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Local vortex mobility below the irreversibility line of Tl2Ba2CaCuO8. A205Tl NMR study of the transverse relaxation in single crystals
PHYSICA 8 ELSEVIER
Physica C 282-287 (1997) 2121-2122
Local vortex mobility below the irreversibility ‘05T1 NMR study of the transverse relaxation J. Witteveena, aKamerlingh
E. G. Nikolaeva*, Onnes
Laboratory,
H. B. Broma, Leiden
line of TlzBazCaCuOs. in single crystals.
A
M. L. de Kok a
University,
2300 RA Leiden,
The Netherlands
The ‘05T1 nuclear spin-spin relaxation rate in single crystals of TlzBazCaCu2Os is studied at different angles 0 The peak between the c-axis and the magnetic field. We observe a peak caused by vortex motion at T/Tcc 0.2. temperature increases, and height decreases with increasing 8. From the data, we extract information about the hopping distance and frequency.
NMR is a powerful tool for the study of the local magnetic field fluctuations caused by mov-
ing vortices [l], as it gives values for the time To observe and length scales of the motion. directly the fluctuating fields, one can use the NMR linewidth, the spin lattice relaxation time Tl, and the spin spin relaxation time 2’2, the former being sensitive to fluctuations near the NMR frequency, the latter at much lower frequencies. Here, we report the results of a 205T1 transverse relaxation study in a crystalline sample of TlzBa2CaCu20s (T, = 115 K) in the superconducting state, and a numerical symulation to obtain information about the vortex hopping distance, and frequency[2]. In our system, 10% of the Ca positions are replaced by Tl. These Tl(1) sites provide excellent probes for T2 studies, as they are far away form other Tl atoms and thus have smaller spin-spin contribution in the relaxation. Below the irreversibility temperature (25 K at 4.7 T), we have found a peak in the T;l temperature dependence. This may be considered as a result of a relatively slow and confined vortex motion in this temperature region. The crystal orientation dependence of these peaks has been studied. Numerical simulations give information about the vortex hopping distance and frequency. To exclude a dipolar origin of the observed peak, we evaluated the Tl-Cu coupling discussed *Permanent address: P.L.Kapitza Institute for Physical Problems RAS ul. Kosygina 2, Moscow 117334, Russia; with finantial support from The Netherlands Organisation of Scientific Research (NWO). 0921-4534/97/$17.000 Elsevier Science B.V. All rights reserved. PI1 SO921-4534(97)01153-2
14
’
12 IO zk
7
’
od---
450 _-*__ 67.60 --a--900 . * . 0: TZ - via Cu ^ ‘c]1-
45” ‘li wa C;u Yi -----
8
67'Tzvia&
Tl -----.
6
h” 4 2 0 0
20
40
60
80
100
T W
Figure 1. T;l(I) vs. T at various 8. The lines below in the graph are calculated using the Tl(I)Cu coupling, see text
in [4]. As the Cu Tl decreases from very short at room temperature, to hours at low temperatures, we pass a point where the unlike coupling between the Cu-TI(1) has an optimal value, predicting a maximum in TF1.This explanation also holds for angles other than B 1) c,and it is of the right order of magnitude. However, evaluation of the rate shows that the temperature at which the peak occurs is approximately 200 K (see figure l), thus ruling it out as the cause of our T;' peak. The temperature dependences of relaxation rates of Tl(1) is shown on fig.1 for various sample orientations. As the angle 8 increases, the sharp peak of the relaxation rate for TI(I) near 20 K moves to higher temperatures correlating with Tirr (measured by comparing the in field and zero
J: Witteveen et al./Physica C 282-287 (1997) 212162122
2122
104
lo3
Figure 2. Tzel vs. rc for the independent (dashed) The diaand collective (dotted) simulations. monds are the experimental data points for 0 = 45” (see text), along with the fit used in figure 1
field cooled linewidths) which increases as the field along the c-axis decreases. Also the peak amplitude (a measure for the size of the fluctuating fields) decreases with increasing 8. The 90”peak is probably due to a small misalignment between the field direction and c-axis. For information about the hop frequency and hop field, we use the approximate formula (see [3]), with T2&ex = y;tb$-,/ [2 + (@zrc)2] rc the average hop time, 7n the gyromagnetic ratio of the Tl nucleus, and b, the average change in magnetic field for each hop. The solid lines in figure 1 show the result of a fit to the data using the above formula and assuming an Ahrrenius law rc = te exp U/kBT for the correlation time temperature dependence. The fit is not perfect but this simplified model gives the right qualitative description of the observed peaks. The resulting h, = 0.2 mT for B 5 45’ is much smaller the average field inhomogeneity in the vortex state AB2)‘j2 = O.O609@a/X~, = 9mT (X,, = 1250 8, ). The average value of the field gradient in the vortex lattice is evaluated as G x (AB2)‘i2/d =0.5 G/A (d = 200A is the average intervortex spacing at 4.7 T). To extract information about the hopping distances, as well as more reliable information about the hopping frequencies, simulations were per-
formed. Using well known expressions for the field distribution around a vortex, we simulated the hopping vortices and the resulting magnetisation decay of the 205T1 nuclei in an NMR pulse experiment, using different values for the average hop distance and time. To compare the results with the measurements, we converted the temperature axis in figure 1 to a rc scale using the Arrhenius low, with the fit parameters mentioned above, see figure 2. As expected, the results depend strongly on how we allow the vortices to move: completely independent motion produces much stronger fields and thus shorter relaxation times than collective motion. The activation energy U obtained from our results ((80 f 20)K at 8 5 45” and (170 f 20) K near 90”) is comparable with values reported by others[l] (taken from Tl data), and in [5] (magnetisation relaxation data). Our average collective hop-distance corresponds nicely with the Lindeman criterium, but shows clearly that the vortices cannot move 0.2d relative to each other (the independent model). REFERENCES
1. J.T.Moonen, H.B.Brom, Physica C 244 D.R.Torgeson, (1995) 1; 10; B.J.Suh, F.Borsa, Phys. Rev. Lett. 71 (1993) 3011; Y.&. Song et al., Phys. Rev. B 50 (1994) 16570; B.J.Suh et al., Phys. Rev. Lett. 76 (1996) 1928. 2. E. N. Nikolaev et al., Phys. Rev. B, act. for publication. 3. J. Witteveen, Phys. Rev. B, act. for publication. 4. R. E. Walstedt et al. Phys. Rev. B 51 (1995) 3163. 5. G. Blatter et al., Rev. Mod. Phys. 66 (1994) 1125.
Physica C 282-287 (1997) 2121-2122
Local vortex mobility below the irreversibility ‘05T1 NMR study of the transverse relaxation J. Witteveena, aKamerlingh
E. G. Nikolaeva*, Onnes
Laboratory,
H. B. Broma, Leiden
line of TlzBazCaCuOs. in single crystals.
A
M. L. de Kok a
University,
2300 RA Leiden,
The Netherlands
The ‘05T1 nuclear spin-spin relaxation rate in single crystals of TlzBazCaCu2Os is studied at different angles 0 The peak between the c-axis and the magnetic field. We observe a peak caused by vortex motion at T/Tcc 0.2. temperature increases, and height decreases with increasing 8. From the data, we extract information about the hopping distance and frequency.
NMR is a powerful tool for the study of the local magnetic field fluctuations caused by mov-
ing vortices [l], as it gives values for the time To observe and length scales of the motion. directly the fluctuating fields, one can use the NMR linewidth, the spin lattice relaxation time Tl, and the spin spin relaxation time 2’2, the former being sensitive to fluctuations near the NMR frequency, the latter at much lower frequencies. Here, we report the results of a 205T1 transverse relaxation study in a crystalline sample of TlzBa2CaCu20s (T, = 115 K) in the superconducting state, and a numerical symulation to obtain information about the vortex hopping distance, and frequency[2]. In our system, 10% of the Ca positions are replaced by Tl. These Tl(1) sites provide excellent probes for T2 studies, as they are far away form other Tl atoms and thus have smaller spin-spin contribution in the relaxation. Below the irreversibility temperature (25 K at 4.7 T), we have found a peak in the T;l temperature dependence. This may be considered as a result of a relatively slow and confined vortex motion in this temperature region. The crystal orientation dependence of these peaks has been studied. Numerical simulations give information about the vortex hopping distance and frequency. To exclude a dipolar origin of the observed peak, we evaluated the Tl-Cu coupling discussed *Permanent address: P.L.Kapitza Institute for Physical Problems RAS ul. Kosygina 2, Moscow 117334, Russia; with finantial support from The Netherlands Organisation of Scientific Research (NWO). 0921-4534/97/$17.000 Elsevier Science B.V. All rights reserved. PI1 SO921-4534(97)01153-2
14
’
12 IO zk
7
’
od---
450 _-*__ 67.60 --a--900 . * . 0: TZ - via Cu ^ ‘c]1-
45” ‘li wa C;u Yi -----
8
67'Tzvia&
Tl -----.
6
h” 4 2 0 0
20
40
60
80
100
T W
Figure 1. T;l(I) vs. T at various 8. The lines below in the graph are calculated using the Tl(I)Cu coupling, see text
in [4]. As the Cu Tl decreases from very short at room temperature, to hours at low temperatures, we pass a point where the unlike coupling between the Cu-TI(1) has an optimal value, predicting a maximum in TF1.This explanation also holds for angles other than B 1) c,and it is of the right order of magnitude. However, evaluation of the rate shows that the temperature at which the peak occurs is approximately 200 K (see figure l), thus ruling it out as the cause of our T;' peak. The temperature dependences of relaxation rates of Tl(1) is shown on fig.1 for various sample orientations. As the angle 8 increases, the sharp peak of the relaxation rate for TI(I) near 20 K moves to higher temperatures correlating with Tirr (measured by comparing the in field and zero
J: Witteveen et al./Physica C 282-287 (1997) 212162122
2122
104
lo3
Figure 2. Tzel vs. rc for the independent (dashed) The diaand collective (dotted) simulations. monds are the experimental data points for 0 = 45” (see text), along with the fit used in figure 1
field cooled linewidths) which increases as the field along the c-axis decreases. Also the peak amplitude (a measure for the size of the fluctuating fields) decreases with increasing 8. The 90”peak is probably due to a small misalignment between the field direction and c-axis. For information about the hop frequency and hop field, we use the approximate formula (see [3]), with T2&ex = y;tb$-,/ [2 + (@zrc)2] rc the average hop time, 7n the gyromagnetic ratio of the Tl nucleus, and b, the average change in magnetic field for each hop. The solid lines in figure 1 show the result of a fit to the data using the above formula and assuming an Ahrrenius law rc = te exp U/kBT for the correlation time temperature dependence. The fit is not perfect but this simplified model gives the right qualitative description of the observed peaks. The resulting h, = 0.2 mT for B 5 45’ is much smaller the average field inhomogeneity in the vortex state AB2)‘j2 = O.O609@a/X~, = 9mT (X,, = 1250 8, ). The average value of the field gradient in the vortex lattice is evaluated as G x (AB2)‘i2/d =0.5 G/A (d = 200A is the average intervortex spacing at 4.7 T). To extract information about the hopping distances, as well as more reliable information about the hopping frequencies, simulations were per-
formed. Using well known expressions for the field distribution around a vortex, we simulated the hopping vortices and the resulting magnetisation decay of the 205T1 nuclei in an NMR pulse experiment, using different values for the average hop distance and time. To compare the results with the measurements, we converted the temperature axis in figure 1 to a rc scale using the Arrhenius low, with the fit parameters mentioned above, see figure 2. As expected, the results depend strongly on how we allow the vortices to move: completely independent motion produces much stronger fields and thus shorter relaxation times than collective motion. The activation energy U obtained from our results ((80 f 20)K at 8 5 45” and (170 f 20) K near 90”) is comparable with values reported by others[l] (taken from Tl data), and in [5] (magnetisation relaxation data). Our average collective hop-distance corresponds nicely with the Lindeman criterium, but shows clearly that the vortices cannot move 0.2d relative to each other (the independent model). REFERENCES
1. J.T.Moonen, H.B.Brom, Physica C 244 D.R.Torgeson, (1995) 1; 10; B.J.Suh, F.Borsa, Phys. Rev. Lett. 71 (1993) 3011; Y.&. Song et al., Phys. Rev. B 50 (1994) 16570; B.J.Suh et al., Phys. Rev. Lett. 76 (1996) 1928. 2. E. N. Nikolaev et al., Phys. Rev. B, act. for publication. 3. J. Witteveen, Phys. Rev. B, act. for publication. 4. R. E. Walstedt et al. Phys. Rev. B 51 (1995) 3163. 5. G. Blatter et al., Rev. Mod. Phys. 66 (1994) 1125.