DOCSLIB.ORG

Chapter 7 Micromagnetism, Domains and Hysteresis

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chapter 7 Micromagnetism, Domains and Hysteresis Chapter 7 Micromagnetism, domains and hysteresis 7.1 Micromagnetic energy 7.2 Domain theory 7.5 Reversal, pinning and nucleation TCD March 2007 1 The hysteresis loop spontaneous magnetization remanence coercivity virgin curve initial susceptibility major loop The hysteresis loop shows the irreversible, nonlinear response of a ferromagnet to a magnetic field . It reflects the arrangement of the magnetization in ferromagnetic domains. The magnet cannot be in thermodynamic equilibrium anywhere around the open part of the curve! M and H have the same units (A m-1). TCD March 2007 2 Domains form to minimize the dipolar energy Ed TCD March 2007 3 TCD March 2007 4 Magnetostatics Poisson’s equarion Volume charge Boundary condition en 2. air + 1. solid + M + M( r) ! H( r) BUT H( r) ! M( r) Experimental information about the domain structure comes from observations at the surface. The interior is inscruatble. TCD March 2007 5 7.1 Micromagnetic energy TCD March 2007 6 1.1 Exchange eM = M( r)/Ms (",#) Exchange length A = kTC/2a 2 A = 2JS Zc/a0 A ~ 10 pJ m-1 Lex ~ 2 - 3 nm Exchange energy of vortex 2 $Eex = JS ln (R/a) TCD March 2007 7 1.2 Anisotropy 2 2 7 -3 EK = K1sin " Bulk K1 ~ 10 - 10 J m -2 Surface Ksa ~ 0.1 - 1 mJ m . -2 Interface Kea ~ 1 mJ m . Exchange and anisotropy govern the width of the domain wall. TCD March 2007 8 1.3 Demagnetizing field Demagnetizing field governs the formation of the wall (integral over all space) and B = µ0(H + M) Hd is determined by the volume and surface charge distributions %.M and en.M 2 &m = qm/4'r; % &m= -(m H = - %&m TCD March 2007 9 1.4 Stress Magnetoelastic strain tensor For isotropic material, uniaxial stress Induced uniaxial anisotropy TCD March 2007 10 1.5 Magnetosriction Local stresses can be created by the magnetostriction of the ferromagnet itself: Magnetostrictive stress Deviation due to magnetostriction Elastic tensor Usually this term is small < 1 kj m-3 , but it can influence the formation of closure domains. TCD March 2007 11 1.6 Charge Avoidance A guide to how nature minimizes the micromagnetic free energy is the charge avoidance principle. Avoid forming bulk or surface chage, and keep charge of like sign as far apart as possible e.g Keep magnetization parallel to the surface, wherever possible. Toroid Picture frame TCD March 2007 12 General statement of the micromagnetic problem: No torque on the magnetization at any point. Brown’s Micromagnetic equations TCD March 2007 13 7.1 Domain Theory A ~ 10-11 J m-1 5 -3 K1 ~ 10 J m TCD March 2007 14 2.1 Bloch Wall TCD March 2007 15 TCD March 2007 16 2.1 Néel Wall Neel walls form in thin films of soft material thinner than ~ 6 nm TCD March 2007 17 2.3 Magnetization processes There are two magnetization processes for a ferromagnet: 1) Domain-wall motion 2) Magnetization rotation H’ If the domain walls are perfectly free to move, they will do so until H =0; H’ = 1/N TCD March 2007 18 7.3 Nucleation, reversal and pinning TCD March 2007 19 Brown’s paradox Brown’s theorem; for a homogeneous, uniformly- magnetized ellipse TCD March 2007 20 TCD March 2007 21 A very small particle will be single-domain. Larger particles form domain walls to reduce demagnetizing energy Single-domain particle size: Cost of making two 90 degree walls is 2!R2(AK)1/2 should offset the N 2 gain in demagnetizing energy -(1/2) Ms TCD March 2007 22 3.2 The Stoner Wohlfarth model Assume coherent rotation of the magnetization. H makes an angle ) with the axis of the particle. NB R < Rsd does not guarantee coherent rotation. When ) = 0, Hc=2Ku/µ0Ms TCD March 2007 23 The energy landscape of a Stoner Wohlfarth particle TCD March 2007 24 Hc = 0.479 Mr = 0.5 Area = 0.99 TCD March 2007 25 Preisach Model Model hysteresis loops with a distribution of elementary square loops. These are known as ‘hysterons’ M H TCD March 2007 26 Other reversal modes TCD March 2007 27 3.3 Reversal in thin films and small elements Consider a thin film as a 2D S-W ‘particle’. The reversal The Stoner Wohlfarth asteroid. is assumed to be coherent Locus of points where a bifurcation of energy occurs Switching occurs on the surface, never within it. Take components of H along easy and hard directions, and normalize them by the anisotropy field 2Ku/Ms dEtot/d"=0 TCD March 2007 28 TCD March 2007 29 TCD March 2007 30 3.4 The two-hemisphere model A sphere made up of two halves with different anisotropy K) and K* Exchange + dipole interactions Anisotropy + Zeeman interactions If K1 = K) and K* = 0, Independent reveral of the soft hemisphere occurs when H ≈ (1/8) Ms l Except if R < ex , when the soft hemisphere cannot reverse independently. TCD March 2007 31 Exchange stiffening operates on a length scale of up to ≈ 4lex ≈ 10 nm. TCD March 2007 32 3.4 Switching dynamics; Torque on a magnetic moment in a field causes precession at the Larmor precession frequency i.e. 28 GHz/T when g=2 and + = -e/m In the presence of unixial anisotropy: H Gilbert damping term M TCD March 2007 33 3.5 Domain wall pinning Barkhausen jumps Domain wall velocity. TCD March 2007 34 3.6 Real hysteresis loops TCD March 2007 35 Kronmuller Equation TCD March 2007 36 TCD March 2007 37 Approach to saturation TCD March 2007 38 Time Dependence Magnetic Viscosity M = M0 - S ln t spontaneous magnetization remanence coercivity virgin curve initial susceptibility major loop The hysteresis loop shows the irreversible, nonlinear response of a ferromagnet to a magnetic field . It reflects the arrangement of the magnetization in ferromagnetic domains. The magnet cannot be in thermodynamic equilibrium anywhere around the open part of the curve! M and H have the same units (A m-1). TCD March 2007 39.
Load more

Recommended publications
  • Stress Dependence of the Magnetic Properties of Steels Michael K
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1992 Stress dependence of the magnetic properties of steels Michael K. Devine Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Metallurgy Commons Recommended Citation Devine, Michael K., "Stress dependence of the magnetic properties of steels" (1992). Retrospective Theses and Dissertations. 227. https://lib.dr.iastate.edu/rtd/227 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Stress dependence of the magnetic properties of steels by Michael Kenneth Devine A Thesis Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Department: Materials Science and Engineering Major: Metallurgy Approved: Signature redacted for privacy In Charge of Major Work For the Major Department For the Graduate College Iowa State University Ames, Iowa 1992 ii TABLE OF CONTENTS Page CHAPTER 1. INTRODUCTION • • • • • • 0 . • • 1 Origin of Ferromagnetism • . 3 Influence of Microstructure and Composition 5 Influence of Stress . • • • 0 • • 11 NDE Applications • • 28 Statement of Problem and Experimental Approach • 29 CHAPTER 2. EXPERIMENTAL PROCEDURE FOR MAGNETIC MEASUREMENTS • • • • • • • • ~0 Magnescope Instrumentation 30 Inspection Head Design • • • 32 CHAPTER 3. LABORATORY SCALE STRESS DETECTION WITH A SOLENOID • • • • • • • • • • • • • • • • • • 37 Introduction • • . 37 Materials and Experimental Procedure 37 Results and Discussion • • 38 Conclusions • • • • • • • • • • • • • • • • 0 • • • 45 CHAPTER 4.
    [Show full text]
  • Thermal Fluctuations of Magnetic Nanoparticles: Fifty Years After Brown1)
    THERMAL FLUCTUATIONS OF MAGNETIC NANOPARTICLES: FIFTY YEARS AFTER BROWN1) William T. Coffeya and Yuri P. Kalmykovb a Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland b Laboratoire de Mathématiques et Physique (LAMPS), Université de Perpignan Via Domitia, 52, Avenue Paul Alduy, F-66860 Perpignan, France The reversal time (superparamagnetic relaxation time) of the magnetization of fine single domain ferromagnetic nanoparticles owing to thermal fluctuations plays a fundamental role in information storage, paleomagnetism, biotechnology, etc. Here a comprehensive tutorial-style review of the achievements of fifty years of development and generalizations of the seminal work of Brown [W.F. Brown, Jr., Phys. Rev., 130, 1677 (1963)] on thermal fluctuations of magnetic nanoparticles is presented. Analytical as well as numerical approaches to the estimation of the damping and temperature dependence of the reversal time based on Brown’s Fokker-Planck equation for the evolution of the magnetic moment orientations on the surface of the unit sphere are critically discussed while the most promising directions for future research are emphasized. I. INTRODUCTION A. THERMAL INSTABILITY OF MAGNETIZATION IN FINE PARTICLES B. KRAMERS ESCAPE RATE THEORY C. SUPERPARAMAGNETIC RELAXATION TIME: BROWN’S APPROACH II. BROWN’S CONTINUOUS DIFFUSION MODEL OF CLASSICAL SPINS A. BASIC EQUATIONS B. EVALUATION OF THE REVERSAL TIME OF THE MAGNETIZATION AND OTHER OBSERVABLES III. REVERSAL TIME IN SUPERPARAMAGNETS WITH AXIALLY-SYMMETRIC MAGNETOCRYSTALLINE ANISOTROPY A. FORMULATION OF THE PROBLEM B. ESTIMATION OF THE REVERSAL TIME VIA KRAMERS’ THEORY C. UNIAXIAL SUPERPARAMAGNET SUBJECTED TO A D.C. BIAS FIELD PARALLEL TO THE EASY AXIS IV. REVERSAL TIME OF THE MAGNETIZATION IN SUPERPARAMAGNETS WITH NONAXIALLY SYMMETRIC ANISOTROPY 1) Published in Applied Physics Reviews Section of the Journal of Applied Physics, 112, 121301 (2012).
    [Show full text]
  • Dynamic Symmetry Loss of High-Frequency Hysteresis Loops in Single-Domain Particles with Uniaxial Anisotropy
    Journal of Magnetism and Magnetic Materials 324 (2012) 466–470 Contents lists available at SciVerse ScienceDirect Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm Dynamic symmetry loss of high-frequency hysteresis loops in single-domain particles with uniaxial anisotropy Gabriel T. Landi Instituto de Fı´sica da Universidade de Sao~ Paulo, 05314-970 Sao~ Paulo, Brazil article info abstract Article history: Understanding how magnetic materials respond to rapidly varying magnetic fields, as in dynamic Received 2 June 2011 hysteresis loops, constitutes a complex and physically interesting problem. But in order to accomplish a Available online 23 August 2011 thorough investigation, one must necessarily consider the effects of thermal fluctuations. Albeit being Keywords: present in all real systems, these are seldom included in numerical studies. The notable exceptions are Single-domain particles the Ising systems, which have been extensively studied in the past, but describe only one of the many Langevin dynamics mechanisms of magnetization reversal known to occur. In this paper we employ the Stochastic Landau– Magnetic hysteresis Lifshitz formalism to study high-frequency hysteresis loops of single-domain particles with uniaxial anisotropy at an arbitrary temperature. We show that in certain conditions the magnetic response may become predominantly out-of-phase and the loops may undergo a dynamic symmetry loss. This is found to be a direct consequence of the competing responses due to the thermal fluctuations and the gyroscopic motion of the magnetization. We have also found the magnetic behavior to be exceedingly sensitive to temperature variations, not only within the superparamagnetic–ferromagnetic transition range usually considered, but specially at even lower temperatures, where the bulk of interesting phenomena is seen to take place.
    [Show full text]
  • Selecting the Optimal Inductor for Power Converter Applications
    Selecting the Optimal Inductor for Power Converter Applications BACKGROUND SDR Series Power Inductors Today’s electronic devices have become increasingly power hungry and are operating at SMD Non-shielded higher switching frequencies, starving for speed and shrinking in size as never before. Inductors are a fundamental element in the voltage regulator topology, and virtually every circuit that regulates power in automobiles, industrial and consumer electronics, SRN Series Power Inductors and DC-DC converters requires an inductor. Conventional inductor technology has SMD Semi-shielded been falling behind in meeting the high performance demand of these advanced electronic devices. As a result, Bourns has developed several inductor models with rated DC current up to 60 A to meet the challenges of the market. SRP Series Power Inductors SMD High Current, Shielded Especially given the myriad of choices for inductors currently available, properly selecting an inductor for a power converter is not always a simple task for designers of next-generation applications. Beginning with the basic physics behind inductor SRR Series Power Inductors operations, a designer must determine the ideal inductor based on radiation, current SMD Shielded rating, core material, core loss, temperature, and saturation current. This white paper will outline these considerations and provide examples that illustrate the role SRU Series Power Inductors each of these factors plays in choosing the best inductor for a circuit. The paper also SMD Shielded will describe the options available for various applications with special emphasis on new cutting edge inductor product trends from Bourns that offer advantages in performance, size, and ease of design modification.
    [Show full text]
  • Magnetic Switching of a Stoner-Wohlfarth Particle Subjected to a Perpendicular Bias Field
    electronics Article Magnetic Switching of a Stoner-Wohlfarth Particle Subjected to a Perpendicular Bias Field Dong Xue 1,* and Weiguang Ma 2 1 Department of Physics and Astronomy, Texas Tech University, Lubbock, TX 79409-1051, USA 2 Department of Physics, Umeå University, 90187 Umeå, Sweden; [email protected] * Correspondence: [email protected]; Tel.: +1-806-834-4563 Received: 28 February 2019; Accepted: 21 March 2019; Published: 26 March 2019 Abstract: Characterized by uniaxial magnetic anisotropy, the Stoner-Wohlfarth particle experiences a change in magnetization leading to a switch in behavior when tuned by an externally applied field, which relates to the perpendicular bias component (hperp) that remains substantially small in comparison with the constant switching field (h0). The dynamics of the magnetic moment that governs the magnetic switching is studied numerically by solving the Landau-Lifshitz-Gilbert (LLG) equation using the Mathematica code without any physical approximations; the results are compared with the switching time obtained from the analytic method that intricately treats the non-trivial bias field as a perturbation. A good agreement regarding the magnetic switching time (ts) between the numerical calculation and the analytic results is found over a wide initial angle range (0.01 < q0 < 0.3), as h0 and hperp are 1.5 × K and 0.02 × K, where K represents the anisotropy constant. However, the quality of the analytic approximation starts to deteriorate slightly in contrast to the numerical approach when computing ts in terms of the field that satisfies hperp > 0.15 × K and h0 = 1.5 × K. Additionally, existence of a comparably small perpendicular bias field (hperp << h0) causes ts to decrease in a roughly exponential manner when hperp increases.
    [Show full text]
  • Module 2C: Micromagnetics
    Module 2C: Micromagnetics Debanjan Bhowmik Department of Electrical Engineering Indian Institute of Technology Delhi Abstract In this part of the second module (2C) we will show how the Stoner Wolfarth/ single domain mode of ferromagnetism often fails to match with experimental data. We will introduce domain walls in that context and explain the basic framework of micromagnetics, which can be used to model domain walls. Then we will discuss how an anisotropic exchange interaction, known as Dzyaloshinskii Moriya interaction, can lead to chirality of the domain walls. Then we will introduce another non-uniform magnetic structure known as skyrmion and discuss its stability, based on topological arguments. 1 1 Brown's paradox in ferromagnetic thin films exhibiting perpendicular magnetic anisotropy We study ferromagnetic thin films exhibiting Perpendicular Magnetic Anisotropy (PMA) to demonstrate the failure of the previously discussed Stoner Wolfarth/ single domain model to explain experimentally observed magnetic switching curves. PMA is a heavily sought after property in magnetic materials for memory and logic applications (we will talk about that in details in the next module). This makes our analysis in this section even more relevant. The ferromagnetic layer in the Ta/CoFeB/MgO stack, grown by room temperature sput- tering, exhibits perpendicular magnetic anisotropy with an anisotropy field Hk of around 2kG needed to align the magnetic moment in-plane (Fig. 1a). Thus if the ferromagnetic layer is considered as a giant macro-spin in the Stoner Wolfarth model an energy barrier equivalent to ∼2kG exists between the up (+z) and down state (-z) (Fig. 1b). Yet mea- surement shows that the magnet can be switched by a field, called the coercive field, as small as ∼50 G, which is 2 orders of magnitude smaller than the anisotropy field Hk, as observed in the Vibrating Sample Magnetometry measurement on the stack (Fig.
    [Show full text]
  • Magnetically Multiplexed Heating of Single Domain Nanoparticles
    Magnetically Multiplexed Heating of Single Domain Nanoparticles M. G. Christiansen,1) R. Chen,1) and P. Anikeeva1,a) 1Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA Abstract: Selective hysteretic heating of multiple collocated sets of single domain magnetic nanoparticles (SDMNPs) by alternating magnetic fields (AMFs) may offer a useful tool for biomedical applications. The possibility of “magnetothermal multiplexing” has not yet been realized, in part due to prevalent use of linear response theory to model SDMNP heating in AMFs. Predictive successes of dynamic hysteresis (DH), a more generalized model for heat dissipation by SDMNPs, are observed experimentally with detailed calorimetry measurements performed at varied AMF amplitudes and frequencies. The DH model suggests that specific driving conditions play an underappreciated role in determining optimal material selection strategies for high heat dissipation. Motivated by this observation, magnetothermal multiplexing is theoretically predicted and empirically demonstrated for the first time by selecting SDMNPs with properties that suggest optimal hysteretic heat dissipation at dissimilar AMF driving conditions. This form of multiplexing could effectively create multiple channels for minimally invasive biological signaling applications. Text: Magnetic fields provide a convenient form of noninvasive electronically driven stimulus that can reach deep into the body because of the weak magnetic properties and low
    [Show full text]
  • High Coercivity Vs
    Card Testing International Ltd Level 4, 105 High Street PO Box 30 356 Lower Hutt 5040, NZ Phone: Asia/Pacific +64 4 903 4990 North America (800) 438 9036 Email: [email protected] Website: www.cardtest.com High Coercivity vs. Low Coercivity Accidental magnetic card erasure, a problem today? We have come to expect reliability in our electronic system. Yes, repairs are required, but when you add up all the electronic gadgets in our homes and businesses it's a miracle that service isn't needed more often. Banking, vending, identification and security are some of the most important systems in our lives, and it is critical that they work smoothly. Some of the cards we use in these systems are subject to reliability problems depending on the material used in their tape. The standard magnetic tape that is used on many bank cards are made with iron oxide, effectively rust. The magnetism needed to erase this medium is called coercive force. Units of coercivity are named Oersted. The coercivity of the iron oxide tape used in banking and many other application is 300 Oersted. Ordinary magnets with which we come into contact can easily erase this tape. The magnets that are sometimes used to hold messages onto our refrigerators fall into this category. Some handbags/wallets have magnetic latches that can be a problem. Magnetic force falls off rapidly as the card distance from the offending magnet is increased. It's unlikely that an ordinary magnet kept at least 10 to 15mm from the stripe will damage the tape.
    [Show full text]
  • Magnetic Materials: Hysteresis
    Magnetic Materials: Hysteresis Ferromagnetic and ferrimagnetic materials have non-linear initial magnetisation curves (i.e. the dotted lines in figure 7), as the changing magnetisation with applied field is due to a change in the magnetic domain structure. These materials also show hysteresis and the magnetisation does not return to zero after the application of a magnetic field. Figure 7 shows a typical hysteresis loop; the two loops represent the same data, however, the blue loop is the polarisation (J = µoM = B-µoH) and the red loop is the induction, both plotted against the applied field. Figure 7: A typical hysteresis loop for a ferro- or ferri- magnetic material. Illustrated in the first quadrant of the loop is the initial magnetisation curve (dotted line), which shows the increase in polarisation (and induction) on the application of a field to an unmagnetised sample. In the first quadrant the polarisation and applied field are both positive, i.e. they are in the same direction. The polarisation increases initially by the growth of favourably oriented domains, which will be magnetised in the easy direction of the crystal. When the polarisation can increase no further by the growth of domains, the direction of magnetisation of the domains then rotates away from the easy axis to align with the field. When all of the domains have fully aligned with the applied field saturation is reached and the polarisation can increase no further. If the field is removed the polarisation returns along the solid red line to the y-axis (i.e. H=0), and the domains will return to their easy direction of magnetisation, resulting in a decrease in polarisation.
    [Show full text]
  • High Coercivity, Anisotropic, Heavy Rare Earth-Free Nd-Fe-B by Flash Spark Plasma Sintering
    www.nature.com/scientificreports OPEN High coercivity, anisotropic, heavy rare earth-free Nd-Fe-B by Flash Spark Plasma Sintering Received: 29 June 2017 Elinor Castle 1, Richard Sheridan2, Wei Zhou2, Salvatore Grasso1, Allan Walton2 & Michael J. Accepted: 17 August 2017 Reece1 Published: xx xx xxxx In the drive to reduce the critical Heavy Rare Earth (HRE) content of magnets for green technologies, HRE-free Nd-Fe-B has become an attractive option. HRE is added to Nd-Fe-B to enhance the high temperature performance of the magnets. To produce similar high temperature properties without HRE, a crystallographically textured nanoscale grain structure is ideal; and this conventionally requires expensive “die upset” processing routes. Here, a Flash Spark Plasma Sintering (FSPS) process has been applied to a Dy-free Nd30.0Fe61.8Co5.8Ga0.6Al0.1B0.9 melt spun powder (MQU-F, neo Magnequench). Rapid sinter-forging of a green compact to near theoretical density was achieved during the 10 s process, and therefore represents a quick and efficient means of producing die-upset Nd-Fe-B material. The microstructure of the FSPS samples was investigated by SEM and TEM imaging, and the observations were used to guide the optimisation of the process. The most optimal sample is compared directly to commercially die-upset forged (MQIII-F) material made from the same MQU-F powder. It is shown that the grain size of the FSPS material is halved in comparison to the MQIII-F material, leading to a 14% −1 −3 increase in coercivity (1438 kA m ) and matched remanence (1.16 T) giving a BHmax of 230 kJ m .
    [Show full text]
  • Tailored Magnetic Properties of Exchange-Spring and Ultra Hard Nanomagnets
    Max-Planck-Institute für Intelligente Systeme Stuttgart Tailored Magnetic Properties of Exchange-Spring and Ultra Hard Nanomagnets Kwanghyo Son Dissertation An der Universität Stuttgart 2017 Tailored Magnetic Properties of Exchange-Spring and Ultra Hard Nanomagnets Von der Fakultät Mathematik und Physik der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung Vorgelegt von Kwanghyo Son aus Seoul, SüdKorea Hauptberichter: Prof. Dr. Gisela Schütz Mitberichter: Prof. Dr. Sebastian Loth Tag der mündlichen Prüfung: 04. Oktober 2017 Max‐Planck‐Institut für Intelligente Systeme, Stuttgart 2017 II III Contents Contents ..................................................................................................................................... 1 Chapter 1 ................................................................................................................................... 1 General Introduction ......................................................................................................... 1 Structure of the thesis ....................................................................................................... 3 Chapter 2 ................................................................................................................................... 5 Basic of Magnetism .......................................................................................................... 5 2.1 The Origin of Magnetism .......................................................................................
    [Show full text]
  • The Role of Cobalt in Neodymium Iron
    TECHNotes The Role of Cobalt in NdFeB Permanent Magnets Neodymium iron boron (“Neo”) permanent magnets, discovered in 1980 and commercialized by 1984, remain the strongest magnets known to man – at least near room temperature. All magnets experience a change in properties as a function of temperature. As the Neo magnet temperature increases, both intrinsic coercivity, HcJ, and magnetic field strength, Br, decrease. Over a limited temperature range, these changes are non-destructive and reversible and are quantified by what are called Reversible Temperature Coefficients of Induction, (Br), and Intrinsic Coercivity (HcJ). These coefficients are the average rate of change between temperature limits. The changes are non-linear so it is necessary to state the temperature range over which the coefficients are calculated. To permit Neo magnets to operate at elevated temperatures, two composition changes are introduced. Figure 1. Magnetic field strength of iron, cobalt and nickel as a 1. The substitution of the heavy rare earth elements function of temperature. [1] (HREEs) dysprosium and/or terbium for a portion of the neodymium increases the anisotropy field. This provides higher room temperature intrinsic coercivity and reduces the rate at which coercivity drops as temperature increases – smaller reversible temperature coefficient of (intrinsic) coercivity. 2. Substitution of cobalt for a portion of iron raises the magnet Curie temperature, Tc, and reduces the rate at which magnetic field strength, B, changes as a function of temperature. This TECHNote focuses on the effects of cobalt on magnet Curie temperature, residual induction, intrinsic coercivity and corrosion resistance. Curie Temperature Figure 2. Magnetization versus magnetic field strength for Both ferro- and ferrimagnetic materials exhibit a NdFeB magnets with three levels of cobalt.
    [Show full text]