Journal of Magnetism and Magnetic Materials 101 (1991) 291-292 North-Holland

Measurement of magnetic anisotropy in ferrimagnetic powders by applied field M6ssbauer spectroscopy

Q.A. Pankhurst Department of Physics, University of Liverpool, Liverpool L69 3BX, UK

A technique for measuring the magnetic anisotropy in ferrimagnetic powders is described. The method is based on a uniaxial anisotropy mean-field model, and uses applied-field M6ssbauer spectroscopy. It is shown that the model predicts a coherent magnetisation reversal.

There are many experimental techniques for mea- suring the magnetic anisotropy field in ferr imagnetic materials. However, methods such as magnetisation curve analysis, work and torque measurements , and microwave ferr imagnetic resonance rely on the avail- ability of ei ther single-crystal or highly or iented partic- ulate samples. Recently, some methods have been de- veloped for use with powder samples, including rota- tional hysteresis loss [1], reversible transverse suscepti- bility [2] and d Z M / d H 2 singular point detection [3] methods. Such developments are welcome in the field of information storage research, where the particulate nature of the recording medium is of intrinsic interest.

One factor that all these techniques have in com- mon is that the anisotropy that is measured is the sum of the contributions from the different lattice sites. We have recently introduced a method that provides a means of distinguishing and measuring the individual sublattice anisotropies. The method uses a microscopic model of the response of a two-sublattice ferr imagnet to an applied field to predict the shape of the applied- field M6ssbauer spectra of the powder. The model is an extension of earl ier work on ant iferromagnetic pow- ders in applied fields [4], and was first presented in ref. [5]. In this paper it is shown that the model predicts coherent magnetisat ion reversal. The effects of inco- herent reversal mechanisms are then discussed.

The Hamil tonian of a two-sublattice ferr imagnet with a nearest-neighbour exchange constant J, sublat- tice anisotropy constants K and K ' , and sublattice spins S and S ' is

Y f = - 2 J Y'. S i " S] - K Y ' . ( S z i ) 2 - K ' Y ' . (Sz i ) 2 ( i j ) i j

B is the local field at an atomic site, which in SI units for the case of cubic symmetry is given by

B =Bap p - / z 0 ( N , - ½)M, (2)

where Nil is the demagnetisat ion factor parallel to the 1

direction of magnetisation and g/z0M is the Lorentz cavity field. The mean-field energy of the system may be expressed in terms of the orientat ions of the two sublattice spins:

E =NSglzB[BE~ cos(0 - 0 ' ) - ½B A cos2(0 - t )

-- ~UAS'R' ~:2 COS2(0 , -- t ) - B ( c o s 0 + ~: COS 0 ' ) ]

(3)

Here N is the number of sublattice spins, and 0, 0' and t are the polar angles of the two sublattice spins and the easy anisotropy axis with respect to the local field direction, s ~ is the ratio of the spin magnitudes, S ' / S , the exchange field is B E = - 2 J z S / g t z B where z is the number of nearest neighbours, and B A = 2KS/g tx a and B ~ = 2 K ' S / g t z B are the anisotropy fields. K and K ' are the effective anisotropy constants that incorporate both crystalline and shape anisotropy terms.

For a given value of t the equilibrium spin configu- ration is obtained numerically by minimizing E with respect to both 0 and 0'. In a powder t is sampled continuously between 0 and 360 o, with the range 0 to 180 o encompassing all the unique solutions. The mag- netic response of a ferr imagnetic powder to an applied field is therefore a sin t weighted superposition of the responses corresponding to each value of t. It may be model led by choosing a finite number of representative values of t, e.g.,

t = c o s - l [ ( Z n - 1 - N , ) / N , ] , n = 1 . . . . . U,.

0312-8853/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved

180-

1 5 0 -

120-

90- N

~ 6 o -

N 3o-

o - -

-3o-

-60

O. I

0.5 ' I ' I I ' I ' I I I ' P

0.1 0 .2 0 .3 0.4 LOCAL FIELO (T)

IO 20 30 40 50 60 70 80 90 ALIGNMENT ANGLE (DEGREES)

Fig. 1. Variation as a function of local field B of the angle 0 between B and the major spin S of a two-sublattice uniaxial ferrimagnet with exchange field B E = 500 T, anisotropy fields

t _ B A = B A - 0.005 T and sublattice spin ratio ~: = S ' / S = 0.95.

The angle 0 be tween the major spin S and the local field B, as d e t e r m i n e d by solving eq. (3) for the case B E = 500 T, B A = B~ = 0.005 T and ~: = 0.95, is shown in fig. 1 for a variety of values of t. Note tha t t is equal to the initial ( B = 0) value of 0. As the exchange is large the spins r emain almost ant ipara l le l t h roughou t the i r reor ien ta t ions . For t > 90 ° abrup t changes are a p p a r e n t in fig. 1, which cor respond to large changes in the d i rec t ion of S as the ne t fe r r imagnet ic m o m e n t of the sample is r eo r i en ted towards B, i.e. at the critical field for magne t i sa t ion reversal. The d e p e n d e n c e of the critical field on the angle 180 ° - t, shown in fig. 2, is the same as the angular var ia t ion of the coercive force requi red to induce magne t i sa t ion reversal in sin- g le-domain particles, see, e.g., ref. [7]. Thus the Hamil- ton ian given in eq. (1) cor responds to a microscopic model l ing of the cohe ren t response of a f e r r imagne t to an appl ied field. I n c o h e r e n t reversal mechanisms, such as curl ing and fanning, resul t in r educed coercivities.

To date the model has b e e n used to fit the 57Fe M6ssbaue r spectra of bo th ba r ium ferr i te [5] and Co- adsorbed ~ - F e 2 0 3 [6]. M6ssbaue r spectroscopy is well sui ted to the technique , especially when the ~-ray b e a m is d i rec ted paral lel to the appl ied field, since the intensi t ies of the A m / = 0 lines are sensitively depen- dent on the angle be tween the spins and the appl ied field. In the case of ba r ium ferr i te the sublat t ice anisot ropies were found to be indis t inguishable , so a single value of B A was fitted. Good-qual i ty fits were ob ta ined for all the spectra, which were recorded at 4.2 K in appl ied fields of 0, 3, 6 and 9 T. C o : ~ / - F e 2 0 3 spectra were recorded at 4.2 K in appl ied fields of 0, 3, 6 and 7.6 T. The two sublat t ice anisot ropies could be dis t inguished. Good fits were ob ta ined by simulta-

2 0 0 -

180-

160-

140- N -

120- u

1 o o - ~ _

Bo-

g 6o-

40-

20-

292 Q.A. Pankhurst / Anisotropy in ferrimagnetic powders

Fig. 2. Field at which the major spin S reorients to a direction close to the local field B, as a function of the angle between - S and B. The alignment angle corresponds to 180 ° - 0 in

fig. 1.

neously fitt ing the Bap o = 0, 6 and 7.6 T spectra, but the cor responding fit of the 3 T spec t rum showed some misfit in the intensi ty of the A m / = 0 lines, with the model predic t ing too large an intensity. This may be in t e rp re t ed as an overes t imate of the coercivity of the sample in response to the 3 T field, and might be indicative of the p resence of incoheren t reversal mech- anisms.

It is concluded tha t by using the mean-f ie ld theory model descr ibed in this pape r it is possible to measure sublatt ice anisot ropies in fe r r imagnet ic powders via applied-field M6ssbaue r spectroscopy. Fu r the rmore , it may be possible to de t e rmine w h e t h e r or not the response of the system is coherent .

R e f e r e n c e s

[1] D.M. Paige, S.R. Hoon, B.K. Tanner and K. O'Grady, IEEE Trans. Magn. MAG-20 (1984) 1852.

[2] L. Pareti and G. Turilli, J. Appl. Phys. 61 (1987) 5098. [3] R. Scholl, K. Elk and L. Jahn, J. Magn. Magn. Mater. 82

(1989) 235. [4] Q.A. Pankhurst and R.J. Pollard, J. Phys.: Condens. Mat-

ter 2 (1990) 7329. [5] Q.A. Pankhurst, J. Phys.: Condens. Matter 3 (1991) 1323. [6] Q.A. Pankhurst and R.J. Pollard, Phys. Rev. Lett. 67

(1991) 248. [7] E.P. Wohlfarth, in: Magnetism, vol. 3, eds. G.T. Rado and

H. Suhl (Academic Press, New York, 1963) p. 367.