- Email: [email protected]
Freezing of magnetic domain motion in a reentrant spin glass as seen by elastic measurements
Solid State Communications, Vol. 83, No. 10, pp. 829-832, 1992. Printed in Great Britain.
0038-1098/92 $5.00 + .00 Pergamon Press Ltd
FREEZING OF M A G N E T I C D O M A I N M O T I O N IN A R E E N T R A N T SPIN GLASS AS SEEN BY ELASTIC M E A S U R E M E N T S P.K. Mukhopadhyay and A.K. Raychaudhuri Department of Physics, Indian Institute of Science, Bangalore 560 012, India
(Received 10 April 1992 by C.N.R. Rao) We report here measurements of elastic modulus of a reentrant spin glass (RSG) across the reentrant transition temperature (Tsg). By measuring the Young modulus (E) in a magnetic field we obtained the " A E " effect, which is the contribution of the ferromagnetic domains to the E. While a small but finite " A E " effect has been observed in the RSG below the first ferromagnetic transition temperature (T¢), it vanishes for T < Tsg. In contrast to the RSG, in a ferromagnet the " A E " effect is temperature independent at T << T c . We explained this observation as arising due to freezing of magnetic domain motion at or below Tsg • This experiment in conjunction with previous magnetic experiments show that the observed "reentrant" transition is determined by freezing of domain motion.
MANY MAGNETIC alloys exhibit at lower temperatures a reentrant behavior to a spin glass like state after undergoing a ferromagnetic transition at higher temperatures. In the magnetic phase diagram these phases generally occur inbetween a spin glass phase and a long range ordered ferromagnetic phase in the critical region of composition for the onset of ferromagnetism [1]. The spin glass like second transition, referred to as the "reentrant" spin glass transition (RSG), shows up in various magnetic measurements. One important question which has received much current attention, has to do with the structure and dynamics of the magnetic domains which are expected to form at the first ferromagnetic transition (at T = Tc) in these alloys. It now appears that at least in some alloys the RSG transition may largely be determined by the blocking of the magnetic domain motions at T ~ Tsg (Tsg----- reentrant spin glass transition temperature). It has been claimed that the onset of strong irreversibility and the rapid rise of the coercive force (Hc) at or below Tsg can be explained by a model based on thermally activated domain wall movement [2-4]. In this model, the RSG transition is not a phase transition but a kinetic freezing process. Activated motions of domain walls have also been seen in direct measurements of low temperature mobility of domain walls [5, 6] and in recent neutron depolarization studies [7]. Of particular interest are the recent transmission electron microscope (TEM) studies of magnetic domains in
two reentrant spin glass alloys [8]. The TEM studies showed that: (1) the gross macroscopic domain structure as it appears at T = Tc remains unaltered as the alloy is cooled across Tsg and (2) the response time of the domain structure after a step like variation in applied magnetic field becomes very large below Tsg. The above discussion shows that magnetic domains play a major role in the RSG transition. We have investigated this particular issue through the elastic measurements (Young's modulus, E) in a magnetic field across the reentrant transition. We shall show that RSG transition manifests itself distinctly in elastic measurements done at low magnetic fields and it is a powerful tool to study the dynamics of domain motion in these alloys. Magnetic measurements in a ferromagnetic alloy probe the response of magnetic domains to an applied magnetic field. In particular the initial slope of the M - H curve or the low field susceptibility (X0) is determined by the dynamics of the domain motions [9]. Similarly, elastic measurements can also probe the response of magnetic domains in an applied strain field [9, 10]. The linear magnetostriction (As) and its sign determine the alignments of non-spherical magnetic domains when the magnetic field and the strain field are applied together. The alignment of domains parallel or perpendicular to an applied stress determines the contribution of magnetic domains to E and is generally known as the " A E effect". (This is different from contributions arising out of volume-
829
830
F R E E Z I N G OF M A G N E T I C D O M A I N M O T I O N IN A SPIN GLASS
RSG 8 /
-
~
12.& ob
6
1.8"E 1.2
2 !
1
o 5 lo
|
;0 2; T(K)
3'0 3s
Fig. 1. The initial susceptibility X0 and the A E effect in the reentrant spin glass Fe57Ni23Cr20 (T~ = 35K, r,~ = 18K). magnetostriction, exchange effects, etc.). In an applied magnetic field (HII to stress) the " A E effect" is given as [9, 12], (Ae/e)~0
= [ e ( n ) - e ( H = 0 ) ] / E ( H = 0) 2 2 3 (2.7AsEH )/H~ff,
(1)
where Heft is an effective internal field against which domain walls move. It may have an elastic contribution and contributions arising out of magnetic anisotropy and exchange fields. At finite measurement frequency w, the effect will get modified as,
( A E / E L = (AE/E)~_o/(1 + .;.~2),
(2)
where r is the domain response time. The effective internal field H , rr also determines the low field susceptibility X0 and they are related by the relation [12, 13],
Xo "~"(2/3)(Ms/Herr),
(3)
where M~ is the saturation magnetization which can be obtained from experiment. In the " d o m a i n " model [2] of RSG transition, the fall of X0 below Tsg arises due to increase of Herr at lower temperatures and not due to a fall in the saturation magnetization Ms. If the domain wall motion is by an activated process the effective field is found to follow a relation [2],
Herr(T) = Herr(O) Ht exp(-Ea/kBT), (4) where Ea is the activation energy associated with the -
domain wall motions. It may be seen from equation (1) and (3) that there is a close parallel between the A E effect and the susceptibility X0We expect that if ferromagnetic domains form at the upper ferromagnetic transition (T~) then in the RSG alloys also we will see a A E effect similar to ferromagnets in the temperature range Tc > T > Tsg.
Vol. 83, No. 10
However, if the domain wall motion is blocked at the RSG transition, the magnetic contribution to Young's modulus (AE effect) should also vanish below Tsg. This can happen due to an increase of Herr [see equation (4)] below T~g and also due to the increase o f domain response time I- which follows an Arrhenius relation with activation energy E~ arising from the thermally activated domain wall motion. With the above motivation, we have measured the A E effect (in a field H = 0.02T) as a function o f temperature in two alloys o f the series Fes0_xNixCr20. This 7 phase f.c.c, alloy series has a critical concentration for ferromagnetism at x = xc -~ 22. One o f the alloys with x = 23 (Fe57Ni23Cr20, referred to as RSG) has a Tc ~ 35 K and Tsg ,.~ 18 K. The other alloy with x = 30 (FesoNia0Cr20, referred to as FM) has a Tc ~ 140K. (This alloy shows no RSG transition until 4 K.) The phase diagram of the alloy system has been extensively studied by different groups [14, 15]. Alloys used in this investigation are the same as those used in Ref. [15] for phase diagram studies. The measurement of E was carried out at around 1 kHz by using a vibrating reed technique [16]. A phase locked loop technique was used to track the resonance. Computer controlled data acquisition [17] and subsequent digital filtering allowed a precision in E ~ 20ppm. The A E effect was measured in an applied field up to 0.02 T, which was created by a pair of Helmholtz coils. T o avoid any effect of remanence during measurement of the A E effect, the samples were first demagnetized at each temperature and then the magnetic field was applied. We found that this particular treatment was essential to get reproducible data. Otherwise we observed hysteresis effects. Also the measuring field was kept low to avoid excessive correction coming from the pole effect [18]. In Fig. 1 we have shown AE/E for the RSG alloy at a few temperatures below the To. In the same graph the l o w field magnetic susceptibility (X0) measured at a similar applied field (H ,~ 0.016 T) has been shown. The qualitative similarity between X0 and A E / E is at once obvious. The A E / E in the RSG alloy is small but finite only in the temperature range T~ > T > T~g, and it vanishes (or at the level of the instrumental resolution) at T << T~g . For comparison the same quantities for the F M alloy are shown in Fig. 2. In the FM alloy AE/E is about 10 times larger than that in RSG alloy and for T<< To A E / E as well as X0 are more or less temperature independent. In view of the preceding discussions, we can conclude that the absence of a measurable A E effect at T < Tsg can be explained as a manifestation of the blocking or freezing of magnetic domain wall
831
FREEZING OF M A G N E T I C D O M A I N M O T I O N IN A SPIN GLASS
Vol. 83, No. 10
FM RS6
FM
8J 6 %
Sl
FM
O
o
~o x
,
~g
i2
2 I
0
50
100
150
"r(K)
Fig. 2. The initial susceptibility X0 and the A E effect in the ferromagnet Fes0Ni30Cr20 (T c = 140K). motions. (The A E effect vanishes as Tc is approached from below because As---~0 as T---~ To.) Our conclusion is in agreement with the previous magnetic measurements [2,4,7] and T E M observations [8] made on similar RSG alloys. We must point out that the AE effect in ferromagnetic alloys (both crystalline and glassy) had been studied extensively in the past [19]. But these are the first measurements of this type carried out on an alloy showing RSG transition [17, 20]. The observed A E / E in the F M alloy is about an order of magnitude smaller than that observed in pure Ni and about two orders of magnitude smaller than that measured in typical ferromagnetic metallic glasses [10, 18]. The small value of A E / E in our case most likely arises from small As [equation (1)]. In typical iron and nickel containing ferromagnetic alloys IAsl ~ 10-4-10 -5. However, both the alloys studied by us lie in the region x , ~ x c , where ferromagnetism is about to vanish. Thus As is also expected to vanish in the range x ~ x c. Estimates of As(T = 0) can be obtained from experimental data as we have shown below. For the FM alloy the As(T= 0) has been estimated to be ~ 5.7 x 1 0 - 6 and for the RSG alloy As(T = 0) ~ 2.9 × l 0 - 7 . The smallness of the AE effect can thus be explained as due to the smallness of As since both the alloys are close to the critical compositiion (xc) for ferromagnetism. At the end by using simple models of A E / E [equations (1) and (2)] and X0 [equation (3)], we would like to show that the drops in X0 and A E / E below Tsg can both be explained as arising from the same thermally activated process with the same activation energy. A good check that equation (1) is indeed valid can be seen from the experimental observation that A E / E
0
0
I 0.2
I 0.4
I 0.6
i 0.8
1.0
~'/Tc Fig. 3. The calculated A E effects in the F M and the RSG alloys. for both the FM and the RSG alloys are proportional to 1-/2. We can obtain Hen"from equation (3) using the experimentally measured X0 and Ms. At the lowest temperatures (4.2 K), for both alloys, Heft are around 0.025-0.030T. However, while for the F M alloy Hen` is nearly constant, for the RSG alloy it shows a temperature dependence obeying equation (4) below To. From the experimental data the Ea for the RSG alloy has been found to be ~ 15 K. For the FM alloy the Eo ~ 0. The domain response time -r, in presence of thermally activated domain wall motion should follow the Arrhenius relation,
"r = "ro exp( Ea/ksT).
(5)
Using equations (1), (2) and (5) we have calculated the A E / E for both the FM and the RSG alloys. The results are shown in Fig. 3. The only adjustable quantity in the calculation was A,(0) and r 0 which were determined by matching the calculated value to the observed A E / E at one temperature. [The temperature dependence of A,(T) is generally given as A~(T) ~ A(0)(1 - t2), where t = T/Tc.] It can be seen that the agreement of the calculated values with the observed data are rather good considering the fact that in the calculation most of the quantities are fixed by experiment. For the RSG alloy, due to smallness of the AE effect, the noise is rather large. We can therefore claim that both the fall of X0 and A E / E below Tsg can be explained as arising from the same thermally activated process. In conclusion, we have shown by elastic experiments that there is clear evidence of freezing or blocking of magnetic domain walls below the RSG transition. This is in agreement with previous magnetic, neutron depolarization and TEM studies. Further experiments of this type on different systems
832
FREEZING OF MAGNETIC D O M A I N MOTION IN A SPIN GLASS
showing similar transition are needed to check the general validity of our observation as well as the conclusion.
Acknowledgements - We want to thank Professor A.K. Mazumdar for supplying the samples. Financial supports from DST and CSIR (Government of India) are acknowledged. Part of the equipment used was a gift to AKR by the Alexander von Humboldt Foundation.
9.
10. 11. 12. 13.
REFERENCES 1.
2. 3. 4. 5. 6. 7. 8.
K.H. Fischer, Phys. Status Solidi (b) 116, 357 (1983); K.H. Fischer, Phys. Status Solidi (b) 130, 13 (1985); K. Binder & A.P. Young, Rev. Mod. Phys. 59, 801 (1986). U. Gfintzel & K. Westerholt, J. Magn. Magn. Mater. 69, 124 (1987). D.G. Rancourt, S. Chehab & G. Lamarche, J. Magn. Magn. Mater. 78, 129 (1989). D.G. Rancourt, J. Magn. Magn. Mater. 78, 153 (1989). D. Simers & E. Nembachi, J. Appl. Phys. 50, 4895 (1979). W. Richeman & E. Nembachi, J. Magn. Magn. Mater. 26, 273 (1982). J. Mirebeau, S. Itoh, S. Mitsuda, F. Watanabe, Y. Endoh, M. Hemion & P. Calmetes, J. Appl. Phys. 67, 5232 (1990). S. Senoussi, S. Hadjoudj & R. Fourmeaux, Phys. Rev. Lett. 61, 1013 (1988).
14.
15. 16. 17. 18. 19. 20.
Vol. 83, No. 10
R.M. Bozoroth, Ferromagnetism. D. van Nostrand, New York (1951); S. Chikazumi & S.H. Charap, Physics of Magnetism, John Wiley, New York (1964). A.S. Nowick & B.S. Berry, Anelastie Relaxation in Crystalline Solids, Academic Press, New York (1972). B.S. Berry & W.C. Pritchet, IBM J. Res. Dev. 19, 334 (1975). J.D. Livingston, Phys. Status Solidi (a) 70, 591 (1982). J.S. Kouvel, W. Abdul-Razzaq & Kh. Ziq, Phys. Rev. B35, 1768 (1987) (and references contained therein). A.Z. Men'shikov, S.K. Sidorov & A.Ye. Teplykh, Phys. Met. Metall. (USSR) 45, 42 (1979); W. Benedick & W. Pepperkhoff, J. Phys. FI1, 57 (1981); M. Acet, W. Stratum, H. Zahres & E.F. Wassermann, J. Magn. Magn. Mater. 68, 233 (1987). A.K. Mazumder & P.V. Blanckenhagen, Phys. Rev. B29, 4079 (1984). P.K. Mukhopadhyay & A.K. Raychaudhuri, J. Phys. E: Sei. Instrum. 20, 507 (1987). P.K. Mukhopadhyay, Ph.D thesis, Indian Institute of Science, Bangalore, India (1989). A. Wagner & E. Torok Jr, J. Magn. Magn. Mater. 12, 283 (1979). B.S. Berry & W.C. Pritchet, J. Appl. Phys. 47, 3295 (1976). P.K. Mukhopadhyay & A.K. Raychaudhuri, J. Appl. Phys, 67, 5235 (1990).
0038-1098/92 $5.00 + .00 Pergamon Press Ltd
FREEZING OF M A G N E T I C D O M A I N M O T I O N IN A R E E N T R A N T SPIN GLASS AS SEEN BY ELASTIC M E A S U R E M E N T S P.K. Mukhopadhyay and A.K. Raychaudhuri Department of Physics, Indian Institute of Science, Bangalore 560 012, India
(Received 10 April 1992 by C.N.R. Rao) We report here measurements of elastic modulus of a reentrant spin glass (RSG) across the reentrant transition temperature (Tsg). By measuring the Young modulus (E) in a magnetic field we obtained the " A E " effect, which is the contribution of the ferromagnetic domains to the E. While a small but finite " A E " effect has been observed in the RSG below the first ferromagnetic transition temperature (T¢), it vanishes for T < Tsg. In contrast to the RSG, in a ferromagnet the " A E " effect is temperature independent at T << T c . We explained this observation as arising due to freezing of magnetic domain motion at or below Tsg • This experiment in conjunction with previous magnetic experiments show that the observed "reentrant" transition is determined by freezing of domain motion.
MANY MAGNETIC alloys exhibit at lower temperatures a reentrant behavior to a spin glass like state after undergoing a ferromagnetic transition at higher temperatures. In the magnetic phase diagram these phases generally occur inbetween a spin glass phase and a long range ordered ferromagnetic phase in the critical region of composition for the onset of ferromagnetism [1]. The spin glass like second transition, referred to as the "reentrant" spin glass transition (RSG), shows up in various magnetic measurements. One important question which has received much current attention, has to do with the structure and dynamics of the magnetic domains which are expected to form at the first ferromagnetic transition (at T = Tc) in these alloys. It now appears that at least in some alloys the RSG transition may largely be determined by the blocking of the magnetic domain motions at T ~ Tsg (Tsg----- reentrant spin glass transition temperature). It has been claimed that the onset of strong irreversibility and the rapid rise of the coercive force (Hc) at or below Tsg can be explained by a model based on thermally activated domain wall movement [2-4]. In this model, the RSG transition is not a phase transition but a kinetic freezing process. Activated motions of domain walls have also been seen in direct measurements of low temperature mobility of domain walls [5, 6] and in recent neutron depolarization studies [7]. Of particular interest are the recent transmission electron microscope (TEM) studies of magnetic domains in
two reentrant spin glass alloys [8]. The TEM studies showed that: (1) the gross macroscopic domain structure as it appears at T = Tc remains unaltered as the alloy is cooled across Tsg and (2) the response time of the domain structure after a step like variation in applied magnetic field becomes very large below Tsg. The above discussion shows that magnetic domains play a major role in the RSG transition. We have investigated this particular issue through the elastic measurements (Young's modulus, E) in a magnetic field across the reentrant transition. We shall show that RSG transition manifests itself distinctly in elastic measurements done at low magnetic fields and it is a powerful tool to study the dynamics of domain motion in these alloys. Magnetic measurements in a ferromagnetic alloy probe the response of magnetic domains to an applied magnetic field. In particular the initial slope of the M - H curve or the low field susceptibility (X0) is determined by the dynamics of the domain motions [9]. Similarly, elastic measurements can also probe the response of magnetic domains in an applied strain field [9, 10]. The linear magnetostriction (As) and its sign determine the alignments of non-spherical magnetic domains when the magnetic field and the strain field are applied together. The alignment of domains parallel or perpendicular to an applied stress determines the contribution of magnetic domains to E and is generally known as the " A E effect". (This is different from contributions arising out of volume-
829
830
F R E E Z I N G OF M A G N E T I C D O M A I N M O T I O N IN A SPIN GLASS
RSG 8 /
-
~
12.& ob
6
1.8"E 1.2
2 !
1
o 5 lo
|
;0 2; T(K)
3'0 3s
Fig. 1. The initial susceptibility X0 and the A E effect in the reentrant spin glass Fe57Ni23Cr20 (T~ = 35K, r,~ = 18K). magnetostriction, exchange effects, etc.). In an applied magnetic field (HII to stress) the " A E effect" is given as [9, 12], (Ae/e)~0
= [ e ( n ) - e ( H = 0 ) ] / E ( H = 0) 2 2 3 (2.7AsEH )/H~ff,
(1)
where Heft is an effective internal field against which domain walls move. It may have an elastic contribution and contributions arising out of magnetic anisotropy and exchange fields. At finite measurement frequency w, the effect will get modified as,
( A E / E L = (AE/E)~_o/(1 + .;.~2),
(2)
where r is the domain response time. The effective internal field H , rr also determines the low field susceptibility X0 and they are related by the relation [12, 13],
Xo "~"(2/3)(Ms/Herr),
(3)
where M~ is the saturation magnetization which can be obtained from experiment. In the " d o m a i n " model [2] of RSG transition, the fall of X0 below Tsg arises due to increase of Herr at lower temperatures and not due to a fall in the saturation magnetization Ms. If the domain wall motion is by an activated process the effective field is found to follow a relation [2],
Herr(T) = Herr(O) Ht exp(-Ea/kBT), (4) where Ea is the activation energy associated with the -
domain wall motions. It may be seen from equation (1) and (3) that there is a close parallel between the A E effect and the susceptibility X0We expect that if ferromagnetic domains form at the upper ferromagnetic transition (T~) then in the RSG alloys also we will see a A E effect similar to ferromagnets in the temperature range Tc > T > Tsg.
Vol. 83, No. 10
However, if the domain wall motion is blocked at the RSG transition, the magnetic contribution to Young's modulus (AE effect) should also vanish below Tsg. This can happen due to an increase of Herr [see equation (4)] below T~g and also due to the increase o f domain response time I- which follows an Arrhenius relation with activation energy E~ arising from the thermally activated domain wall motion. With the above motivation, we have measured the A E effect (in a field H = 0.02T) as a function o f temperature in two alloys o f the series Fes0_xNixCr20. This 7 phase f.c.c, alloy series has a critical concentration for ferromagnetism at x = xc -~ 22. One o f the alloys with x = 23 (Fe57Ni23Cr20, referred to as RSG) has a Tc ~ 35 K and Tsg ,.~ 18 K. The other alloy with x = 30 (FesoNia0Cr20, referred to as FM) has a Tc ~ 140K. (This alloy shows no RSG transition until 4 K.) The phase diagram of the alloy system has been extensively studied by different groups [14, 15]. Alloys used in this investigation are the same as those used in Ref. [15] for phase diagram studies. The measurement of E was carried out at around 1 kHz by using a vibrating reed technique [16]. A phase locked loop technique was used to track the resonance. Computer controlled data acquisition [17] and subsequent digital filtering allowed a precision in E ~ 20ppm. The A E effect was measured in an applied field up to 0.02 T, which was created by a pair of Helmholtz coils. T o avoid any effect of remanence during measurement of the A E effect, the samples were first demagnetized at each temperature and then the magnetic field was applied. We found that this particular treatment was essential to get reproducible data. Otherwise we observed hysteresis effects. Also the measuring field was kept low to avoid excessive correction coming from the pole effect [18]. In Fig. 1 we have shown AE/E for the RSG alloy at a few temperatures below the To. In the same graph the l o w field magnetic susceptibility (X0) measured at a similar applied field (H ,~ 0.016 T) has been shown. The qualitative similarity between X0 and A E / E is at once obvious. The A E / E in the RSG alloy is small but finite only in the temperature range T~ > T > T~g, and it vanishes (or at the level of the instrumental resolution) at T << T~g . For comparison the same quantities for the F M alloy are shown in Fig. 2. In the FM alloy AE/E is about 10 times larger than that in RSG alloy and for T<< To A E / E as well as X0 are more or less temperature independent. In view of the preceding discussions, we can conclude that the absence of a measurable A E effect at T < Tsg can be explained as a manifestation of the blocking or freezing of magnetic domain wall
831
FREEZING OF M A G N E T I C D O M A I N M O T I O N IN A SPIN GLASS
Vol. 83, No. 10
FM RS6
FM
8J 6 %
Sl
FM
O
o
~o x
,
~g
i2
2 I
0
50
100
150
"r(K)
Fig. 2. The initial susceptibility X0 and the A E effect in the ferromagnet Fes0Ni30Cr20 (T c = 140K). motions. (The A E effect vanishes as Tc is approached from below because As---~0 as T---~ To.) Our conclusion is in agreement with the previous magnetic measurements [2,4,7] and T E M observations [8] made on similar RSG alloys. We must point out that the AE effect in ferromagnetic alloys (both crystalline and glassy) had been studied extensively in the past [19]. But these are the first measurements of this type carried out on an alloy showing RSG transition [17, 20]. The observed A E / E in the F M alloy is about an order of magnitude smaller than that observed in pure Ni and about two orders of magnitude smaller than that measured in typical ferromagnetic metallic glasses [10, 18]. The small value of A E / E in our case most likely arises from small As [equation (1)]. In typical iron and nickel containing ferromagnetic alloys IAsl ~ 10-4-10 -5. However, both the alloys studied by us lie in the region x , ~ x c , where ferromagnetism is about to vanish. Thus As is also expected to vanish in the range x ~ x c. Estimates of As(T = 0) can be obtained from experimental data as we have shown below. For the FM alloy the As(T= 0) has been estimated to be ~ 5.7 x 1 0 - 6 and for the RSG alloy As(T = 0) ~ 2.9 × l 0 - 7 . The smallness of the AE effect can thus be explained as due to the smallness of As since both the alloys are close to the critical compositiion (xc) for ferromagnetism. At the end by using simple models of A E / E [equations (1) and (2)] and X0 [equation (3)], we would like to show that the drops in X0 and A E / E below Tsg can both be explained as arising from the same thermally activated process with the same activation energy. A good check that equation (1) is indeed valid can be seen from the experimental observation that A E / E
0
0
I 0.2
I 0.4
I 0.6
i 0.8
1.0
~'/Tc Fig. 3. The calculated A E effects in the F M and the RSG alloys. for both the FM and the RSG alloys are proportional to 1-/2. We can obtain Hen"from equation (3) using the experimentally measured X0 and Ms. At the lowest temperatures (4.2 K), for both alloys, Heft are around 0.025-0.030T. However, while for the F M alloy Hen` is nearly constant, for the RSG alloy it shows a temperature dependence obeying equation (4) below To. From the experimental data the Ea for the RSG alloy has been found to be ~ 15 K. For the FM alloy the Eo ~ 0. The domain response time -r, in presence of thermally activated domain wall motion should follow the Arrhenius relation,
"r = "ro exp( Ea/ksT).
(5)
Using equations (1), (2) and (5) we have calculated the A E / E for both the FM and the RSG alloys. The results are shown in Fig. 3. The only adjustable quantity in the calculation was A,(0) and r 0 which were determined by matching the calculated value to the observed A E / E at one temperature. [The temperature dependence of A,(T) is generally given as A~(T) ~ A(0)(1 - t2), where t = T/Tc.] It can be seen that the agreement of the calculated values with the observed data are rather good considering the fact that in the calculation most of the quantities are fixed by experiment. For the RSG alloy, due to smallness of the AE effect, the noise is rather large. We can therefore claim that both the fall of X0 and A E / E below Tsg can be explained as arising from the same thermally activated process. In conclusion, we have shown by elastic experiments that there is clear evidence of freezing or blocking of magnetic domain walls below the RSG transition. This is in agreement with previous magnetic, neutron depolarization and TEM studies. Further experiments of this type on different systems
832
FREEZING OF MAGNETIC D O M A I N MOTION IN A SPIN GLASS
showing similar transition are needed to check the general validity of our observation as well as the conclusion.
Acknowledgements - We want to thank Professor A.K. Mazumdar for supplying the samples. Financial supports from DST and CSIR (Government of India) are acknowledged. Part of the equipment used was a gift to AKR by the Alexander von Humboldt Foundation.
9.
10. 11. 12. 13.
REFERENCES 1.
2. 3. 4. 5. 6. 7. 8.
K.H. Fischer, Phys. Status Solidi (b) 116, 357 (1983); K.H. Fischer, Phys. Status Solidi (b) 130, 13 (1985); K. Binder & A.P. Young, Rev. Mod. Phys. 59, 801 (1986). U. Gfintzel & K. Westerholt, J. Magn. Magn. Mater. 69, 124 (1987). D.G. Rancourt, S. Chehab & G. Lamarche, J. Magn. Magn. Mater. 78, 129 (1989). D.G. Rancourt, J. Magn. Magn. Mater. 78, 153 (1989). D. Simers & E. Nembachi, J. Appl. Phys. 50, 4895 (1979). W. Richeman & E. Nembachi, J. Magn. Magn. Mater. 26, 273 (1982). J. Mirebeau, S. Itoh, S. Mitsuda, F. Watanabe, Y. Endoh, M. Hemion & P. Calmetes, J. Appl. Phys. 67, 5232 (1990). S. Senoussi, S. Hadjoudj & R. Fourmeaux, Phys. Rev. Lett. 61, 1013 (1988).
14.
15. 16. 17. 18. 19. 20.
Vol. 83, No. 10
R.M. Bozoroth, Ferromagnetism. D. van Nostrand, New York (1951); S. Chikazumi & S.H. Charap, Physics of Magnetism, John Wiley, New York (1964). A.S. Nowick & B.S. Berry, Anelastie Relaxation in Crystalline Solids, Academic Press, New York (1972). B.S. Berry & W.C. Pritchet, IBM J. Res. Dev. 19, 334 (1975). J.D. Livingston, Phys. Status Solidi (a) 70, 591 (1982). J.S. Kouvel, W. Abdul-Razzaq & Kh. Ziq, Phys. Rev. B35, 1768 (1987) (and references contained therein). A.Z. Men'shikov, S.K. Sidorov & A.Ye. Teplykh, Phys. Met. Metall. (USSR) 45, 42 (1979); W. Benedick & W. Pepperkhoff, J. Phys. FI1, 57 (1981); M. Acet, W. Stratum, H. Zahres & E.F. Wassermann, J. Magn. Magn. Mater. 68, 233 (1987). A.K. Mazumder & P.V. Blanckenhagen, Phys. Rev. B29, 4079 (1984). P.K. Mukhopadhyay & A.K. Raychaudhuri, J. Phys. E: Sei. Instrum. 20, 507 (1987). P.K. Mukhopadhyay, Ph.D thesis, Indian Institute of Science, Bangalore, India (1989). A. Wagner & E. Torok Jr, J. Magn. Magn. Mater. 12, 283 (1979). B.S. Berry & W.C. Pritchet, J. Appl. Phys. 47, 3295 (1976). P.K. Mukhopadhyay & A.K. Raychaudhuri, J. Appl. Phys, 67, 5235 (1990).