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THE MAGNETOCRYSTALLINE ANISOTROPY OF W-TYPE HEXAGONAL FERRITE5

Y.Xu, G,L.Yang, H. Cai, H.R.Zhai

ABSTRACT

Single ion anisotropy of Fe3' i o n s a t each site of the 7 s u b l a t t i c e s 2d, 4e, 4 f ~ , 4fv1, 68, 12k, and 4f i n t h e f e r r i t e Zn2W has been calculated by c r y s t a l f i e l d

theory using point charge approximation. As expected, t h e r e s u l t s show tha t t he con t r ibu t ions o f d i f f e ren t s i t e s a r e d i f f e r e n t which may be pos i t ive o r negative. This model can explain the experimental results of subs- t i t u t e d W-type f e r r i t e s .

I. INTRODUCTION

W-type f e r r i t e i s a kind of hexagonal ferri tes with i t s chemical formula as BaM2Fe16027, i n which M repre-

sen ts a di-valent metal ion. I t has an abbrevia t ion as M2W. For example, when M i s Zn o r Fe, the abbreviat ion

i s Zn2W o r Fe2W. The general propert ies and the struc-

tu res o f W-type f e r r i - t e s can be found i n t h e famous book wr i t ten by smit and wijn[l]. W-type hexagonal f e r r i t o i s a new candidate for oxide permanent magnet with mag- net izat ion higher than M-type f e r r i t e . I t has been re- ported that permanent magnet using Fe W t y p e f e r r i t e s has been 'made with (BH),=3.7-4.3 x 10 GOe[2]. A number of invest igat ions on Zn2W have been conducted. !The

measured value of magnetocrystalline anisotropy constant of ZnzW a t O°K i s K1=6.74 cm-l/molecule while i t s calcu-

la ted va lue due to c l a s s i ca l d ipo le i n t e rac t ion i s K,&=-0.26 cm-1/molecule[3]. Thus the magnetic anisofr-

opy constant K =7.0cm-'/molecule from o the r o r ig in should exist. ?t i s considered to be from s ing le i on mechanism. The e f f ec t o f i on subs t i t u t ion on the pro- p e r t i e s o f Zn2W has been studied by G.Albanese e t a1.[41

They f i n d t h a t f o r BaZnZFe16xMex027, where Me represen-

ts Al, Ga, I n and Sc non-magnetic i ons , d i f f e ren t k inds o f i ons have d i f f e ren t i n f luence on the magnetocrystl- l ine an iso t ropy . They a r e a ) f o r Ga3+, Kl increases

s l igh t ly wi th x a t first and than decreases gradually; b) f o r A13', as x i s small, the change o f X, i s not evident while with x%, K1 increases notably; and c) f o r

l 0 1 A

I

0 1 2 3 4 5 6 7 8 ~

Fig. 1 X, vs. x f o r BaZn2Fe,6_xMex027 a t O°K with Me=Al, Ga, I n and Sc.

Manuscript received March 23, 1984. The aur thors a re wi th the Ins t i tu te of Solid State

Physics, Nanjing University, Nanjing, China. The work was supported by the science foundation of the Academy of Sciences of China.

1n3' and Sc3', even small subs t i t u t ion l eads t o r ap id decrease of KI. Fig. 1 shows the concentration depen- dence of K1 evaluated from the experimental results[4). They a l so gave the preference s i tes occupat ion of Ga,Al, I n and Sc i o n s i n Zn2W crys ta l . So f a r t h e r e h a s been no explana t ion in the l i t e ra ture for these observa t ions . A possible explanat ion, in our opinion, i s tha t s ince t h e r e a r e 7 d i f f e r e n t i n e q u i v a l e n t l a t t i c e s i t e s f o r

Fe3' i n Zn2W with different local environments , Fe3'

i o n s i n d i f f e r e n t s i t e s may g ive d i f fe ren t cont r ibu t ions to anisotropy which may be p o s i t i v e as well as negat ive with various absolute values. The subs t i t u t ion o f Fe3+ i n d i f f e r e n t s i t e s by var ious kinds of non-magnetic i o n s may be the reason of different appearance of concentra- t i o n dependence of K, shown i n t h e above f igure. To ver i fy this assumption we car r ied ou t theore t ica l ca lcu- la t ions o f s ing le ion an iso t ropy of Fe3+ i o n s i n t h e seven l a t t i c e sites i n Zn2W by c r y s t a l f i e l d t h e o r y

udng point charge approximation. Our r e s u l t s show the validity of this assumption and the model. can explain the above experimental facts quali tatively.

11. METHOD OF CALCULATION

Neglecting the spin-crbit coupling, the Hamiltonian

of Fe3+ i o n system can be expressed as H=Ho+IIc (7)

where Ho i s the Hamiltonian of free ion without spin- orbi t coupl ing and H e i s t h e c r y s t a l f i e l d p o t e n t i a l . Expressions for Ho and Hc are:

The c o e f f i c i e n t s i n He were calculated using point charge model accord ing to the da ta o f c rys ta l s t ruc ture of Zn2W measured by P.B.Broun[5].

The electron configurat ion o f FeSf i s 3d5. The f i rs t order per turba t ion of H e does no t l ead t o sp l i t - t ing of spectral terms. Thus we have to perform the ca lcu la t ion of second order perturbation, which i s equi- va len t to d iagonal iz ing &r%~.il.~ simul.taneously. Since these two terms do not include operator of e lectron spin, the ca lcu la t ion of d iagonal iza t ion may be car r ied ou t separately with respect to the spectral terms of Fe3.t 'on with the ame mul t ip l ic i ty . In our ca lcu la t ion on ly 'G ,%,4D and f F terms were retained. The doublet terms with higher energy, 2I e t c , we're neglected.

energy of these four terms (considering 6s as zero) are: 4G=32b00 em", 4F=35100 cm-' , 'D=38500 em", 4F=52100 em-', respect ively. Rased on S l a t e r r a d i a l wave funct ion we have<r2>=9.03 x lO-17cm2, (r4>=1.311 x 10-~~cmL. Hence we determined the energy levels of S=3/2 terms o f Fe3f i o n s and t h e i r wave func t ions a t var ious sites.

According to t he da t a from o p t i c a l spectrum, the

The magnetocrystalline an' sotropy depends on the

b i n e d e f f e c t o f c r y s t a l f i e l d and spin-orbi t in terac- t ions. The ground s t a t e 6S i s an o rDi t a l s lng le s t a t e . The f i rs t order per turba t ion of Hsl does not lead to

s p l i t t i n g o f t h e ground state t, S of Fe3' under the com-

removal of spin degeneracy and thus second order pertu-

0018-9464/84/0900-1227%01.0001984 IEEE

1228

bation modification was considered. The energy modifica- t i o n by second order per turbat ion was determined by the following 6x6 matrix: 2 <%,&I HslI %,sA)<$&l %I I%,@> d 5.L LEX65 ) - €4

where E i corresponds to the energy levels of the four terms 'G, %, %, 'F a f t e r c r y s t a l f i e l d s p l i t t i n g , w i t h t h e i r wave functions and X, g=f1/2, i3/2, f5/2.

In case tha t on ly the e f fec t o f neares t ne ighbors i s con-

of the seven s i tes for Fe3f. Taking t h e axis o f three- sidered, an axis of three-fold symmetry e x i s t s i n e v e r y

fo ld ax is as Z-axis, the above matrix diagonalizes auto- mat ical ly , and the energy modification of second order perturbation simply equals:

i, si,

Now the s p l i t t i n g o f ground s t a t e can be described by the spin Hamiltonian:

Hs=DSz 2 (5)

i n which D=1/4[E( Sz=5/2)-E( Sz=3/2)] and the magnetocrys- ta l l ine anisotropy constant of a s ingle Fe3+ i o n a t O'K i s K1=-5D.

<pi, s~ I Hsl 1 %SYSz> can be car r ied ou t in the represen-

ta t ion with Slater determinant as i t s base. For conve- nience the HS1 i s expressed as:

The calcul t ion of the matrix element

<%(Mz=l,Sz=1/2)[ H s l ( 6 S ( S z = 3 / 2 ) > = - . 3 ( f i ) 2 ~

and so on.

take <3(r)> =440 em-' (experimental value) in the ca lcu- l a t i o n .

According t o Fuchikami[6] and o u r own work[71 we

111, RESULTS AND DISCUSSION

Our resu l t s o f ca lcu la t ion a re l i s t as fol lows:

S i t e s hf 12k 6g l+f 4.f 4e 2d 4.07

cm-I 0.29 -0.39 -0.18 -0.02 -0.27 0.21 4.85 K1

cm-I 0.06 -0.18 -0.02 -0.21 -0.24 -0.19

the upper row re fe r s t o t he r e su l t s on ly cons ide r ing t he effect of nearest neighboring 02- i o n s i n c r y s t a l f i e l d ca lcu la t ion and i n t h e lower row the ca lcu la ted resu l t s considering further the next nearer neighboring metal i o n s a r e shown. Among the next neighbors o f the three s i t e s 6g, 12k and 4f, there are Zn2+ ions. With the supposition of random d i s t r ibu t ion o f Znzt i o n s i n t h e two t e t r a h e d r a l s i t e s 4e and 4fiV, we ca l cu la t ed t he e f f ec t of a l l the poss ib le d i s t r ibu t ion of ZnZt and found l i t t l e difference. Therefore we took the d i f fe ren t d i s t r ibu t ions as equal probabi l i ty and made the average. In the case of including the next nearer neighbors z-axis i s s t i l l approximately three-fold symmetrical.

of 2d and 4f s i t e s t o an i so t ropy a r e pos i t i ve and the rest s i tes give negat ive Contr ibut ions. Only the calcu- la ted value of 4e s i t e s changes sign when d i f f e r e n t l a y e r s of neighboring ions are considered. The contr ibut ion of 2d s i t e i s h igher than tha t o f the o ther s i tes by one order of magnitude. However, the number of ions of the o t h e r s i t e s p e r u n i t c e l l i s larger than tha t o f 2d. Thus the e f f ec t o f t he o the r s i t e s canno t be neglected. This

Our ca lcu la t ed r e su l t s show tha t the cont r ibu t ions

i s ju s t s imi l a r t o t he ca l cu la t ed r e su l t s fo r M-type hexagonal f e r r i t e s done by usI73. Our recent calcula- t ion of the anisotropy o f C02t i o n s u b s t i t u t i n g i n t h e 12k s i t e i n BaM gave a very large negative value as ob- t a i n e d i n a number o f experiments. The d e t a i l s a r e t o be published elsewhere.

With our t heo re t i ca l r e su l t s we can tentatively ex- plain the experimental results obtained in[&]. (a) Acco- rding to the analysis of Albanese 141, In3' and Sc3+ ions e n t e r mainly i n t o 2d and 4f s i t e s . The contr ibut ions of Fe3+ i n these two s i t e s a r e p o s i t i v e w i t h a very la rge va lue for 2d s i te . Tnis may be the reason why K1 decreases rapidly with increasing concentration of subs- t i t u t i o n o f In3' and Sc3+. (b) For A13+, when the subs- t i t u t i o n o f x<5, Al3+ i ons en t e r mainly i n t o 6g and 4f s i t e s and then to 1%. Owing to the compensation effect of 6g and 4f s i t e s (when they are occupied by non-magne- t i c A13+ ions) the value of K 1 changes very l i t t l e when x<3 and then K 1 increases gradually with x. Around 4<x<6, K1 increases conspicuously and reaches a maximum, which may be accounted for by the occupation of A13' i n 1% where the contr ibut ion of Fe3' i o n i s r e l a t i v e l y l a r g e anti negative. The decrease of K1 upon fur ther in - crease of x can be explained when a fur ther information about the d i s t r ibu t ion of Al3+ i o n s f o r l a r g e x i s avai- l a b l e . ( e ) Ga3+ i o n s a r e s a i d t o d i s t r i b u t e randomly among the oc t ahedra l s i t e s and the probabili ty of ente- r i n g 2d s i t e i s small when x<5. According t o o u r r e s u l t s the contr ibut ions of Fe3+ i o n s i n a l l o c t a h e d r a a r e ne- gative except that i n hf , which may expla in the s l igh t increase of K1 f o r small x. When x35, the p robabi l i ty f o r Ga3' t o occupy 2d s i t e i n c r e a s e s and thus the value of K1 decreases with a r e l a t i v e l y l a r g e r a t e .

REFERENCES

J.Smit and H.P.J.Wijn, t tFer r i tesT1, (Phi l ips Techni- cal Library, 1959) Chapter I X . F.K.Lotgering,P.H,G.M.Vromans and M.A.H.Huyberts, IIPermanent-magnet material obtained by s i n t e r i n g the hexagonal ferr i te U=Bh.Fe1802711, J.Appl.Phys.,

F.K.Lotgering,P.R.Locher and R.P.van Sta.pele, "Anisotropy of hexagonal f e r r i t e s w i t h M , W and Y structures containing Fe3' and Fe2+ as magnetic ionsll, J.Phys.Chem.Solids,Vo1.41, No.5,pp.481-487, 1980. G.Albanese,M.Garbucicchio,L.Pareti,S.Rinaldi,E. Lucchini and G.Slokar, "Magnetic and Mdssbauer study of Al,Ga,In and Sc subs t i tu ted Zn W hexagonal fe r r i tes" , Journa l o f Magnetism an8-Magnetic Materi- als,Vol.l5-18,Part 3,pp.1453-1454,1980. P.B.Braun,"The c rys t a l s t ruc tu res o f a new group of ferromagnetic compoundstl,Philips Res.Rep., Vol. 12, ~~.491-548,Dec.,l957. Nobuko Fuchikami,"Magnetic anisotropy of magneto- plumbite BaFe1201 I I , Journal o f the Physical Socie- ty of Japan, Vol.%,N0.5,pp.760-769,Xay,1')65. Y.Xu,G.L.Yang,D.P.Chu and H.R.Zhai,flMagnetic ani- sotropy o f BaM ferr i tes" , Journal of Kagnetism and Magnetic Materials, Vol.31-34,Part 2, pp.851-816, 1983.

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