- Email: [email protected]
2d dynamic exponent derived from CuMn spin glass films
Journal of Magnetism and Magnetic Materials 140-144 (1995) 1721-1722
~ ,~
Journalof magnotlcm and magnetic materials
ELSEVIER
2d dynamic exponent derived from CuMn spin glass films C. Djurberg a,*, j. Mattsson a, p. Nordblad a, L. Hoines b, J.A. Cowen b a Department of Technology, Uppsala University, Box 534, S-751 21 Uppsala, Sweden b Department of Physics and Centerfor FundamentalMaterials Research, Michigan State University, East Lansing, Michigan 48824, USA Abstract
The slowing down of the magnetic relaxation of thin multilayered CuMn spin glass films on approaching, T = 0 K, is investigated using SQUID magnetometry. In 2d spin glasses the slowing down follows a generalised Arrhenius law, log(t/t o) cx T - ° ÷*~, with a spin glass transition at 0 K. Magnetically decoupled films of thickness < 30 ,~ are found to exhibit 2d critical behaviour and the dynamical exponent Sv = 0.9 is determined.
Theoretical and experimental results agree that there is no spin glass phase at finite temperatures in two dimensional spin glasses [1]. Only at zero temperature the spin glass correlation length diverges. The dynamic slowing down towards the transition has experimentally been found to be well described by the generalised Arrhenius law, l o g ( t / t o ) ~ T -(1 + ~J'),
(1)
predicted by the droplet scaling model [2]. In CuMn spin glass, the anisotropy due to Dzyaloshinskii-Moriya interaction, causes an Ising behaviour on long length scales [3]. In Eq. (1), t is the maximum relaxation time and t o = 10-13 s is a microscopic spin-flip time. In the droplet model, the dynamics is governed by thermal activation over energy barriers B. The barrier height for an excitation of length L, scales as B ~ L ¢', activated dynamics implies Bct T log(t/t o) and in a 2d system the correlation length diverges as: T-", giving Eq. (1). Although Eq. (1) is found to adequately describe the slowing down of the magnetic relaxation in experimental realisations of 2d spin glasses, reported values of the dynamic exponent ~bu differ substantially [4-6]. In a multilayered sample consisting of 20 ,~ thick Cu(12% Mn) spin glass layers, separated by interlayers of 300 ,~ Cu, dynamic scaling resulted in ~bu = 1.5 [5]. Dynamic scaling performed on ac-susceptibility data from measurements on the layered spin glass crystal, Rb2Cuo.78Coo.22F4, yielded a value ~bu = 2.2 [6]. In contrast to these results, relaxation and susceptibility measurements, at temperatures well below the freezing (irreversibility) temperatures, on the thin
* Corresponding author. Fax + 46-18555095; email: [email protected].
multilayered 2d spin glass films have indicated ~bv< 1 [5,7,8]. This paper reports a study aiming at a reliable determination of the 2d value of the dynamic exponent ~bv using thin spin glass films. The measurements have been performed in a non-commercial SQUID magnetometer on dc-sputtered multilayered spin glass samples. The samples consist of Cu(12% Mn) spin glass layers of thickness, wsg, separated by Cu interlayers of thickness, Wiroln this study samples with Wsg> 20 A and wit = 600 A have been investigated by zero field cooled magnetisation measurements. The sample is cooled in zero field to a measurement temperature where a small field, h = 10 Oe, is applied and the relaxation of the magnetisation, m(t), is recorded as a function of time in the interval 0.3 < t < 104 S. Multilayered spin glass films behave as two-dimensional spin glasses, if wiL is large enough to completely decouple the individual spin glass layers and if the length scales relevant to experimental time scales are much larger than Wsg. From earlier investigations on multilayered spin glass films with varying interlayer thickness, a thickness wij = 600 .~ has been found to completely decouple the spin glass layers magnetically on experimental time scales
[8]. Fig. 1 shows the temperature dependence of X ( t ) = m(t)/h, at different observation times, for a sample with Wsg= 20 ,~ and wil = 600 A. Defining the position of the maximum in a x(T, t) vs. T curve as the freezing temperature, Te, at the corresponding observation time, t, Tf(t) has been derived from the different curves in Fig. 1. The slowing down of the relaxation times of this sample are found to be well described by Eq. (1). In Fig. 2, a best fit, given by log t vs. Tf-1.9, is plotted. This implies ~bu = 0.9 and gives t o = 10-13 s. Scaling of the freezing tempera-
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)01362-4
C. Djurberg et al. /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1721-1722
1722
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Fig. 1. Susceptibility m(t)[h vs. T at different observation times, for the 20 A CuMn/600 A Cu film. tures for a sample with wsg = 30/~ and wil = 600 -A yields the same values of ~bv and t o as the Wsg = 20 A sample. When the results from a sample with even thicker spin glass layers, Wss = 40 A and wu = 600 ,~ are scaled, the value of the exponent ~bv increases significantly whereas the value of t o decreases. This is an indication that the dynamics already have been somewhat affected by a 3d-2d crossover occurring on short time-length scales. On experimental time scales, the sample with Wsg = 40 A still exhibits essentially 2d relaxational behaviour. T h e multilaYered spin glass films with thicknesses Wsg < 30 A are seen to yield true 2d spin glass scaling behaviour.
4
2 0 .~ C u M n / 6 0 0
A Cu
1
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Fig. 2. log t vs T~ 1.9 for the 20 ~. CuMn/600 ~ Cu film, implying ~rv = 0.9.
If the interlayer thickness, wu is decreased, the coupling between adjacent spin glass layers gradually becomes effective. Already at a interlayer thickness around 500 ,~ the coupling starts to affect the relaxation behaviour on the time scales of our exeoeriments. In a sample with Wsg = 20 ,~ and Wil = 300 A there is a very weak but significant coupling through the interlayers [5], a scaling analysis of the slowing down of the relaxation times according to Eq. (1) of this sample yielded ~bv= 1.5. On further decreasing Wil, the coupling strength increases and a fit of the data to Eq. (1) becomes poor. In conclusion, even very weak magnetic coupling of 3d nature affects the dynamic behaviour of 2d spin glasses on experimental time scales. The dynamic exponent ~bv is found to be critically sensitive to any non-2d properly of the spin glass. This is probably the reason why all experimental values of @v hitherto reported from dynamic scaling on experimental 2d spin glasses have been quite divergent and > 1. In this investigation, using completely decoupled 2d spin glass layers, ~bv= 0.9 is found from dynamic scaling of the freezing temperatures. Acknowledgement: Financial support from the Swedish Natural Science Research Council (NFR) is acknowledged.
References [1] See e.g.J. Bass and J.A. Cowen, in: Recent Progress in Random Magnets, ed. D.H. Ryan (World Scientific, 1993) p. 177; K.H. Fischer and J.A. Hertz, Spin Glasses (Cambridge University Press, 1991). [2] D. Fisher and D. Huse, Phys. Rev. B 36 (1987) 8937. [3] P.M. Levy and A. Fert, Phys Rev B 23 (1981) 4667. [4] L. Sandlund, P. Granberg, L. Lundgren, P. Nordblad, P. Svedlindh, J.A. Cowen and G.G. Kenning, Phys. Rev. B 40 (1989) 869. [5] P. Granberg, P. Nordblad, P. Svedlindh, L. Lundgren, R. Stubi, G.G. Kenning, D.L. Leslie-Pelecky, J. Bass and J. Cowen, J. Appl. Phys. 67 (1990) 5252. [6] C. Dekker, A. Arts, H. de Wijn, A. Duyneveldt and J. Mydosh, Phys. Rev. Lett. 61 (1988) 1780. [7] J. Mattsson, P. Granberg, P. Nordblad, L. Lundgren, R. Stubi, D. Leslie-Pelecky, J. Bass and J. Cowen, Physica B 165 & 166 (1990) 461. [8] P. Granberg, J. Mattsson, P. Nordblad, L. Lundgren, R. Stubi, J. Bass, D.L. Leslie-Pelecky and J.A. Cowen, Phys. Rev. B 44 (1991) 4410.
~ ,~
Journalof magnotlcm and magnetic materials
ELSEVIER
2d dynamic exponent derived from CuMn spin glass films C. Djurberg a,*, j. Mattsson a, p. Nordblad a, L. Hoines b, J.A. Cowen b a Department of Technology, Uppsala University, Box 534, S-751 21 Uppsala, Sweden b Department of Physics and Centerfor FundamentalMaterials Research, Michigan State University, East Lansing, Michigan 48824, USA Abstract
The slowing down of the magnetic relaxation of thin multilayered CuMn spin glass films on approaching, T = 0 K, is investigated using SQUID magnetometry. In 2d spin glasses the slowing down follows a generalised Arrhenius law, log(t/t o) cx T - ° ÷*~, with a spin glass transition at 0 K. Magnetically decoupled films of thickness < 30 ,~ are found to exhibit 2d critical behaviour and the dynamical exponent Sv = 0.9 is determined.
Theoretical and experimental results agree that there is no spin glass phase at finite temperatures in two dimensional spin glasses [1]. Only at zero temperature the spin glass correlation length diverges. The dynamic slowing down towards the transition has experimentally been found to be well described by the generalised Arrhenius law, l o g ( t / t o ) ~ T -(1 + ~J'),
(1)
predicted by the droplet scaling model [2]. In CuMn spin glass, the anisotropy due to Dzyaloshinskii-Moriya interaction, causes an Ising behaviour on long length scales [3]. In Eq. (1), t is the maximum relaxation time and t o = 10-13 s is a microscopic spin-flip time. In the droplet model, the dynamics is governed by thermal activation over energy barriers B. The barrier height for an excitation of length L, scales as B ~ L ¢', activated dynamics implies Bct T log(t/t o) and in a 2d system the correlation length diverges as: T-", giving Eq. (1). Although Eq. (1) is found to adequately describe the slowing down of the magnetic relaxation in experimental realisations of 2d spin glasses, reported values of the dynamic exponent ~bu differ substantially [4-6]. In a multilayered sample consisting of 20 ,~ thick Cu(12% Mn) spin glass layers, separated by interlayers of 300 ,~ Cu, dynamic scaling resulted in ~bu = 1.5 [5]. Dynamic scaling performed on ac-susceptibility data from measurements on the layered spin glass crystal, Rb2Cuo.78Coo.22F4, yielded a value ~bu = 2.2 [6]. In contrast to these results, relaxation and susceptibility measurements, at temperatures well below the freezing (irreversibility) temperatures, on the thin
* Corresponding author. Fax + 46-18555095; email: [email protected].
multilayered 2d spin glass films have indicated ~bv< 1 [5,7,8]. This paper reports a study aiming at a reliable determination of the 2d value of the dynamic exponent ~bv using thin spin glass films. The measurements have been performed in a non-commercial SQUID magnetometer on dc-sputtered multilayered spin glass samples. The samples consist of Cu(12% Mn) spin glass layers of thickness, wsg, separated by Cu interlayers of thickness, Wiroln this study samples with Wsg> 20 A and wit = 600 A have been investigated by zero field cooled magnetisation measurements. The sample is cooled in zero field to a measurement temperature where a small field, h = 10 Oe, is applied and the relaxation of the magnetisation, m(t), is recorded as a function of time in the interval 0.3 < t < 104 S. Multilayered spin glass films behave as two-dimensional spin glasses, if wiL is large enough to completely decouple the individual spin glass layers and if the length scales relevant to experimental time scales are much larger than Wsg. From earlier investigations on multilayered spin glass films with varying interlayer thickness, a thickness wij = 600 .~ has been found to completely decouple the spin glass layers magnetically on experimental time scales
[8]. Fig. 1 shows the temperature dependence of X ( t ) = m(t)/h, at different observation times, for a sample with Wsg= 20 ,~ and wil = 600 A. Defining the position of the maximum in a x(T, t) vs. T curve as the freezing temperature, Te, at the corresponding observation time, t, Tf(t) has been derived from the different curves in Fig. 1. The slowing down of the relaxation times of this sample are found to be well described by Eq. (1). In Fig. 2, a best fit, given by log t vs. Tf-1.9, is plotted. This implies ~bu = 0.9 and gives t o = 10-13 s. Scaling of the freezing tempera-
0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)01362-4
C. Djurberg et al. /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1721-1722
1722
i
°~°
i
"*!~!,
e o D
f
-,|!
:i!!"
...i
!!t
t
1000Os 3000s lOOOs 3~s l~s
3Os
15
116
17
3s is 0.3s
I
I
18 T [K]
19
I
20
21
Fig. 1. Susceptibility m(t)[h vs. T at different observation times, for the 20 A CuMn/600 A Cu film. tures for a sample with wsg = 30/~ and wil = 600 -A yields the same values of ~bv and t o as the Wsg = 20 A sample. When the results from a sample with even thicker spin glass layers, Wss = 40 A and wu = 600 ,~ are scaled, the value of the exponent ~bv increases significantly whereas the value of t o decreases. This is an indication that the dynamics already have been somewhat affected by a 3d-2d crossover occurring on short time-length scales. On experimental time scales, the sample with Wsg = 40 A still exhibits essentially 2d relaxational behaviour. T h e multilaYered spin glass films with thicknesses Wsg < 30 A are seen to yield true 2d spin glass scaling behaviour.
4
2 0 .~ C u M n / 6 0 0
A Cu
1
o -1 0.0032
I
I 0.0036
I
I 0.004 T -~.9
I
I 0.0044
Fig. 2. log t vs T~ 1.9 for the 20 ~. CuMn/600 ~ Cu film, implying ~rv = 0.9.
If the interlayer thickness, wu is decreased, the coupling between adjacent spin glass layers gradually becomes effective. Already at a interlayer thickness around 500 ,~ the coupling starts to affect the relaxation behaviour on the time scales of our exeoeriments. In a sample with Wsg = 20 ,~ and Wil = 300 A there is a very weak but significant coupling through the interlayers [5], a scaling analysis of the slowing down of the relaxation times according to Eq. (1) of this sample yielded ~bv= 1.5. On further decreasing Wil, the coupling strength increases and a fit of the data to Eq. (1) becomes poor. In conclusion, even very weak magnetic coupling of 3d nature affects the dynamic behaviour of 2d spin glasses on experimental time scales. The dynamic exponent ~bv is found to be critically sensitive to any non-2d properly of the spin glass. This is probably the reason why all experimental values of @v hitherto reported from dynamic scaling on experimental 2d spin glasses have been quite divergent and > 1. In this investigation, using completely decoupled 2d spin glass layers, ~bv= 0.9 is found from dynamic scaling of the freezing temperatures. Acknowledgement: Financial support from the Swedish Natural Science Research Council (NFR) is acknowledged.
References [1] See e.g.J. Bass and J.A. Cowen, in: Recent Progress in Random Magnets, ed. D.H. Ryan (World Scientific, 1993) p. 177; K.H. Fischer and J.A. Hertz, Spin Glasses (Cambridge University Press, 1991). [2] D. Fisher and D. Huse, Phys. Rev. B 36 (1987) 8937. [3] P.M. Levy and A. Fert, Phys Rev B 23 (1981) 4667. [4] L. Sandlund, P. Granberg, L. Lundgren, P. Nordblad, P. Svedlindh, J.A. Cowen and G.G. Kenning, Phys. Rev. B 40 (1989) 869. [5] P. Granberg, P. Nordblad, P. Svedlindh, L. Lundgren, R. Stubi, G.G. Kenning, D.L. Leslie-Pelecky, J. Bass and J. Cowen, J. Appl. Phys. 67 (1990) 5252. [6] C. Dekker, A. Arts, H. de Wijn, A. Duyneveldt and J. Mydosh, Phys. Rev. Lett. 61 (1988) 1780. [7] J. Mattsson, P. Granberg, P. Nordblad, L. Lundgren, R. Stubi, D. Leslie-Pelecky, J. Bass and J. Cowen, Physica B 165 & 166 (1990) 461. [8] P. Granberg, J. Mattsson, P. Nordblad, L. Lundgren, R. Stubi, J. Bass, D.L. Leslie-Pelecky and J.A. Cowen, Phys. Rev. B 44 (1991) 4410.