domain Structures in Magnetization Reversal Process of Write Head in Hard Disk Drives Observed by Strain Imaging, K. Takata (2006)
    TitleSmall Domain Structures in Magnetization Reversal Process of Write Head in Hard Disk Drives Observed by Strain Imaging
    AuthorK. Takata
    PublicationJapanese Journal of Applied Physics
    DateMarch, 2006
    AbstractDetection and imaging of magnetic-field-induced strains using scanning probe microscopy enable us to observe magnetic domain structures. Using strain imaging, domain structures in a magnetization reversal process of a thin film write head in a hard disk drive were investigated by scanning the air-bearing surface of the head. An external magnetic field was applied by the head coil. In the process, a characteristic small domain structure appeared in several portions in the bottom pole of the write head. The domain structure was hemispherical with a diameter of around 0.6 µm, consisting of two opposite magnetizations in the direction of the applied magnetic field. The domain structures appeared under a head coil current of less than 10 mA but vanished at larger currents. The portions where the domain structures were created should impede smooth magnetization reversal.
  • Micromagnetic simulation of ferromagnetic part-spherical particles, Richard P. Boardman et al. (2004)
    TitleMicromagnetic simulation of ferromagnetic part-spherical particles
    AuthorsRichard P. Boardman, Hans Fangohr, Simon J. Cox, Alexander V. Goncharov, Alexander A. Zhukov, Peter A. J. de Groot
    DateJune 01, 2004
  • Micromagnetism and the Microstructure of Ferromagnetic Solids, H. Kronmüller et al. (2003)
    TitleMicromagnetism and the Microstructure of Ferromagnetic Solids
    AuthorsH. Kronmüller, M. Fähnle
    PublisherCambridge University Press
    AbstractThe main theme of this book is micromagnetism and microstructure as well as the analysis of the relations between characteristic properties of the hysteresis loop and microstructure. Also presented is an analysis of the role of microstructure in the fundamental magnetic properties (for example magnetorestriction or critical behaviour) of crystalline and amorphous alloys. The authors apply the theory of micromagnetism to all aspects of advanced magnetic materials including domain patterns and magnetization processes under the influence of defect structures. Coverage includes modern developments in computational micromagnetism and its application to spin structures of small particles and platelets. It will be of interest to researchers and graduate students in condensed matter, physics, electrical engineering and materials science, as well as to industrial researchers working in the electrotechnical and recording industry. * The first book to deal with the relations between magnetic properties and microstructure * Includes micromagnetism of advanced metallic materials * Describes computational micromagnetism of magnetization processes as well as the magnetic structures of small particles and thin films Contents 1. Introduction 2. Magnetic Gibbs free energy 3. Basic micromagnetic equilibrium conditions 4. Domain walls in crystalline and amorphous solids 5. Interaction of domain walls with defects 6. Coercivity of modern magnetic materials 7. Statistical theory of domain wall pinning 8. Law of approach to ferromagnetic saturation and high-field susceptibility 9. Microstructure and domain patterns 10. Magnetic after-effects in amorphous alloys 11. Magnetorestriction in amorphous and polycrystalline ferromagnets 12. Micromagnetic theory of phase transitions in spatially disordered spin systems 13. Computational micromagnetism of thin platelets and small particles 14. Computational micromagnetism of dynamic magnetization processes.
  • General relation for the vector magnetic field of a circular current loop: a closer look, R.A. Schill (2003)
    TitleGeneral relation for the vector magnetic field of a circular current loop: a closer look
    AuthorR.A. Schill
    PublicationMagnetics, IEEE Transactions on
    AbstractThis paper presents a general theory for the fields generated by a circular current loop and compares it with existing theories. The existing, general, closed solution for the vector magnetic field may be expressed in a number of seemingly different but equivalent forms. These relations offer alternative closed-form solutions that may find various applications, including the characterization of Helmholtz coils. The paper provides alternative closed forms in both spherical and cylindrical coordinate systems. It employs Gauss's magnetic law to show that the alternative closed form is self-consistent and correct and also shows agreement with well-known solutions. Finally, it develops a new (or not readily found) tabulated mathematical identity.
  • Magnetic size effects in iron nanoparticles and nanoparticle arrays, Y. Ijiri et al. (2002)
    TitleMagnetic size effects in iron nanoparticles and nanoparticle arrays
    AuthorsY. Ijiri, D. F. Farrell, S. Yamamuro, S. A. Majetich
    PublicationAPS Meeting Abstracts
    DateMarch 1, 2002
    AbstractIn order to probe magnetic size effects on the nanometer length scale, we have investigated a series of different size-selected iron nanoparticles which self-assemble into ordered arrays. The particles were synthesized in solution from the decomposition of iron pentacarbonyl and coated with surfactant molecules. Concentrations, reaction rates, and surfactants were varied to produce particles with mean diameters from 5 to 10 nm and tight size distributions of 5-10%. Magnetization measurements reveal unusual features in the dependencies of the blocking temperature and the time-dependent decay of the magnetization as a function of particle size. The results are interpreted by considering the expected changes to the magnitude of the relevant dipolar and exchange interactions.
  • Analysis of the Demagnetisation Process and Possible Alternative Magnetic Treatments for Naval Vessels, T. Baynes (2002)
    TitleAnalysis of the Demagnetisation Process and Possible Alternative Magnetic Treatments for Naval Vessels
    AuthorT. Baynes
    DateFebruary, 2002
    AbstractNaval submarines and surface ships are regularly subjected to a treatment called “deperming” that seeks to design the vessel’s permanent magnetisation for optimal magnetic camouflage. A scaled model of a magnetic treatment facility (MTF) has been established as a valid system to simulate deperming and used to investigate various aspects of the deperm process including: magnetic anisotropy and demagnetising fields as factors in the physical modelling of magnetism in whole vessels; a comparison of current and alternative deperm procedures; the application of theoretical models of bulk magnetisation to calculate deperm outcomes in the physical model and in actual vessels. A “laboratory MTF” was constructed to imitate the applied field geometry at a naval MTF. The system was calibrated and it was determined that the laboratory MTF could make magnetic measurements on a CU200T-G steel bar sample with an equivalent accuracy (error = ±5%) to that of standard magnetometric equipment. Experiments were conducted with emphasis on a holistic approach to modelling the deperm process and describing magnetisation changes in whole objects. The importance of the magnetic anisotropic changes to steel with cold rolling was confirmed. In CU200T-G steel sheet the initial susceptibility (ci) was found to increase by a factor of 3 ±0.1 in the rolling direction, from a value of ~ 110 in the un-rolled steel sheet (thickness dependent). ci in the rolled sheet transverse to the rolling direction was decreased by a factor of 0.94 ±0.09 to ci in the un-rolled sheet steel. Previous studies on hull steel have neglected to account for this transformation through cold work. The demonstration on mild steel here is expected to have an analogy in the final state of the hull sheet steel as it resides in a submarine pressure hull. Future studies either on hull material or on modelling whole vessels should include the same or similar magnetic anisotropic properties in the steel(s) under investigation. Hollow circular tubes made from CA2S-E and CU200T-G steel sheet were selected as models for vessels. It was shown that these steel tubes were a good choice in this regard: minimising the complexity of the experiment whilst maintaining the validity of XI a deperm simulation. During a deperm there was an excellent qualitative likeness in the permanent longitudinal magnetisation (PLM) for the steel tubes to PLM in both a submarine and a surface vessel. Permanent vertical magnetisation (PVM) deperm results from the tubes displayed a close qualitative match with PVM in a submarine but not in a surface vessel. A theoretical treatment for demagnetisation factors (Nd) in hollow ellipsoids was used in conjunction with a geometrical approximation to calculate Nd for finite hollow objects of revolution. Subsequent theoretical calculations correlated well with experimental results for measured effective ci (ceff) in hollow circular CU200T-G steel tubes of various lengths and aspect ratios. Using an estimate of 100 as ci for submarine hull steel, the same analysis produces Nd for the axial and transaxial directions in a submarine equal to 5.97´10-3 and 0.0142 respectively. Three items for potential improvement were identified in the current deperm protocol used on naval vessels (Flash-D): redundancy in the protocol; the duration of the deperm and a theoretical basis for predicting the final magnetisation or changes in magnetisation during a deperm. Simulations of a novel “anhysteretic deperm” method, designed to combat these issues, compared favourably to the Flash-D protocol. The standard deviation (s) of the final PVM from 30 Flash-D deperms on steel tubes was 206 A/m; for the final PVM from 30 anhysteretic deperms of the same duration, this was 60 A/m. The s for the final PLM for Flash-D and anhysteretic deperms of the same duration were 416 A/m and 670 A/m respectively. The conclusion is that adopting the anhysteretic deperm on actual vessels would improve the reliability of the PVM outcome. Though the procedure would demand the same duration as Flash-D, there is the advantage of saving time by not having to repeat deperms to obtain the desired result. Additionally the anhysteretic deperm is considerably more amenable to theoretical analysis. A modified version of Langevin’s equation was used to predict the final PLM and PVM results for anhysteretic deperms and to provide a useful analysis of the anhysteretic processes in the Flash-D procedure. Using a Preisach analysis of hysteresis, a mathematical description of bulk magnetic changes that occur to a specific object, XII within a deperm, has been developed. Theoretical calculations of PLM in a steel tube during and after both types of deperm are in excellent agreement with experimental data. The same theoretical approach was also used to retrospectively model PLM results from previous Flash-D deperms on a submarine with equal success. With this analysis it is proposed that anhysteretic deperm outcomes could be predicted a priori. The influence of magnetic cargo on hull magnetisation was demonstrated to be of significance during and after deperming. “Sympathetic deperming” occurs where a magnetic source is located close to the hull during a deperm. It was found that a vessel or model vessel hull could still be demagnetised even when they contain magnetic cargo that would normally resist the direct application of the same magnetic fields. This was explained using the principles of demagnetising fields and anhysteretic magnetisation. A possible explanation was provided for a PVM measurement anomaly common to the model and vessel deperm results. From measurement, alternating longitudinal applied fields apparently induce corresponding changes in the PVM. This effect could be explained by the depermed object being offset longitudinally from the position expected by the measurement system. This offset could be estimated using an analysis of the changes to PLM and PVM after a longitudinal applied field. The offset displacements calculated for the vessels were too small to be verified experimentally (< 0.1m), but the predicted offset for the steel tubes coincided with the limit of precision for their placement in the laboratory MTF = 0.5mm The aim of this work was to look at the deperm process with reference to a system that demonstrated qualitative similarities to deperms on actual vessels. The laboratory MTF is a unique facility, permitting a useful practical analysis of deperming based on sound magnetostatic measurements The experimental and theoretical results gained here have direct application to future deperms on naval vessels with particular reference to submarines.
  • Small inexpensive diamagnetic levitation apparatus, Charles A. Sawicki (2001)
    TitleSmall inexpensive diamagnetic levitation apparatus
    AuthorCharles A. Sawicki
    PublicationThe Physics Teacher
    DateDecember 00, 2001
    AbstractA small, inexpensive (5 x 5 x 9 cm and $17) diamagnetic levitation apparatus is described in which a cubic NdFeB magnet 0.476 cm on a side is suspended in a potential energy well created using small ceramic disk magnets and two graphite plates.
  • Exchange bias theory, Miguel Kiwi (2001)
    TitleExchange bias theory
    AuthorMiguel Kiwi
    PublicationJournal of Magnetism and Magnetic Materials
    DateSeptember 2001
    AbstractResearch on the exchange bias (EB) phenomenon has witnessed a flurry of activity during recent years, which stems from its use in magnetic sensors and as stabilizers in magnetic reading heads. EB was discovered in 1956 but it attracted only limited attention until these applications, closely related to giant magnetoresistance, were developed during the last decade. In this review, I initially give a short introduction, listing the most salient experimental results and what is required from an EB theory. Next, I indicate some of the obstacles in the road towards a satisfactory understanding of the phenomenon. The main body of the text reviews and critically discusses the activity that has flourished, mainly during the last 5 years, in the theoretical front. Finally, an evaluation of the progress made, and a critical assessment as to where we stand nowadays along the road to a satisfactory theory, is presented.
  • Layered Magnetic Structures: History, Highlights, Applications, Peter Grunberg (2001)
    TitleLayered Magnetic Structures: History, Highlights, Applications
    AuthorPeter Grunberg
    PublicationPhysics Today
    DateMay 00, 2001
    AbstractThe study of layered magnetic structures is one of the hottest topics in magnetism today, due largely to growing applications in magnetic sensors and in magnetic storage media like computer disks and random-access memories (see the article by L. M. Falicov in PHYSICS TODAY, October 1992, page 46, and the special issue of PHYSICS TODAY on magnetoelectronics, April 1995). Magnetic random-access memories (MRAMs) based on structures of magnetic metallic films interspersed with nonmagnetic metallic or insulating interlayers could be the next generation in magnetic-storage technology, replacing the semiconductor-based dynamic random-access memories (DRAMs) that are now the standard. Advantages of MRAMs include nonvolatility (they retain information when the computer is switched off), high storage density, and low energy consumption. Until the introduction of DRAMs in the 1970s, MRAM technology—using minute ferrite rings, or “core”—was dominant. Thin magnetic film was suggested as a replacement for core as early as 1955, and the first research results were presented in 1959, but problems with reliability of film-based MRAMs led instead to the adoption of DRAMs.
  • Introduction to the Theory of Ferromagnetism, Amikam Aharoni (2001)
    TitleIntroduction to the Theory of Ferromagnetism
    AuthorAmikam Aharoni
    PublisherOxford University Press
  • Measuring the exchange-stiffness constant of nanocrystalline solids by elastic small-angle neutron scattering, A. Michels et al. (2000)
    TitleMeasuring the exchange-stiffness constant of nanocrystalline solids by elastic small-angle neutron scattering
    Authors A. Michels, J. Weissmüller, A. Wiedenmann, J. S. Pedersen, J. G. Barker
    PublicationPhilosophical Magazine
    DateDecember 2000
    AbstractIn ferromagnets with a non-uniform magnetocrystalline and/or magnetoelastic anisotropy, such as nanocrystalline or cold-worked polycrystalline materials, the static magnetic microstructure gives rise to elastic magnetic small-angle neutron scattering (SANS). The paper explores a method for determining the exchange-stiffness constant A by analysis of the dependence of the elastic SANS cross-section on the applied magnetic field. Experimental results for A and for the spin-wave stiffness constant D in cold-worked or nanocrystalline Ni and Co are found to agree with literature data obtained by inelastic neutron scattering on single-crystal specimens.
  • Deviation from the superparamagnetic behaviour of fine-particle systems, I. Malaescu et al. (2000)
    TitleDeviation from the superparamagnetic behaviour of fine-particle systems
    AuthorsI. Malaescu, C. N. Marin
    PublicationJournal of Magnetism and Magnetic Materials
    DateJuly 2, 2000
    AbstractStudies concerning superparamagnetic behaviour of fine magnetic particle systems were performed using static and radiofrequency measurements, in the range 1-60 MHz. The samples were: a ferrofluid with magnetite particles dispersed in kerosene (sample A), magnetite powder (sample B) and the same magnetite powder dispersed in a polymer (sample C). Radiofrequency measurements indicated a maximum in the imaginary part of the complex magnetic susceptibility, for each of the samples, at frequencies with the magnitude order of tens of MHz, the origin of which was assigned to Neel-type relaxation processes. The static measurements showed a Langevin-type dependence of magnetisation M and of susceptibility [chi], on the magnetic field for sample A. For samples B and C deviations from this type of dependence were found. These deviations were analysed qualitatively and explained in terms of the interparticle interactions, dispersion medium influence and surface effects.
  • Magnet levitation at your fingertips, A. K. Geim et al. (1999)
    TitleMagnet levitation at your fingertips
    AuthorsA. K. Geim, M. D. Simon, M. I. Boamfa, L. O. Heflinger
    DateJuly 22, 1999
  • Exchange bias, J. Nogués et al. (1999)
    TitleExchange bias
    AuthorsJ. Nogués, Ivan K. Schuller
    PublicationJournal of Magnetism and Magnetic Materials
    DateFebruary 15, 1999
    AbstractWe review the phenomenology of exchange bias and related effects, with emphasis on layered antiferromagnetic (AFM)-ferromagnetic (FM) structures. A compilation of materials exhibiting exchange bias and some of the techniques used to study them is given. Some of the applications of exchange bias are discussed. The leading theoretical models are summarized. Finally some of the factors controlling exchange bias as well as some of the unsolved issues associated with exchange bias are discussed.
  • Single-Domain Circular Nanomagnets, R. P. Cowburn et al. (1999)
    TitleSingle-Domain Circular Nanomagnets
    AuthorsR. P. Cowburn, D. K. Koltsov, A. O. Adeyeye, M. E. Welland, D. M. Tricker
    PublicationPhysical Review Letters
  • Controlling magnetic ordering in coupled nanomagnet arrays, R. P. Cowburn et al. (1999)
    TitleControlling magnetic ordering in coupled nanomagnet arrays
    AuthorsR. P. Cowburn, A. O. Adeyeye, M. E. Welland
    PublicationNew Journal of Physics
    AbstractWe have fabricated using high-resolution electron beam lithography circular magnetic particles (nanomagnets) of diameter 60 nm and thickness 7 nm out of the common magnetic alloy supermalloy. The nanomagnets were arranged on rectangular lattices of different periods. A high-sensitivity magneto-optical method was used to measure the magnetic properties of each lattice. We show experimentally how the magnetic properties of a lattice of nanomagnets can be profoundly changed by the magnetostatic interactions between nanomagnets within the lattice. We find that simply reducing the lattice spacing in one direction from 180 nm down to 80 nm (leaving a gap of only 20 nm between edges) causes the lattice to change from a magnetically disordered state to an ordered state. The change in state is accompanied by a peak in the magnetic susceptibility. We show that this is analogous to the paramagnetic-ferromagnetic phase transition which occurs in conventional magnetic materials, although low-dimensionality and kinetic effects must also be considered.
  • Permanent Magnetism, R. Skomski et al. (1999)
    TitlePermanent Magnetism
    AuthorsR. Skomski, J.M.D Coey
    PublisherTaylor & Francis
  • Demagnetizing factors for rectangular ferromagnetic prisms, Amikam Aharoni (1998)
    TitleDemagnetizing factors for rectangular ferromagnetic prisms
    AuthorAmikam Aharoni
    PublicationJournal of Applied Physics
    DateMarch 15, 1998
  • Special Issue: Magnetoelectronics, Gary Prinz et al. (1995)
    TitleSpecial Issue: Magnetoelectronics
    AuthorsGary Prinz, Kristl Hathaway
    PublicationPhysics Today
    DateApril 1, 1995
  • Demagnetizing factors for cylinders, D.-X. Chen et al. (1991)
    TitleDemagnetizing factors for cylinders
    AuthorsD.-X. Chen, J.A. Brug, R.B. Goldfarb
    PublicationIEEE Transactions on Magnetics
    AbstractFluxmetric (ballistic) and magnetometric demagnetizing factors Nf and Nm for cylinders as functions of susceptibility χ and the ratio γ of length to diameter have been evaluated. Using a one-dimensional model when γ&ges;10, Nf was calculated for -1&les;χ<∞ and Nm was calculated for χ→∞. Using a two-dimensional model when 0.01&les;γ&les;50, an important range for magnetometer measurements, Nm and Nf were calculated for -1&les;χ<∞. Demagnetizing factors for χ<0 are applicable to superconductors. For χ=0, suitable for weakly magnetic or saturated ferromagnetic materials, Nf and Nm were computed exactly using inductance formulas
  • Method of images and electrostatic screening by a polarized dielectric sphere, Clinton DeW. Van Siclen (1988)
    TitleMethod of images and electrostatic screening by a polarized dielectric sphere
    AuthorClinton DeW. Van Siclen
    PublicationAmerican Journal of Physics
    DateDecember 00, 1988
  • Magnetic properties of ultrafine ferrite particles, Toshihiko Sato et al. (1987)
    TitleMagnetic properties of ultrafine ferrite particles
    AuthorsToshihiko Sato, Tetsuo Iijima, Masahiro Seki, Nobuo Inagaki
    PublicationJournal of Magnetism and Magnetic Materials
    DateMarch 1, 1987
    AbstractThe morphology and magnetic properties of ultrafine ferrite particles prepared by coprecipitation are studied. Saturation magnetization is found to decrease sharply when the particle size is reduced below 10 nm, and this decrease is found to be related to the crystalline magnetic anisotropy constant K1.
  • Spin wave stiffness constants in some ferrimagnetics, C. M. Srivastava et al. (1987)
    TitleSpin wave stiffness constants in some ferrimagnetics
    AuthorsC. M. Srivastava, R. Aiyar
    PublicationJournal of Physics C: Solid State Physics
    AbstractThe magnitude of the spin wave stiffness parameter. D and its dependence on temperature in YIG, Fe3O4 and Li-Zn ferrite has been examined and compared with theory. It is shown that values of D obtained using the exchange constants that satisfactorily explain the equilibrium magnetic properties of these systems yield results in agreement with experiment for YIG and Fe3O4 but are inappropriate for the Li-Zn ferrite. The temperature dependence of D in YIG and Fe3O4 is satisfactorily explained on the basis of the interaction of acoustic magnons with optic magnons.
  • Magnetocrystalline Anisotropy of Low Temperature Phase of Magnetite, K. Abe et al. (1976)
    TitleMagnetocrystalline Anisotropy of Low Temperature Phase of Magnetite
    AuthorsK. Abe, Y. Miyamoto, S. Chikazumi
    PublicationJournal of the Physical Society of Japan
    DateDecember, 1976
    AbstractThe magnetocrystalline anisotropy of low temperature phase of magnetite (Fe3O4) was measured for a monoclinic single phase specimen by using computerized fully-automatic torque magnetometer. The anisotropy is expressed by Ea=Kaα2a+Kbα2b+Kaaα4a+Kbbα4b+Kabα2aα2b-Kuα2111, where αa, αb and α111 are direction cosines of the magnetization with respect to the monoclinic a-, b- and cubic [111] axes, respectively, the last of which coincides with the longest cube diagonal. The values of the anisotropy constants at 4.2 K are: Ka=25.5, Kb=3.7, Ku=2.1, Kaa=1.8, Kbb=2.4 and Kab=7.0 in 105 erg/cm3. It was found that Ka, Kb and Ku exhibit the temperature dependence of an activation type with the activation energy of about 0.02 eV. It was also found that the constants Kaa, Kbb and Kab are well expressed in terms of cubic K1. The mechanism of the anisotropy is also discussed.
  • Magnetization curling in a sphere, I. Eisenstein et al. (1976)
    TitleMagnetization curling in a sphere
    AuthorsI. Eisenstein, A. Aharoni
    PublicationJournal of Applied Physics
    DateJanuary 00, 1976
    AbstractUsing simplifying assumptions, solutions for the magnetization distribution in the curling mode are obtained for a ferromagnetic sphere with a uniaxial anisotropy. These are used to obtain a magnetization curve for a vanishing anisotropy constant and the remanent domain configuration in a cobalt sphere. In the latter case it is shown that as the radius of the sphere increases, two cylindrically symmetric coaxial domains are being formed. Some features of this configuration are discussed and a comparison is made with previous literature.
  • Introduction to Magnetic Materials, B. D. Cullity (1972)
    TitleIntroduction to Magnetic Materials
    AuthorB. D. Cullity
  • Critical superparamagnetism, K. Stierstadt N. Steigenberger (1972)
    TitleCritical superparamagnetism
    AuthorK. Stierstadt N. Steigenberger
    PublicationPhysica Status Solidi (a)
    AbstractThe behaviour of a magnetic system, which becomes superparamagnetic at a blocking temperature inside its critical region, is called critical superparamagnetism. The system may consist either of small ferromagnetic particles in a non-ferromagnetic matrix, or likewise of a large crystal containing small regions with different Curie temperatures. The conditions for the existence of critical superparamagnetism are studied as functions of temperature, particle size, packing fraction, and anisotropy. The initial susceptibility of such a system depends in a characteristic manner on the measuring frequency. At a frequency corresponding to the reciprocal superparamagnetic relaxation time the susceptibility changes rather abruptly from its rotational to its superparamagnetic value. Numerical calculations are carried out for nickel showing the existence of critical superparamagnetism in this material. The susceptibility difference can reach several orders of magnitude under suitable conditions
  • Magnetization Curling, A. Aharoni (1966)
    TitleMagnetization Curling
    AuthorA. Aharoni
    Publicationphysica status solidi (b)
  • Demagnetizing Field in Nonellipsoidal Bodies, R. I. Joseph et al. (1965)
    TitleDemagnetizing Field in Nonellipsoidal Bodies
    AuthorsR. I. Joseph, E. Schlomann
    PublicationJournal of Applied Physics
    DateMay 00, 1965
  • Magnetization Reversal of Almost Perfect Whiskers, F. E. Luborsky et al. (1964)
    TitleMagnetization Reversal of Almost Perfect Whiskers
    AuthorsF. E. Luborsky, C. R. Morelock
    PublicationJournal of Applied Physics
    DateJuly 00, 1964
  • Thermal Fluctuations of a Single-Domain Particle, W.F. Brown (1963)
    TitleThermal Fluctuations of a Single-Domain Particle
    AuthorW.F. Brown
    PublicationPhysical Review
    DateJune 01, 1963
    AbstractA sufficiently fine ferromagnetic particle has a uniform vector magnetization whose magnitude is essentially constant, but whose direction fluctuates because of thermal agitation. The fluctuations are important in superparamagnetism and in magnetic aftereffect. The problem is approached here by methods familiar in the theory of stochastic processes. The "Langevin equation" of the problem is assumed to be Gilbert's equation of motion augmented by a "random-field" term. Consideration of a statistical ensemble of such particles leads to a "Fokker-Planck" partial differential equation, which describes the evolution of the probability density of orientations. The random-field concept, though convenient, can be avoided by use of the fluctuation-dissipation theorem. The Fokker-Planck equation, in general, is complicated by the presence of gyroscopic terms. These drop out in the case of axial symmetry: then the problem of finding nonequilibrium solutions can be restated as a minimization problem, susceptible to approximate treatments. The case of energy barriers large in comparison with kT is treated both by approximate minimization and by an adaptation of Kramers' treatment of the escape of particles over barriers. The limits of validity of the discrete-orientation approximation are discussed.
  • Spin-Flopping in MnF[sub 2] by High Magnetic Fields, I. S. Jacobs (1961)
    TitleSpin-Flopping in MnF[sub 2] by High Magnetic Fields
    AuthorI. S. Jacobs
    PublicationJournal of Applied Physics
    DateMarch 00, 1961
    AbstractObservations of spin-flopping, or decoupling between the direction of antiferromagnetism and the easyaxis of the crystal, are presented for MnF2 in single crystal and powder form at low temperatures. Magnetizationmeasurements in pulsed fields to 140 koe are employed to explore the critical interaction energy inthis antiferromagnet, as an alternative tool to microwave resonance. The orientation dependence predictedby Néel in 1936 is confirmed. The critical field for spin-flopping given by the combination of anisotropy andexchange, (2HEHA)<sup>(1/2)</sup> is found to be 93±2 koe in excellent agreement with resonance results of S. Foner[(a) Phys. Rev. 107, 683 (1957); (b) J. phys. radium 20, 336 (1959)], and F. M. Johnson and A. H.Nethercot [Phys. Rev. 104, 847 (1956); 114, 705 (1959)]
  • Development of Elongated Particle Magnets, Fred E. Luborsky (1961)
    TitleDevelopment of Elongated Particle Magnets
    AuthorFred E. Luborsky
    PublicationJournal of Applied Physics
    DateMarch 00, 1961
  • Das magnetische Einmündungsgesetz bei plastisch verformten Nickel- und Nickel-Kobalt-Einkristallen, Kronmüller (1959)
    TitleDas magnetische Einmündungsgesetz bei plastisch verformten Nickel- und Nickel-Kobalt-Einkristallen
    Author Kronmüller
    PublicationZeitschrift für Physik A Hadrons and Nuclei
    DateOctober 01, 1959
    AbstractZusammenfassung In der vorliegenden Arbeit wird der Einfluß einer plastischen Verformung auf die Einmündung in die ferromagnetische Sättigung experimentell untersucht. Ni-und NiCo-Einkristalle wurden bei Raumtemperatur und -183° C im Zugversuch plastisch verformt. Abweichend von dem Vorgehen früherer Autoren wurde zur Auswertung der magnetischen Messungen nicht die Feldstärkeabhängigkeit, sondern die Abhängigkeit von der plastischen Verformung benützt. Aus der Temperaturabhängigkeit der differentiellen Suszeptibilität ? ergibt sich, daß die Zunahme von ? mit wachsender Verformung der magnetostriktiven Wirkung der während der Verformung entstandenen Fehlstellen, insbesondere der Versetzungen, zuzuschreiben ist.
  • New Magnetic Anisotropy, W. H. Meiklejohn et al. (1957)
    TitleNew Magnetic Anisotropy
    AuthorsW. H. Meiklejohn, C. P. Bean
    PublicationPhysical Review
    DateFebruary 01, 1957
    AbstractA new type of magnetic anisotropy has been discovered which is best described as an exchange anisotropy. This anisotropy is the result of an interaction between an antiferromagnetic material and a ferromagnetic material. The material that exhibits this exchange anisotropy is a compact of fine particles of cobalt with a cobaltous oxide shell. The effect occurs only below the Néel temperature of the antiferromagnetic material, which is essentially room temperature for the cobaltous oxide. An exchange torque is inferred to exist between the metal and oxide which has a maximum value at 77°K of ∼2 dyne-cm/cm2 of interface.
  • Crucial Experiment Demonstrating Single Domain Property of Fine Ferromagnetic Powders, C. Kittel et al. (1950)
    TitleCrucial Experiment Demonstrating Single Domain Property of Fine Ferromagnetic Powders
    AuthorsC. Kittel, J. K. Galt, W. E. Campbell
    PublicationPhysical Review
    DateMarch 01, 1950
  • Physical Theory of Ferromagnetic Domains, Charles Kittel (1949)
    TitlePhysical Theory of Ferromagnetic Domains
    AuthorCharles Kittel
    PublicationReviews of Modern Physics
    DateOctober 1949
  • Influence des fluctuations thermiques sur l'aimantation de grains ferromagnétiques très fins, L. Néel (1949)
    TitleInfluence des fluctuations thermiques sur l'aimantation de grains ferromagnétiques très fins
    AuthorL. Néel
    PublicationSéance du académie des sciences
    Date21 Feb 1949
  • A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys, E. C. Stoner et al. (1948)
    TitleA Mechanism of Magnetic Hysteresis in Heterogeneous Alloys
    AuthorsE. C. Stoner, E. P. Wohlfarth
    PublicationPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
    DateMay 04, 1948
    AbstractThe Becker-Kersten treatment of domain boundary movements is widely applicable in the interpretation of magnetization curves, but it does not account satisfactorily for the higher coercivities obtained, for example, in permanent magnet alloys. It is suggested that in many ferromagnetic materials there may occur 'particles' (this term including atomic segregates or 'islands' in alloys), distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector, I 0 . As the field changes continuously, the resolved magnetization, I H , may change discontinuously at critical values, H 0 , of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle, and on the orientation of 'easy axes' with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magneto-crystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution (section section 2,3,4), and a less detailed treatment for the general ellipsoidal form (section 5). For the first it is convenient to use the non-dimensional parameter h, such that h = H/(|N a -N b |) I 0 , N a and N b being the demagnetization coefficients along the polar and equatorial axes. The results are presented in tables and diagrams giving the variation with h of I H /I 0 . For the special limiting form of the oblate spheroid there is no hysteresis. For the prolate spheroid, as the orientation angle, θ , varies from 0 to 90 degrees, the cyclic magnetization curves change from a rectangular form with |h 0 | = 1, to a linear non-hysteretic form, with an interesting sequence of intermediate forms. Exact expressions are obtained for the dependence of h 0 and θ , and curves for random distribution are computed. All the numerical results are applicable when the anisotropy is due to longitudinal stress, when h = HI 0 /3 λσ, where λ is the saturation magnetostriction coefficient, and σ the stress. The results also apply to magneto-crystalline anisotropy in the important and representative case in which there is a unique axis of easy magnetization as for hexagonal cobalt. Estimates are made of the magnitude of the effect of the various types of anisotropy. For iron the maximum coercivities, for the most favourable orientation, due to the magneto-crystalline and strain effects are about 400 and 600 respectively. These values are exceeded by those due to the shape effect in prolate spheroids if the dimensional ratio, m, is greater than 1 ⋅1; for m = 10, the corresponding value would be about 10,000 (section 7). A fairly precise estimate is made of the lower limit for the equatorial diameter of a particle in the form of a prolate spheroid below which boundary formation cannot occur. As m varies from 1 (the sphere) to 10, this varies from 1 ⋅5 to 6 ⋅1 × 10 -6 for iron, and from 6 ⋅2 to 25 × 10 -6 for nickel (section 6). A discussion is given (section 7) of the application of these results to (a) non-ferromagnetic metals and alloys containing ferromagnetic 'impurities', (b) powder magnets, (c) high coercivity alloys of the dispersion hardening type. In connexion with (c) the possible bearing on the effects of cooling in a magnetic field is indicated.
  • Theory of the Structure of Ferromagnetic Domains in Films and Small Particles, Charles Kittel (1946)
    TitleTheory of the Structure of Ferromagnetic Domains in Films and Small Particles
    AuthorCharles Kittel
    PublicationPhysical Review
    DateDecember 01, 1946
  • Demagnetizing Factors of the General Ellipsoid, J. A. Osborn (1945)
    TitleDemagnetizing Factors of the General Ellipsoid
    AuthorJ. A. Osborn
    PublicationPhysical Review
    DateJune 01, 1945
  • The Effect of Dislocations on Magnetization Near Saturation, William Fuller Brown (1941)
    TitleThe Effect of Dislocations on Magnetization Near Saturation
    AuthorWilliam Fuller Brown
    PublicationPhysical Review
    DateJuly 15, 1941
    AbstractThe effect of dislocations on the magnetization curve at high fields is calculated by direct use of dislocation theory. The deviation from saturation is assumed to be due to magnetostrictive forces, localized in the stress field about the dislocation rather than at the dislocation itself; their effect is more complicated than that of the simple "line concentrations of force" considered in an earlier article. Pairs of dislocations of opposite sign, separated by a short distance, contribute a term a / H to the deviation from saturation; in this respect they resemble line concentrations. Pairs separated by a long distance and surplus dislocations of one sign contribute a term b / H2, with b theoretically not a constant but a logarithmically varying function of H. From data on the variation of the empirical a and b with plastic strain, it is possible to calculate the density of dislocations and the "block" length if a value is assumed for the distance Y between the members of a dislocation pair. The orders of magnitude obtained agree with those obtained in the theory of hardening if Y is taken ≅2×10-6 cm. It appears that all but about 1 percent of the dislocations are members of such pairs.
  • Theory of the Approach to Magnetic Saturation, William Fuller Brown (1940)
    TitleTheory of the Approach to Magnetic Saturation
    AuthorWilliam Fuller Brown
    PublicationPhysical Review
    DateOctober 15, 1940
  • Some Applications of the Method of Images-I., Jakob Kunz et al. (1921)
    TitleSome Applications of the Method of Images-I.
    AuthorsJakob Kunz, P. L. Bayley
    PublicationPhysical Review
    DateFebruary 1921
  • An Account of an Extraordinary Effect of Lightning in Communicating Magnetism. Communicated by Pierce Dod, M. D. F. R. S. from Dr. Cookson of Wakefield in Yorkshire, Pierce Dod (1735)
    TitleAn Account of an Extraordinary Effect of Lightning in Communicating Magnetism. Communicated by Pierce Dod, M. D. F. R. S. from Dr. Cookson of Wakefield in Yorkshire
    AuthorPierce Dod
    PublicationPhilosophical Transactions (1683-1775)
    Date1735 - 1736