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Frequency dependent ESR of the spinglass Gd.06La.94Al2
Ph.vsica I08B (1981) 773-774 North.Hollmut Publishing Company
MB 5
FREQUENCY DEPENDENT ESR OF THE SPINGLASS Gd.o6La
94AI 2
M. Zomack and K. Baberschke
Institut fSr Atom- und FestkSrperphysik, Freie Universit~t Berlin, Boltzmannstr. 20, D-|OOO Berlin 33, Fed. Rep. Germany We report ESR experiments on a LaAI 2 sample doped with 6% Gd. The experiments were performed at I, 3, 9 and 35 GHz. We find for T ~ T c essentially a frequency independent shift of Hres, but a frequency dependence for the minimum in the linewidth. The results will be discussed in terms of static internal fields and dynamic field fluctuations.
i.
INTRODUCTION
The electron spin resonance (ESR) has been employed to study spinglass systems as, for example, CuMn 11,21, A~Mn 13~, or amorphous (Yi_xGdx-~-AI2 141. rh~-s technique yields in one experiment two informations: (]) from the change of the applied resonance field Hre s at temperatures near the s~inglass temperature T c one can extract either a change of the effective moment of the species in resonance or an internal unidirectional static field. (2) From an upturn of the linewidth at low temperatures again one can get an internal symmetric field distribution (inhomogeneous broadening) or an increase of the relaxation rate. Maybe even both informations do not image the spinglass properties very well, because the conventional ESR requires an application and sweep of the magnetic field when spectra are taken. To shed some light in the possible interference of the different effects we present here ESR results for a (Gd 06 La 94 )AI 2 sample at 4 different frequencies I,'3, 9 and 35 GHz (corresponding to 400 G, I kG, 3 kG and ]2 kG). The spinglass properties of (GdxLa]_x)Al 2 have been published previously 15 . Our Xac measurements (~2OO Hz) agree with iS], for the 6% sample T .... ~ ].7 K A full description of the work including the concentration dependence from ]% to ;5% will be given elsewhere. Because we present here only data for one concentration, we do not deal with the bottleneck behaviour. The thermal broadening for our sample equals b ~ 7 G/K, only |/7 of the Korringarate 161. The g-shift vanishes almost, the g-value equals g = 1.993 for high . 3T temperatures. Crystal fleld effects of the Gd ion can be safely neglected (CEF < 70 mK) 17!. Our experiments were carried out for T > Tc; no remanence or field cooling effects were observed.
The simple resonance condition h ¢ = PB (g + ~g)
From this analysis we conclude tem at a temperature T ~ 3 T c an internal field starts. The pends only on the temperature concentration). /(~ !
FIELD FOR RESONANCE
As proposed in the introduction a change of the experimental Hre s for T > T c can be attributed to a uniform internal field ~H~e s in our case obviously parallel to the applxed field or caused by a change of the g-value: g + g + 6g.
0378-4363/81/0000-0000/$02.50
© North-HollandPublishingCompany
I
that in our systhe formation of absolute value de(and on the Gd
I
O| v''M
~
-100
g~
-20C x
•
2.
(Hres + 6Hres)
shows that the first term is independent of the microwave frequency ~, the later not. Fig. ] shows the change of Hr~ s from its high temperature values correspondlng to g a 2. Independent of frequency there appears a field shift of about 280 G at i.5 K. A change of the g-value [8 I would result in frequency dependent fieldshifts; for the highest frequency the shift should be 30 times larger than for ] GHz!
0
I
I
I
5
10
15
TIK
Figure 1: Here we plotted 6Hres, the experimental shift in the field for resonance at ].} GHz (~), 3.3 GHz (o), 9.5 GHz (A), and 34.7 GHz (x). The high temperature resonance fields correspond to 0.4 kG, 1.2 kG, 3.4 kG, and ]2.4 kG, respectively. Because of the low Hre s at ].] GHz and AH ~ 200 G the errorbar of H is in the order res of 10%.
773
774
3.
LINEWIDTH
IN CONCLUSION
In Fig. 2 we show the linewidth versus T. As in Fig. ], the ] GHz and 35 GHz data are only taken in 4He temperature range. For 35 GHz the high T data at low concentrations were taken previously 16!. The dashed line is just a guide for the eye. The figure clearly shows a strong frequency dependence. A line broadening at low temperatures and higher concentrations of magnetic ions is quite com~non and cannot be elaborated here ]8 I. One reason might be inhomogeneous broadening (with a symmetric field distribution at Hres)- This appears certainly at higher temperatures than Hre s starts to shift. Here the frequency dependence would be due to the different part of the fluctuation spectra picked up with 35 GHz or ] GHz Larmor precession. I GHz averages 35 times longer and faster fluctuations cancel to zero. For CuMn the increase of the linewidth at T > T ¢ has been interpreted in terms of critical dynamics III. We feel that this model is not adequate for our system: i.e. the strong frequency (field) dependence, the onset of broadening for 2 < T/r f< |O and the change of lineshape at low temperatures. A very general ESR feature of linewidth broadening 191 seems to explain our data more easily. There exists also a difference to the Ag___~ system. For (LaGd)A] 2 the high temperature linewidth (Fig. 2, T > 18 K) shows no frequency dependence and reflects perfect the single ion behavlour (for AgMn see Fig. 4 in ref. 3).
I
500
I
400 300 ~
o
A•~.
o~
•
100 0
We enjoyed helpful discussions and M. Hardlman.
I1
M.B.
with S.E. Barnes
Salomon, Phys. Rev. Lett. 21 (1978)
1506.
12
For a review see P.A. Beck, Progr. Science, 23 (]978) 1.
13
E.D. Dahlberg, M. Hardiman, R. Orbach, J. Souletie, Phys. Rev. Lett. 42 (1979) 401 and E.D. Dahlberg, M. Hardiman, J. Soultie, J. Phys. Lett. 39 (1978) L-389.
in Mat.
A.P. Malozemoff, L. Kresin - Elbaum, R.C. Taylor, Proc. Mag. Mag. Mat. Conf., Dallas (]980), to appear.
5I
H.V. L6hneysen, J.L. Tholence, Z. Phys. B29 (1978) 319.
61
G. Koopmann, U. Engel, K. Baberschke, S. HUfner, Sol. St. Com. II (1972) 1197.
71
K. Baberschke, B. Bachor, S.E. Barnes, Phys. Rev. B21 (1980) 2666.
F. Steglich,
I
~H/G
20C
The experiments demonstrate that ESR at several frequencies is needed before a full analysis of the relaxation phenomena and the static local susceptibility can be given. This analysis will include a lineshape analysis involving a convolution of the Lorenzian relaxation part with a field distribution function. Furthermore, we will discuss that Yoslda's theorem (_[Mtotal' HRKKy] = O) may not be applicable for sptnglasses, blnce in a spinglass the individual moments are highly correlated, the definition of Mtota I is in question. Under those circumstances HRKKY can quite well contribute to line broadening IIOI .
l
I
I
I
5
10
15
20
TIK
Figure 2: Linewidth versus T; symbols as in Fig. I. Again the 1 G H z data have large errorbars of approx. 15%. For these data we had to include in the analysis the resonance at "negative" fields. Dashed lines are guides for the eye.
f81
See for example the review article by S.E. Barnes, Adv. in Phys.,to be published.
191
See for example E. Dormann, V. Jaccorino, Phys. Lett. 48A (]974) 81.
11ol
S.E. Barnes,
to be published.
MB 5
FREQUENCY DEPENDENT ESR OF THE SPINGLASS Gd.o6La
94AI 2
M. Zomack and K. Baberschke
Institut fSr Atom- und FestkSrperphysik, Freie Universit~t Berlin, Boltzmannstr. 20, D-|OOO Berlin 33, Fed. Rep. Germany We report ESR experiments on a LaAI 2 sample doped with 6% Gd. The experiments were performed at I, 3, 9 and 35 GHz. We find for T ~ T c essentially a frequency independent shift of Hres, but a frequency dependence for the minimum in the linewidth. The results will be discussed in terms of static internal fields and dynamic field fluctuations.
i.
INTRODUCTION
The electron spin resonance (ESR) has been employed to study spinglass systems as, for example, CuMn 11,21, A~Mn 13~, or amorphous (Yi_xGdx-~-AI2 141. rh~-s technique yields in one experiment two informations: (]) from the change of the applied resonance field Hre s at temperatures near the s~inglass temperature T c one can extract either a change of the effective moment of the species in resonance or an internal unidirectional static field. (2) From an upturn of the linewidth at low temperatures again one can get an internal symmetric field distribution (inhomogeneous broadening) or an increase of the relaxation rate. Maybe even both informations do not image the spinglass properties very well, because the conventional ESR requires an application and sweep of the magnetic field when spectra are taken. To shed some light in the possible interference of the different effects we present here ESR results for a (Gd 06 La 94 )AI 2 sample at 4 different frequencies I,'3, 9 and 35 GHz (corresponding to 400 G, I kG, 3 kG and ]2 kG). The spinglass properties of (GdxLa]_x)Al 2 have been published previously 15 . Our Xac measurements (~2OO Hz) agree with iS], for the 6% sample T .... ~ ].7 K A full description of the work including the concentration dependence from ]% to ;5% will be given elsewhere. Because we present here only data for one concentration, we do not deal with the bottleneck behaviour. The thermal broadening for our sample equals b ~ 7 G/K, only |/7 of the Korringarate 161. The g-shift vanishes almost, the g-value equals g = 1.993 for high . 3T temperatures. Crystal fleld effects of the Gd ion can be safely neglected (CEF < 70 mK) 17!. Our experiments were carried out for T > Tc; no remanence or field cooling effects were observed.
The simple resonance condition h ¢ = PB (g + ~g)
From this analysis we conclude tem at a temperature T ~ 3 T c an internal field starts. The pends only on the temperature concentration). /(~ !
FIELD FOR RESONANCE
As proposed in the introduction a change of the experimental Hre s for T > T c can be attributed to a uniform internal field ~H~e s in our case obviously parallel to the applxed field or caused by a change of the g-value: g + g + 6g.
0378-4363/81/0000-0000/$02.50
© North-HollandPublishingCompany
I
that in our systhe formation of absolute value de(and on the Gd
I
O| v''M
~
-100
g~
-20C x
•
2.
(Hres + 6Hres)
shows that the first term is independent of the microwave frequency ~, the later not. Fig. ] shows the change of Hr~ s from its high temperature values correspondlng to g a 2. Independent of frequency there appears a field shift of about 280 G at i.5 K. A change of the g-value [8 I would result in frequency dependent fieldshifts; for the highest frequency the shift should be 30 times larger than for ] GHz!
0
I
I
I
5
10
15
TIK
Figure 1: Here we plotted 6Hres, the experimental shift in the field for resonance at ].} GHz (~), 3.3 GHz (o), 9.5 GHz (A), and 34.7 GHz (x). The high temperature resonance fields correspond to 0.4 kG, 1.2 kG, 3.4 kG, and ]2.4 kG, respectively. Because of the low Hre s at ].] GHz and AH ~ 200 G the errorbar of H is in the order res of 10%.
773
774
3.
LINEWIDTH
IN CONCLUSION
In Fig. 2 we show the linewidth versus T. As in Fig. ], the ] GHz and 35 GHz data are only taken in 4He temperature range. For 35 GHz the high T data at low concentrations were taken previously 16!. The dashed line is just a guide for the eye. The figure clearly shows a strong frequency dependence. A line broadening at low temperatures and higher concentrations of magnetic ions is quite com~non and cannot be elaborated here ]8 I. One reason might be inhomogeneous broadening (with a symmetric field distribution at Hres)- This appears certainly at higher temperatures than Hre s starts to shift. Here the frequency dependence would be due to the different part of the fluctuation spectra picked up with 35 GHz or ] GHz Larmor precession. I GHz averages 35 times longer and faster fluctuations cancel to zero. For CuMn the increase of the linewidth at T > T ¢ has been interpreted in terms of critical dynamics III. We feel that this model is not adequate for our system: i.e. the strong frequency (field) dependence, the onset of broadening for 2 < T/r f< |O and the change of lineshape at low temperatures. A very general ESR feature of linewidth broadening 191 seems to explain our data more easily. There exists also a difference to the Ag___~ system. For (LaGd)A] 2 the high temperature linewidth (Fig. 2, T > 18 K) shows no frequency dependence and reflects perfect the single ion behavlour (for AgMn see Fig. 4 in ref. 3).
I
500
I
400 300 ~
o
A•~.
o~
•
100 0
We enjoyed helpful discussions and M. Hardlman.
I1
M.B.
with S.E. Barnes
Salomon, Phys. Rev. Lett. 21 (1978)
1506.
12
For a review see P.A. Beck, Progr. Science, 23 (]978) 1.
13
E.D. Dahlberg, M. Hardiman, R. Orbach, J. Souletie, Phys. Rev. Lett. 42 (1979) 401 and E.D. Dahlberg, M. Hardiman, J. Soultie, J. Phys. Lett. 39 (1978) L-389.
in Mat.
A.P. Malozemoff, L. Kresin - Elbaum, R.C. Taylor, Proc. Mag. Mag. Mat. Conf., Dallas (]980), to appear.
5I
H.V. L6hneysen, J.L. Tholence, Z. Phys. B29 (1978) 319.
61
G. Koopmann, U. Engel, K. Baberschke, S. HUfner, Sol. St. Com. II (1972) 1197.
71
K. Baberschke, B. Bachor, S.E. Barnes, Phys. Rev. B21 (1980) 2666.
F. Steglich,
I
~H/G
20C
The experiments demonstrate that ESR at several frequencies is needed before a full analysis of the relaxation phenomena and the static local susceptibility can be given. This analysis will include a lineshape analysis involving a convolution of the Lorenzian relaxation part with a field distribution function. Furthermore, we will discuss that Yoslda's theorem (_[Mtotal' HRKKy] = O) may not be applicable for sptnglasses, blnce in a spinglass the individual moments are highly correlated, the definition of Mtota I is in question. Under those circumstances HRKKY can quite well contribute to line broadening IIOI .
l
I
I
I
5
10
15
20
TIK
Figure 2: Linewidth versus T; symbols as in Fig. I. Again the 1 G H z data have large errorbars of approx. 15%. For these data we had to include in the analysis the resonance at "negative" fields. Dashed lines are guides for the eye.
f81
See for example the review article by S.E. Barnes, Adv. in Phys.,to be published.
191
See for example E. Dormann, V. Jaccorino, Phys. Lett. 48A (]974) 81.
11ol
S.E. Barnes,
to be published.