Thermoremanent phenomena in disordered systems

Journal of Mqx?im~

ad ivSagneCcMaterials MO-144 (1995) 359-360

ELSEVIER

Themoremanentphenomena in disoderedsyste M. El-Milo %*, K. O’Grady a, R.W. Chantrell b a Magnetic Marerials Research Group, SEECS, Uniuersity College of North Wales, Bangor, Gyw4-l b Dept. of Physics, Keels Uniur sity Keele, Stafi ST5 SBG, UK

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In this paper the effect of particle interactions on the behaviour of the thermoremanent m examined. The variation of the TRM with cooling fieId is well known, and shows an monotonic increase to saturation. In this paper a mean field approach and a Monte Carlo model are corn Carlo calculations predict a peak in the TRM, which is a consequence of the interaction field, whereas approach does not predict a peak.

1. Introduction

The thermoremanent state is obtained by cooling a system in the presence of a magnetic field fiam a temperature at which all moments can fluctuate rapidly, to one at which some of the fluctuations are quenched and hence thermoremanent behaviour is observed. The variation of the TRM with cooling field is well known and is observed in many systems to give rise to a peak. This peak is observed to shift to lower fields as the waiting time after switching off the field is increased [1,2]. These observations of a time dependence, and the suggestion in Ref. [2] that there is a finite time for the field to be switched off, were modelled by Aharoni and Wohlfarth [3]. In their model the time dependence during the field switching was calculated using a linear reduction of field with time. These calculations successfully predicted a peak in the TRM, which was found to shift to a higher field as the waiting time was increased. This effect was not observed experimentally. The effects of time dependence during field reduction have been re-examined [4,5], since measurements of the TRM curve under a constant time of field reduction were also observed to give a peak in the curve [6]. The results of these studies [4,!3] have shown that only a nonlinear reduction of the field will give rise to a peak in the TRM, and with increased waiting time the peak still shifts the wrong way, i.e. to higher fields. Thus from these results, time dependence effects during field reduction alone cannot explain the peak in T’RM, so that other effects such as particle interactions must be considered in the calculations.

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+ 44-248-361429;

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In this paper the effects of particle considered using two different model in which the interaction an interaction field proportional adds lo the applied field; and Carlo model in which the e tion field is calculated.

in

2. TImwy

dM(H,,

T, V, t) dt

=

IcI,(&,

T, V) -M(H,, T(&,

T, V, t)

T, V)

where M, is the equiliirium magnetisation, and 7 is the relaxation time,

,

0) i.e.

M(t =

T-I =fo exp(-AE(H,, V, where +!J is the angle between the easy axis of the and the applied field. For the magnetisation changes given by merica!Iy using the Runge-Kutta me cd solution is not possible since the acting

0304-8853/95/XJ9.50 Q 1995 Elsevier Science B.V. AU rights resemed SSDI 0304-8853(94)01166-4

001,

Coohn~

Field

(0~)

Fig. 3. The variation of the average interaction field (Hi,) remanence with cooling field. axis system of a5y paaide within the system.

a typica! particie particle is given

is shown in Fig. 1; the energy of

at

the

by:

ET = KV sin2a - kXiiT cosp,

(2)

where H, is the total acting field (applied plus interactions). Energy minimisation of momentsis performed by iterating the angles 0 and I$, and the nagnetisationof the systemis then obtained by averagingover all orientations of momentsalong the measurementdirection. A full description of this model will be publishedelsewhere[7]. Fig. 2 showsthe calculatedTRM curve for different waiting tines at a temperatureT= 20 K. Thesecalculationswere made for Fe,O, particleswith a mediandiameter of 80 A and u= 0.3. K = 4,5 x 105 erg/cm3 in a cell with a packing fraction of E= 0.2. Fig. 3 shows tie variation of interaction field along the field direction. Thesedata showthat (Hi,) is negativeand increaseswith increasing cooling field, but does not saturateeven in twice the field required to saturatethe remanence.This causesthe TRM to decreaseat higher fields and gives rise to the peak. We can conclude that in random systemsinteraction effectscangive rise to the peak in the TkM. The failure of the mean field approachis not surprisingsince its effects saturatewhen the remanenceis saturated. Rtduccd

TRM

References

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[I] J. Fe& and J. Rajchenbach, J. Appl. Phys. 52 (1981) 1697. [2] t’k Beck, Phys. Rev. B 24 (1981) 2867. [3] A. Aharoni and E.P. Wohlfarth, J. Appi. Phys. 55 (1984) 1664. [4] M. EtHilo, KO’Grady, H. Pfeiffer and R.W. Chantrell J. Magn. Magn. Mater. IO&lU7 (1992) 1580. [s] M. EI-Hilo, ICO’Grady and R.W. Chantrell, in: Studies of Magnetic Properties of Fine Particles and their Relevance to Material Science, eds. 1-L. Dormann and D. Fiorani (Elsevier, Amsterdam, 1992). [6] M. El-Hilo, KO’Grady and J. Popplewell, J. Appl. Phys. 69 (1991) 5133. 171 M. El-Hilo, USGrady and R.W. Chantrell (to be published).