1 Objective Linear Props Magnetism Ferromagnets Domains Wall

1 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Microstructure-Properties: I Lecture 4 A: Mathematical Descriptions of Properties; Magnetic Microstructure 27 -301 Fall, 2002 Prof. A. D. Rollett

2 Bibliography • • • Objective Linear Props. Magnetism Ferromagnets • • • Domains Wall motion Glossary Magnetism • • De Graef, M. , lecture notes for 27 -201. Nye, J. F. (1957). Physical Properties of Crystals. Oxford, Clarendon Press. Chen, C. -W. (1977). Magnetism and metallurgy of soft magnetic materials. New York, Dover. Chikazumi, S. (1996). Physics of Ferromagnetism. Oxford, Oxford University Press. Attwood, S. S. (1956). Electric and Magnetic Fields. New York, Dover. Newey, C. and G. Weaver (1991). Materials Principles and Practice. Oxford, England, Butterworth-Heinemann. T. Courtney, Mechanical Behavior of Materials, Mc. Graw-Hill, 0 -07 -013265 -8, 620. 11292 C 86 M. Kocks, U. F. , C. Tomé, et al. , Eds. (1998). Texture and Anisotropy, Cambridge University Press, Cambridge, UK. Reid, C. N. (1973). Deformation Geometry for Materials Scientists. Oxford, UK, Pergamon. Braithwaite, N. and G. Weaver (1991). Electronic Materials. The Open University, England, Butterworth-Heinemann.

3 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Objective of Lecture 4 A • The objective of this lecture is to relate magnetic properties to microstructure as an important example of a non-linear, anisotropic property. This example is illustrated by reference to ferromagnetic materials. In these materials the domain structure provides an additional degree of microstructural complexity that affects properties such as permeability. • The presence of defects (microstructure) in the material has a profound on the magnetic properties of a material. For example, the presence of second phase particles makes a material magnetically hard, just as it makes it mechanically hard.

4 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Mathematical Descriptions • Mathematical descriptions of properties are available. • Mathematics, or a type of mathematics provides a quantitative framework. It is always necessary, however, to make a correspondence between mathematical variables and physical quantities. • In group theory one might say that there is a set of mathematical operations & parameters, and a set of physical quantities and processes: if the mathematics is a good description, then the two sets are isomorphous.

5 Math of Microstructure-Property Relationships Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • In order to describe properties, we must first relate a response to a stimulus with a property. • A stimulus is something that one does to a material, e. g. apply a load. • A response is something that is the result of applying a stimulus, e. g. if you apply a load (stress), the material will change shape (strain). • The material property is the connection between the stimulus and the response.

6 Stimulus Property Response Objective Linear Props. Magnetism Ferromagnets • Mathematical framework for this approach? • The Property is equivalent to a function, P, and the {stimulus, F, response, R} are variables. The stimulus is also called a field because in many cases, the stimulus is actually an applied electrical or magnetic field. • The response is a function of the field: Domains Wall motion Glossary Magnetism R = R(F) R = P(F)

7 Scalar, Linear Properties Modulus Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Temperature • In many instances, both stimulus and response are scalar quantities, meaning that you only need one number to prescribe them, so the property is also scalar. • To further simplify, some properties are linear, which means that the response is linearly proportional to the stimulus: R = P F. However, the property is generally dependent on other variables. • Example: elastic stiffness in tension/compression as a function of temperature: R = P(T) F.

8 Objective Scalar, non-linear properties • Unfortunately not all properties are linear! • What do we do? In many cases, it useful to expand about a known point (Taylor series). Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • The response function (property) is expanded about the zero field value, assuming that it is a smooth function and therefore differentiable according to the rules of calculus.

9 Scalar, non-linear properties, contd. Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • In the previous expression, the state of the material at zero field is defined by R 0 which is sometimes zero (e. g. elastic strain in the absence of applied stress) and sometimes non-zero (e. g. in ferromagnetic materials in the absence of an external magnetic field). • Example: magnetization of iron-3%Si alloy, used for transformers [Chen].

10 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Example: magnetization • Magnetization, or B-H curve, in a ferromagnetic material measures the extent to which the atomic scale magnetic moments (atomic magnets, if you like) are aligned. • The stimulus is the applied magnetic field, H, measured in Oersteds (Oe). The response is the Induction, B, measured in kilo-Gauss (k. G). • As shown in the plot, the magnetization is a nonlinear function of the applied field. Even more interesting is the hysteresis that occurs when you reverse the stimulus. For alternating directions of field, this means that energy is dissipated in the material during each cycle.

11 Example: magnetization: linearization Objective Linear Props. Magnetism Ferromagnets Domains • An important feature of this example is the possibility of linearization. • How? Take a portion of the property curve and fit a straight line to it. Around H=0, this is the magnetic permeability. B Slope µ permeability Wall motion Glossary Magnetism H

12 Example: magnetization: µstructure Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • How does magnetization depend on microstructure? • In a soft magnetic material, of which Fe-3 Si is an example, all the atomic moments are aligned with one another, i. e. the material is fully magnetized. However, there are domains within which all the atomic moments point the same way. The magnetization within each domain, however, points in a different direction. • Generally speaking, domains are smaller than grains. • Anisotropy means that the magnetization within each domain points along a <100> direction.

13 Magnetism: basics • • Objective • Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism An elementary understanding of magnetism at the atomic level is assumed. The basic magnetic properties of a material are often described by a “BH curve. ” Non-magnetic materials either slightly reject magnetic fields (diamagnetism) or reinforce them (paramagnetism). A limited set of materials (Fe, Co, Ni, Gd and some transition metal oxides) exhibit ferromagnetism, i. e. spontaneous alignment of atomic spins.

14 Notation BS Br Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Hc µ 0 µr Ms Wh BHmax Saturation flux density/ induction Remanence; flux density remaining after applied field is removed Coercivity; field required to bring the net flux density to zero. Permeability; = B/H Susceptibility; = M/H Permeability of free space; 4π. 10 -7 henry per meter Relative permeability, = B/µ 0 H Saturation magnetization; BS=µ 0 Ms Energy lost per cycle; often the most important parameter for a soft magnetic material. Energy product; often the most important parameter for a hard magnetic material.

15 Objective Linear Props. Magnetism Magnetic Domains • A useful exercise is to see how domain walls arise from the anisotropy of magnetism in a ferromagnetic material such as Fe. • The interaction between atomic magnets in Fe is such that the local magnetization at any point is parallel to one of the six <100> directions. [001] Ferromagnets Domains Wall motion Glossary Magnetism [010] _ [100] _ [010] [100] _ [001]

16 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Magnetocrystalline Anisotropy • The fact that different directions magnetize more easily than others in ferromagnetic materials is known as magnetocrystalline anisotropy. This can be measured by applying fields along different directions, e. g. here along 100, 110 and 111 [Chen].

17 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Domains • The local magnetization can point in directions other than a <100> direction, but only if a strong enough external field is applied that can rotate it away from its preferred direction. • Domains are regions in which the local atomic moments all point in the same <100> direction. • At the point (plane, actually) where the local magnetization switches from one <100> direction to another, there is a domain wall.

18 Magnetization: domains <100> Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism DOMAINS in Fe (Chikazumi); domain walls appear as light and dark lines. GRAINS (Smith); Domains within grains

19 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Magnetic Anisotropy • Why does the magnetization always point along a <100> direction (in Fe)? An over-simple answer is that this is a consequence of the interaction between the atomic moments and that different materials prefer to magnetize along different crystal directions. • An important consequence of this anisotropy is that the local direction of magnetization has to change direction at a grain boundary but this raises the energy of the system. As a result, the domain structure is more complex near the boundary. The next few slides review this effect.

20 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Domain Walls • Since domains of like-oriented moments are volumes like grains, there are (planar) interfaces between domains called domain walls. • Bloch first pointed out that the minimum energy configuration means that the magnetization changes gradually across the wall, 3. 10 b, not abruptly, 3. 10 a.

21 90° Domain Walls • Here is an example of a 90° domain wall. Objective Linear Props. [010] Magnetism Ferromagnets Domains Wall motion Glossary Magnetism [100]

22 Objective Linear Props. 180° Domain Wall • By contrast, here is a 180° domain wall with the local magnetic moments pointing in opposite directions. [010] Magnetism Ferromagnets Domains Wall motion Glossary Magnetism [100]

23 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Domain Walls, contd. • In a cubic material with 6 different <100> directions, it is possible to have both 180° walls, and 90° walls. • Domain walls have the lowest energy when they coincide with low index planes (one can say that there is an inclination dependence of the domain wall energy). • Example: in iron, the lowest energy domain walls lie on {001}, {110} and {111}. This explains the way in which the domain walls are straight lines along a small number of directions in the figure. • Just as for grain boundaries, the free energy of a domain wall is always positive.

24 Grain Boundary Domain Structure Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • Note how the domain structure, visible as stripes of alternating gray contrast, changes in the vicinity of a grain boundary [Chen].

25 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Demagnetizing Effect (Field) • In a single crystal (no grain boundaries), why does a ferromagnetic material not magnetize in a single direction, with no domains? At the surface of the mono-domain body, there would be free magnetic poles because of the change in magnetization (as for a permanent magnet). A large magnetic field would exist outside the body with which a large amount of (magnetostatic) energy would be associated. By rearranging the internal directions into domains, there is a large reduction in total energy by (near) elimination of the magnetostatic energy.

26 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Hard versus Soft Magnets • We can now understand qualitatively at least, the difference between hard and soft magnets. • In soft magnets, e. g. Fe-3 Si, the body has no external field but the domains can be easily brought into alignment with an externally applied field. • In hard magnets, e. g. Alnico, the body does have an external field because the domains have been prevented from changing their alignment.

27 Hard versus Soft Magnets, contd. Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • The reasons for some materials being soft and some being hard lie in the microstructure, which we will examine further. In simple terms, soft magnets are single phase and coarse grained: hard magnets are multiphase and fine grained. • There is an important parallel between magnetic and mechanical hardness. The same microstructural features that promote magnetic hardness also promote mechanical hardness.

28 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Soft magnetic materials Material Composition Iron Fe 1043 2. 2 4 2. 105 0. 1 30 Mild steel Fe-C 1000 2. 1 143 2. 105 0. 10 500 Transformer steel Fe-3 Si 1030 2. 0 12 4. 104 0. 5 30 Permalloy Fe 79 Ni 800 1. 1 4 1. 105 0. 2 Supermalloy Fe 79 Ni 5 Mo 0. 80 0. 16 1. 106 0. 6 570 0. 25 0. 8 1. 5. 103 106 13 630 1. 6 > 105 103 13 Ferroxcube Amorphous iron Fe. BSi Tc (K) Bs (T) Hc (A. m-1) µr Resistivity (µWm) WH (J. m 3. cycle-1)

29 Hard magnetic materials Material Composition Objective Alnico IV H 12 Al 26 Ni 8 Co 2 Cu 1160 0. 6 63 13 Linear Props. Alnico V 8 Al 13. 5 Ni 24 Co 3 Cu 1160 1. 35 64 44 Barium ferrite Ba. O(Fe 2 O 3)6 720 0. 4 264 28 Samarium colbalt Sm. Co 5 1000 0. 85 600 140 Neodymium iron boron Nd 2 Fe 14 B 620 1. 1 890 216 g iron oxide Fe 2 O 3 0. 21 25 Magnetite Fe. OFe 2 O 3 0. 27 25 Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Tc (K) 850 Remanence BT (T) Coercivity Hc (A. m-1) BH max (k. J. m-3)

30 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Changing Domain Structures • There are two ways in which domain structures can change. • A: the domain wall between two domains moves such that the volume of one domain increases and the other decreases. This applies at small fields. • B: the magnetization within a grain rotates (to become aligned with an external field). This only applies at large external fields.

31 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Magnetization Curve • [Chen] The figure below illustrates the difference between the early part of the curve for which domain wall movement is dominant and the later portion where domain rotation dominates. The external field is applied along a non-easy axis (not <100>).

32 Domain Wall Motion • The process of magnetization can be illustrated with a single crystal example (Fe). Objective Linear Props. Zero field Medium field Magnetism Ferromagnets Low field High field Domains Wall motion Glossary Magnetism Domain wall motion Domain rotation Applied field direction

33 Irreversible Domain Wall Motion • The graph on a previous slide mentioned the “Barkhausen effect” which is observed as a series of jumps in the magnetization curve as the field is increased. Objective • These jumps in magnetization are irreversible - if you take the field off, the domain wall(s) does not make the reverse motion Linear Props. and decrease the net magnetization. Magne • Why the irreversibility? ! There are obstacles to domain wall tism motion that require a certain minimum driving force to force the wall past them. The same barrier exists if you try to force the Ferrowall back in the opposite direction. magnets Domains • The barrier is precisely the same as barriers to dislocation motion and in fact, are also precipitates, solute atoms, for Wall example. motion Glossary • This is the basic explanation for magnetic hardness being the same as mechanical hardness. Magnetism

34 Objective Linear Props. 180° Domain Wall • Moving the domain wall involves “flipping” some of the local magnetic moments to the opposite direction. [010] Magnetism Ferromagnets Domains Wall motion Glossary Magnetism [100]

35 Obstacles to domain wall motion Objective Linear Props. • Anything that interacts with a domain wall will make moving it more difficult. For example, a second phase particle will require some extra driving force in order to pull the domain wall past it. Magnetism Domain wall motion Ferromagnets Domains Wall motion Glossary Magnetism particle

36 Objective Linear Props. Domain Wall obstacles • A more detailed look at what is going on near particles reveals that magnetostatic energy plays a role in forcing a special domain structure to exist next to a [non-magnetic] particle. Magnetism Ferromagnets Domains Wall motion Glossary Domain wall motion Magnetism [Electronic Materials]

37 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Particle Pinning of Interfaces • A domain wall is an example of a (planar) interface. • The reason that particles (or voids) exert a pinning effect on domain wall motion (or any other kind of planar defect) is that some of the interfacial area is removed from the system when the interface intersects the particle. This lowers the free energy of the system. In order for the interface to move away from the particle, energy must be put back into the system in order to re-create interfacial area. • Later on (302) we will estimate the energy of domain walls and thus the magnitude of the pinning effect.

38 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Why Domain Walls? • Why should domain walls exist? Answer: because the atomic magnets only like to point in certain directions (as discussed previously). • Can we estimate how much energy it takes to pull a domain away from its preferred direction? Answer: yes, easily. How? Integrate the area under the curve for an easy direction and compare that to the curve for a hard direction. • The area that we need is given by Hd. M ≈ µ 0 H 2/2. • Think of the difference in areas between the 100 and 111 directions as the difference in energy required to move the crystals of different orientations into the field.

39 Objective Linear Props. Magnetism Area under the curve • The area that we need is given by Hd. M ≈ µ 0 H 2/2. • The energy difference = area(111)-area(100) ≈ area(111). 100 area 111 area Ferromagnets Domains Wall motion Glossary Magnetism [Chen]

40 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Energy anisotropy estimate: Fe • Area(111) ~ 4π x 18. 105 A. m-1 x 3. 104 A. m-1 / 2 = 3. 4. 104 J. m-3 • Compare with the accepted value of the anisotropy coefficient for iron, which is K 1 = 4. 8 104 J. m-3. • The estimated anisotropy is very close to the measured value! 111 area

41 How big are domains? • It is reasonable to ask how big domains have to be. One approach to compare the total energy difference for a particle against the available thermal energy. Objective • Total energy for a particle, comparing magnetization in the easy direction (100 in Fe) against the hard direction (111 in Fe) is just Linear Props. the particle volume multiplied by the anisotropy energy (density): E = VK 1 = 4πr 3/3 K 1. Magnetism • The thermal energy is Ethermal = k. T which at room temperature gives Ethermal = 4. 10 -21 J. Ferromagnets • Thus the radius at which the energies are similar, for Fe, is: Domains Wall motion Glossary Magnetism rcritical = 3√{3 k. T/4πK 1} ~ 1. 3 nm

42 Superparamagnetism? • This limiting size, below which we expect a single particle to not have domains because thermal energy can move the magnetization direction around “randomly” is very important technologically. Objective • Small enough particles (relative to the magnetic anisotropy) are Linear called superparamagnetic because they behave like a Props. paramagnetic material even though the bulk form is Magneferromagnetic. tism • For magnetic recording, you cannot expect the recording (in the sense of regions of magnetization that remain fixed until the next Ferrotime you read them) to be stable if thermal energy can change it. magnets Domains • Thus a physical limit exists to the bit density on disks or tapes. • To be safe, the particles need to be much bigger than our Wall estimate - say, 10 times larger. motion Glossary Magnetism

43 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Magnetocrystalline Anisotropy • The fact that different directions magnetize more easily than others in ferromagnetic materials is known as magnetocrystalline anisotropy. This can be measured by applying fields along different directions, e. g. here along 100, 110 and 111 [Chen].

44 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Labs • Later in the course we will do a lab exercise on imaging domain structures in a sample of Fe-3 Si, which is the standard material for manufacturing transformers. We will use cross-polars and rely on the Kerr effect which is where the presence of a magnetic field at the surface of a material rotates the plane of polarization of light. Different directions of magnetization in different domains rotate the polarization differently. This is how the example image of domain structure was obtained.

45 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Application of soft magnetic materials: transformers • A major application of soft magnetic materials is in transformers that step alternating current electrical power up or down in voltage (and therefore current). • The requirement is that a sufficient field is contained within the transformer core, and that it switches each AC cycle with minimal losses (from the hysteresis of the magnetization curve)

46 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Transformer materials, contd. • Other important issues constrain the selection of transformer materials. • Saturation magnetization is a function of atomic species and iron has the highest value for low cost materials. • Silicon is added to iron to raise the resistivity in order to minimize losses. The 3% level represents the maximum that still permits conventional thermomechanical processing (TMP). • Specialized TMP is used to develop near-singlecrystal texture, called the Goss texture, {110}<001>.

47 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Supplemental Slides • The following slides contain some useful definitions of terms in magnetism and magnetic materials.

48 Appendix: Glossary of Magnetism • • Objective Linear Props. Magnetism • • Ferromagnets • • Domains • Wall motion Glossary Magnetism • • • Ageing: Change in magnetic properties with time, especially in the apparent remanence of a permanent magnet; can be reduced or anticipated by artificial ageing (magnetic, thermal, mechanical). Air Gap: Space between the poles of a magnet in which there exists a useable magnetic field. AMR-effect: Non isotropic magneto resistive effect, (see also XMR-effect). Alnico: Magnet alloys composed of Aluminium, Nickel, Cobalt, Iron and other additives - produced by casting or sintering - can only be processed by grinding. Alnico P: DIN 17410 designation for plastic bonded Alnico materials. A/m: amperes per meter : unit of magnetic field strength; 1 A/m= 0, 01 A/cm (= 0, 01256 Oersted). Anisotropy: Directional dependence of a physical quantity ; in the case of permanent magnets this relates to remanence, coercivity etc. Axial magnetization: Magnetization along the symmetric achsis of a bar magnet or along one edge of a block magnet. B = Induction or flux density: Unit: 1 Tesla = 1 Vs/m 2 = 10 -4 Vs/cm 2 = 104 Gauß. B (H) Curve: A curve representing the relationship between induction B and field strength H (see also hysteresis loop). (B • H): Product of the respective induction B and field strength H within a magnet (see also energy density). Unit: 1 J/m 3 = 10 -3 k. J/m 3 = 125, 6 Gauß • Oersted = 125, 6 • 10 -6 MGOe (B • H)max - Value: Maximum product resulting from B and H on the demagnetization curve, i. e. the largest rectangle which can be drawn within the B (H) curve in the second quadrant of the hysteresis curve; this usually corresponds to the optimal working point. cgs-units: Physical units which are based on the three fundamental units cm, gram and second (see also SI-units). CMR-effect: Colossal magneto resistive effect (see also XMR-effect). Coercive Field Strength Hc, Coercivity: Strength of the demagnetizing field where B = 0 ( Hc. B ) or J = 0 ( Hc. J ). Columnar crystalline materials: Especially Al. Ni. Co alloys where an orientation of the crystals is formed by a controlled solidification of the melting charge. The material Al. Ni. Co 700 shows a very distinct anisotropy. in contrast to those types where an anisotropy is produced only by applying a magnetic field during heat treatment. Curie Temperature: The temperature above which the remanence of polarization in a ferro-magnetic material becomes Jr = 0. At all temperatures above the Curie temperature all ferromagnetic materials are paramagnetic. Demagnetization: Reduction of induction to B = 0; this is obtained practically by the application of an alternating field of decreasing amplitude. Demagnetization Curve: The second quadrant of the hysteresis loop which is of great importance for permanent magnets. Demagnetization Factor N: Shape dependent factor which determines the angle between working line and B-axis. N is the tangent of this angle. Diamagnetism: Magnetic property of materials whose permeability m is smaller than 1, e. g. bismuth. Dimensional Relationship: Relationship L/D = length / diameter of a bar magnet. For each magnet material the optimal working point corresponds to a fixed L/D value.

49 Glossary of Magnetism: 2 • • • Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • • • • • Dipole field: first approximation of the field of a magnet at a large distance. The dipole field is defined only by orientation and amount of the magnetic moment and decreases according to 1/r 3 with increasing distance r. Dipole moment: see moment (magnetic) Eddy current: A current induced in a conductor by a changing magnetic field. It is exploited for example in electricity meters for retarding without any contact. On the other hand it causes losses and undesirable heating in motors, transformers etc. Effective Flux: Part of the magnetic flux which passes through the air gap. Energy Density: 1/2 B • H = half of the product resulting from the magnetic induction B and the field strength H (half of the rectangle within the demagnetization curve with its corner at the working point) Ferromagnetism: Magnetic property of materials with a permeability m >>1, e. g. iron, nickel, cobalt and many of their alloys and compounds. Field: space having physical properties (see also magnetic field). Field Constant, Magnetic: m 0 = B/H in the vacuum, with m 0 = 1, 256 -10 -6 T m / A = 1, 256 - 10 -6 /s / Am. Field Line: Means of evident representation of fields. In force fields (e. g. magnetic fields) the tangents to the field lines represent the direction of the effective forces; the density of field lines is a measure of the strength of effective forces. Field Strength (magnetic) H : a quantitative representation of the strength and the direction (vector) of a magnetic field. Unit 1 A/m = 0, 01 A/cm = 0, 01256 Oersted. Flux Density B: No. of field lines per unit of surface. Unit: 1 Tesla = 1 Vs/m 2 = 10 -4 Vs/cm 2 = 104 Gauss. Flux, magnetic: When a magnetic field is represented by field lines, the total number of lines through a given surface is known as the magnetic flux: measured as an electrical impulse in a coil surrounding this surface on appearance or disappearance of this flux. Unit : 1 Weber (Wb) = 1 Vs = 108 Maxwell. Fluxmeter: Electronic integrator for measuring a magnetic flux or induction. Force Line: Visible representation of a force field, especially a magnetic field. Gauß: Old unit of magnetic induction, 1 Gauß = 10 -4 Tesla = 10 -8 Vs/cm. Gaußmeter: Instrument for measuring magnetic induction B. Instruments for measuring magnetic field strength H (Oerstedmeters) are often referred to as Gaußmeters. Gilbert: Old unit of magnetic tension; 1 Gilbert = 1 Oe cm = 0, 796 A. GMR-effect: Gigantic magneto resistive effect (see also XMR-effect). H = magnetic field strength, Unit : 1 A/m = 0, 01 A/cm = 0, 01256 Oe. Halbach-system: An arrangement of magnets named after the American physicist K. Halbach which produces precise and very homogeneous multipole fields( for example a dipole field). Hall probe: Semiconductor probe for measuring magnetic fields (e. g. in an air gap of a magnet system). Hall-probes always are used connected to a gaußmeter.

50 Glossary of Magnetism: 3 • • Objective Linear Props. Magnetism • • Ferromagnets • • Domains • • Wall motion • Glossary Magnetism Hard Ferrite: Term used in DIN 17410 for Oxide magnet materials. Hard Ferrite P: Term used in DIN 17410 for plastic bonded oxide magnet materials. Helmholtz-coil: A double coil to produce extremely homogeneous fields. The distance between the two coils is equivalent to their radius. The coil is used for measuring magnetic moments. Hybrid-material: Plastic bonded material containing several kinds of magnetic powders to adjust certain magnetic properties by using for example Neofer and oxide-powders to reach a predicted price. Hysteresis - loop: Representation of induction B resp. Polarization J in relation to the magnetizing field strength H. Induction: 1. The ability of the magnetic field to surround itself with an electric field whilst it is changing. 2. The term induction is also used to mean flux density B. Induction Constant: See field constant, magnetic. Isotropy: Equality of physical properties in all directions. J = magnetic polarization: Density of aligned magnetic moments in a magnetized material Unit 1 T = 1 VS / m 2 = 10 -4 VS / m 2. Magnetic: Commonly used to denote all materials with noticeably high permeability (especially iron, nickel, cobalt and their alloys); all other materials (gold, brass, copper, wood, stone, etc. ) are considered to be non-magnetic. Magnetic Circuit: Total of parts and gaps through which a magnetic flux passes; in the case of a permanent magnet this consists of the magnet itself, the pole shoes, the air gap and the stray field. Magnetic Field: Space in which mechanical forces have an effect on magnetic charges or where induction occurs. Magnetic Field Strength H: See field strength (magnetic). Magnetic flux: See Flux, magnetic. Magnetization: 1) The noun arising from "magnetizing” 2) Polarization divided by the magnetic field constant M = J / m 0, B = m 0 (H+M) = m 0 H + J. Magnetizing: Process of aligning the molecular magnets by an external magnetic field. Magnetism: Sum of magnetic phenomena as a part of the electromagnetic interaction(force) being one of the four fundamental forces in physics. They are characterized by magnetic field H and magnetic induction B. All the magnetic phenomena are a consequence of moving electric charges (electric currents) whereas electrostatics describes the forces between unmoved electric charges. Electrodynamics finally deals with the connection of electric and magnetic fields varying with time. With the magnetism of matter an orientation of magnetic moments (colloquial elementary magnets)is defined by polarization J. These moments are composed of the orbital moment of electrons moving around the nucleus of the atom and the so called electron spin moment which is caused by the rotation of the electron around its own axis. If all these moments are compensated the material is called diamagnetic.

51 Glossary of Magnetism: 4 • • Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism • • • • Concerning para- ferro- antiferro- and ferrimagnetic materials the sum of these moments is different from zero. They differ by the kinds of coupling of adjoining atomic moments: In the case paramagnetic materials there is no coupling; with ferromagnetic materials adjacent atomic moments are parallel; with antiferromagnetic materials they are adjusted antiparallel. If the antiparallel adjusted atomic moments do not compensate each other completely and a resulting magnetization remains it is called ferrimagnetism. Magnetomotive Force: Q Term for the line-integral of field strength H along any path. For the case of a closed path the magneto motive force is the sum of the electrical currents enclosed within the curve : . Unit: 1 A = 1, 256 Oe cm = 1, 256 Gilbert. Magneto resistive sensor: (MR)-sensor using the change of electric resistance in a magnet field to measure it. Because of recent developments of thin layers showing extremely high magneto resistive effects we have a renaissance of MR-sensors. ( see also XMR-effect ) Magnet Pole: Part of the surface of a magnet where the magnetization is rectangular to the surface. This part corresponds to the regions where the magnetic flux leaves the magnet. Maxwell: Former unit of magnetic flux 1 Maxwell = 10 -8 Wb = 10 -8 Vs. Melt spin process: Method of an extremely fast cooling of a melting charge being sprayed on a rotating cylinder which leads to alloys with different physical properties than melting charges cooled down under normal conditions. This method is used to produce the basic powder of Neofer p ®. Moment (magnetic), (dipolar moment): Product of polarization J and Volume V of a homogeneously magnetized magnet. The moment in units of Vsm corresponds to the mechanic torque in Nm of the magnet in a magnetic field perpendicular to the magnetization of 1 A/m. The moment is designated by m, better by m. Coul (Coulomb's magnetic moment ) to not confuse it with m. Amp ( Ampers's magnetic moment ) the formerly often used quantity. m. Amp = m. Coul / m 0 is the product of Magnetization M and Volume V. Multicomponent injection moulding: Injection moulding process where two or more different materials are injected one after another for example a non-magnetic material is injected on top of a magnetic compound. Neofer â: Permanent magnet material based on neodymium, iron and boron. Neofer p â: Permanent magnet material based on neodymium, iron and boron with a bonding agent. Oersted: Former unit of magnetic field strength 1 Oersted = 79, 6 A/m = 0, 796 A/cm = 0, 0796 k. A/m. Oerstedmeter: Instrument for measuring the magnetic field strength H (also known as Gaußmeter). Oxide Magnet: Hard ferrite, ceramic magnet material, e. g. composed of iron oxide and barium oxide (Ba 0 x 6 Fe 2 03). Paramagnetism: Magnetic property of materials with permeability m > 1. All ferromagnetic materials exhibit paramagnetism above the Curie temperature. Permagraph: Measuring instrument for plotting the entire hysteresis loop of a magnet. It consists of an electromagnetic yoke to apply an external field measuring instruments for measuring field strength H and induction B and a calculator or a chart recorder to describe the curve.

52 Objective Linear Props. Magnetism Ferromagnets Domains Wall motion Glossary Magnetism Glossary of Magnetism: 5 • Permeability: m = B/H; relationship between induction B and the magnetic field H. In permanent magnet technology permanent permeability is important as this gives the change in B when small changes in H take place (dp = d. B/d. H) especially in the proximity of the optimal working point. Unit: 1 Tm / A. • • • The permeability of the vacuum (magnetic field constant) is m 0 = 1, 256 -10 -6 T m / A = 1, 256 - 10 -6 /s / Am. • Polarization J: Grade of magnetic orientation in a magnetic material (magnetization multiplied by field constant). It is J = m 0 M = B - m 0 H. • Potential, magnetic: Physical quantity of which the gradient gives the magnetic field H. Only a potential difference can be measured (magnetic tension between two points) as an integral of the field strength over any path between these two points, provided this path does not enclose an current-carrying conductor. • • Prac Ò: Pressed magnet composed of Al. Ni. Co powder and bonding agent. • • Pressed Magnet: A magnet manufactured by a pressing process from powdered magnet material and a bonding agent. Permeance: Ratio of magnetic flux to magnetic potential difference ( in the case of an air gap surface : length) Plastic bonded magnet material: If a magnet powder is blended with plastic material it is possible to apply methods of plastic industry (injection moulding, rolling etc. ) to produce magnets of very complex shapes. The advantages: cheap manufacturing processes, small tolerances and many kinds of shapes must be compared with the disadvantages: expensive tools and lower magnetic properties. Preferred Direction: Direction in a permanent magnet in which magnetic properties are at a maximum. This direction is determined by the manufacturing process. Prox Ò: Pressed magnet composed of oxide powder and a bonding agent. Quality: (see also (BH)max –value) Rare earth magnet materials: The rare earth metals Nd and Sm are applied to different alloys for manufacturing permanent magnets with very high magnetic properties. The nowadays commercially exploited materials Seco and Neofer are based on the compositions Sm. Co 5, Sm 2(Fe. Co)17 and Nd 2 Fe 14 B.

53 Glossary of Magnetism: 6 • • Objective • Linear Props. • Magnetism • • Ferromagnets • • • Domains • Wall motion Glossary Magnetism • Radial magnetization: Magnetizing a ring magnet between two coils carrying currents of opposite directions leads to a radial magnetization. One pole is on the inner circumference of the magnet the other pole on the outer circumference. Reed switch: Magnetomechanic switch where two metal reeds in a inert gas get into contact by applying a magnetic field actuating the switch. The unit of the sensitivity of the switch is ampere windings. Remanence BR: Residual induction in a solid which has been subjected to a magnetizing field (true remanence in the case of a closed magnetic circuit, apparent remanence in the case of an open magnetic circuit). Residual magnetism: Because of the manufacturing process delivered magnets show more or less a residual magnetism. This can only be reduced by a demagnetization process. Saturation: Better termed saturation polarization Saturation Polarization: Highest practically achievable magnetic polarization of a material when exposed to a sufficient strong magnetic field. . Seco Ò: A magnet material composed of an alloy of rare earths and cobalt. Seco P Ò: A magnet material composed of a rare earth cobalt alloy and a plastic bonding agent Sintered Magnet: A permanent magnet pressed from a mixture of metallic or ceramic powders and solidified by heating below the melting point (burning). SI-units: Physical units according to the System International (SI) which is based on the units kilogram, meter second ampere. All other units are a product, a quotient or a power of these four basic units. The traditional cgs-units resp. the Gauß-units in magnetism are still in use but have to be adapted by law. The following table shows some magnetic units and their conversion. REFERENCE: http: //www. magnetfabrik. de/english/abc/service. htm