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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) Title Including effects of microstructure and anisotropy in theoretical models describing hysteresis of ferromagnetic materials Authors H. Hauser, Y. Melikhov, D. C. Jiles Publication Applied Physics Letters Volume 91 Issue 17 Pages 172512-3 Date October 22, 2007 URL http://link.aip.org/link/?APL/91/172512/1 Solid-state physics: Response with a twist, Karin M. Rabe (2007) Title Solid-state physics: Response with a twist Author Karin M. Rabe Publication Nature Volume 449 Issue 7163 Pages 674-675 Date October 11, 2007 DOI 10.1038/449674a Observation of ferrotoroidic domains, Bas B. Van Aken et al. (2007) Title Observation of ferrotoroidic domains Authors Bas B. Van Aken, Jean-Pierre Rivera, Hans Schmid, Manfred Fiebig Publication Nature Volume 449 Issue 7163 Pages 702-705 Date October 11, 2007 DOI 10.1038/nature06139 Magnetism & Magnetic Materials; 3S100 course syllabus 2007-2008, H.M. Swagten (2007) Title Magnetism & Magnetic Materials; 3S100 course syllabus 2007-2008 Author H.M. Swagten Date 29/08/2007 Publisher Eindhoven University of Technology Electrical switching of the vortex core in a magnetic disk, Keisuke Yamada et al. (2007) Title Electrical switching of the vortex core in a magnetic disk Authors Keisuke Yamada, Shinya Kasai, Yoshinobu Nakatani, Kensuke Kobayashi, Hiroshi Kohno, Andre Thiaville, Teruo Ono Publication Nat Mater Volume 6 Issue 4 Pages 270-273 Date April 2007 DOI 10.1038/nmat1867 The role of nucleation field of media in heat-assisted magnetic probe recording, Li Zhang (2007) Title The role of nucleation field of media in heat-assisted magnetic probe recording Author Li Zhang Publication Physica B: Condensed Matter Volume 390 Issue 1-2 Pages 373-376 Date March 1, 2007 Abstract We 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. DOI 10.1016/j.physb.2006.08.040 URL http://www.sciencedirect.com/science/article/B6TVH-4M57H7Y-1/1/bdd38706c178dbc442b1b9354d25425e Current-induced magnetic vortex core switching in a Permalloy nanodisk, Y. Liu et al. (2007) Title Current-induced magnetic vortex core switching in a Permalloy nanodisk Authors Y. Liu, S. Gliga, R. Hertel, C. M. Schneider Publication Applied Physics Letters Volume 91 Issue 11 Pages 112501-3 Date 2007 Abstract The 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. URL http://link.aip.org/link/?APL/91/112501/1 Current induced switching of vortex polarity in magnetic nanodisks, Denis D. Sheka et al. (2007) Title Current induced switching of vortex polarity in magnetic nanodisks Authors Denis D. Sheka, Yuri Gaididei, Franz G. Mertens Publication Applied Physics Letters Volume 91 Issue 8 Pages 082509-3 Date 2007 Abstract It 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. DOI 10.1063/1.2775036 URL http://link.aip.org/link/?APL/91/082509/1 The breakdown of the fingerprinting of vortices by hysteresis loops in circular multilayer ring arrays, V. Rose et al. (2007) Title The breakdown of the fingerprinting of vortices by hysteresis loops in circular multilayer ring arrays Authors V. Rose, X. M. Cheng, D. J. Keavney, J. W. Freeland, K. S. Buchanan, B. Ilic, V. Metlushko Publication Applied Physics Letters Volume 91 Issue 13 Pages 132501-3 Date 2007 DOI 10.1063/1.2786856 URL http://link.aip.org/link/?APL/91/132501/1 Supermagnetism in magnetic nanoparticle systems, S. Bedanta (2006) Title Supermagnetism in magnetic nanoparticle systems Author S. Bedanta Date 11 Dec, 2006 URL http://deposit.ddb.de/cgi-bin/dokserv?idn=983630305 Micromagnetic energy barriers, R. Skomski et al. (2006) Title Micromagnetic energy barriers Authors R. Skomski, J. Zhou, R. D. Kirby, D. J. Sellmyer Volume 99 Pages 08B906-3 Date April 15, 2006 Proceedings Title 50th Annual Conference on Magnetism and Magnetic Materials Conference Name 50th Annual Conference on Magnetism and Magnetic Materials Place San Jose, California (USA) Publisher AIP Abstract The 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. URL http://link.aip.org/link/?JAP/99/08B906/1 Small Domain Structures in Magnetization Reversal Process of Write Head in Hard Disk Drives Observed by Strain Imaging, K. Takata (2006) Title Small Domain Structures in Magnetization Reversal Process of Write Head in Hard Disk Drives Observed by Strain Imaging Author K. Takata Publication Japanese Journal of Applied Physics Volume 45 Pages 1189-1981 Date March, 2006 Abstract Detection 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. DOI 10.1143/JJAP.45.1889 URL http://jjap.ipap.jp/link?JJAP/45/1889/ Micromagnetic simulation of ferromagnetic part-spherical particles, Richard P. Boardman et al. (2004) Title Micromagnetic simulation of ferromagnetic part-spherical particles Authors Richard P. Boardman, Hans Fangohr, Simon J. Cox, Alexander V. Goncharov, Alexander A. Zhukov, Peter A. J. de Groot Volume 95 Pages 7037-7039 Date June 01, 2004 Publisher AIP URL http://link.aip.org/link/?JAP/95/7037/1 Micromagnetism and the Microstructure of Ferromagnetic Solids, H. Kronmüller et al. (2003) Title Micromagnetism and the Microstructure of Ferromagnetic Solids Authors H. Kronmüller, M. Fähnle Pages 448 Date 2003-09-29 Publisher Cambridge University Press Abstract The 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) Title General relation for the vector magnetic field of a circular current loop: a closer look Author R.A. Schill Publication Magnetics, IEEE Transactions on Volume 39 Issue 2 Pages 961-967 Date 2003 Abstract This 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) Title Magnetic size effects in iron nanoparticles and nanoparticle arrays Authors Y. Ijiri, D. F. Farrell, S. Yamamuro, S. A. Majetich Publication APS Meeting Abstracts Pages 15002 Date March 1, 2002 Abstract In 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. URL http://adsabs.harvard.edu/abs/2002APS..MARJ15002I Analysis of the Demagnetisation Process and Possible Alternative Magnetic Treatments for Naval Vessels, T. Baynes (2002) Title Analysis of the Demagnetisation Process and Possible Alternative Magnetic Treatments for Naval Vessels Author T. Baynes Date February, 2002 Abstract Naval 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. URL http://www.phys.unsw.edu.au/~tmb/Thesis_online/Thesis.htm Small inexpensive diamagnetic levitation apparatus, Charles A. Sawicki (2001) Title Small inexpensive diamagnetic levitation apparatus Author Charles A. Sawicki Publication The Physics Teacher Volume 39 Issue 9 Pages 556-558 Date December 00, 2001 Abstract A 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. DOI 10.1119/1.1482567 URL http://link.aip.org/link/?PTE/39/556/1 Exchange bias theory, Miguel Kiwi (2001) Title Exchange bias theory Author Miguel Kiwi Publication Journal of Magnetism and Magnetic Materials Volume 234 Issue 3 Pages 584-595 Date September 2001 Abstract Research 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. DOI 10.1016/S0304-8853(01)00421-8 URL http://www.sciencedirect.com/science/article/B6TJJ-4417P2D-11/2/0f126091e72e284b134c543dba3ed809 Layered Magnetic Structures: History, Highlights, Applications, Peter Grunberg (2001) Title Layered Magnetic Structures: History, Highlights, Applications Author Peter Grunberg Publication Physics Today Volume 54 Issue 5 Pages 31-37 Date May 00, 2001 Abstract The 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. DOI 10.1063/1.1381100 URL http://link.aip.org/link/?PTO/54/31/1 Introduction to the Theory of Ferromagnetism, Amikam Aharoni (2001) Title Introduction to the Theory of Ferromagnetism Author Amikam Aharoni Pages 336 Date 2001 Publisher Oxford University Press URL http://books.google.nl/books?id=9RvNuIDh0qMC Measuring the exchange-stiffness constant of nanocrystalline solids by elastic small-angle neutron scattering, A. Michels et al. (2000) Title Measuring 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 Publication Philosophical Magazine Volume 80 Issue 12 Pages 785-792 Date December 2000 Abstract In 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. DOI 10.1080/0950083001000180S URL http://www.informaworld.com/smpp/content?content=10.1080/0950083001000180S Deviation from the superparamagnetic behaviour of fine-particle systems, I. Malaescu et al. (2000) Title Deviation from the superparamagnetic behaviour of fine-particle systems Authors I. Malaescu, C. N. Marin Publication Journal of Magnetism and Magnetic Materials Volume 218 Issue 1 Pages 91-96 Date July 2, 2000 Abstract Studies 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. URL http://www.sciencedirect.com/science/article/B6TJJ-40NG387-G/2/48fee798a553e9bd67ad30f66f52ee71 Magnet levitation at your fingertips, A. K. Geim et al. (1999) Title Magnet levitation at your fingertips Authors A. K. Geim, M. D. Simon, M. I. Boamfa, L. O. Heflinger Publication Nature Volume 400 Issue 6742 Pages 323-324 Date July 22, 1999 DOI 10.1038/22444 Exchange bias, J. Nogués et al. (1999) Title Exchange bias Authors J. Nogués, Ivan K. Schuller Publication Journal of Magnetism and Magnetic Materials Volume 192 Issue 2 Pages 203-232 Date February 15, 1999 Abstract We 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. DOI 10.1016/S0304-8853(98)00266-2 URL http://www.sciencedirect.com/science/article/B6TJJ-3W1XP6M-1/2/8429da7f21810fe1baec27e9c0879396 Single-Domain Circular Nanomagnets, R. P. Cowburn et al. (1999) Title Single-Domain Circular Nanomagnets Authors R. P. Cowburn, D. K. Koltsov, A. O. Adeyeye, M. E. Welland, D. M. Tricker Publication Physical Review Letters Volume 83 Issue 5 Pages 1042 Date 1999 URL http://link.aps.org/abstract/PRL/v83/p1042 Controlling magnetic ordering in coupled nanomagnet arrays, R. P. Cowburn et al. (1999) Title Controlling magnetic ordering in coupled nanomagnet arrays Authors R. P. Cowburn, A. O. Adeyeye, M. E. Welland Publication New Journal of Physics Volume 1 Pages 16 Date 1999 Abstract We 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) Title Permanent Magnetism Authors R. Skomski, J.M.D Coey Pages 416 Date 1999 Publisher Taylor & Francis Demagnetizing factors for rectangular ferromagnetic prisms, Amikam Aharoni (1998) Title Demagnetizing factors for rectangular ferromagnetic prisms Author Amikam Aharoni Publication Journal of Applied Physics Volume 83 Issue 6 Pages 3432-3434 Date March 15, 1998 DOI 10.1063/1.367113 URL http://link.aip.org/link/?JAP/83/3432/1 Special Issue: Magnetoelectronics, Gary Prinz et al. (1995) Title Special Issue: Magnetoelectronics Authors Gary Prinz, Kristl Hathaway Publication Physics Today Volume 48 Pages 24-25 Date April 1, 1995 Demagnetizing factors for cylinders, D.-X. Chen et al. (1991) Title Demagnetizing factors for cylinders Authors D.-X. Chen, J.A. Brug, R.B. Goldfarb Publication IEEE Transactions on Magnetics Volume 27 Issue 4 Pages 3601-3619 Date 1991 Abstract Fluxmetric (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 DOI 10.1109/20.102932 Method of images and electrostatic screening by a polarized dielectric sphere, Clinton DeW. Van Siclen (1988) Title Method of images and electrostatic screening by a polarized dielectric sphere Author Clinton DeW. Van Siclen Publication American Journal of Physics Volume 56 Issue 12 Pages 1142-1143 Date December 00, 1988 URL http://link.aip.org/link/?AJP/56/1142/1 Magnetic properties of ultrafine ferrite particles, Toshihiko Sato et al. (1987) Title Magnetic properties of ultrafine ferrite particles Authors Toshihiko Sato, Tetsuo Iijima, Masahiro Seki, Nobuo Inagaki Publication Journal of Magnetism and Magnetic Materials Volume 65 Issue 2-3 Pages 252-256 Date March 1, 1987 Abstract The 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. URL http://www.sciencedirect.com/science/article/B6TJJ-46JGPB6-P0/2/b02f6b48576eb18e8b94a0093a3ad106 Spin wave stiffness constants in some ferrimagnetics, C. M. Srivastava et al. (1987) Title Spin wave stiffness constants in some ferrimagnetics Authors C. M. Srivastava, R. Aiyar Publication Journal of Physics C: Solid State Physics Volume 20 Issue 8 Pages 1119-1128 Date 1987 Abstract The 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) Title Magnetocrystalline Anisotropy of Low Temperature Phase of Magnetite Authors K. Abe, Y. Miyamoto, S. Chikazumi Publication Journal of the Physical Society of Japan Volume 41 Issue 6 Pages 1894-1902 Date December, 1976 Abstract The 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. DOI 10.1143/JPSJ.41.1894 URL http://jpsj.ipap.jp/link?JPSJ/41/1894 Magnetization curling in a sphere, I. Eisenstein et al. (1976) Title Magnetization curling in a sphere Authors I. Eisenstein, A. Aharoni Publication Journal of Applied Physics Volume 47 Issue 1 Pages 321-328 Date January 00, 1976 Abstract Using 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. DOI 10.1063/1.322318 URL http://link.aip.org/link/?JAP/47/321/1 Introduction to Magnetic Materials, B. D. Cullity (1972) Title Introduction to Magnetic Materials Author B. D. Cullity Pages 666 Date 1972-06 Publisher Addison-Wesley Critical superparamagnetism, K. Stierstadt N. Steigenberger (1972) Title Critical superparamagnetism Author K. Stierstadt N. Steigenberger Publication Physica Status Solidi (a) Volume 12 Issue 1 Pages 133-142 Date 1972 Abstract The 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 DOI 10.1002/pssa.2210120113 Magnetization Curling, A. Aharoni (1966) Title Magnetization Curling Author A. Aharoni Publication physica status solidi (b) Volume 16 Issue 1 Pages 3-42 Date 1966 DOI 10.1002/pssb.19660160102 Demagnetizing Field in Nonellipsoidal Bodies, R. I. Joseph et al. (1965) Title Demagnetizing Field in Nonellipsoidal Bodies Authors R. I. Joseph, E. Schlomann Publication Journal of Applied Physics Volume 36 Issue 5 Pages 1579-1593 Date May 00, 1965 URL http://link.aip.org/link/?JAP/36/1579/1 Magnetization Reversal of Almost Perfect Whiskers, F. E. Luborsky et al. (1964) Title Magnetization Reversal of Almost Perfect Whiskers Authors F. E. Luborsky, C. R. Morelock Publication Journal of Applied Physics Volume 35 Issue 7 Pages 2055-2066 Date July 00, 1964 URL http://link.aip.org/link/?JAP/35/2055/1 Thermal Fluctuations of a Single-Domain Particle, W.F. Brown (1963) Title Thermal Fluctuations of a Single-Domain Particle Author W.F. Brown Publication Physical Review Volume 130 Issue 5 Pages 1677 Date June 01, 1963 Abstract A 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. DOI 10.1103/PhysRev.130.1677 Spin-Flopping in MnF[sub 2] by High Magnetic Fields, I. S. Jacobs (1961) Title Spin-Flopping in MnF[sub 2] by High Magnetic Fields Author I. S. Jacobs Publication Journal of Applied Physics Volume 32 Issue 3 Pages S61-S62 Date March 00, 1961 Abstract Observations 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)] DOI 10.1063/1.2000500 URL http://link.aip.org/link/?JAP/32/S61/1 Development of Elongated Particle Magnets, Fred E. Luborsky (1961) Title Development of Elongated Particle Magnets Author Fred E. Luborsky Publication Journal of Applied Physics Volume 32 Issue 3 Pages S171-S183 Date March 00, 1961 DOI 10.1063/1.2000392 URL http://link.aip.org/link/?JAP/32/S171/1 Das magnetische Einmündungsgesetz bei plastisch verformten Nickel- und Nickel-Kobalt-Einkristallen, Kronmüller (1959) Title Das magnetische Einmündungsgesetz bei plastisch verformten Nickel- und Nickel-Kobalt-Einkristallen Author Kronmüller Publication Zeitschrift für Physik A Hadrons and Nuclei Volume 154 Issue 5 Pages 574-600 Date October 01, 1959 Abstract Zusammenfassung 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. DOI 10.1007/BF01337568 New Magnetic Anisotropy, W. H. Meiklejohn et al. (1957) Title New Magnetic Anisotropy Authors W. H. Meiklejohn, C. P. Bean Publication Physical Review Volume 105 Issue 3 Pages 904 Date February 01, 1957 Abstract A 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. DOI 10.1103/PhysRev.105.904 URL http://link.aps.org/abstract/PR/v105/p904 Crucial Experiment Demonstrating Single Domain Property of Fine Ferromagnetic Powders, C. Kittel et al. (1950) Title Crucial Experiment Demonstrating Single Domain Property of Fine Ferromagnetic Powders Authors C. Kittel, J. K. Galt, W. E. Campbell Publication Physical Review Volume 77 Issue 5 Pages 725 Date March 01, 1950 DOI 10.1103/PhysRev.77.725 URL http://prola.aps.org/abstract/PR/v77/i5/p725_1 Physical Theory of Ferromagnetic Domains, Charles Kittel (1949) Title Physical Theory of Ferromagnetic Domains Author Charles Kittel Publication Reviews of Modern Physics Volume 21 Issue 4 Pages 541 Date October 1949 DOI 10.1103/RevModPhys.21.541 URL http://link.aps.org/abstract/RMP/v21/p541 Influence des fluctuations thermiques sur l'aimantation de grains ferromagnétiques très fins, L. Néel (1949) Title Influence des fluctuations thermiques sur l'aimantation de grains ferromagnétiques très fins Author L. Néel Publication Séance du académie des sciences Volume 228 Issue 8 Pages 664-666 Date 21 Feb 1949 A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys, E. C. Stoner et al. (1948) Title A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys Authors E. C. Stoner, E. P. Wohlfarth Publication Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences Volume 240 Issue 826 Pages 599-642 Date May 04, 1948 Abstract The 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. URL http://links.jstor.org/sici?sici=0080-4614%2819480504%29240%3A826%3C599%3AAMOMHI%3E2.0.CO%3B2-Q Theory of the Structure of Ferromagnetic Domains in Films and Small Particles, Charles Kittel (1946) Title Theory of the Structure of Ferromagnetic Domains in Films and Small Particles Author Charles Kittel Publication Physical Review Volume 70 Issue 11-12 Pages 965 Date December 01, 1946 URL http://link.aps.org/abstract/PR/v70/p965 Demagnetizing Factors of the General Ellipsoid, J. A. Osborn (1945) Title Demagnetizing Factors of the General Ellipsoid Author J. A. Osborn Publication Physical Review Volume 67 Issue 11-12 Pages 351 Date June 01, 1945 DOI 10.1103/PhysRev.67.351 URL http://link.aps.org/abstract/PR/v67/p351 The Effect of Dislocations on Magnetization Near Saturation, William Fuller Brown (1941) Title The Effect of Dislocations on Magnetization Near Saturation Author William Fuller Brown Publication Physical Review Volume 60 Issue 2 Pages 139 Date July 15, 1941 Abstract The 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. DOI 10.1103/PhysRev.60.139 URL http://link.aps.org/abstract/PR/v60/p139 Theory of the Approach to Magnetic Saturation, William Fuller Brown (1940) Title Theory of the Approach to Magnetic Saturation Author William Fuller Brown Publication Physical Review Volume 58 Issue 8 Pages 736 Date October 15, 1940 URL http://link.aps.org/abstract/PR/v58/p736 Some Applications of the Method of Images-I., Jakob Kunz et al. (1921) Title Some Applications of the Method of Images-I. Authors Jakob Kunz, P. L. Bayley Publication Physical Review Volume 17 Issue 2 Pages 147 Date February 1921 DOI 10.1103/PhysRev.17.147 URL http://link.aps.org/abstract/PR/v17/p147 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) Title 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 Author Pierce Dod Publication Philosophical Transactions (1683-1775) Volume 39 Pages 74-75 Date 1735 - 1736 URL http://links.jstor.org/sici?sici=0260-7085%281735%2F1736%2939%3C74%3AAAOAEE%3E2.0.CO%3B2-S

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