Spin-glass behavior in CuM Mn alloys

1357

Journal of Magnetism and Magnetic Materials 31-34 (1983) 1357-1358 SPIN-GLASS

BEHAVIOR

IN CuM Mn ALLOYS

J.A. C O W E N ,

C.L. F O I L E S a n d J a m e s S H E L L

Physws Department, Michigan State Umversttv, East Lansing, M1 48828, USA

An extensive study of the magnetic properties of ternary spin-glasses of the form (Cu I _, M ~)l , Mn, with M = Au, Pd and Pt, 0 08 _
The increasing use of an R K K Y interaction for interpreting various properties of dilute, conducting spin-glasses reqmres some experimental tests of systematic behavior intrinsic to this interaction The C u r i e - W e i s s temperature (0), the spin-glass temperature (To) and the hysteresis loop parameters form a good set of test quantities since each one probes a different feature of the interaction 0 is related to the average of the exchange interactions, To is related to the first m o m e n t of the exchange Interactions and the hysteresis loop is related to the amsotropy of the interactions Initial studies [1,2] on alloy systems (Cul_ M ~ , ) l _ c M n c ( y > > c ) which can exist m atomically ordered and disordered forms have clearly estabhshed that i n d e p e n d e n t changes can occur m TO and 0 Changes in the associated hysteresis loops have been observed but the data are preliminary and too limited to permit any conclusions at this time

In the present paper we restrict ourselves to alloys m the atomically disordered form reporting magnetic behavior for high concentrations of several non-magnetic constituents and comparing the results to a theoretical expression due to Larsen [3,4]. We have measured the suscepttbihty of several alloys with M = Au, Pd, Pt with 0.08 < y < 0.5 and c = 0 . 0 1 The samples were rapidly cooled from the melt so that all alloys have an FCC crystal structure and are atomically disordered Table 1 gives To , Pelf and 0 for nine samples and for pure CuMn001 prepared in the same fashion In these ternary systems the constituent M would be expected to cause a d a m p i n g and phase shift of the R K K Y interaction and thus produce changes in all of the magnetic properties Larsen has related To to the d a m p i n g in the following manner Starting from the E d w a r d - A n d e r s o n assumption that TO depends on the width of a Gausslan distribution of exchange interactions, he adds (a) a damping, exp( - R/)~), to the R K K Y

Table 1 Magnetic parameters of several ternary alloys with 1% Mn Host system Cu I ,M v M=Au V=012 v=025 y=055 M = Pd v=008 y=017 v = 0 25 y=040

Pelf(S) (~n)

TO

0

Pm

~k

(K) (_+02)

(K) (error _+1 5)

( ~ cm) (+_15%)

(,~)

60(254) 52(215) 48(1 95)

101 59 44

30 30 05

92 134 161

210 150 135

52(2 15) 53(22) 5 0(2 05)

70 55 35 <16

-1 8 -20 -3 5 -23

124 162 248 34 1

152 11 8 78 58

M = Pt

y=025 v = 0 50

5 1(21) 4 9(2 0)

40 24

-46 - 10 5

Pure Cu

5 1(2 1)

99

30

0304-8853/83/0000-0000/$03.00

© 1983 N o r t h - H o l l a n d

43 86 -4

45 24 472

J A ('owen et a l /

1358

Spm-Elaa9 behat~lol in ( u M Mn alloys'

interaction, (b) f l u c t u a t i o n s m the & s t a n c e R b e t w e e n m a g n e t i c runs to r e p r e s e n t the r a n d o m n a t u r e o f the & s o r d e r e d alloys F r o m this he derives T()[(2S + I) 4 -

1] 1 / 2 [ A 1 / 1 2 ,

(])

I/2

A=

a ~ - ( 2 / + 1)2(3c)

/'

4Erku

1

f':- dx "I1 x 4

(exp[-2d0x/)~

]

1/2

× e x p [ - ~ ' ( 1 - x~)] }

(2)

w h e r e d o = a o ( 3 / 1 6 ~ r ) I/~, a 0 )s the lattice c o n s t a n t . <'=~/(l-c). J )s the effective s d e x c h a n g e m t e r a c tlon a n d the o t h e r s y m b o l s have thmr usual m e a n i n g In our s a m p l e s the m e a n - f r e e - p a t h )~ ts d e t e r m i n e d primarily by the d~sordered host alloy, Quant~tatwe values of ), were d e t e r m i n e d from the total res~stwJty using the e x p r e s s m n

)~=a2h/2,Se213/16"n]1/'(p.,)

'.

(3)

w h e r e ,8 ~s an adJustable p a r a m e t e r set equal to 3.5 and P~,, ~s the total resistivity Pm and X are also g w e n in table 1 A q u a h t a t l v e test o f L a r s e n ' s t h e o r y Is possible once S )s k n o w n W e have d e t e r m i n e d S from the effective m o m e n t s o f the h~gh t e m p e r a t u r e suscepttbJllty data a n d used these values to d e t e r m i n e A. Fig 1 ~s a plot of A as a f u n c t i o n o f ~, the clear r e l a u o n b e t w e e n these p a r a m e t e r s ~s a q u a l l t a u v e c o n f i r m a t i o n of t a r s e n X t h e o r y In o r d e r for th)s q u a h t a t l v e test to b e c o m e

2#

3

/

1

•

O f

f

)

o

q u a n t i t a t i v e s o m e a s s u m p t i o n s a b o u t J a n d E~ m u s t be m a d e "lhe simplest a s s u m p t i o n is that b o t h J and E t ,ire c o n s t a n t C h o o s i n g E l = 7 eV, a p p r o p r . a t e for pure c o p p e r , the d a s h e d a n d sohd hnes are calculations using J = 0 153 a n d 0.126 eV, respectively T h e former value Js c h o s e n to r e p r o d u c e the pure C u M n d a t u m and the w__ latter value )s c h o s e n as a fit to the ternar~ allov data Several i m p o r t a n t features e m e r g e from fig 1 F)r~t, the e x p e r i m e n t a l d a t a d o not have the a s y m p t o t m form which the theoretical curves shov, for c o n s t a n t J Smcc the knee o f the curve is i n d e p e n d e n t of J and since any a t t e m p t to scale E r m a k e s relatively small c h a n g e s m the positron of the knee, no single value of J w)ll p r o d u c e a g r e e m e n t b e t w e e n theory and e x p e r i m e n t Second, a suitable choice of J as a f u n c u o n of ) can p r o d u c e q u a n t t t a t w e a g r e e m e n t b e t w e e n theory a n d e x p e r i m e n t , however, as s h o w n m fig 1, the necessary values of .l to p r o d u c e such a g r e e m e n t are m o r e than an o r d e r of m a g m t u d e smaller than those d e d u c e d from m a g n e n c m e a s u r e m e n t s on C u M n [5] T h e s e values are, though, c o m p a r a b l e to t h o s e d e d u c e d m a similar stud'/ of (Au C u) )Mn by S n v a s t a v a et al [6] Finally. our (Cu0 sPt0 s )Mn s a m p l e has a spin-glass transition a n d a n o n - z e r o 0 even t h o u g h its " m e a n - f r e e - p a t h " )s less than one lattice spacing a n d much less than tile average Mn- Mn spacing F o r all alloy s y s t e m s except (Cuu 1 ) P t )Mn the varmUon In 0 is less systematic a n d m u c h weaker (generally c o n s t a n t w ) t h m e x p e r i m e n t a l error) than the vat)at)on m T0 Th)s suggests that the average interact)on ts relatively i n d e p e n d e n t of the m e a n free path A l t h o u g h the general t r e n d of the e x p e r i m e n t a l data for Tu agrees with the theory, the s l g m f i c a n c e of the a g r e e m e n t in unclear The small values of J n e e d e d to fit the e x p e r i m e n t s and the ex)stence ol a spin-glass t r a n s m o n with 2t less than the lattice p a r a m e t e r ,ire lwo p r o b l e m s w h i c h m u s t be resolved before a real agreem e n t b e t w e e n theor> and e x p e r i m e n t can be c l a i m e d A reah~tlc i n t r o d u c t i o n of p h a s e shifts into the R K K Y Interaction a n d / o r the d e v e l o p m e n t of theoretical m o d els for c o n c e n t r a t e d alloys 0 e v ~ 0 5) may resolve these p r o b l e m s

Reference,,

lb

210

a'o

4bMA

Fig 1 The RKKY mteracnon parameter zx vs the mean free path ), of the conduction electron The dashed and sohd lines are the results of the Larsen theory f o r J = 0 153 and J = 0 126 eV, respectively The exper, mental results are for 1% Mn in • pure Cu, 0 CuAu, • CuPd, • CuPt hosts v, lth various ratios of ('u to M

[1] I Shell, J A ('owen and C L Fodes, PtDs Re~ B 25 (19~;2) 6015 [2} J A ( o w e n and C L Folios, to be published [3] U Larsen, Solid StateCommun 28 (1977) 311 [4] U Larsen, Phys Re,, B 18 (1978) 5014 [5] F W Smith, Ph>s Rev B 14(1976) 241 [6] ( M Sn,,astava, A W Sheikh and G Chandra, J Magn Magn Mat 25(1981)147