1. Permanent magnet materials
Magnetic core memory
Magnetic fridge memory 2011

2. Hårdmagnetiska material / permanent magnet materials
Magnetiseras först med stort magnetfält H1 (ofta pulsat), när det yttre
fältet är bortaget finns fortfarande det avmagnetiserande fältet Hd och
arbetsinduktionen (-magnetiseringen) är Bd (Md)

3. Tillämpningar delas in i 3 kategorier
elektrisk-till-mekanisk omvandling
mekanisk-till-elektrisk omvandling
magnetisk kraft

4. 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 < MR after field removal.
Desired properties:
high (large magnetic anisotropy),
high ,
high and
high
Coercive field
A material is classified as magnetically hard if Hc > 104 A/m, distinguish between
I Hci defined by M vs. Hi curve and
II Hc defined by B vs. Hi curve, Hc < Hci.
Good permanent magnets like Nd2Fe14B or SmCo5 have Hci ≥ 106 A/m.
Remanence
MR 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 MR.
Good permanent magnets like Nd2Fe14B or SmCo5 MR ~ 106 A/m.
Saturation magnetization
Desired to have MR / Ms ~ 1, implies rectangular hysteresis curve.
Nd2Fe14B have Ms ~ A/m.

5. Ampere's circulation law (i = 0) Field equations
Curie temperature
Working temperature << Tc , 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/m3]. 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/m3

6. 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
-m0Ms/2
m0 Hi m0 Hci
m0 M , B
m0 M
m0 Ms
Maximum?
m0 Hc

7. is called permeance coefficient
How large can the energy product become? Fe-Co alloy has Ms = 1.96106 A/m →
J/m3. Today we have reached kJ/m3.
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. Hi ;
ii) B vs. Hi ;
is called permeance coefficient
working point
For B vs. Hi the load line is defined by = Hi B
load line

8. 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

9. 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) 2a Ms H q0 q 2b x z y
easy axis
q0+p
In case of shape anisotropy, the anisotropy axis is given by the long axis and the anisotropy constant by

10. Back to the Stoner-Wohlfarth model. The total energy is for
+ fields
- fields
At equilibrium it holds
where
q 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) q0 q
q0+p Ms H

11. q0 q
q0+p Ms H

12. where H0 corresponds to the critical field
where H0 corresponds to the critical field. For every value of there exists a corresponding H0.
At the instability of , (1) and (2) can be written
where
… after some work we obtain
Relation

13. 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 q0
H/Han q0
M/Ms

14. H Ms H0
Instabilt läge för Ms → 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

15. 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.

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

17. The a2 phase pins domain walls; the a1 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, weight-%, and a small amount Ti, 5-8 weight-% (increases Hc).
Energy product for oriented Alnico is kJ/m3, kA/m, while for isotropic Alnico it is 5-10 kJ/m3, kA/m.

19. Hard ferrites
Developed in the 50'th (Stoner-Wohlfarth model), sintered material, hexagonal crystal structure and plate like grains with size ~ 1 mm, which is larger than the single domain limit, c-axis perpendicular to plate, magnetocrystalline anisotropy dominates, K1 = 3.3∙105 J/m3.
Most common are BaO-6Fe2O3 and SrO-6Fe2O3, cheap to produce – large industry. Larger Hc compared to Alnico, kA/m, but smaller energy product kJ/m3.
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 Ms for light RE-elements.
coercivity governed by domain
wall nucleation and motion

20. SmCo5 m0MR ≈ 0.9 T, m0Hc ≈1 T (m0Hci ≈ 2 T) and kJ/m3 and
Tc = 720 oC.
Hexagonal crystal structure, sintered material, grain size 3-10 mm, magnetocrystalline anisotropy dominates, experimental results obtained for single crystals (H // hard direction) show that
Sm2Co17 m0MR ≈ 1.1 T, m0Hc ≈1 T and kJ/m3, consists of bands of SmCo5 separating regions of SmCo17, higher Tc compared to pure SmCo5 (Tc = 820 oC).
grains larger than the
single domain limit

21. Coercivity controlled by nucleation of
reverse domains or by pinning of
domain walls, SmCo5 is one example
of nucleation controlled coercivity
The Sm2Co17 magnets consists
of SmCo5 bands separating
regions of Sm2Co17
SmCo5
Sm2Co17

22. Nd-Fe-B
Was developed in the 80'th, Nd2Fe14B, the magnetic properties are sensitive to details of the fabrication process, two methods are commonly used:
I. Sintered material with grain size ~ 3 mm and
II. 'melt-spun' material with grain size nm.
Tetragonal structure, strong magnetocrystalline anisotropy K1 ≈ 5·106 J/m3.
mMR ≈1.2 T, m0Hc ≈1 T (m0Hci ≈ T) and kJ/m3 for oriented material. One problem with this material is the comparably low Curie-temperature, Tc ≈ 300 oC.
tillsatser av Co och Dy
vanliga...

23. Stability of permanent magnets against external field and
temperature changes (page )
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 oC
Rectangular M vs Hi curve

24. 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

25. Novel Permanent Magnetic material without Rare Earth Elements or Pt
Objectives
(BH)max ~
100–150 kJ/m3
Tc > 600 K