LOW-FIELD MAGNETIC HYSTERESIS IN IRON, COBALT, NICKEL AND STEEL

Journal of Magnetism and Magnetic Materials 65 (1987) 71-75
North-Holland, Amsterdam

71

LOW-FIELD MAGNETIC H Y S T E R E S I S IN IRON, COBALT, NICKEL AND S T E E L
G.H.J. W A N T E N A A R , S.J. CAMPBELL, D.H. C H A P L I N and G.V.H. WILSON
Department of Physics *, University College, University of New South Wales,
A ustrafian Defence Force Academy, Campbell A CT 2600, A ustrafia
Received 15 August 1986

Spheroidal samples of high purity iron, cobalt and nickel and carbon steel have been examined in a low field (10 -3 to 103
Am -1 rms) ac magnetisation study of their hysteresis losses. Detailed comparisons of the field dependences of the fundamental and higher harmonic components show that only cobalt exhibits the features of the empirical Rayleigh-like behaviour for which both linear and quadratic dependences of magnetisation upon magnetic field are present.

1. Introduction
Recent low field ac magnetic hysteresis studies
[1] report considerable departures from the empirical Rayleigh law in describing magnetic hysteresis losses in toriodal samples of ferromagnetic gadolinium and terbium. This law has been formulated theoretically in terms of small discontinuous field-induced irreversible displacements of domain walls between a series of small potential wells [2]. For these rare earth ferromagnets the linear plus quadratic dependence of the initial magnetisation with applied field expected from
Rayleigh's law was not reflected in measurements of the third harmonic of the ac magnetisation for which log-log plots should exhibit a distinct linear region with slopes of m = 2. The deviations from m = 2 were marked, being closer on average, to m = 3. These findings prompted the present more detailed scrutiny of Rayleigh-like behaviour in 3d transition metals which are more generally associated with exhibiting the above simple Rayleigh power law dependences upon the magnetic field.
The present study is therefore an extension of the elemental rare earth work to measurements on
* Former address: Department of Physics, Faculty of Military
Studies, University of New South Wales, Royal Military
College, Duntroon, ACT 2600, Australia.

high purity iron, cobalt and nickel and also includes measurements on carbon steel. Preliminary results for iron and steel are reported elsewhere
[31.
In the present study the possibility of Rayleighlike behaviour has been examined critically by sensitive measurements of the fundamental and harmonic dispersive components, and, in certain cases, the absorptive component of the ac magnetisation. The room temperature ac magnetisation of the samples was studied as functions of applied magnetic field amplitude (10-3-1010
Am -1 rms) and frequency (0.2-100 Hz).

2. Experimental
Spheroidal samples formed removable cores of a solenoidal transformer, thereby allowing measurements of the voltage induced in the secondary coil with and without the sample present. The free space contribution to the total magnetisation could therefore be determined independently. Lock-in amplifiers were used to detect synchronously the complex fundamental components and the magnitude of the third harmonic component. A square wave from the same source as the applied field provided a synchronised fundamental and a harmonic reference signal via a selective amplifier.

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72

G.H.J. Wantenaar et al. / Low-field hysteresis in iron, cobah, nickel and steel

2.1. Samples
The samples of purity 5N were precision machined into spheroids from rods 15 cm long and diameter 5 mm. An identical sample was made from commercial carbon steel rod (diameter 5 mm), giving prolate spheroids with major axis 75 mm and minor axis 2.5 mm. N o subsequent heat treatment was applied to the cold worked spheroids. The fraction of space occupied by the samples (filling factor ~) was accurately determined from the weight and dimensions of samples before machining, the weight after machining and the dimensions of the secondary coil.
2.2• Solenoid
The sample assembly consisted of a two layer fine gauge secondary coil of length 15 cm placed centrally within a primary coil of length 35 cm. A uniform field along the secondary coil was provided by the narrow diameter of the solenoid ( = 5 mm), which was lined with thin Teflon sheeting.
The cross section of the secondary coil was measured accurately by slicing an identically constructed solenoid•
2•3. Magnetic measurements
The experiments were similar to those carried out on the toroidal samples of gadolinium and terbium [1] in which an air-cored transformer was used to back off unwanted signals in the harmonic measurements• As already noted, greater accuracy was achieved by having removable samples. Corrections were applied for demagnetising effects•
Although the demagnetising factor [4] for these toroids was small (D = 0.003444), the high magnetic susceptibility of iron and steel meant that the internal field at our highest applied fields was nevertheless reduced to about one half of the external field• In these cases, a combination of limited oscillator current and demagnetising field effects restricted susceptibility measurements to maximum internal fields of H = 400 A m - t rms. It should be noted that, for samples of high susceptibility, demagnetising effects can lead to phase and amplitude distortion of the applied wave-

forms at magnetic fields well above the region of initial susceptibility• With the low susceptibility of cobalt such sources of distortion were negligible.
Current studies on long thin wire (0.5 mm) samples of steel and high purity (5N) iron confirm that the internal magnetic field distortion on the present spheroidal samples over the field values studied was insignificant.

3. Results and discussion

The field dependences of dispersion X', loss X" and third harmonic components X3 of ac magnetic susceptibility for the samples are shown in log-log form in fig. 1. Initial relative susceptibilities and the magnetic fields below which disper-

3

/

2

log Z

I

,

steel
- t ~
Fe
steel
.
• .•

0

!

(a)
-" - - :

- - l -

•~

~

,

,

~=.

"

~

m=l / < . J

,

i

_ . ~ X '
~
-~;X"~...... f steel

Fe

..................................

o

~ u ~n
~
u~

X'

(b)
~ X n

-I log X_2

co

m

X3

-3
".~

I
1

I

(c)

I

I

I

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X.'

0

Ni

./ X"

.....~J-

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• • .'..,
-3

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X3

t

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3

(Am -l )

Fig. 1. log-log plots of ac magnetic susceptibility (X = X' +Jx" and the third harmonic component X3) versus rms internal magnetic field (f = 3 Hz): (a) iron (solid curves) and steel; (b) cobalt; (c) nickel.

G.H.J. Wantenaar et aL / Low-field hysteresis in iron, cobalt, nickel and steel

sion becomes field independent are given in table
1. In the case of magnetic hysteresis described by
Rayleigh's law [1,4], the field dependence of the dispersive component is given by X ' = Xo + otH where X0 is defined as the initial susceptibility, is Rayleigh's constant, and the hysteretic components X" and X3 are both proportional to field with constants containing a. Hence if Rayleigh's law applies, log-log plots will feature linear graphs of slope unity for X" and X3 and a field independent portion for X' at low field values (where
X0 >> a l l ) .
For iron and nickel, fig. 1 shows that there are no linear field dependences evident in the hysteretic components and therefore their hysteresis cannot be described in terms of Rayleigh's law.
X" of steel has a linear field dependence of unit slope for 10 Am - t < H < 60 Am -1, but the corresponding Rayleigh-like behaviour is not present in
X3- Therefore, while steel might be considered
Rayleigh-like on the basis of the field dependences of dispersion and loss [3], the third harmonic measurements show clearly that this is not the case. Only cobalt exhibits consistent behaviour in that the slopes of each of its hysteretic components are essentially unity within the range 200
A m - 1 < H < 600 A m - t rms. Below the initial fields all samples have their third harmonic signals diminishing rapidly at low fields. This effect was also observed in gadolinium and terbium, and presumably indicates the approach of reversible domain wall motion of pinned domain walls. It can be concluded therefore that the iron, nickel and steel samples do not follow the simple
Rayleigh power law, but at the lowest fields all samples do exhibit field independent susceptibilities as observed originally by Rayleigh [5].

73

As in previous studies of ferromagnets [1] it is found that additional loss mechanisms which are field independent remain in the loss component
X" as the dominant hysteretic contribution (as evidenced by X3) falls off at low fields (fig. 1).
These losses can originate either in eddy current effects or, as in gadolinium [6], as a diffusion after-effect. The possible existence of an after-effect in the present samples was investigated by measuring the frequency dependence of the susceptibility: fig. 2 shows the frequency dependence of the phase lag ~ = arctan X"/X'- The dependence of an identical spheroid of gadolinium
(formed from stock for which an after-effect is known to exist [6]) was used for comparison. Fig.
2 suggests that only losses related to eddy current effects can be observed in iron, nickel and steel, whereas there is a possibility of a very weak after-effect in cobalt as indicated by the trend towards a peak at low frequencies (cf the well established frequency peak for gadolium). Such an additional contribution to X" in cobalt could account for the observed ratio in the linear region of X " / X 3 = 7 / 1 rather than the 5 : 1 ratio expected for Rayleigh hysteresis [1].
2
I

steel,

I Fe

phase lag arctan

O~o_oG d ~

J

Co

XZ'

X'
Table 1
Initial magnetic behaviour of the iron, cobalt, nickel and steel samples Initial relative susceptibility Carbon steel
Iron
Cobalt
Nickel

Initial magnetic field
( A m - x rms)

81.5 _+0.5
54.5 + 1.0
3.645 + 0.010
13.43 +0.03

_.