Growth-induced site preferences in rare earth garnets

Solid State Communications,

Vol. 9, Pp. 1691—1694, 1971. Pergamon Press.

Printed in Great Britain

GROWTH-INDUCED SITE PREFERENCES IN RARE EARTH GARNETS A. Rosencwaig and W.J. Tabor Bell Telephone Laboratories, Incorporated Murray Hill, New Jersey

(Received 28 July 1971 by N.B. Hannay)

A recent ESR experiment has provided experimental verification of the theoretically-predicted growth-induced non-random distribution of rare earth ions in flux-grown garnets. We show that the observed site preferences are in good agreement with the predictions of the site models proposed for the magnetically noncubic garnets.

THE NONCUBIC magnetic anisotropies which have been observed in certain flux-grown mixed 2have been explained rare earth iron garnets’ ‘ with the hypothesis that there exists a growthinduced non-random distribution of the rare earth ions in the dodecahedral sublattice.2~ It has also been proposed in the models of references 2—6 that this non-random ionic distribution is facet dependent. Recently electron spin resonance measurements on YAG: Nd and YAG : Yb7 have provided experimental verification of the above hypothesis. Noticeable differences in the site populations of the Nd34 and Yb34 ions have been observed under both facets, and these differences have been found to be facet-dependent.

preference is present, we can define the probability for ion A occupying site i as = ~ ,~A) (1) is the relative concentration of ion A in the solid and 7~’ is the growth-induced preference of ion A for the ith site. Since ~ = nA, it is clear that ~Th’~’ = 0 (2) ~A

Similarly for ion B we have B = flB(1 ± 7~) and

~

=

0.

(3)

P~ Since p,A

p~ = 1, it is clear that

+

=

In this letter we show that the observed site preferences are in general agreement with the predictions of the theoretical site models ~ (the site models of H. Callen5 and Rosencwaig, Tabor and Pierce4 are basically similar though developed independently). We will consider first the site preferences developed from the pair-bond preference parameters,2’3 and then the site preferences determined from an expression6 involving the local orthorhombic axes of the dodecahedral rare earth sites.

(4)

If we assume that the site preferences are functions of the facet normal /3, then i~(/3) can be written in terms of a local axis of symmetry ~ as6 77~(f3) = c ~

/3)2

—

1/3

(5)

If the d~represent pair-bond directions,2 ,3 then 77~(/3)can be written as in equation (5) of reference (4), i.e.,

=

If we consider two rare earth ions A and B distributed among the dodecahedral garnet sites, and assume that some growth-induced site

—n B~~B

c(A:B){m1~ (~~)(/3) 4

+

m~ ~ “i

4

~~k)

(~)+ mi!i ~ l=i

(6) 1691

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Vol.9, No. 19

Table 1. Theoretical and experimental site preferences Facet

Site preference

Pair bond cos — sin O~ }

c(A : B)~0.67m’ 0.22&’— 0.31mm~ —

7~

~110~

—~1c~

c~,+-~ c

—

2

—0.05

+0.14

+0.12

—0.26

+0.07

—0.31

c(A:B)1—1.33tn~+0.48m”+ 2.68m~’~_4c~+-~.c

1,.-fc~

i

c(A:B)t_1.33mI+0.48m~_1.44mm}

c(A : B) ~112I

E.S.R. results YAG: Yb YAG: Nd

Orthorhombic

—

0.50m’

+

0.35mg

+

1.87m’~}

1

+

0.35mg

-

1.29m”~

c(A : B)I-0.50m c(A : B)~m’— 0.68m”

—

0.O4mm}

~

c~+ c1, c~ —~-c~ 1c~, 1c~ 12 4 6

— ~—

-

+

0.03

—0.39

-

+0.03

-0.39

—0.04

+0.41

—0.07

+1.14

—~-c 2,~

c(A:B){m’ -0.68m”-1.34m~

—

c~

_~-c~,++cz

c(A:B)12.67m’ ~0.44mh1_mI!l~

~100~ c(A:B)~_1.67mI_0.22mhI~~0.50mt~ +icx+ic~_J-cz

c(A:B)~1.60m’~

~11l~ c(A:B)3-l.60m”~

where I, II, III represent the nearest-neighbor tetrahedral (N.N.T.) bonds, the nearest-neighbor octahedral (N.N.O.) bonds and the next-nearestneighbour tetrahedral (N.N.N.T.) bonds, respectively. The m are weighting factors for the different bond classes, and the E~1,hh1 are the appropriate pair preference parameters for the ith site. The coefficient c(A B) is a scalar preference function for ion A in an A—B mixture, and is dependent solely on the properties of the rare earth ions, such as the mass and radii. It is clear from equation (4) that c(A : B) has the opposite sign of c(B: A). In Table 1 we list the various sitedodecahedral preferences, for the six magnetically inequivalent

!~ _l~~ garnet sites under both the ~110~and {112~ facets. These preferences have been evaluated from equation (6) and tables of bonds such as Table 1 in reference (4). We have used the angular dependence for the E”s that has been used in reference (2) and (3), i.e., ~ a ~ cosO~ — sinO~I where O~is the angle between the pair-bond direction and the normal to the growth facet. So far we have characterized the dodecahedral sites in terms of the set of nearestneighbor bonds at each site. A simpler but equivalent way is to characterize each site by 6 The its local orthorhombic crystal field axes. general expression for the preference of an A ion

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SITE PREFERENCES IN RARE EARTH GARNETS

for the ith site will then be given by =

ci,, 1(d~~ 1/31 1/31 + c~1(d .

—

where d~, d,,~ and

—

.

+

cv 1(d~~. ~)2 —

1/31

(7)

are the local crystal field

axes at the ith site, and ~ is again the facet normal. The c’s are weighting factors which are dependent on the rare earth properties and determine the relative importance of the local orthorhombic axes in establishing the site preferences. Equation (7) reduces to equation (5) for the case where the three axes reduces to one local axis of symmetry and with c~+ c~,+ c,, c(A : B). =

Using equation (7) and the local axes for the six magnetically inequivalent sites, we can evaluate the three different preference parameters under the 11101 facet, and the four different parameters under the 11121 facet. These parameters are listed in Table 1 under the heading of ‘orthorhombic’. Upon examining the two sets of theoretical preference parameters listed in Table 1 we can draw the following conclusions: (1) Since the magnitudes of the weighting factors m1’11’~11 decrease with increasing nearestneighbor distance (that is, the closer neighbors are more important in determining the preference than the farther neighbors) then mt > m~1> m111. Equivalently, this results in c, > c~ c~,since the local crystal field z-axis is always a <100> direction. This then implies that the induced -‘-‘

1693

(5) From equation (4) it is clear that c (A: B) and c (B: A) differ in sign. This in turn indicates that c(Nd: Y) and c(Yb: Y) will also differ in 3~is larger than Y34, while Yb34 sign since Nd is smaller. (6) Furthermore, since Nd34 is 12% larger

than Y34 while Yb34 is only 7% smaller than Y34, we expect I c (Nd: Y) > c (Yb: Y) I. It should be noted that all three sets of preference parameters give essentially the same results, thus again demonstrating the equivalence between the various ways of characterizing the dodecahedral sites. In the last two columns of Table 1 we list the induced preferential site occupation of Yb34 and Nd3~in YAG as derived from the experiment of reference (7). In comparing the above theoretical conclusions with these experimental results we find good agreement with the YAG: Yb system. The results on YAG : Nd are in general agreement and differ essentially only in the unexpectedly high value ~ under the 11121 facet. It is not clear at this point why YAG: Nd does show this difference while the YAG: Yb does not. In addition to the bulk crystals which grow with 11101 and 11121 facets only, garnet films grown epitaxially on 11001 and 11111 substrates8 have also exhibited noncubic magnetic properties which can be attributed to growth-induced site

preferences.9 For the 11001 substrate we find only two different parameters: ~ 7) y, 7)y T)z, 77z 2 ‘ 2. For the 11111 substrate we again have ‘~7z, only two 77Y, ‘7x different parameters: ?)x, 2 ‘r~z2. The predicted site preferences for the 11001 and 11111 substrates have been evaluated both in terms of the pair-bond characterization (equation 6) and in terms of the crystal field axes characterization =

=

=

=

preference of ion A for a site, such as X1, will change sign when one proceeds from the 11101 facet to the 11121 facet. (2) Under both the 11101 and 11121 facets, the difference between an X site and a Z site should be larger than the difference between the two Z sites. (3) The difference between the two Z sites under the 11101 facet should be larger than the same difference under the 11121 facet. (4) There is no difference between the two X sites under the 11101 facet but some difference between these two under the 11121 facet.

=

=

=

~

=

(equation 7). It would be of considerable interest

to perform an E.S.R. experiment on these garnet films to further test the theoretical models. Finally it should be noted that the site preference parameters 77 are all 3-parameter expressions. is true both for those determined by the This pair-bond characterization, and those determined by the orthorhombic characterization. The use, in the expressions for 77, of only

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Vol.9, No.19

the second power of the scalar product involving the facet normal, will result, as shown in

data is as yet not consistent enough to warrant a careful evaluation of c1 and c2, a first order

reference 6 in expressions which contain only two independent parameters. For the case of the orthorhombic 77’s it can be shown that the two independent parameters are c, c2 + c~,— 2c2 and c c c . All of the site preferences can be written in terms of c, and c2. Although the

analysis clearly reveals that c, >> c2, a result in full accord with our previous assumption that C2 > C~

‘~

C~.

=

=

—

Acknowledgements The authors wish to thank R. Wolfe and M.D. Sturge for helpful discussions. —

REFERENCES 1.

BOBECK A.H., SPENCER E.G., VAN UITERT L.G., ABRAHAMS S.C., BARNS R.C., GRODKIEWICZ W.H., SHERWOOD R.C., SCHMIDT P.H., SMITH D.H. and WALTERS E.M., Appi. Phys. Left. 17, 131 (1970); LECRAW R.C., WOLFE R., BOBECK A.H., PIERCE R.D. and VAN UITERT L.G., J. appi. Phys. 42, 1641 (1971).

2.

ROSENCWAIG A., TABOR W.J., HAGEDORN F.B. and VAN UITERT L.G., Phys. Rev. Lett. 26, 775 (1971).

3.

ROSENCWAIG A. and TABOR W.J., J. appi. Phys. 42, 1643 (1971).

4.

ROSENCWAIG A., TABOR W.J. and PIERCE R.D., Phys. Rev. Leti. 26, 779 (1971).

5.

CALLEN H., Appi. Phys. Left. 18, 311 (1971).

6.

GYORGY E.M., ROSENCWAIG A., BLOUNT E.I., TABOR W.J. and LINES M.E., Appi. Phys. Lets.

7.

18, 479 (1971). WOLFE R., STURGE M.D., MERRITT F.R. and VAN UITERT L.G., Phys. Rev. Left. 26, 1570 (1971).

8.

SHICK L.K., NIELSEN J.W., BOBECK A.H., KURTZIG A.J., MICHAELIS P.C. and REEKSTEN J.P., J. appi. Phys. 42, 1277 (1971).

9.

KURTZIG A.J. and HAGEDORN F.B., to be published.

Une experience recente en resonance paramagnétique électronique sur des grenats, obtenus en presence d’un fondant, a fourni une verification expérimentale de la repartition non-aléatoire, prédite théoriquement, des ions de terres rares, induite par la croissance.

On montre que les préférences de site observées, s’accordent bien avec les predictions selon les modèles de sites, proposes pour les grenats magnétiquement non-cubiques.