The frequency and field dependence of the ac susceptibility of the Ag Mn spin glass

Physica l13B (1982) 123-126 North-Holland Publishing Company

123

LETTER TO THE EDITOR T H E F R E Q U E N C Y AND F I E L D D E P E N D E N C E OF T H E ac S U S C E P T I B I L I T Y OF T H E AgMn SPIN GLASS

C.A.M. M U L D E R and A.J. V A N D U Y N E V E L D T Kamerlingh Onnes Laboratorium der Rijksuniversiteit Leiden, Nieuwsteeg 18, 2311 SB Leiden, The Netherlands Received 19 November 1981 The spin-glass freezing temperature of AgMn with 0.98 at.% Mn [Tf(v = 29.3 Hz) = 4.76 ---0.02 K] was found to vary as = (4.5 -----0.4) × 1 0 - 3 per decade of frequency and to be independent of external magnetic field. Furthermore we report the out-of-phase component g" and the frequency-dependent part of X' as a function of temperature. A Tf/Tf

F r o m earlier investigations on the differential susceptibility of the metallic spin-glass system A g M n [1,2] a frequency dependence of the freezing t e m p e r a t u r e Tf was not detected in the frequency range from 1 6 H z to 2 . 8 M H z . Recently, the frequency dependence of Tf has been r e m e a s u r e d by Tholence [3]. Within the f r a m e w o r k of a m o r e general study of the frequency d e p e n d e n c e of the ac susceptibility of the archetypical metaliic spin-glass [4] we studied the differential susceptibility of the A g M n spinglass in some detail. A g M n containing 0.98 at.% Mn was obtained in the well-established m a n n e r [5] by repeated arc melting, followed by a homogenizing anneal at 900°C and a rapid quench in ice-water. After filing, the A g M n powder (grain size ~<100 g m) was mixed with non-conducting A1203 powder (grain size ~ 6 0 / z m ) to avoid electrical contact between the A g M n grains (cf. ref. [6]). Susceptibility data were collected using a mutual inductance method, simultaneously registering the in-phase and the out-of-phase c o m p o n e n t of the complex susceptibility, X' and X", respectively. For details on the experimental equipment and the accuracy of the measurements, see refs.

[5, 71. 0378-4363/82/0000-0000/$02.75 O 1982 North-Holland

In fig. 1 we present the zero-field susceptibility as a function of t e m p e r a t u r e in the range from 1 . 2 K to 2 0 K for a frequency v = 29.3Hz. A relatively sharp peak in X' is observed, leading to a freezing temperature Tf(v = 29.3 Hz) = 4.76-_+ 0.02 K. It is seen from fig. 1 that X" displays a small anomaly around the freezing temperature also, the broad m a x i m u m in X" lying somewhat below Tf(v). The inflection point in the X" (T) curve occurs at the t e m p e r a t u r e of the m a x i m u m in the x ' ( T ) curve. This typical behaviour of X" in the vicinity of the freezing t e m p e r a t u r e was previously observed in various spin-glass systems [4, 6, 8-10]. In the frequency region from 7.32Hz to 1.87kHz the behaviour of the susceptibility around the freezing t e m p e r a t u r e was measured with a high relative accuracy. The result for several frequencies is given in fig. 2. As usual, we determined the relative shift in Tf per decade of frequency, i.e. ATf/(TfA log v) = (4.5 -- 0.4) x 10-3. F r o m the frequency-dependent susceptibility m e a s u r e m e n t s on A g M n alloys containing 1 - 1 0 a t . % Mn by Tholence [3] we deduce for the relative shift i n Tf: (6_+2)x 10 -3 p e r decade of frequency. T h e behaviour of t h e s.usceptibility with respect to the frequency was

C.A.M. Mulder and A.J. van Duyneveldt / ac susceptibility of the AgMn spin glass

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also followed for temperatures well below the freezing temperature. In fact, the separation for the different frequencies is still observed down to 1.2K and is reversible with temperature and frequency, but the various X' (T) curves seem to converge towards a single, non-zero, frequency independent X' value at T = 0 K, just as in the case of C_.uuMn[5] and A___uuMn[6]. This situation is illustrated in fig. 3 where we have plotted the normalized susceptibility as a function of frequency for several different temperatures. It is seen that the frequency dependence of X' gradually decreases on lowering the temperature (T < T,). The susceptibility as a function of an external static magnetic field H (up to 4.5 kOe, applied parallel to the ac driving field) measured at T = Tf is depicted in fig. 4. We found no H-field shift of the peak in the X' (T) curve, i.e. Tf is not field dependent. In addition, no irreversible effects in the susceptibility were observed upon the application of the magnetic field. The dashed and dotted lines in fig. 4 represent similar measure-

C.A.M. Mulder and A.J. van Duyneveldt / ac susceptibility of the A g M n spin glass r

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ved, is strongly dependent on the homogeneity of the sample and on the magnitude of the measuring field. In fields below about 400 Oe homogeneous samples exhibited a sharper peak in the magnetization, and TR was found to coincide with the freezing temperature. In higher fields the systems displayed a cross-over behaviour with mixed magnetic properties, indicating that the temperature at which the magnetization goes through a broad maximum no longer has a physical meaning. From the above measurements we conclude that the behaviour of the susceptibility for Ag____Mn is very much alike to that for the similar spinglass systems C___quMnand AuMn. A comparison of the behaviour of the out-of-phase component X" in the vicinity of the freezing temperature with the recent theoretical results of Lundgren et al. [10] is in progress, together with a detailed discussion of the frequency and field dependences of the differential susceptibility [4, 12].

T = Tf Acknowledgement

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Fig. 4. The susceptibility X' divided by the zero-field susceptibility X~ as a function of the static external magnetic field at T = Tr for ~ (0.98at.% Mn, Tf(J,=29.3Hz)=4.76K, circles). The CuMn (0.70 at.% Mn, T = Tf = 7.65 K) result from ref. [5] and the A._.uuMn(2.98at.% Mn, T = Tt(~,= 234Hz)= 10.23 K) result from ref. [6] are shown by the dashed and dotted lines, respectively.

ments for CuMn (0.70 at.% Mn, Tt = 7.65 K) [5], and for A____uuMn(2.98 at.% Mn, Tf(v = 234 Hz) = 10.23 K) [6], respectively. The reversibility and time dependence of the dc magnetization in AgMn (containing 1-8 at.% Mn) was studied by Chamberlin et al. [11]. It was shown that the temperature TR at which the magnetization becomes reversible, defined by the temperature above which no difference between the zero-field cooled and field cooled magnetization is obser-

We are very grateful to Prof. W.J. Huiskamp and Prof. J.A. Mydosh for their interest and support in this work.

References [1] E.D. Dahlberg, M. Hardiman and J. Souletie, J. de Physique 39 (1978) L389. [2] E.D. Dahlberg, H. Hardiman, R. Orbach and J. Souletie Phys. Rev. Letters 42 (1979) 401. [3] J.L. Tholence, Physica 108B (1981) 1287. [4] C.A.M. Mulder, Ph.D. thesis, Leiden (1982). [5] C.A.M. Mulder, A.J. van Duyneveldt and J.A. Mydosh, Phys. Rev. B23 (1981) 1384. [6] C.A.M. Mulder, A.J. van Duyneveldt and J.A. Mydosh, Phys. Rev. B25 (1982), to be published. [7] H.A. Groenendijk, A.J. van Duyneveldt and R.D. Willett, Physiea 101B (1980) 320. [8] L.E. Wenger, C.A.M. Mulder, A.J. van Duyneveldt and J.A. Mydosh, Phys. Letters 77A (1980) 378; L.E. Wenger, C.A.M. Mulder, A.J. van Duyneveldt and M. Hardiman, to be published.

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C.A.M. Mulder and A.J. van Duyneveldt / ac susceptibility of the A g M n spin glass

[9] C.A.M. Mulder, A.J. van Duyneveldt, H.W.M. van der Linden, B.H. Verbeek, J.C.M. van Dongen, G.J. Nieuwenhuys and J.A. Mydosh, Phys. Letters 83A (1981) 74. [10] L. Lundgren, P. Svedlindh and O. Beckman, J. Magn. Magn. Mat. 25 (1981) 33.

[11] R.V. Chamberlin, M. Hardiman and R. Orbach, J. Appl. Phys. 52 (1981) 1771; R.V. Chamberlin, M. Hardiman, L.A. Turkevich and R. Orbach, to be published. [12] M. Hardiman, C.A.M. Mulder and A.J. van Duyneveldt, to be published.