ELECTRONIC RELAXATION IN RARE EARTH METALS AND ALLOYS - A NON-KRAMERS EXAMPLE : Tm3+

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ELECTRONIC RELAXATION IN RARE EARTH METALS AND ALLOYS - A NON-KRAMERS

EXAMPLE : Tm3+

N. Dixon, L. Fritz, Y. Mahmud, B. Triplett, S. Hanna, G. von Eynatten

To cite this version:

N. Dixon, L. Fritz, Y. Mahmud, B. Triplett, S. Hanna, et al.. ELECTRONIC RELAXATION IN

RARE EARTH METALS AND ALLOYS - A NON-KRAMERS EXAMPLE : Tm3+. Journal de

Physique Colloques, 1980, 41 (C1), pp.C1-25-C1-31. �10.1051/jphyscol:1980104�. �jpa-00219574�

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JOURNAL DE PHYSIQUE

Colloque

C1,

suppl4ment au n

^O

1 , Tome 41, janvier 1980, page

C1-25

ELECTRONIC R E W T I O N

IN

RARE EARTH METALS AND ALLOYS

-

A NON-KRAFZERS

W P L E :

m3+

N.S. Dixon, L.S. F r i t z , Y. Mahmud, B.B. T r i p l e t t , S.S. Hanna and G.Von ~ y n a t t e n

*

Physics dept., S t a n f o r d U n i v e r s i t y , S t a n f o r d , Ca 94305 USA.

" P h y s i c s dept., U n i v e r s i t y o f Konstanz, Konstanz, Germany.

A b s t r a c t

-

E l e c t r o n i c r e l a x a t i o n i n r a r e e a r t h m a t e r i a l s h a s been a s u b j e c t of c o n s i d e r a b l e i n t e r e s t i n r e c e n t y e a r s . S e v e r a l m e t a l l i c thulium compounds, Tm, TmA1, h C u , and Tm,Y1-xCu, were s t u d i e d u s i n g MEssbauer spectroscopy o v e r t h e temperature range o f 65,mK t o T > TNgel. A l l o f t h e s p e c t r a can b e w e l l d e s c r i b e d by i n c l u d i n g e l e c t r o n i c r e l a x a t i o n u s i n g t h e m a t r i x formalism o f L. L. H i r s t . The g e n e r a l f e a t u r e s o f t h e s p e c t r a f o r a l l t h e s e m a t e r i a l s a r e s i m i l a r , even though Tm is hexagonal and shows a com- p l e x s p i n s t r u c t u r e i n neutron d i f f r a c t i o n s t u d i e s , TmAl i s orthorhombic, and TmCu and Tm Y Cu a r e cubic.

x 1-x

1. INTRODUCTION

-

The presence o f e l e c t r o n i c r e - l a x a t i o n means t h a t a Mzssbauer nucleus is i n an environment o f f l u c t u a t i n g h y p e r f i n e f i e l d s pro- duced by t h e v a r i o u s c r y s t a l f i e l d s t a t e s of t h e e l e c t r o n i c system, c o n s i d e r e d h e r e f o r t h e r a r e e a r t h s t o b e t h e 4f e l e c t r o n s o n l y . I f t h e s e f i e l d s a r e f l u c t u a t i n g a t f r e q u e n c i e s much g r e a t e r t h a n t h e c h a r a c t e r i s t i c n u c l e a r p r e c e s s i o n frequen- c i e s , t h e nucleus w i l l be a b l e t o respond t o o n l y t h e average s t a t i c Boltzmann f i e l d s of t h e c r y s t a l f i e l d s t a t e s . I n t h i s f a s t r e l a x a t i o n l i m i t , t h e M6ssbauer e f f e c t w i l l produce a s i n g l e h y p e r f i n e s t r u c t u r e spectrum; f o r i n s t a n c e , t h e f a m i l i a r s i x - l i n e spectrum of m a g n e t i c a l l y o r d e r e d 571?e. I f , on t h e o t h e r hand, t h e mean l i f e t i m e s o f t h e crys- t a l f i e l d s t a t e s a r e much g r e a t e r t h a n t h e i n v e r s e o f t h e c h a r a c t e r i s t i c n u c l e a r p r e c e s s i o n frequen- c i e s , t h e nucleus w i l l b e a b l e t o respond t o t h e s t a t i c h y p e r f i n e f i e l d s o f each c r y s t a l f i e l d s t a t e s e p a r a t e l y . I n t h i s slow r e l a x a t i o n l i m i t , a M6ssbauer spectrum w i l l c o n s i s t of a s u p e r p o s i t i o n of component s p e c t r a , e a c h weighted according t o t h e Boltzmann p o p u l a t i o n o f t h e c r y s t a l f i e l d s t a t e producing it. I n t h e i n t e r m e d i a t e o r r e l a x a t i o n r e g i o n , where t h e t r a n s i t i o n r a t e s between c r y s t a l f i e l d s t a t e s a r e w i t h i n s e v e r a l o r d e r s of magni-

s e e s f l u c t u a t i n g h y p e r f i n e f i e l d s , and r a t h e r com- p l e x ' s p e c t r a can r e s u l t . F i g u r e 1 i l l u s t r a t e s t h e s e t h r e e r e g i o n s o f i n t e r e s t f o r Tm m e t a l below i t s magnetic o r d e r i n g temperature.

F i g . 1. T h e o r e t i c a l l i n e s h a p e s f o r Tm m e t a l below Ty&el i n t h e f a s t , i n t e r m e d i a t e , and slow r e l a x a - t r o n r e g i o n s .

E l e c t r o n i c r e l a x a t i o n e f f e c t s i n Mijssbauer s p e c t r a of heavy r a r e e a r t h m a t e r i a l s have been recognized s i n c e t h e 1960's 1 1

-

131, b u t v e r y t u d e o'f t h e p r e c e s s i o n f r e q u e n c i e s , t h e nucleus l i t t l e work h a s been r e p o r t e d on t h e non-Kramers

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980104

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C1-26 JOURNAL DE PHYSIQUE

i o n s , such as Tm 3+ [141. I n a l l the Tm compounds then gluing t h e powdered and annealed samples t o and a l l o y s t h a t we have studied, e l e c t r o n i c relaxa- beryllium d i s k s with a l i g h t varnish. The Tm metal t i o n e f f e c t s on the ~ i j s s b a u e r s p e c t r a a r e apparent, absorber kindly provided by R. L. Cohen was vqpor d e s p i t e the f a c t t h a t a l l the m a t e r i a l s t r e a t e d deposited d i r e c t l y onto a beryllium disk.

here order magnetically, i n d i c a t i n g an appreciable To a t t a i n the necessary Doppler v e l o c i t i e s of exchange i n t e r a c t i o n . I n metals one a l s o expects up t o

+

80 cm/sec, a transducer motor w a s modified the conduction-electron exchange coupling t o en- 1151 by adding a matched s e t of four c o i l springs hance t h e spin-spin r e l a x a t i o n , and thus one may t o the l i g h t p a i r of concentric centering springs o f t e n expect t h e f a s t r e l a x a t i o n l i m i t t o be a t - of the d r i v e t o increase i t s resonant fyequency t o

tained. about 40 Hz.

2. EXPERIMENTAL DETAILS

-

A l l s p e c t r a discussed here were obtained with absorbers attached t o the mixing chamber of a 3 ~ e - 4 He d i l u t i o n r e f r i g e r a t o r [15] (shown schematically i n Fig. 2)

,

which could

Fig. 2. Schematic diagram of t h e Mossbauer s p e c t r e meter and lower portion of t h e 3 ~ e - 4 ~ e d i l q t i o n re- f r i g e r a t o r : (1) o u t e r dewar w a l l , (2) 77 K s h i e l d ,

(3) 4 K wall, (4) 1 K s h i e l d , (5) copper mixing chamber, (6) germanium r e s i s t a n c e thermometer and S i diode thermometer, (7) copper absorber mount,

(8) absorber on beryllium, (9) Xe-CO2 proportional counter, (10) 16'3r (Al) source i n a "hot f i n g e r "

attached t o t h e 4 K w a l l , (11) thin-wall s t a i n l e s s skeel d r i v e rod, (12) modified Ranger E l e c t r o n i c s , Inc. VT-700 d r i v e motor, (13) beryllium vacuum s e a l windows.

be regulated a t temperatures between approximately 0.05 K and 300 K.

The Mcssbauer source used was. 16'3r i n A l .

3 . THEORY

-

The ~ g s s b a u e r t r a n s i t i o n i n 1691tn is a 3/2+ + 1/2+ t r a n s i t i o n , s o t h a t one expects *he f a m i l i a r s i x - l i n e o r two-line p a t t e r n f o r a s t a t i c magnetic f i e l d o r e l e c t r i c f i e l d g r a d i e n t a t t h e nucleus. The excited s t a t e h a l f - l i f e i s 3.5 nsec, s o t h e n a t u r a l linewidth i s

TO

= 0.8 cm/sec. The t o t a l magnetic s p l i t t i n g i n t h e Tm 34- f r e e ion l i m i t hyperfine f i e l d of nearly 7 MOe f161 i s around 110 cm/sec, and t h e Tm3+ f r e e ion l i m i t q u a d r u p l e s h i f t i s taken t o be 7 . 8 4 cm/sec from t h e value observed i n W e 2 [171.

The Tm3+ e l e c t r o n i c ground m u l t i p l e t of t h e 4f1' configuration i s 'H6, with t h e f i r q t e x c i t e d m u l t i p l e t well separated a t about 11,000 K [16J.

The t o t a l e l e c t r o n i c angular momentum J = 6 i s t h e r e f o r e a good quantum number, and t h e r e w i l l be 13 w e l l defined c r y s t a l f i e l d s t a t e s . I n cubic symmetry i n t h e absence of magnetic f i e l d s , these w i l l be s p l i t i n t o 2 s i n g l e t s , 1 non-Kramers doublet, and 3 t r i p l e t s [18]. I n a magqetically ordered ma- t e r i a l , we may define a m ~ l e e u l a r exchange f i e l d , Hex

,

and thus w r i t e t h e c r y s t a l f i e l d H m i l t o n i a n f o r t h e ground m u l t i p l e t a s :

The m1, TmCu, and wY1-xCu absorber m a t e r i a l s

were prepared by a r c melting the appropriate m

$ i ~ = Hex ?Z +

C

^'n ^OJI^J>

^2nm

n,m amounts of c o n s t i t u e n t s i n an argon atmosphere, and

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where the &-direction i s defined a s t h e d i r e c t i o n of? maqnetizafion, 0 a r e s p h e r i c a l tensor o p e r a t o r

-n

equ$,vqlents 1191,

<JI~

8

11

J > a r e t h e a,

B,

y of E l l i o t n

and Stevens 5201 and C n a r e c r y s t a l f i e l d para- a\eters ( i n energy u n i t s ) . Diagonalizing t h i s Hamiltonian. we then have c r y s t a l f i e l d s t a t e s of t h e form

The

hyperfine i n t e r a c t i o n a t t h e nucleus from t h e s e c r y s t a l f i e l d s t a t e s may then be w r i t t e n :

Hare A F -qNa#gff/Jr where the l i m i t i n g e f f e c t i v e field H z f f ipeludes t h e f r e e ion l i m i t f i e l d from t h e 4f e l e c t r o n s p l u s core p ~ l a r i z a t i o n and conduc-

2 4f t i o n e l e c t r o n p o l a r i z a t i o n ; B = 1/4e Q q, /

[ 3

-

~q ( J + I ) ~

I

where -eqtf i s the l i m i t i n g value of

%he e l e c t r i c f i e l d g r a d i e p t from t h e 4f e l e c t r o n s , including atomic Sternheimer s h i e l d i n g s ; and Q I l a t t fo t h e l a f t i o e quadrupole i n t e r a c t i o n including con- duqtion e l e c t r o n e f f e c t s .

For t h e f a s t r e l a x a t i o n l i m i t , t h e expectation values tJz> and < 3

-

J ( J + l ) > a r e taken t o be ~ ~ ~ thqstq of t h e Boltzmann averageso£ t h e e n t i r e c r y s t a l f i e l d m u l t i p l e t . For t h e slow r e l a x a t i o n l i m i t and f o r thq r e l a x a t i o n a n a l y s i s t h e s e a r e taken t o be the expectation values f o r e a ~ h of t h e c r y s t a l f i e l d states, s e p a r a t e l y .

~ o l l o w i n g t h e p e r t u r b a t i o n approach of H i r s t

[I),

the energy absorption spectrum f o r the M&- hauer e f f e c t i s then given by:

Here

5

i s t h e column matrix of t h e electromagnetic multipole o p e r a t o r y i e l d i n g t h e i n t e n s i t i e s of t h e

various l i n e s of the spectrum;

g -

i s t h e u n i t diagonal matrix; W_ is - a diagonal matrix containing the equilibrium (Boltzmann) populations of t h e s t a t e s

(both e l e c t r o n i c and n u c l e a r ) ;

- 2'

i s a diagonal matrix of elements

wi + iri,

where t h e index i r e f e r s t o a given electro-nuclear ~ G s s b a u e r tran- s i t i o n , w. i s t h e y-ray frequency, a s determined from Eq. 2, and

r .

i s t h e (minimum) experimental linewidth; and

g -

i s t h e r e l a x a t i o n matrix y e t t o be discussed.

For diagonal hyperfine i n t e r a c t i o n s t h e nucleus alone may be taken a s t h e quantum mechanical resonant system so t h a t t h e multipole operator a c t s only on the nuclear s t a t e s , and t h e r e l a x a t i o n processes a c t only on the e l e c t r o n i c s t a t e s . The matrices of E q . 3 can then be p u t i n t o block diagonal form by an a p p r o p r i a t e ordering of s t a t e s , such t h a t f o r Tm 3+

t h e r e w i l l be s i x s i m i l a r 13 x 13 blocks, one f o r each of t h e s i x allowed Mb;ssbauer t r a n s i t i o n s .

These blocks 5

-

f o r t h e r e l a x a t i o n matrix

E w i l l

^-

a l l be i d e n t i c a l , and a r e given by:

Here

Ir.

> i s an e l e c t r o n i c c r y s t a l f i e l d s t a t e ; the K~~ s a r e t h e e l e c t r o n i c operators of t h e r e l a x a t i o n

*

d r i v i n g mechanism; and J (w T) i s t h e s p e c t r a l q i j '

d e n s i t y function representing t h e p r o b a b i l i t y t h a t t h e thermal b a t h ( l a t t i c e o r conduction e l e c t r o n s ) give a quantum hw t o the system through t h e coup-

i j

l i n g ..K ~ , . where h \ j i s t h e enerqy d i f f e r e n c e between the two c r y s t a l f i e l d s t a t e s

Iri>

and

Ir

₃

^.>.

For magnetic r e l a x a t i o n mechanisms, such a s spin-spin i n t e r a c t i o n s (including spin-conduction e l e c t r o n i n t e r a c t i o n s ) o r varying magnetic f i e l d s

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c1-28 JOURNAL DE PHYSIQUE

from l a t t i c e v i b r a t i o n s , t h e K q ' s may g e n e r a l l y b e

-

t a k e n a s J Z , _J+, J-, and t h e s e l e c t i o n r u l e A m =

,.,

-

^J

+

1, 0 h o l d s f o r t r a n s i t i o n s induced between t h e c r y s t a l f i e l d s t a t e s . This i s t a k e n a s one l i m i t - i n g case i n our a n a l y s i s , r e f e r r e d t o h e r e a s s e l e c t i o n r u l e r e l a x a t i o n .

For e l e c t r o n i c r e l a x a t i o n mechanisms such a s l a t t i c e v i b r a t i o n s of t h e c r y s t a l l i n e e l e c t r i c f i e l d t h e K q ' s

-

may be taken a s t h e c r y s t a l f i e l d o p e r a t o r s 0 m

,

b u t w i t h o u t t h e s t r i n g e n t symmetry

,n

l i m i t a t i o n s on t h e allowed v a l u e s of n and m t h a t h o l d f o r t h e s t a t i c c r y s t a l f i e l d . T r a n s i t i o n s between c r y s t a l f i e l d s t a t e s w i l l t h e r e f o r e be almost completely u n r e s t r i c t e d . To approximate t h i s c a s e

Eq. 2, a s w e l l a s t h e l i n e w i d t h s and r e l a t i v e i n t e n - s i t i e s of t h e s i x t r a n s i t i o n s , f o r t h e Tm metal.

The maximum e f f e c t i v e magnetic f i e l d a t t h e nucleus (< JZ> = 6) i s t h u s found t o be 6.5 MOe, l e s s t h a n t h e c a l c u l a t e d f r e e i o n l i m i t of 6.95 MOe 1161, i m - p l y i n g a n e g a t i v e c o n t r i b u t i o n from conduction e l e c - t r o n p o l a r i z a t i o n . The l i n e i n t e n s i t i e s d i f f e r from t h e u s u a l 3:2:1:1:2:3 r a t i o s because of p a r t i a l pre- f e r e n t i a l o r i e n t a t i o n from t h e vapor d e p o s i t i o n pro- c e s s .

I n 1968, Cohen 1241 suggested a m u l t i p l e - s i t e i n t e r p r e t a t i o n o f Tm m e t a l ~ b ' s s b a u e r s p e c t r a based on t h e e a r l y neutron d i f f r a c t i o n r e s u l t s . This i n - t e r p r e t a t i o n assumed t h e f a s t r e l a x a t i o n l i m i t and we a l l o w a l l p o s s i b l e c r y s t a l f i e l d t r a n s i t i o n s accounted f o r t h e s t r u c t u r e of t h e s p e c t r a i n o n l y w i t h e q u a l p r o b a b i l i t y , i - e . , ri<j = J ( w .

.

,T) i n

9 11 a l i m i t e d temperature range. A s i n g l e - s i t e r e l a x a -

~ q . 4. T h i s w i l l be r e f e r r e d t o a s random r e l a x a - t i o n a n a l y s i s , however, p r o v i d e s an adequate des-

t i o n . c r i p t i o n o f t h e s p e c t r a throughout t h e e n t i r e tem-

We a l s o adopt t h e white n o i s e approximation p e r a t u r e range o f i n t e r e s t . F i g u r e 3 shows repre- which assumes a c o n s t a n t phonon d e n s i t y o v e r t h e

range o f c r y s t a l f i e l d s p l i t t i n g s . For i s o t r o p i c r e l a x a t i o n mechanisms, J (w ,T) can be t a k e n a s

s

i j

J ( O , T ) and be f a c t o r e d o u t of t h e r e l a x a t i o n m a t r i x and becomes an o v e r a l l r a t e parameter, where i t i s understood t h a t t h e e x p o n e n t i a l f a c t o r of Eq. 4 must be e x p l i c i t l y r e t a i n e d .

4. RESULTS AND DISCUSSION

-

C r y s t a l f i e l d parameters f o r Tm m e t a l (hexagonal c r y s t a l s t r u c t u r e ) have been determined from s u s c e p t i b i l i t y measure-

ments [21]

.

Neutron d i f f r a c t i o n s t u d i e s 1223 show VELOCITY k m l a e c I M L O C I T Y (cm/sec)

magnetic s p i n wave s t r u c t u r e below TNgel = 56 K , F i g . 3 . Mijssbauer s p e c t r a of Tm m e t a l w i t h random r e l a x a t i o n f i t s and TmAl w i t h s e l e c t i o n r u l e r e l a x - with ferromagnetism commencing below 30 K. From a t i o n f i t s .

t h e s e and m a g n e t i z a t i o n s t u d i e s 123 1

,

t h e e l e c - s e n t a t i v e s p e c t r a below TNgel w i t h f i t s o b t a i n e d t r o n i c ground s t a t e a t low temperature i s known t o from o u r random r e l a x a t i o n a n a l y s i s . T h i s a n a l y s i s be p u r e mJ = 6. Our low temperature s p e c t r a a t a l s o d e s c r i b e s w e l l t h e asymmetric quadrupole doub- 65mK and 1.1 K ( s e e Fig. 3) t h u s determine t h e con- l e t s observed above t h e magnetic o r d e r i n g tempera- s t a n t A and t h e low temperature v a l u e o f o f t u r e . S e l e c t i o n r u l e r e l a x a t i o n a n a l y s i s y i e l d s

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s i m i l a r f i t s t o t h e s p e c t r a below TNeCel, b u t h a s n o t y e t been completed f o r s p e c t r a above TNgel. I t should be noted t h a t t h e value of t h e exchange f i e l d required t o o b t a i n t h e f i t s below T de-

gel v i a t e s considerably from t h a t expected from a mole- c u l a r f i e l d approximation c a l c u l a t i o n . Since t h i s i s t r u e only i n Tm metal, we f e e l t h i s may be due t o t h e s p i n wave s t r u c t u r e .

C r y s t a l f i e l d parameters f o r TmAl (orthorhom- b i c c r y s t a l s t r u c t u r e ) were derived from t h e tem- p e r a t u r e dependence of t h e quadrupole i n t e r a c t i o n and low temperature parameters from our s p e c t r a . The e f f e c t i v e magnetic f i e l d a t t h e nucleus i n TmAl is found from t h e spectrum a t 2.8 K t o be 6.69 MOe.

A s can be seen i n Fig. 3, TmAl s p e c t r a d i s p l a y mag- n e t i c hyperfine s p l i t t i n g above t h e ordering tem- p e r a t u r e TNGel = 11 K (251.

m

o b t a i n t h e observed

s t r u c t u r e , it i s necessary t o r e t a i n a small b u t non-zero value of t h e exchange f i e l d above TNgel,

VELOCITY (cn/rec) VELOCITY (crnhec)

Fig. 4. ~ Z s s b a u e r s p e c t r a of TmCu w i t h ( a ) random r e l a x a t i o n f i t s , and (b) s e l e c t i o n r u l e r e l a x a t i o n f i t s .

and a l s o t o be i n t h e slow o r intermediate region.

The f i t s shown i n t h e f i g u r e were obtained w i t h our s e l e c t i o n r u l e r e l a x a t i o n a n a l y s i s , and again t h e random r e l a x a t i o n a n a l y s i s y i e l d s s i m i l a r r e s u l t s . S p e c t r a o f hnAl a t temperatures above t h e c o l l a p s e of t h e magnetic hyperfine s t r u c t u r e show a s y m e t r i c quadrupole doublets s i m i l a r t o those of Tm metal.

C r y s t a l f i e l d parameters were obtained f o r m c u by matching t h e ground s t a t e moments < J > and

< 33z2

-

J ( J + ~ ) > with t h e observed s p l i t t i n g s a t 65mK, ( s e e Fig. 4) t a k i n g values f o r A and B of Eq. 2 from Tm metal and W e 2 , r e s p e c t i v e l y , and using an exchange f i e l d derived from a molecular f i e l d approximation c a l c u l a t i o n w i t h TNgel = 11 K

[26]. C r y s t a l f i e l d parameters f o r Tm 0.85'0. 1!?icu were taken t o be t h e same a s those of TmCu, w i t h a decreased exchange f i e l d accounting f o r t h e observed decrease i n ordering temperature. For

m0

70Y0 3 0 C ~ , it was necessary t o a l s o include non-zero CZ0 and Q ~ l a t t t o match t h e observed low temperature s p l i t t i n g s and account f o r a small quadrupole s p l i t t i n g observed above t h e ordering temperature. A s seen i n Fig. 5, t h e low tempera-

VELOCITY (crn/sec I

Fig. 5. Mijssbauer s p e c t r a of Tm 85Y0 l S ~ u and and

no.

7oY0. 3 0 C ~ w i t h random r e k x a t x b n f l t s .

(7)

C1-30 JOURNAL DE PHYSIQUE

t u r e s p e c t r a of Tm

0.85'0.

isCU

and

%.

^70'0. ^3oCU

Show l i n e broadening due t o a d i s t r i b u t i o n of hy- P e r f i n e f i e l d s caused by d i l u t i o n s i m i l a r t o t h a t seen by Abbundi e t a l . I271 i n Dy-Sc a l l o y s .

The W u and v l - x C ~ s p e c t r a a t higher tem- p e r a t u r e s show the now f a m i l i a r r e l a x a t i o n l i n e - shapes. Figure 4 s h m s f i t s t o t h e W u d a t a with both t h e random and s e l e c t i o n r u l e r e l a x a t i o n ana- lysesand Fig. 5 shows s p e c t r a of !rm0-85Y0.15C~ and Tm0.70Y0.30C~ with random r e l a x a t i o n f i t s . Similar f i t s a r e obtained f o r t h e Tm0*85Y0.15C~ with t h e s e l e c t i o n r u l e a n a l y s i s , b u t t h i s a n a l y s i s i s not y e t complete f o r t h e Tm

0.70~0. 3ocu'

Figure 6 shows t h e temperature dependence of t h e r e l a x a t i o n r a t e s derived from f i t s t o t h e W u and !rmxYl-xCu spectra. A f e a t u r e t o note i s t h a t t h e r e l a x a t i o n r a t e s increase with decreasing Tm concentration, which i s a r e f l e c t i o n of t h e decreasing ordering temperatures due t o a decreased exchange i n t e r a c t i o n between t h e !Cm ions. This i s again s i m i l a r t o the Dy-Sc a l l o y s .

The most s t r i k i n g f e a t u r e apparent i n t h e f i - gure, however, i s t h e strong temperature dependence of t h e r e l a x a t i o n r a t e s . The T m metal and TmAl r e l a x a t i o n r a t e s shown i n Fig. 7 show s i m i l a r temperature dependences much g r e a t e r than l i n e a r with temperature. This i s o f t e n i n d i c a t i v e of spin- l a t t i c e r e l a x a t i o n , b u t h e r e could a l s o possibly be due t o spin-spin r e l a x a t i o n with higher c r y s t a l f i e l d s t a t e s c o n t r i b u t i n g a s they become populated.

Selection Rules Selection Rules

Fig. 7. Relaxation r a t e s vs. temperature f o r Tm and TmA1.

I t should be noted t h a t t h e absolute magni-

T ( K ) tudes of t h e r e l a x a t i o n r a t e s derived can be r a t h e r

Fig. 6. Relaxation r a t e s vs. tempprature f o r TmCu s e n s i t i v e t o t h e c r y s t a l f i e l d parameters and ex- and RnxYl-xCu.

change f i e l d used, i n d i c a t i n g a need f o r indepen- dent determinations of t h e s e parameters.

I n conclusion we have seen e l e c t r o n i c relaxa-

(8)

t i o n e f f e c t s i n a l l of t h e thulium m a t e r i a l s we have studied. By simply including r e l a x a t i o n i n our a n a l y s i s , we have been a b l e to c o n s i s t e n t l y d e s c r i b e t h e Mdssbauer s p e c t r a of a number of various thulium compounds.

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