1. Hårdmagnetiska material / permanent magnet materials Magnetiseras först med stort magnetfält H 1 (ofta pulsat), när det yttre fältet är bortaget finns fortfarande det avmagnetiserande fältet H d och arbetsinduktionen (-magnetiseringen) är B d (M d )

2. Tillämpningar delas in i 3 kategorier i)elektrisk-till-mekanisk omvandling ii)mekanisk-till-elektrisk omvandling iii)magnetisk kraft

3. Hard magnetic materials Always used as passive component, the energy is stored in the material before use by applying and removing a large magnetic field, the magnetization is < M R after field removal. Desired properties: high (large magnetic anisotropy), high, high and high. Coercive field A material is classified as magnetically hard if H c > 10 4 A/m, distinguish between I H ci defined by M vs. H i curve and IIH c defined by B vs. H i curve, H c < H ci. Good permanent magnets like Nd 2 Fe 14 B or SmCo 5 have H ci ≥ 10 6 A/m. Remanence M R defined for closed magnetic circuit (no demagnetizing field), applications require open circuit → magnetization for a permanent magnet when used in an application always smaller than M R. Good permanent magnets like Nd 2 Fe 14 B or SmCo 5 M R ~ 10 6 A/m. Saturation magnetization Desired to have M R / M s ~ 1, implies rectangular hysteresis curve. Nd 2 Fe 14 B have M s ~ 1.2 10 6 A/m.

4. Curie temperature Working temperature << T c, otherwise (strongly) temperature dependent magnetic parameters, risc that the permanent magnet material ages and in the worst case the material will be demagnetized; producers give information... Energy product Ampere's circulation law (i = 0)Field equations Energy/unit area in air-gap where B and H are the magnetic flux density and magnetic field in the material, respectively, B ∙ H is called energy product, SI unit is [J/m 3 ]. Note that ideal magnetic circuit, the core is a permanent magnet material and the field in the material is a demagnetizing field B, M H + - CGS units: [M G Oe] 1 M G Oe = 7.96 kJ/m 3

5. The working point for a permanent magnet in an application is always found in the second quadrant of the hysteresis curve (the magnetic field is a demagnetizing field). How large is the energy product for the ideal permanent magnet material with a “rectangular” hysteresis curve? The maximum energy product thus is B  0 M s /2 0 Hi0 Hi  0 M, B 0 M0 M  0 M s Maximum?

6. How large can the energy product become? Fe-Co alloy has M s = 1.96  10 6 A/m → J/m 3. Today we have reached kJ/m 3. To reach higher values, we must improve… The demagnetizing curve Defined as the second quadrant of the hysteresis curve, contains all information being important for a permanent magnet. Geometrical considerations determine the working point in an application, since the demagnetizing field is determined by the geometrical shape of the material. Two cases (i = 0): i) M vs. H i ; ii)B vs. H i ; is called permeance coefficient working point For B vs. H i the load line is defined by =. HiHi B load line

7. Demagnetizing curves, lines of constant energy product and permeance coefficients in the same figure How should one choose the permanent magnet material for a specific application? Always the material exhibiting the largerst ? No! Given a value for the permeance coefficient, choose the material exhibiting the largest energy product at the working point for the material! 0.0244

8. Stoner-Wohlfarth model Model that was developed ~ 1950, guided the search for new permanent magnet materials at that time. Start out by assuming uniaxial anisotropy (magnetocrystalline or shape anisotropy) and that the material is built up of single domain particles (implies a magnetization process governed only by...) Uniaxial magnetocrystalline or shape anisotropy (lecture 4) 2a2a MsMs H   2b2b x z y easy axis    In case of shape anisotropy, the anisotropy axis is given by the long axis and the anisotropy constant by

9. Back to the Stoner-Wohlfarth model. The total energy is for + fields - fields At equilibrium it holds + fields - fields where.  thus determined is used to calculate the magnetization as Moreover, holds for energy minimum, and for – fields rotates with increasing field towards the field and decreases, instability for when. (1)

11. where H 0 corresponds to the critical field. For every value of there exists a corresponding H 0. At the instability of, (1) and (2) can be written where … after some work we obtain Relation

12. Starting condition, angle between field and easy axis of magnetization, field decreases from a large positive value: I. For positive fields, the magnetization first rotates reversibly away from the field direction; at zero field the magnetization is along the easy axis. II. For negative fields, the magnetization continues to rotate reversibly towards the field direction, when the field magnitude reaches the magnetization rotates irreversibly to a new equilibrium direction. III. Finally, there is a reversible rotation of the magnetization towards the applied field direction. Hysteresis curves for different  0 H/H an 00 M/MsM/Ms

13. H MsMs MsMs H MsMs H MsMs H MsMs H MsMs H MsMs H0H0 Instabilt läge för M s → irreversibel rotation H ≈0 IV. If the field decreases from a large negative value, the behavior of the magnetization is repeated and the irreversible rotation occurs at.

14. For a polycrystalline material consisting of grains exhibiting uniaxial anisotropy, averaging over a random distribution of (random with respect to…) yields By aligning the grains during fabrication (how?), the coercive field can be increased to Grain aligning also yields a material exhibiting. The S-W model has been useful as a guide when researching for new permanent magnet materials and is also useful for e.g. magnetic storage media consisting of single domain magnetic particles. Modern permanent magnet materials are best explained by domain wall motion and/or nucleation of domains with reverse magnetization. Materials Alnico Was developed in ~ 1930, Fe-Co-Ni-Al alloy, small amount of other elements may also be used.

15. The magnetic properties can be improved by precipitation (step2) in magnetic field and/or columnar growth of grains. Steps in fabrication heat to 1250 o C to form a homogeneous solid solution cool at a rate of ~ 1 o C/sec to about 500 o C reheat at 600 o C for a few hours Sintered bcc material, mixed two-phase material: I. Fe-Co phase strongly magnetic II. Ni-Al phase weakly magnetic/paramagnetic

16. The  2 phase pins domain walls; the  1 phase consists of elongated single domain grains (long axis // [100]), l / d ~ 600 nm / 30 nm, shape anisotropy. Distinguish between isotropic (1-4) and oriented Alnico (5-9), oriented Alnico contain somewhat more Co, 20-40 weight-%, and a small amount Ti, 5-8 weight-% (increases H c ). Energy product for oriented Alnico is 40-100 kJ/m 3, kA/m, while for isotropic Alnico it is 5-10 kJ/m 3, kA/m.

18. Hard ferrites Developed in the 50'th (Stoner-Wohlfarth model), sintered material, hexagonal crystal structure and plate like grains with size ~ 1  m, which is larger than the single domain limit, c-axis perpendicular to plate, magnetocrystalline anisotropy dominates, K 1 = 3.3 ∙ 10 5 J/m 3. Most common are BaO-6Fe 2 O 3 and SrO-6Fe 2 O 3, cheap to produce – large industry. Larger H c compared to Alnico, kA/m, but smaller energy product kJ/m 3. Sm-Co Intensive research in the 60'th to find compounds based on rare-earth (4f) and transition metal (3d) elements, highest anisotropy for Co-RE, moreover higher M s for light RE-elements. coercivity governed by domain wall nucleation and motion

19. SmCo 5  0 M R ≈ 0.9 T,  0 H c ≈1 T (  0 H ci ≈ 2 T) and kJ/m 3 and T c = 720 o C. Hexagonal crystal structure, sintered material, grain size 3-10  m, magnetocrystalline anisotropy dominates, experimental results obtained for single crystals (H // hard direction) show that Sm 2 Co 17  0 M R ≈ 1.1 T,  0 H c ≈1 T and kJ/m 3, consists of bands of SmCo 5 separating regions of SmCo 17, higher T c compared to pure SmCo 5 (T c = 820 o C). grains larger than the single domain limit

20. Coercivity controlled by nucleation of reverse domains or by pinning of domain walls, SmCo 5 is one example of nucleation controlled coercivity The Sm 2 Co 17 magnets consists of SmCo 5 bands separating regions of Sm 2 Co 17 SmCo 5 Sm 2 Co 17

21. Nd-Fe-B Was developed in the 80'th, Nd 2 Fe 14 B, the magnetic properties are sensitive to details of the fabrication process, two methods are commonly used: I. Sintered material with grain size ~ 3  m and II. 'melt-spun' material with grain size 20-80 nm. Tetragonal structure, strong magnetocrystalline anisotropy K 1 ≈ 5·10 6 J/m 3.  M R ≈1.2 T,  0 H c ≈1 T (  0 H ci ≈ 1 - 2 T) and kJ/m 3 for oriented material. One problem with this material is the comparably low Curie-temperature, T c ≈ 300 o C. tillsatser av Co och Dy vanliga...

22. Stability of permanent magnets against external field and temperature changes (page 495-497) may be a problem in this case but not in this case Irreversible changes for sufficiently large temperature increase, e.g. for NdFeB the temperature limit is 150 – 200 o C Rectangular M vs H i curve

23. Mål Känna till hur hårdmagnetiska material förbereds för att kunna användas i tillämpningar Känna till önskvärda egenskaper för hårdmagnetiska material Känna till vad energiprodukten innebär och hur man utifrån magnetisering/magnetisk induktion versus inre fält kan beräkna energiprodukten Känna till begreppen avmagnetiseringskurva, arbetslinje och permeanskoefficient och vad de innebär Känna till Stoner-Wohlfarth modellen, inte härledningar men vad modellen beskriver Känna till egenskaper hos Alnico, hårdferriter, SmCo och NdFeB permanentmagneter Känna till hur man utifrån hystereskurvan kan avgöra om koercivfältet bestäms av nukleering av omvända domäner eller fastlåsning av domänväggar