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A.C. susceptibility of Cu Mn and Ag Mn spin-glasses
TC 3
Physica 108B (1981) 1287-1288 North-Holland Publishing Company
A.C. SUSCEPTIBILITY
OF C u Mn and A g Mn SPIN-GLASSES
J.L. Tholence
Centre de Recherches
sur les Tr~s Basses Temperatures, C.N.R.S., 38042 Grenoble C~dex, France
B.P.
166 X,
The a.c. susceptibility of CuMn ( 1 % < x < 10 %) and AgMn ( 1 , 1 % < x < 10 %) is found to be frequency dependent below and around Tf, temperature of the a.c. susceptibility maximum. The frequency dependence of Tf can be characterized by an absolute variation ATf per decade of time, roughly proportional to the concentration or to x 2/3 and similar in magnitude in both systems as well as in AuFe. Neutron measurements made on CuMn 10 % by A.P. Murani and F. Mezei are in agreement with a Fulcher law ~-= Vo exp(-Ea/k(T-To)) to describe the frequency dependence of Tf, with Vo = 1011s-1
INTRODUCTION An important frequency dependence of Tf (temperature of the maximum of the a.c. susceptibilit~ is observed in several spin-glass systems (1,2, 3). On the contrary, this frequency dependence is much smaller in canonical spin-glasses (AuFe,__ Cu___Mn, Au___Mn, etc...) which is indicative of a more cooperative freezing (4,5,6,7,8). The description of the frequency dependence of Tf by a Fulcher law has been used to underline similarities between the spin-glass and the real glass transitions. We present here new a.c. susceptibility data which show the frequency dependence of Tf in the AgHn and Cu___Hn systems. These data associated with neutron measurements (9) tend to confirm the validity of a Fulcher law in spinglasses.
frequency (17-104Hz). Typical data are shown on fig. ] for AgMn 5 % and the frequency dependence of Tf is given in the table I.
AgMr~ ~(HZ I0 300 ,.,'/. ,5oo 3000 10000 17.3
"if (K)CuMn 6.32 6.35 I'/o 6.40 6.42 6.45 8.75 3,3'/°
2%
2103 8.80
5'/,,
17.3 198 2103
17.3 10% 198 2103
~)(Hz) 173 198 z,03 I0
Tf(K) CuMn I ~)(Hz) I f ( K ) 9.86 20 39.2 9.96 200 39.4 ,0.08 8% 5.,10 '~26°° % ,9.7 19,70 52* 3
300 20,0 IO0(X 20.24 5.6J0]C 30",3
1772 10 17.88 1(30 18.02 4.6'/° IOOO 3000 31.41 10000 31.60 8 31.81 I0
17.3 48.2 198 48.5 10% 2106 48.9 1.6d~- 55*3 1.6,,10t~ 62* 3
27.7 27.85 283 8.9 i32.03 28,2 ~1Fe 17.4 32,13 28.4 159 32.28 10°1" 32*2 1302 32.73
RESULTS AND DISCUSSION Table I : Tf of several C__uuMn, AgMn, __AuFe samples is given for different measuring frequencies.
400
X
~,
I
I
I
!
A_~qMn5Olo
350
, 16
17
ttl
, 18
19
Fig. l : A.C. susceptibility vicinity of Tf.
,
,
20 K
of AgMn 5 % in the
The a.c. susceptibility of AgHn and Cu___Mn samples furnished by A.P. Murani has been measured to determine its frequency dependence at low
03784363/81/0000-0000/$02.50
Table l also summarize some data presented in other papers (5,6). As already observed the relative variation of Tf : gTf/Tf is similar to the relative variation of the temperature dependent part of the susceptibility : Xc(T) below Tf :-AXc(T)/Xc(T) (6) if x(T) is written : X(T) = Xo + Xc(T) below Tf. For a given system ATf/Tf is proportional to the logarithmic variation of the frequency : A log ~ (1,6,7). In a previous paper and supposing Tf ~ x, I had proposed that ATf was proportional to x. Mulder and al. (7) arguing of the fact that T~ was proportional to x 2/3 in a large concentration range, have proposed the law ATf ~ x 2/3 A log v for CuMn.
© North-Holland Publishing Company
Figure 2 represents the absolute variation ATf of Tf per decade of time as a function of the concentration for Cu___Mn, Ag___Mn and AuFe. The large error bars allow to say that ATf ~ x as well as ATf ~ x 2/3. However this last fit is quite reasonable and one respectly finds ATf/Alog]o V = 1.44 x 273 and ATf/Aloglo v ~ 0.95 x 2/3 for Cu___Mn and Ag__~Jn
1287
1288
0.4
A 'Tf_
'
'
'
I
'
'
'
Alog1~• Au.Fe 0.3 ,K
•
.(;_~Mn
•
Ag-Mn
'
I
r e a c h ~ a lower limit for long measuring times (12).This would indicate a transition stronger thamthe glass-like transition suggested by a Fulcherlaw. In the present situation more data are needed to better understand the nature of the spin-glass transition.
'
~ I /
ACKNOWLEDGMENTS I thank A.P. Murani and F. Mezei for the determination of Tf from neutron meas,rements and the lending of samples.
j j LJ'[-
0.2
REFERENCES
0.I
A,/i
I
(I' T II
0 0
I
zibold [] Cu-Mn Meert et al
I
I
I
0.05
I
I
I
I
I
I
Xl
0.I
Fig. 2 : The absolute variation of T~ per decade of time reported vs x, can be represented by a x 2/3 law.
(dashed curve of fig. 2). So, we observe comparative frequency dependence for the absolute variation of Tf in AuFe, __CuMn and Ag__Mn. This frequency dependence for long measuring times is much smaller than in other systems, it is indicative of a more cooperative freezing. It can not be reasonnably described by an Arrhenius law T = T o exp(Ea/kT) which would give non physical parameters. The validity of a Fulcher law, T = T o exp(Ea/k(Tf-To)) , to describe the variation of Tf in a large frequency range (6) needs to be confirmed. It has been used by analogy to what is observed in real glasses. In recent papers F. Mezei and A.P. Murani have proposed a model to describe the time dependence of the susceptibility in a large frequency range (9,10,11). They determine a distribution N(log t) of the relaxation times t which is consistent with neutron spin echo and a.c. susceptibility measurements. Tf has also been determined from neutron measurements (9) for short measuring times (108 < v < 5.6 x lO10s -I) for CuMn (see table). The description of Tf(~) using a Fulcher law ~ = ~o exp(-Ea/k(Tf-Tn)) gives the following parameters : ~o = ;Ol~s-l, T o = 17.4 K, Ea/k = 63 K for CuMn ~ 3 % ; Vo = IO11s-l, To = 26 K, Ea/k--Z 39~K for CuMn 4 6 % ; ~o = lOl2s-I, To = 3 7 . 1 K . E-~/k ='51 °K for C___~In 8 % ; ~o = 101]s-l, T o = 45 K, Ea/j = 68 K for CuMn IO %The frequency dependence of Tf in Euo.4Sro.6S has been analysed as a constant value for long measuring times and an Arrhenius law for shorter times (3). In CuMn too, it appears that Tf(v)
I) LShneysen H.v., Tholence J.L. and Tournier R., J. Phys. 39, C6-922 (1978). 2) Maletta H., Felsch W. and Tholence J.L., J. Magn. and Magn. Mat. 9, 41 (1978). 3) Bontemps N., Rivoal J.C., Billardon M., Rajchenbach J., Ferr~ J., ~ Conf. Dallas (1980) to appear in J. of Appl. Physics. 4) Zibold G., J. Phys. F 9, 917 (1979) and 8, L 229 (1978). 5) Holtzberg F., Tholence J.L., Godfrin H. and Tournier R., J. Appl. Phys. 50, 1717 (1979). 6) Tholence J.L., J. Applied Phys. 50, 7310 (1980), and Solid State Comm. 35, 113 (1980) 7) Mulder C.A.M., Van Duyneveldt A.J. and ~lydosh J.A., Phys. Rev. B23, 1384 (1981). 8) Meert T.A. and Wenger L.E., 1979 March Meeting of the A.P.S. 9) Mezei F., Murani A.P. and Tholence J.L., these Proceedings. IO) Hezei F. and Murani A.P., J. Magn. and Magn. Mat. 14, 211 (1979). 11) Murani A.P., J. of Magn. and Magn. Mat. 22, 271 (1981). 12) Malozemoff A.P. and Imry Y., Preprint.
Physica 108B (1981) 1287-1288 North-Holland Publishing Company
A.C. SUSCEPTIBILITY
OF C u Mn and A g Mn SPIN-GLASSES
J.L. Tholence
Centre de Recherches
sur les Tr~s Basses Temperatures, C.N.R.S., 38042 Grenoble C~dex, France
B.P.
166 X,
The a.c. susceptibility of CuMn ( 1 % < x < 10 %) and AgMn ( 1 , 1 % < x < 10 %) is found to be frequency dependent below and around Tf, temperature of the a.c. susceptibility maximum. The frequency dependence of Tf can be characterized by an absolute variation ATf per decade of time, roughly proportional to the concentration or to x 2/3 and similar in magnitude in both systems as well as in AuFe. Neutron measurements made on CuMn 10 % by A.P. Murani and F. Mezei are in agreement with a Fulcher law ~-= Vo exp(-Ea/k(T-To)) to describe the frequency dependence of Tf, with Vo = 1011s-1
INTRODUCTION An important frequency dependence of Tf (temperature of the maximum of the a.c. susceptibilit~ is observed in several spin-glass systems (1,2, 3). On the contrary, this frequency dependence is much smaller in canonical spin-glasses (AuFe,__ Cu___Mn, Au___Mn, etc...) which is indicative of a more cooperative freezing (4,5,6,7,8). The description of the frequency dependence of Tf by a Fulcher law has been used to underline similarities between the spin-glass and the real glass transitions. We present here new a.c. susceptibility data which show the frequency dependence of Tf in the AgHn and Cu___Hn systems. These data associated with neutron measurements (9) tend to confirm the validity of a Fulcher law in spinglasses.
frequency (17-104Hz). Typical data are shown on fig. ] for AgMn 5 % and the frequency dependence of Tf is given in the table I.
AgMr~ ~(HZ I0 300 ,.,'/. ,5oo 3000 10000 17.3
"if (K)CuMn 6.32 6.35 I'/o 6.40 6.42 6.45 8.75 3,3'/°
2%
2103 8.80
5'/,,
17.3 198 2103
17.3 10% 198 2103
~)(Hz) 173 198 z,03 I0
Tf(K) CuMn I ~)(Hz) I f ( K ) 9.86 20 39.2 9.96 200 39.4 ,0.08 8% 5.,10 '~26°° % ,9.7 19,70 52* 3
300 20,0 IO0(X 20.24 5.6J0]C 30",3
1772 10 17.88 1(30 18.02 4.6'/° IOOO 3000 31.41 10000 31.60 8 31.81 I0
17.3 48.2 198 48.5 10% 2106 48.9 1.6d~- 55*3 1.6,,10t~ 62* 3
27.7 27.85 283 8.9 i32.03 28,2 ~1Fe 17.4 32,13 28.4 159 32.28 10°1" 32*2 1302 32.73
RESULTS AND DISCUSSION Table I : Tf of several C__uuMn, AgMn, __AuFe samples is given for different measuring frequencies.
400
X
~,
I
I
I
!
A_~qMn5Olo
350
, 16
17
ttl
, 18
19
Fig. l : A.C. susceptibility vicinity of Tf.
,
,
20 K
of AgMn 5 % in the
The a.c. susceptibility of AgHn and Cu___Mn samples furnished by A.P. Murani has been measured to determine its frequency dependence at low
03784363/81/0000-0000/$02.50
Table l also summarize some data presented in other papers (5,6). As already observed the relative variation of Tf : gTf/Tf is similar to the relative variation of the temperature dependent part of the susceptibility : Xc(T) below Tf :-AXc(T)/Xc(T) (6) if x(T) is written : X(T) = Xo + Xc(T) below Tf. For a given system ATf/Tf is proportional to the logarithmic variation of the frequency : A log ~ (1,6,7). In a previous paper and supposing Tf ~ x, I had proposed that ATf was proportional to x. Mulder and al. (7) arguing of the fact that T~ was proportional to x 2/3 in a large concentration range, have proposed the law ATf ~ x 2/3 A log v for CuMn.
© North-Holland Publishing Company
Figure 2 represents the absolute variation ATf of Tf per decade of time as a function of the concentration for Cu___Mn, Ag___Mn and AuFe. The large error bars allow to say that ATf ~ x as well as ATf ~ x 2/3. However this last fit is quite reasonable and one respectly finds ATf/Alog]o V = 1.44 x 273 and ATf/Aloglo v ~ 0.95 x 2/3 for Cu___Mn and Ag__~Jn
1287
1288
0.4
A 'Tf_
'
'
'
I
'
'
'
Alog1~• Au.Fe 0.3 ,K
•
.(;_~Mn
•
Ag-Mn
'
I
r e a c h ~ a lower limit for long measuring times (12).This would indicate a transition stronger thamthe glass-like transition suggested by a Fulcherlaw. In the present situation more data are needed to better understand the nature of the spin-glass transition.
'
~ I /
ACKNOWLEDGMENTS I thank A.P. Murani and F. Mezei for the determination of Tf from neutron meas,rements and the lending of samples.
j j LJ'[-
0.2
REFERENCES
0.I
A,/i
I
(I' T II
0 0
I
zibold [] Cu-Mn Meert et al
I
I
I
0.05
I
I
I
I
I
I
Xl
0.I
Fig. 2 : The absolute variation of T~ per decade of time reported vs x, can be represented by a x 2/3 law.
(dashed curve of fig. 2). So, we observe comparative frequency dependence for the absolute variation of Tf in AuFe, __CuMn and Ag__Mn. This frequency dependence for long measuring times is much smaller than in other systems, it is indicative of a more cooperative freezing. It can not be reasonnably described by an Arrhenius law T = T o exp(Ea/kT) which would give non physical parameters. The validity of a Fulcher law, T = T o exp(Ea/k(Tf-To)) , to describe the variation of Tf in a large frequency range (6) needs to be confirmed. It has been used by analogy to what is observed in real glasses. In recent papers F. Mezei and A.P. Murani have proposed a model to describe the time dependence of the susceptibility in a large frequency range (9,10,11). They determine a distribution N(log t) of the relaxation times t which is consistent with neutron spin echo and a.c. susceptibility measurements. Tf has also been determined from neutron measurements (9) for short measuring times (108 < v < 5.6 x lO10s -I) for CuMn (see table). The description of Tf(~) using a Fulcher law ~ = ~o exp(-Ea/k(Tf-Tn)) gives the following parameters : ~o = ;Ol~s-l, T o = 17.4 K, Ea/k = 63 K for CuMn ~ 3 % ; Vo = IO11s-l, To = 26 K, Ea/k--Z 39~K for CuMn 4 6 % ; ~o = lOl2s-I, To = 3 7 . 1 K . E-~/k ='51 °K for C___~In 8 % ; ~o = 101]s-l, T o = 45 K, Ea/j = 68 K for CuMn IO %The frequency dependence of Tf in Euo.4Sro.6S has been analysed as a constant value for long measuring times and an Arrhenius law for shorter times (3). In CuMn too, it appears that Tf(v)
I) LShneysen H.v., Tholence J.L. and Tournier R., J. Phys. 39, C6-922 (1978). 2) Maletta H., Felsch W. and Tholence J.L., J. Magn. and Magn. Mat. 9, 41 (1978). 3) Bontemps N., Rivoal J.C., Billardon M., Rajchenbach J., Ferr~ J., ~ Conf. Dallas (1980) to appear in J. of Appl. Physics. 4) Zibold G., J. Phys. F 9, 917 (1979) and 8, L 229 (1978). 5) Holtzberg F., Tholence J.L., Godfrin H. and Tournier R., J. Appl. Phys. 50, 1717 (1979). 6) Tholence J.L., J. Applied Phys. 50, 7310 (1980), and Solid State Comm. 35, 113 (1980) 7) Mulder C.A.M., Van Duyneveldt A.J. and ~lydosh J.A., Phys. Rev. B23, 1384 (1981). 8) Meert T.A. and Wenger L.E., 1979 March Meeting of the A.P.S. 9) Mezei F., Murani A.P. and Tholence J.L., these Proceedings. IO) Hezei F. and Murani A.P., J. Magn. and Magn. Mat. 14, 211 (1979). 11) Murani A.P., J. of Magn. and Magn. Mat. 22, 271 (1981). 12) Malozemoff A.P. and Imry Y., Preprint.