CRYSTAL ANISOTROPY LUBORSKY (32!
J6 but neither was it as large as expected for shape anisotropy.
Frei, Shtrikman and Treves (57) and Jacobs and Bean (58) were both soon to show that there were, under certain circumstances
alternative mechanisms to the uniform rotation of magnetisation in the absence of domain walls. Frei et al obtained solutions of Brown’s equations by the methods of micromagnetics (57*59) and give two new mechanisms of demagnetisation referred to as ’’buckling” and ’’curling”. The deviations in magnetic moment within the particle at some point during demagnetisation are shown schematically in Fig 12. In buckling
%
spin or magnetic moment deviation occurs only in one plane in a
direction at right angles to the long axis. . The deviation is a periodic function of displacement in the direction of the long axis. With the curling mechanism the magnetisation aquires a circumferential component that depends only on distance from the axis. This mechanism is
particularly interesting since,unlike buckling in which the applied field must overcome anisotropy and exchange forces, however in the case of curling, for an infinitely long or cylindrical particle at least, the magnetisation aquires no extra magnetostatic forces because during reversal all new components of the magnetisation are circumfer ential, and the flux is therefore continuous. Half way through reversal by this method, the spins are all parallel to planes normal to the
long axis and form closed circles of flux in all cross sections, In contrast, coherent rotation produces increases in anisotropy and
magnetostatic forces but no exchange forces during reversal. A further conclusion that reversal by curling of highly elongated particles
should be independant of the packing function may also be expected because no magnetostatic energy is involved (*f8) again this is in sharp contrast to coherent rotation theory.
The reversal mode considered by Jacobs and Bean (5 8) was
suggested by the shape of the electrodeposited iron particles
observed by electron microscopy. « The particles were considered to be chains of spheres where rotation occurs by a fanning mechanism in
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v (0 (0 (c) ( A)(a) Rotation in unison, (b) Cnrli.no-, (c) buckling, (d) fanning
05 BUCKLING 02 CURLING 005 0 02 fl-0 I 05
Fig 12. Calculated fields for nuclcation of magnetisation reversal in infinite cylindrical particles (n,b and. c) or chains of spheres (d) for various modes of reversal (d0,57,58,)
The axial field is o-iven hv H~rJ h CT s cj'A n ' o . j The particle diameter is given by d= 2. Ma S C 2
where C is the exchange constant Js
between two neighbouring spins.
which the magnetisation in successive spheres rotates in alternate directions. They also considered rotation in unison (symmetric fanning) in which the magnetisation of all the spheres is always parallel. Each sphere is assumed to be a single domain with no anisotropy of its own and within which the spins reverse coherently. Each sphere is treated as a magnetic dipole and overall anisotropy energy obtained by interaction between them. They showed that the energy barrier for reversal by the fanning mode is only one third of that for coherent rotation with the same particle system.
Fig 12 shows diagramatically the variation of H „ T for the various modes for long particles as a function of the (reduced)
diameter (57). Buckling is in practice not very important because it is found to give a lower coercivity than the other modes only over a very restricted range of diameter near to the maximum critical diameter for coherent rotation. The critical diameter for long iron-or cobalt iron particles above which the curling mode is energetically more favourable is calculated to be about 17 nm which explaines why the
coercive force found is lower than the maximum J , the value fors
uniform rotation. By contrast the particle sizi^at which actual domain walls can start to appear for materials of moderate crystal anisotropy such as iron or nickel is expected to be greater than the natural domain wall thickness which is about 10 - 50 nm. Information on not only the distribution of anisotropy and alignment of particle » assemblies but also the mode of reversal of the particle magnetism may be obtained from the analysis of torque magnetometry measurements
(6 0,1 3). If torque curves are measured for assemblies of fine particles,
the measurements in very high’fields can give information about particle alignment. For randomly aligned particles no torque curve has an amplitude which is characteristic of the distribution. Torque
curves taken in a clockwise and anticlockwise direction in high fields are identical.
In fields of the order of half the anisotropy field there is a difference between such torque curves and the area between them is referred to as rotational hysteresis loss.
It has been shown (59*27* 60 *4-8) that the variation of
magnetisation reversal. Moreover, these curves also differ for random and aligned particles and this type of analysis permits some far reaching conclusions about the demagnetisation of fine particle systems.
hysteresis loss, has a value of about 0,4- for random or aligned particles with coherent rotation of magnetisation, but a value of 1 or 1,5 for random and aligned particles respectively in which the magnetisation changes by fanning,
Shtrikman et al (57*59*60,4-8) have made similar calculations for curling and buckling in long cylindrical particles and found that
the shape of the -H! curve and the value of R depends on the
particle diameter,
1,3* Fine Particle permanent magnets from alloys
1.3,1. Alnico alloys technological developments
The discovery of an alloy system,which it is now universally agreed, derives its permanent magnet properties from fine particle shape anisotropy, was made some years before the cause of the magnetic hysteresis was known. In 1931 Mishima in Japan discovered that-an
alloy of 5 6 percent Fe, 30 percent Ni and 12 percent Al had a coerc
ivity of over 30 kA/m or about double that of the best magnet material, a magnet steel, previously available.
rotational hysteresis loss with field differs for different modes of
Jacobs and Luborsky also find that the rotational hysteresis
Work by Bradley and Taylor (6l) and Bradley (62) established the broad metallurgical behaviour of the iron-nickel-aluminium alloys and showed that in the ternary diagram the alloys with interesting permanent magnet properties lay close to the line from Fe to Ni Al and centred around the composition corresponding to Fe^ Ni Al, The Alnico permanent magnet alloys comprise a wide range of alloys based on Fe-Ni-Al with major additions of cobalt, copper and titanium and additions of niobium, silicon, sulphur and other elements,
Gould (6 3) lists the compositions and outlines manufacturing
techniques for the Alnico alloys which are currently the most important commercial permanent magnet materials, principally because the metals from which they are made are relatively inexpensive and abundant in contrast to the best permanent magnet materials based on rare-earth- cobalt intermetallic alloys.
Among the possible additions allowed for in the Mishima patent (64-) was 0,5 to 40% Cobalt, However the realisation of economically justifiable improvements in properties from additions of cobalt came
from independent work in Germany (6 5) and in Sheffield (66),
Other additions such as titanium and niobium (which also neutralised the effects of impurity levels of carbon) and copper were also made resulting in a range of alloys with (BH) max of 10-16 kj/m
and coercivities 54-60 kA/m (6 3). Optimum magnetic properties are
obtained by cooling slowly from a temperature of about 1250°C followed
by annealing or tempering for several hours in the region 550 - 6 0 0°C,
In 1938 Oliver and Sheddon (6 7) obtained slight improvements
in the (BH) max and remanence of an alloy containing 12% cobalt and 6% copper by cooling in a magnetic field of 350 kA/m. The improvements were found when the alloy was tested in the same direction as the
previously applied field and reduced properties when tested at right angles to this direction. This was quickly followed by the discovery
of a range of alloys containing 1 6 - 30% cobalt which responds so well
to magnetic field treatment that energy products two or three times those of the isotropic properties could be obtained in the field treatment direction (68). The significant change is the very large
increase in remenance Br or Cooling in the absence of a field
gives ^r = 0*5 - 0*7 but with the field jr values of over 0*9 are
J Js
achieve?• This change is accompanied by squaring of the demagnet
isation curve so that the fullness factor (BH) max/ B r CBH^t, increases
from about O.^f in the isotropic alloys to 0.6 or more for the best field cooled alloys.
Further improvements in the directional magnetic properties were achieved by making magnets with columnar grains and then field
cooling in the direction of the long axis of the grains (6 9), giving
values of J /J in this direction approaching 1 and up to a furtherr s
70% improvement in energy product.
Other developments have stemmed mainly from composition
adjustments, notably substantial quantities of titanium (up to 8 wt.%) with a simultaneous increase of the cobalt content up to 35-*KD%» have achieved much higher coercivity and some improvement in (BH) max; however, at the expense of the reraanence (70). Difficulties of achieving columnar growth due to the presence of both aluminium and titanium (71) were solved by small additions of sulphur or tellurium (72). These titanium bearing alloys require isothermal annealing in a magnetic field in contrast to the other alloys which are cooled from the high temperature conditions in the field.
Details of these materials are conveniently summarised by
Gould (6 3) and a few representative BH demagnetisation curves are