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Time dependent magnetic properties of (La , Gd)Al2 spin-glasses
T I M E D E P E N D E N T M A G N E T I C P R O P E R T I E S OF (La, Gd)A1 z S P I N - G L A S S E S H. v. L O H N E Y S E N 2. Physikalisches lnstitut der Rheinisch-Westfiilischen Technischen Hochschule Aachen, 5100 Aachen, and Sonderforschangsbereich 125 Aachen-Julic,i-Ki~ln, Fed. Rep. Germany
and J. L. T H O L E N C E Centre de Recherches sar les Tres Basses Tempkratures, CNRS, BP 166 X, 38042 Grenoble-Cedex, France
The frequency dependent freezing temperature T~ of (La, Gd)AI 2 continues to decrease as the measuring time is extended to 103 s. This observation is related to time effects in the ~ g n e t i z a t i o n and remanence.
1. Introduction 25
The existence of a small remanent magnetization below the freezing temperature Tf is an intrinsic property of spin-glasses, observed in such different systems as CuMn, (La, Gd)A1 z, or insulating spin-glasses. It has been associated with the maxim u m in the "reversible" susceptibility Xrev which is obtained after zero field cooling [1, 2]. The thermoremanent magnetization o rth is related to the "irreversible" susceptibility: Xirr = O°~/OHc)nc-~o [1]. The total susceptibility Xt = Mt/Hc obtained from the total magnetization M t after cooling the sample through Tf in a field H c, is equal to Xrev + Xir~" Since both, Xrev and o rth, depend on the measuring time t m, it is necessary to determine both quantities with t m fixed. Experiments on a variety of spinglasses, including (La, Gd)A12 [3] have indeed shown that Xrev and in particular Tf, the temperature of the maximum of Xrev depend on frequency. On the other hand Xt is time-independent and depends only weakly on temperature in moderate fields H e. However, recent measurements suggest that Xt exhibits a (time-independent) maximum in very small fields [4-6] thus posing the question of a lower limit of Tf for very long measuring times. Some of the time effects observed in (La, Gd)A12 in the ac susceptibility [3], the remanence [7] and low-field magnetization [8] have already been reported. We shall focus here on long time measurements.
no a
%
rco
E ,2,o
o° o
Q
8
o% °o o o
15
o
X
a
•---'--'ILa,L~Cl)A|2
° o o
x =0.594 at°/o
I 02
0.5 0.1
I 0.3
04
T(K) Fig. l
measuring time. In terms of the model of magnetic regions in a spin-glass [1] Xt is essentially independent of T because all regions susceptible to the cooling field H c are turned into the direction of H c above Tf before being blocked at their respective blocking temperature Tb. T b is given by the Arrhenius relation E a = ln(tm/zo)kBTb where ~'0 is a characteristic time. The anisotropy energy E a is related to the anisotropy field H a through E a = MsHa/2 where M g --- ~0V'nn is the resulting moment of a region containing n magnetic moments /~o. Ha presumably has its origin in the dipolar coupling. The regions with largest T b then determine the freezing temperature Tf. Qualitatively, interaction between regions can explain the different types of temperature dependence of Xt below
2. Results and discussion
%
Fig. 1 shows the total susceptibility Xt (triangles) for H c = 16 Oe. Xt increases slowly with decreasing temperature below Tf and is independent of the
We now turn to the curves obtained after zero field cooling. The first one (fig. 1, circles) has been obtained from the magnetization measured in a null field and in a dc measuring field (16 Oe)
Journal of Magnetism and Magnetic Materials 15-18 (1980) 171-172 ©North Holland
171
172
H. v. Lo'hneysen, J. L. Tholence/ Time-dependent properties of ( La , Gd)AI2
applied only for the necessary time of a measurement (40 s). The field was turned off when the temperature was changed allowing the r e m a n e n t magnetization (obtained after 40 s in the field) to decrease to zero, since the time spent between two measurements is m u c h larger than 40 s. Therefore, the measuring time for this curve is rather well k n o w n and equal to 40 s. In that case Tf is equal to 120 mK, which is m u c h smaller than the value of 160 m K for a frequency of 7.2 Hz [3]. To further increase the measuring time we also measured the magnetization with increasing temperature after applying a field of 16 Oe at low temperature (fig. 1, squares). Since the field is left on while taking data for the total curve, the time effects are additive. F o r the lowest temperature, the total measuring time is of about 40 s, it progressively increases to b e c o m e ~ 103 s near Tf. T h e increase of the measuring time a n d - - i n a d d i t i o n - - t h e decrease of the relaxation times as the temperature is raised result in the strong upward curvature of x(T). We note that a similar type of "cumulative" time effect is also seen in the magnetization curves M ( H ) below T t as observed in (La, Gd)A12 [8] and the classical C u M n spin-glass [9, 10]. In this case the temperature is kept constant and only t m increases which leads to s-shaped M ( H ) - c u r v e s below Tf with a temperature-dependent inflection point. F o r the measuring time of t m ~ 103 s, the maxim u m of Xrev is f o u n d at Tf = 110 mK, cf. fig. 1. Fig. 2 shows the values of l / T f vs. log u, v = 1 / t m, together with the previously reported data obtained by ac measurements [3] for two alloys of roughly the same G d concentration ( ~ 0.6 at%). F o r both sets of data, ac and dc, the slope of l / T f vs. log l, is the same, yielding E a / k 8 = l0 K. The systematic difference in the absolute values of T r is p r o b a b l y due to the different measuring field employed: already small external fields shift Tf to lower temperatures [8].
10
f
T
I
I
T
•
(Lo,__Gd) A[ 2
.
]
o x= 0 5 9 L atVo x: 0 6 0 4 at°/°
i - "
--L
o~ H ~ O | O e
-
H=160e
10 -3
10 -2
10 1
1
10 ~
~...
/
'" . ~ ' { ~
q
10 2
10 3
v(Hz)
Fig. 2
In conclusion, the time dependent properties of (La, Gd)A12 spin-glasses, most spectacularly seen in the frequency dependent freezing temperature, are present over six decades in frequency with no indication of reaching a (frequency independent) limit for ~0 ~ 0.
References
[I] J. L. Tholence and R. Tournier, J. de Phys. 35 (1974) C4-229; Physica 86-88B (1977) 873. [2] C. N. Guy, J. Phys. F 7 (1977) 1505. [3] H. v. L6hneysen, J. L. Tholence and R. Tournier, J. de Phys. 39 (1978) C 6-922. [4] T. Mizoguchi, T. R. McGuire, S. Kirkpatrick and R. J. Gambino, Phys. Rev. Lett. 38 (1977) 89. [5] L. Krusin-Elbaum, R. Raghavan and S. J. Williamson, Phys. Rev. Lett. 42 (1979) 1762. [6] C. N. Guy, private communication. [7] H. v. L/Jhneysen and J. L. Tholence, Phys. Rev. B 19 (1978) 5858. [8] H. v. L6hneysen, J. L. Tholenee and F. Steglich, Z. Phys. B 29 (1978) 319. [9] R. W. Knitter, J. S. Kouvel and H. Claus, J. Magn. Magn. Mat. 5 (1977) 356. [10] C. Schwink, K. Emmerich and U. Sehulze, Z. Phys. B 31 (1978) 385.
and J. L. T H O L E N C E Centre de Recherches sar les Tres Basses Tempkratures, CNRS, BP 166 X, 38042 Grenoble-Cedex, France
The frequency dependent freezing temperature T~ of (La, Gd)AI 2 continues to decrease as the measuring time is extended to 103 s. This observation is related to time effects in the ~ g n e t i z a t i o n and remanence.
1. Introduction 25
The existence of a small remanent magnetization below the freezing temperature Tf is an intrinsic property of spin-glasses, observed in such different systems as CuMn, (La, Gd)A1 z, or insulating spin-glasses. It has been associated with the maxim u m in the "reversible" susceptibility Xrev which is obtained after zero field cooling [1, 2]. The thermoremanent magnetization o rth is related to the "irreversible" susceptibility: Xirr = O°~/OHc)nc-~o [1]. The total susceptibility Xt = Mt/Hc obtained from the total magnetization M t after cooling the sample through Tf in a field H c, is equal to Xrev + Xir~" Since both, Xrev and o rth, depend on the measuring time t m, it is necessary to determine both quantities with t m fixed. Experiments on a variety of spinglasses, including (La, Gd)A12 [3] have indeed shown that Xrev and in particular Tf, the temperature of the maximum of Xrev depend on frequency. On the other hand Xt is time-independent and depends only weakly on temperature in moderate fields H e. However, recent measurements suggest that Xt exhibits a (time-independent) maximum in very small fields [4-6] thus posing the question of a lower limit of Tf for very long measuring times. Some of the time effects observed in (La, Gd)A12 in the ac susceptibility [3], the remanence [7] and low-field magnetization [8] have already been reported. We shall focus here on long time measurements.
no a
%
rco
E ,2,o
o° o
Q
8
o% °o o o
15
o
X
a
•---'--'ILa,L~Cl)A|2
° o o
x =0.594 at°/o
I 02
0.5 0.1
I 0.3
04
T(K) Fig. l
measuring time. In terms of the model of magnetic regions in a spin-glass [1] Xt is essentially independent of T because all regions susceptible to the cooling field H c are turned into the direction of H c above Tf before being blocked at their respective blocking temperature Tb. T b is given by the Arrhenius relation E a = ln(tm/zo)kBTb where ~'0 is a characteristic time. The anisotropy energy E a is related to the anisotropy field H a through E a = MsHa/2 where M g --- ~0V'nn is the resulting moment of a region containing n magnetic moments /~o. Ha presumably has its origin in the dipolar coupling. The regions with largest T b then determine the freezing temperature Tf. Qualitatively, interaction between regions can explain the different types of temperature dependence of Xt below
2. Results and discussion
%
Fig. 1 shows the total susceptibility Xt (triangles) for H c = 16 Oe. Xt increases slowly with decreasing temperature below Tf and is independent of the
We now turn to the curves obtained after zero field cooling. The first one (fig. 1, circles) has been obtained from the magnetization measured in a null field and in a dc measuring field (16 Oe)
Journal of Magnetism and Magnetic Materials 15-18 (1980) 171-172 ©North Holland
171
172
H. v. Lo'hneysen, J. L. Tholence/ Time-dependent properties of ( La , Gd)AI2
applied only for the necessary time of a measurement (40 s). The field was turned off when the temperature was changed allowing the r e m a n e n t magnetization (obtained after 40 s in the field) to decrease to zero, since the time spent between two measurements is m u c h larger than 40 s. Therefore, the measuring time for this curve is rather well k n o w n and equal to 40 s. In that case Tf is equal to 120 mK, which is m u c h smaller than the value of 160 m K for a frequency of 7.2 Hz [3]. To further increase the measuring time we also measured the magnetization with increasing temperature after applying a field of 16 Oe at low temperature (fig. 1, squares). Since the field is left on while taking data for the total curve, the time effects are additive. F o r the lowest temperature, the total measuring time is of about 40 s, it progressively increases to b e c o m e ~ 103 s near Tf. T h e increase of the measuring time a n d - - i n a d d i t i o n - - t h e decrease of the relaxation times as the temperature is raised result in the strong upward curvature of x(T). We note that a similar type of "cumulative" time effect is also seen in the magnetization curves M ( H ) below T t as observed in (La, Gd)A12 [8] and the classical C u M n spin-glass [9, 10]. In this case the temperature is kept constant and only t m increases which leads to s-shaped M ( H ) - c u r v e s below Tf with a temperature-dependent inflection point. F o r the measuring time of t m ~ 103 s, the maxim u m of Xrev is f o u n d at Tf = 110 mK, cf. fig. 1. Fig. 2 shows the values of l / T f vs. log u, v = 1 / t m, together with the previously reported data obtained by ac measurements [3] for two alloys of roughly the same G d concentration ( ~ 0.6 at%). F o r both sets of data, ac and dc, the slope of l / T f vs. log l, is the same, yielding E a / k 8 = l0 K. The systematic difference in the absolute values of T r is p r o b a b l y due to the different measuring field employed: already small external fields shift Tf to lower temperatures [8].
10
f
T
I
I
T
•
(Lo,__Gd) A[ 2
.
]
o x= 0 5 9 L atVo x: 0 6 0 4 at°/°
i - "
--L
o~ H ~ O | O e
-
H=160e
10 -3
10 -2
10 1
1
10 ~
~...
/
'" . ~ ' { ~
q
10 2
10 3
v(Hz)
Fig. 2
In conclusion, the time dependent properties of (La, Gd)A12 spin-glasses, most spectacularly seen in the frequency dependent freezing temperature, are present over six decades in frequency with no indication of reaching a (frequency independent) limit for ~0 ~ 0.
References
[I] J. L. Tholence and R. Tournier, J. de Phys. 35 (1974) C4-229; Physica 86-88B (1977) 873. [2] C. N. Guy, J. Phys. F 7 (1977) 1505. [3] H. v. L6hneysen, J. L. Tholence and R. Tournier, J. de Phys. 39 (1978) C 6-922. [4] T. Mizoguchi, T. R. McGuire, S. Kirkpatrick and R. J. Gambino, Phys. Rev. Lett. 38 (1977) 89. [5] L. Krusin-Elbaum, R. Raghavan and S. J. Williamson, Phys. Rev. Lett. 42 (1979) 1762. [6] C. N. Guy, private communication. [7] H. v. L/Jhneysen and J. L. Tholence, Phys. Rev. B 19 (1978) 5858. [8] H. v. L6hneysen, J. L. Tholenee and F. Steglich, Z. Phys. B 29 (1978) 319. [9] R. W. Knitter, J. S. Kouvel and H. Claus, J. Magn. Magn. Mat. 5 (1977) 356. [10] C. Schwink, K. Emmerich and U. Sehulze, Z. Phys. B 31 (1978) 385.