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Magnetic properties of some rare earth ferrites
Mat. Res. Bull. Vol. 8, pp. 1337-1342, 1973. Printed in the United States.
P e r g a m o n P r e s s , Inc.
MAGNETIC PROPERTIES OF SOME RARE EARTH FERRITES M. Drofenik, D. Han~el and J. Zupan Institute "Jo~ef Stefan" University of Ljubljana 61000 Ljubljana, Jamova 39, Yugoslavia (Received July 10, 1973 and in final form October 2, 1973; Refereed) ABSTRACT The tetragonal SrEu2Fe207 and BaEu2Fe20 7 have been investigated using MSssbauer spectroscopy and magnetic susceptibility techniques. The m e a s u r e m e n t s of magnetic susceptibility have ° been c a r r i•e d out m the t e m p e r a t u r e range 1 00 to 700 O K. The data have been fitted to C u r i e - W e i s s law X = ~ + .4 using a nonlinear least square curve fitting procedure. These f e r r i t e compounds are paramagnetic above 534°K and 537°K respectively, with a n t i f e r r o m a g n e t i c o r d e r i n g below these t e m p e r a t u r e s . Int roduct ion The preparation of new t e r n a r y compounds SrEu2Fe20 7 and BaEu2Fe20 7 has been recently d e s c r i b e d (1, 2). gonal and isomorphous.
Both compounds are t e t r a -
In the p r e s e n t work the magnetic p r o p e r t i e s of these
two compounds were examined in relation to t h e i r c r y s t a l structure (3). Experimental Samples were p r e p a r e d by standard c e r a m i c techniques from a mixture containing SrCO3(BaCO3) , Eu203 and Fe203 in a mole ratio 1:1:1.
The mix-
tures were fired at 1300°C in a i r for 3 hours with intermittent cooling, crushing and mixLng to facilitate homogenization. X - r a y powder analyses showed only the p r e s e n c e of the tetragonal phase. For the M0ssbauer m e a s u r e m e n t s , finely powdered s a m p l e s of BaEu2Fe20 7 and S r E u 2 F e 2 0 7 were mixed with 8 mg,/cm 2 of iron enriched to 1337
1338
RARE EARTH F E R R I T E S
80% of 57Fe w e r e u s e d a s the a b s o r b e r s .
Vol. 8, No. 12
The 57Fe s p e c t r a w e r e t a k e n on the
512 c h a n n e l a n a l y z e r o p e r a t e d in t i m e m o d e in c o m b i n a t i o n with the E l r o n AME30 M S s s b a u e r s p e c t r o m e t e r .
57Co in Pd m a t r i x was u s e d a s a s o u r c e of
g a m m a r a y s w h i c h w e r e d e t e c t e d with the X e n o n - m e t h a n e p r o p o r t i o n a l c o u n t e r . The v e l o c i t y s c a l e was c a l i b r a t e d with Na2Fe(CN)5NO. H 2 0 and with m e t a l l i c iron. The m a g n e t i c s u s c e p t i b i l i t y m e a s u r e m e n t s w e r e p e r f o r m e d using the F a r a d a y m e t h o d on a m o d i f i e d N e w p o r t I n s t r u m e n t s a p p a r a t u s .
The i n s t r u -
m e n t was c a l i b r a t e d with m e r c u r y (2+) t h i o c i n a t o c o b a l t a t e (II) (4).
The m a g -
n e t i c s u s c e p t i b i l i t y ~ ( g w a s found to be i n d e p e n d e n t f r o m the applied m a g n e t i c field which d e m o n s t r a t e s the a b s e n c e of f e r r o m a g n e t i c i m p u r i t i e s (5). m e a s u r e m e n t s w e r e c a r r i e d out in the t e m p e r a t u r e r a n g e 100 to 700°K.
The The
m e a s u r e m e n t s and the t e m p e r a t u r e c o n t r o l of the s a m p l e s w e r e v e r y s i m i l a r to t h o s e d e s c r i b e d by D a n l e y and Mulay (6). In the m e a s u r e d t e m p e r a t u r e r e g i o n all w e i g h i n g s w e r e c a r r i e d out on the Cahn RG e l e c t r o b a l a n c e c o n n e c t e d with a d i g i t a l v o l t m e t e r .
Since s m a l l
f l u c t u a t i o n s in the w e i g h i n g s at d i f f e r e n t fields w e r e o b s e r v e d , e a c h s u s c e p t i bility value at one t e m p e r a t u r e point w a s t a k e n a s an a v e r a g e obtained by m e a s u r e m e n t s at five m a g n e t i c fields.
T h e s e v a l u e s have b e e n s t a t i s t i c a l l y c u r v e -
fitted to the e q u a t i o n (7) C ")(M= T + 8 + A w h i c h i n c l u d e s a l s o a t e m p e r a t u r e independent p a r t A. A c o m p u t e r p r o g r a m m e (7) f o r the n o n l i n e a r f o r m of this e q u a t i o n w a s u s e d to obtain the b e s t v a l u e s of the p a r a m e t e r s C, 8 and A.
The r e s u l t s a r e shown in Table 2.
This s t a t i s -
t i c a l fitting w a s c a r r i e d out f o r the t e m p e r a t u r e r e g i o n , w h e r e the C u r i e - W e i s s law w a s obeyed. R e s u l t s and D i s c u s s i o n The m a g n e t o c r y s t a l l i n e s t r u c t u r e of both c o m p o u n d s is c h a r a c t e r i z e d by l a r g e n e g a t i v e e x c h a n g e i n t e r a c t i o n s b e t w e e n n e i g h b o u r i n g i r o n a t o m s in the (X, Y, A) planes (A = 0. 09, 0.39) and by m u c h w e a k e r i n t e r a c t i o n s b e t w e e n t h e s e planes.
T h e s e p l a n e s c o n s i s t of oxygen and i r o n ions on 8h, 4e
and 8j l a t t i c e s i t e s in P 4 2 / m n m s p a c e g r o u p (Fig. 1).
F o r the c a s e of a n t i -
Vol. 8, No. 12
RARE EARTH FERRITES
1339
f e r r o m a g n e t i c l a y e r s with equal numbers of p a r a l l e l and anti-
~ /
p a r a l l e l interplane n e a r e s t neigh-
~
~ .... ~
F/
bours the ordering in the third dimension is not favored.
~
Regarding the above facts
{
2
and the detailed discussion by Lines
/
(8), it could be a s s u m e d that two
~ .
~
dimensional magnetism ts present
~'J
in these phases and may result in
_ ~ q
an indistinct indication of T N. Both compounds yielded simple six-line s p e c t r a below the Neel t e m p e r a t u r e
~.8(
~(e) 8(h)
/
~(g)---~(
)J
TN, and a split line above T N is in
C) Oxygen 0 Strontium ~ Europium • iron
a g r e e m e n t with the existence of only one type of c r y s t a l l o g r a p h i c site of iron (8j).
,..~(f)
Typical spectra
FIG.
for SrEu2Fe207 are shown on Fig. 2.
1
C r y s t a l structure of SrEu2Fe207.
The solid curve through the experimental points r e p r e s e n t s the least square fit to six Lorentzian lines at T = 300°K and to two lines at 600°K.
The same well-resolved six line pattern be-
low TN, and the two line s p e c t r a above T N a r e obtained for BaEu2Fe207 too. Two line s p e c t r a above T N may be interpreted as the quadrupole interaction of the Q and the electric field gradient tensor at the iron nucleus.
The
d 5 electronic configuration and the cubic environment of Fe 3+ ions should not give a quadrupole splitting.
The observed splitting (Table 1) is due to the lo-
cal distortion of the cubic environment around Fe 3+ ions. The values for the effective magnetic fields, quadrupole splitting and i s o m e r shift p a r a m e t e r s obtained from the fitted s p e c t r a are given in Table 1. F r o m the t e m p e r a t u r e dependence of the magnetic hyperfine coupling it follows that the long range magnetic ordering exists to 534 °K for S r E u 2 F e 2 0 7 and to 537°K for BaEu2Fe20 7.
1340
RARE EARTH FERRITES
1.00
"
Vol. 8, No. 12
~
0.85
~-
0.70
.,,,,-,
0.85
0.70 10
I
I
I
I
I
I
I
I
I
8
5
~
2
0
2
~
5
8
I 10
I 12
mm/s relative to iron
FIG. 2 Fitted M5ssbauer s p e c t r a of SrEu2Fe207 at 300°K and 600°K. The i s o m e r shift in both compounds is c h a r a c t e r i s t i c trivalent highspin iron with a s m a l l covalent contribution (9). The value of the internal field is c h a r a c t e r i s t i c for the 6S5 / state of Fe 3+ ion in a cubic environment.
ground
The effective field per/2unpaired 3d
e l e c t r o n for iron at 90°K a g r e e s to within 15% with the field for a free ion calculated by Watson and F r e e m a n (10). The variation of magnetic susceptibility as a function of t e m p e r a t u r e is TABLE 1 M5ssbauer p a r a m e t e r s and T N for SrEu2Fe207 and BaEu2Fe207. T
=
T
300°K
=
545°K
TN
Compound
H(KG)
5 (mm/s)
E(mm/s)
6 (mm/s)
~E(mm/s)
T(°K)
SrEu2Fe207
466
0.37
0.16
0.16
0. 68
534 -+ 8
BaEu2Fe207
462
0. 38
0. 15
0. 13
0. 66
537 +- 5
Vol. 8, No. 12
RARE EARTH FERRITES
1341
/
,("
~0-
.=
o
/
o/;
o/'/
o
Sr Eu~Fe207
.
B(I Eu2Fe20,
~0I
I
1
I
1
I
100
200
300
bOO
500
600
3
FIG. Inverse susceptibility vs. temperature shown T N.
I
700 T i°K ]
for SrEu2Fe207
and BaEu2Fe207.
on Fig. 3. A very slight change in the slope I/~(g was observed Curie constants,
and effective magnetic
Weiss
temperatures,
moments
The effective magnetic
are shown moment
temperature
independent
near term
in Table 2.
(Pelf) has been calculated from the re-
TABLE 2 Magnetic p a r a m e t e r s for S r E u 2 F e 2 0 7 and BaEu2Fe207. Compound
Mol. unit
C
8(°K)
A (emu/mole)
peff(B. M)
SrEu2Fe207
(SrOT)0. 25Eu (SrOT)0.25Fe
1.51 3.33
402 515
(0. 8 + 1.0)10 -6 (0. 3 + 0. 8)10 -6
3.46 5. 18
BaEu2Fe20 7
(BaOT)0.25Eu
1.79
447
(0. 0 + 0. 1)10 -6
3.80
(BaO7)0.25Fe
3.56
524
(1.4 + 0. 6)10 -6
5.36
1342
RARE EARTH FERRITES
lation Peff = 2. 828 C'C = 2. 828 ~/;~(T + 0). A is small and has been ignored.
Vol. 8, No. 12
The t e m p e r a t u r e independent t e r m
In the comparison with the l i t e r a t u r e data
the effective m o m e n t s obtained by our m e a s u r e m e n t s a r e lower in the case of Fe 3+ and higher in the case of Eu 3+.
In the t e m p e r a t u r e region below T N the
iron sublattice is a n t i f e r r o m a g n e t i c a l l y coupled, the europium is p a r a m a g netic, that the exchange coupling between Fe and Eu are at least two o r d e r s of magnitude below the F e - F e coupling. The curvature of 1 / ~ g observed at t e m p e r a t u r e s below 200°K (Fig. 3) may be a result of some localized clustering of the europium ions. Acknowledgements The authors a r e indebted to P r o f e s s o r D. Kolar for generous support. Financial support from Boris Kidri~ Found is gratefully acknowledged. References 1. J. C. Janbert, D. Samaros, A. Collomb, G. Le Flem et A. Daoudi, Mat. Res. Bull. 6, 341 (1971). 2. M. Drofenik, D. Kolar and L. GolLY, J. L e s s - C o m . Met. 3_..00, 309 (1973). 3. M. Drofenik, D. Kolar and L. GolLY, J. Crystal Growth 2_..00, 75 (1973). 4. B. N. Figgis and R. S. Nyholm, J. Chem. Soc. 1958, 9410 (1958). 5. L. F. Bates, Modern Magnetism. York (1951).
Cambridge University P r e s s , New
6. W. J. Danley and L. N. Mulay, Mat. Res. Bull. 7, 739 (1972). 7. D. W. Marquart, Least Squares Estimation of Non-linear P a r a m e t e r . I. M. B. Share Library, Distribution No. 3094 (1964). 8. M. E. Lines, Phys. Rev. 164, 736 (1967). 9. L. R. Walker, G. W. W e r t h e i m and V. Jaccarino, Phys. Rev. Lett. 6, 98 (1961). 10. R. E. Watson and A. J. F r e e m a n , Phys. Rev. 123, 2027 (1961).
P e r g a m o n P r e s s , Inc.
MAGNETIC PROPERTIES OF SOME RARE EARTH FERRITES M. Drofenik, D. Han~el and J. Zupan Institute "Jo~ef Stefan" University of Ljubljana 61000 Ljubljana, Jamova 39, Yugoslavia (Received July 10, 1973 and in final form October 2, 1973; Refereed) ABSTRACT The tetragonal SrEu2Fe207 and BaEu2Fe20 7 have been investigated using MSssbauer spectroscopy and magnetic susceptibility techniques. The m e a s u r e m e n t s of magnetic susceptibility have ° been c a r r i•e d out m the t e m p e r a t u r e range 1 00 to 700 O K. The data have been fitted to C u r i e - W e i s s law X = ~ + .4 using a nonlinear least square curve fitting procedure. These f e r r i t e compounds are paramagnetic above 534°K and 537°K respectively, with a n t i f e r r o m a g n e t i c o r d e r i n g below these t e m p e r a t u r e s . Int roduct ion The preparation of new t e r n a r y compounds SrEu2Fe20 7 and BaEu2Fe20 7 has been recently d e s c r i b e d (1, 2). gonal and isomorphous.
Both compounds are t e t r a -
In the p r e s e n t work the magnetic p r o p e r t i e s of these
two compounds were examined in relation to t h e i r c r y s t a l structure (3). Experimental Samples were p r e p a r e d by standard c e r a m i c techniques from a mixture containing SrCO3(BaCO3) , Eu203 and Fe203 in a mole ratio 1:1:1.
The mix-
tures were fired at 1300°C in a i r for 3 hours with intermittent cooling, crushing and mixLng to facilitate homogenization. X - r a y powder analyses showed only the p r e s e n c e of the tetragonal phase. For the M0ssbauer m e a s u r e m e n t s , finely powdered s a m p l e s of BaEu2Fe20 7 and S r E u 2 F e 2 0 7 were mixed with 8 mg,/cm 2 of iron enriched to 1337
1338
RARE EARTH F E R R I T E S
80% of 57Fe w e r e u s e d a s the a b s o r b e r s .
Vol. 8, No. 12
The 57Fe s p e c t r a w e r e t a k e n on the
512 c h a n n e l a n a l y z e r o p e r a t e d in t i m e m o d e in c o m b i n a t i o n with the E l r o n AME30 M S s s b a u e r s p e c t r o m e t e r .
57Co in Pd m a t r i x was u s e d a s a s o u r c e of
g a m m a r a y s w h i c h w e r e d e t e c t e d with the X e n o n - m e t h a n e p r o p o r t i o n a l c o u n t e r . The v e l o c i t y s c a l e was c a l i b r a t e d with Na2Fe(CN)5NO. H 2 0 and with m e t a l l i c iron. The m a g n e t i c s u s c e p t i b i l i t y m e a s u r e m e n t s w e r e p e r f o r m e d using the F a r a d a y m e t h o d on a m o d i f i e d N e w p o r t I n s t r u m e n t s a p p a r a t u s .
The i n s t r u -
m e n t was c a l i b r a t e d with m e r c u r y (2+) t h i o c i n a t o c o b a l t a t e (II) (4).
The m a g -
n e t i c s u s c e p t i b i l i t y ~ ( g w a s found to be i n d e p e n d e n t f r o m the applied m a g n e t i c field which d e m o n s t r a t e s the a b s e n c e of f e r r o m a g n e t i c i m p u r i t i e s (5). m e a s u r e m e n t s w e r e c a r r i e d out in the t e m p e r a t u r e r a n g e 100 to 700°K.
The The
m e a s u r e m e n t s and the t e m p e r a t u r e c o n t r o l of the s a m p l e s w e r e v e r y s i m i l a r to t h o s e d e s c r i b e d by D a n l e y and Mulay (6). In the m e a s u r e d t e m p e r a t u r e r e g i o n all w e i g h i n g s w e r e c a r r i e d out on the Cahn RG e l e c t r o b a l a n c e c o n n e c t e d with a d i g i t a l v o l t m e t e r .
Since s m a l l
f l u c t u a t i o n s in the w e i g h i n g s at d i f f e r e n t fields w e r e o b s e r v e d , e a c h s u s c e p t i bility value at one t e m p e r a t u r e point w a s t a k e n a s an a v e r a g e obtained by m e a s u r e m e n t s at five m a g n e t i c fields.
T h e s e v a l u e s have b e e n s t a t i s t i c a l l y c u r v e -
fitted to the e q u a t i o n (7) C ")(M= T + 8 + A w h i c h i n c l u d e s a l s o a t e m p e r a t u r e independent p a r t A. A c o m p u t e r p r o g r a m m e (7) f o r the n o n l i n e a r f o r m of this e q u a t i o n w a s u s e d to obtain the b e s t v a l u e s of the p a r a m e t e r s C, 8 and A.
The r e s u l t s a r e shown in Table 2.
This s t a t i s -
t i c a l fitting w a s c a r r i e d out f o r the t e m p e r a t u r e r e g i o n , w h e r e the C u r i e - W e i s s law w a s obeyed. R e s u l t s and D i s c u s s i o n The m a g n e t o c r y s t a l l i n e s t r u c t u r e of both c o m p o u n d s is c h a r a c t e r i z e d by l a r g e n e g a t i v e e x c h a n g e i n t e r a c t i o n s b e t w e e n n e i g h b o u r i n g i r o n a t o m s in the (X, Y, A) planes (A = 0. 09, 0.39) and by m u c h w e a k e r i n t e r a c t i o n s b e t w e e n t h e s e planes.
T h e s e p l a n e s c o n s i s t of oxygen and i r o n ions on 8h, 4e
and 8j l a t t i c e s i t e s in P 4 2 / m n m s p a c e g r o u p (Fig. 1).
F o r the c a s e of a n t i -
Vol. 8, No. 12
RARE EARTH FERRITES
1339
f e r r o m a g n e t i c l a y e r s with equal numbers of p a r a l l e l and anti-
~ /
p a r a l l e l interplane n e a r e s t neigh-
~
~ .... ~
F/
bours the ordering in the third dimension is not favored.
~
Regarding the above facts
{
2
and the detailed discussion by Lines
/
(8), it could be a s s u m e d that two
~ .
~
dimensional magnetism ts present
~'J
in these phases and may result in
_ ~ q
an indistinct indication of T N. Both compounds yielded simple six-line s p e c t r a below the Neel t e m p e r a t u r e
~.8(
~(e) 8(h)
/
~(g)---~(
)J
TN, and a split line above T N is in
C) Oxygen 0 Strontium ~ Europium • iron
a g r e e m e n t with the existence of only one type of c r y s t a l l o g r a p h i c site of iron (8j).
,..~(f)
Typical spectra
FIG.
for SrEu2Fe207 are shown on Fig. 2.
1
C r y s t a l structure of SrEu2Fe207.
The solid curve through the experimental points r e p r e s e n t s the least square fit to six Lorentzian lines at T = 300°K and to two lines at 600°K.
The same well-resolved six line pattern be-
low TN, and the two line s p e c t r a above T N a r e obtained for BaEu2Fe207 too. Two line s p e c t r a above T N may be interpreted as the quadrupole interaction of the Q and the electric field gradient tensor at the iron nucleus.
The
d 5 electronic configuration and the cubic environment of Fe 3+ ions should not give a quadrupole splitting.
The observed splitting (Table 1) is due to the lo-
cal distortion of the cubic environment around Fe 3+ ions. The values for the effective magnetic fields, quadrupole splitting and i s o m e r shift p a r a m e t e r s obtained from the fitted s p e c t r a are given in Table 1. F r o m the t e m p e r a t u r e dependence of the magnetic hyperfine coupling it follows that the long range magnetic ordering exists to 534 °K for S r E u 2 F e 2 0 7 and to 537°K for BaEu2Fe20 7.
1340
RARE EARTH FERRITES
1.00
"
Vol. 8, No. 12
~
0.85
~-
0.70
.,,,,-,
0.85
0.70 10
I
I
I
I
I
I
I
I
I
8
5
~
2
0
2
~
5
8
I 10
I 12
mm/s relative to iron
FIG. 2 Fitted M5ssbauer s p e c t r a of SrEu2Fe207 at 300°K and 600°K. The i s o m e r shift in both compounds is c h a r a c t e r i s t i c trivalent highspin iron with a s m a l l covalent contribution (9). The value of the internal field is c h a r a c t e r i s t i c for the 6S5 / state of Fe 3+ ion in a cubic environment.
ground
The effective field per/2unpaired 3d
e l e c t r o n for iron at 90°K a g r e e s to within 15% with the field for a free ion calculated by Watson and F r e e m a n (10). The variation of magnetic susceptibility as a function of t e m p e r a t u r e is TABLE 1 M5ssbauer p a r a m e t e r s and T N for SrEu2Fe207 and BaEu2Fe207. T
=
T
300°K
=
545°K
TN
Compound
H(KG)
5 (mm/s)
E(mm/s)
6 (mm/s)
~E(mm/s)
T(°K)
SrEu2Fe207
466
0.37
0.16
0.16
0. 68
534 -+ 8
BaEu2Fe207
462
0. 38
0. 15
0. 13
0. 66
537 +- 5
Vol. 8, No. 12
RARE EARTH FERRITES
1341
/
,("
~0-
.=
o
/
o/;
o/'/
o
Sr Eu~Fe207
.
B(I Eu2Fe20,
~0I
I
1
I
1
I
100
200
300
bOO
500
600
3
FIG. Inverse susceptibility vs. temperature shown T N.
I
700 T i°K ]
for SrEu2Fe207
and BaEu2Fe207.
on Fig. 3. A very slight change in the slope I/~(g was observed Curie constants,
and effective magnetic
Weiss
temperatures,
moments
The effective magnetic
are shown moment
temperature
independent
near term
in Table 2.
(Pelf) has been calculated from the re-
TABLE 2 Magnetic p a r a m e t e r s for S r E u 2 F e 2 0 7 and BaEu2Fe207. Compound
Mol. unit
C
8(°K)
A (emu/mole)
peff(B. M)
SrEu2Fe207
(SrOT)0. 25Eu (SrOT)0.25Fe
1.51 3.33
402 515
(0. 8 + 1.0)10 -6 (0. 3 + 0. 8)10 -6
3.46 5. 18
BaEu2Fe20 7
(BaOT)0.25Eu
1.79
447
(0. 0 + 0. 1)10 -6
3.80
(BaO7)0.25Fe
3.56
524
(1.4 + 0. 6)10 -6
5.36
1342
RARE EARTH FERRITES
lation Peff = 2. 828 C'C = 2. 828 ~/;~(T + 0). A is small and has been ignored.
Vol. 8, No. 12
The t e m p e r a t u r e independent t e r m
In the comparison with the l i t e r a t u r e data
the effective m o m e n t s obtained by our m e a s u r e m e n t s a r e lower in the case of Fe 3+ and higher in the case of Eu 3+.
In the t e m p e r a t u r e region below T N the
iron sublattice is a n t i f e r r o m a g n e t i c a l l y coupled, the europium is p a r a m a g netic, that the exchange coupling between Fe and Eu are at least two o r d e r s of magnitude below the F e - F e coupling. The curvature of 1 / ~ g observed at t e m p e r a t u r e s below 200°K (Fig. 3) may be a result of some localized clustering of the europium ions. Acknowledgements The authors a r e indebted to P r o f e s s o r D. Kolar for generous support. Financial support from Boris Kidri~ Found is gratefully acknowledged. References 1. J. C. Janbert, D. Samaros, A. Collomb, G. Le Flem et A. Daoudi, Mat. Res. Bull. 6, 341 (1971). 2. M. Drofenik, D. Kolar and L. GolLY, J. L e s s - C o m . Met. 3_..00, 309 (1973). 3. M. Drofenik, D. Kolar and L. GolLY, J. Crystal Growth 2_..00, 75 (1973). 4. B. N. Figgis and R. S. Nyholm, J. Chem. Soc. 1958, 9410 (1958). 5. L. F. Bates, Modern Magnetism. York (1951).
Cambridge University P r e s s , New
6. W. J. Danley and L. N. Mulay, Mat. Res. Bull. 7, 739 (1972). 7. D. W. Marquart, Least Squares Estimation of Non-linear P a r a m e t e r . I. M. B. Share Library, Distribution No. 3094 (1964). 8. M. E. Lines, Phys. Rev. 164, 736 (1967). 9. L. R. Walker, G. W. W e r t h e i m and V. Jaccarino, Phys. Rev. Lett. 6, 98 (1961). 10. R. E. Watson and A. J. F r e e m a n , Phys. Rev. 123, 2027 (1961).