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Local field distribution in YNi2B2C superconductor
PHYSlCA® ELSEVIER
Physica C 341--348 (2000) 2137-2138 www.clsevier.nl/locate/physc
Local field distribution in YNi2B2C superconductor D. H. Kim a, K. H. Lee a, S. W. Seoa, K. S. Han a, B. J. Mean a, Moohee Lee a*, B. K. Cho b, and S.I. Lee c aDepartment of Physics, Kon-Kuk University, Seoul 143-701, Korea bDepartment of Material Science and Technology, KJ-IST, Kwangju 500-712, Korea CNational Creative Initiative Center for Superconductivity, POSTECH, Pohang 790-784, Korea Local field distribution in the mixed state of type II superconductors has been numerically calculated and compared with tlB NMR spectra for YNi2B2C single crystals. We find that only small distortion of vortex positions from the perfect lattice points is enough to smear out the low frequency shoulder. It is found that the second moment of the field distribution has a major contribution from the high frequency tall. Consequently, a linewidth calculated from the .second moment assuming for a Gaussian line shape is overestimated.
1. I n t r o d u c t i o n Recently, NMR experiments have played a great role in understanding vortex dynamics in cuprate superconductors. NMR is sensitive to the local field distribution and fluctuation in the precession period of a nuclear spin. The static information is the peak position and the linewidth of NMR resonance signal, which reflect, respectively, the saddle-point field and the local field inhomogeneity in the mixed state. In this paper, we report numerical calculation of local field distribution in the mixed state of YNi2B2C superconductor and compare the results with 11B NMR data.
=
-0.2
Experiment
YNi2B2C single crystal was grown by the Ni2B high-temperature flux growth method. The sample was roughly 11 x 7 × 2mm 3. The pulsed 11B NMR measurements were carried out at 1.8 - 4.0 T parallel to the c-axis. * Corresponding author: mhlee~kkucc.konkuk.ac.kr. M.L. acknowledges financial support from the Korea Science & Engineering Foundation through the Grant No. 1999-2-114-005-5 and through Center for Strongly Correlated Materials Research at Seoul National University in 1999.
-0'.1 '
010
,
=
.
• 011 0 1 2
00
~af (MHz)
Figure 1. l i b NMR spectrum for YNi2B2C single crystal at 1.8 T and 3.8 K.
3. 2.
•"
.
Results
and
Discussion
Figure 1 shows 11B NMR spectrum at 1.8 T and 3.8 K. This line shape exhibits a typical asymmetric shape with a long tall in the high frequency side, which is similar to the characteristic field distribution for Abrikosov vortex lattice of square type, as calculated and shown in Fig. 2. However, a shoulder in the low frequency side is missing in Fig. 1. To understand absence of the shoulder, we have carried out numerical calculation of the local field distribution in the mixed state of YNi2B2C superconductor. Assuming that the local magnetic field for a single vortex decreases as the modified Bessel function,
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)01064-9
D.H. Kim et aL/Physica C 341-348 (2000) 2137-2138
2138
0.10 ...... H=1.8 T ice
0.08
Analytic Calculation- Ref. 3 Numerical Calculation - This Work AH(T) ffi Ic %l'kZ(T)
0.06 Square Lattice YNi2B2C He= 360 Oe Ho~ =I 0,5 T
0.04
I
.
.
.
.
.
.
.
.
Magnetic Field (A.U.)
0.02
0.00
Figure 2. Calculated 11B NMR spectrum of YNi2B2C for the perfect square lattice.
I
I
I
4
6
8
",'"'-,-
10
H(T) Figure 3. The second moment calculation of 11B NMR linewidth in the mixed state of YNi2B2C.
H(r) ~, 2=-~ Ko[(r 2 + 2~2)1/2/A] [1], we sum up the respective local fields of 300 x 300 vortices in a unit cell of 300 x 300 pixels for a square lattice. The square lattice has been observed in this field range [2]. Since we think that the absence of the shoulder may originate from distortion of vortex lattice due to pinning centers, we calculate local field distribution accounting for random distortion of vortices from the regular lattice positions. Then, core finding from our numerical calculation is that a small amplitude (-,,2%) of random distortion is enough to wash out the left shoulder. Furthermore, the line shape for larger distortion becomes much broader approaching a symmetric Gaussian shape. Indeed, at higher magnetic field of 3.0 T for a stronger NMR signal, we have finally observed a NMR line shape, which is very close to the calculated line shape in Fig. 2 . The field inhomogeneity of the perfect vortex lattice can be calculated by taking account of the spatial modulation of the local field in the mixed state. The second moment of the field variation is given as < AH2(T) >1/2= ~@o/A(T)2 where @o is the flux quantum, A(T) is the penetration depth, and ~ is a numerical factor. The formula for ~ has been calculated for Hcz << H << He2 and 0.5Hcl < H < He2 [3]. However, for the intermediate field value as for our magnetic field of 1.8 and 3.0 T, ~ can be only numerically calculated. Using X(0) = 1207 A [4] and the coherence length ~(0) = 55/~ from Hc2(0)--10.5 W [5], we have carried out the numerical calculation and obtained ~ for several values of magnetic field,
which is shown in Fig. 3. Numerical results are compared with the results of analytic calculation [3]. Two results are fairly close. We find that the second moment of local field distribution is dominated mostly by the long tail in the high frequency side. To compare NMR data with calculation, we usually take a linewidth of NMR spectrum as a measure of field inhomogeneity. Then, assuming a Ganssian line shape, the full-width-at-halfmaximum (FWHM) is given by A f = 2.367AH where 7 is the nuclear gyromagnetic ratio of 11B nucleus, 13.67 kHz/Oe. We find this analysis is erroneous since contribution to the second moment of the line shape comes mostly from the long tail in the high frequency side and the line shape is not a Gaussian line shape unless the samples are dirty with many pinning centers. REFERENCES 1. E.H. Brandt, Rep. Prog. Phys. 58 (1995) 1465. 2. M. Yethiraj et aL, Phys. Rev. Lett. 78 (1997) 4849. 3. E.H. Brandt, Phys. l~v. Lett. 66 (1991) 3213. 4. K.D.D. Rathnayaka et al., Phys. Rev. B 55 (1997) 8506. 5. S.V. Shulga et aL, Phys. Rev. Lett. 80 (1998) 1730.
Physica C 341--348 (2000) 2137-2138 www.clsevier.nl/locate/physc
Local field distribution in YNi2B2C superconductor D. H. Kim a, K. H. Lee a, S. W. Seoa, K. S. Han a, B. J. Mean a, Moohee Lee a*, B. K. Cho b, and S.I. Lee c aDepartment of Physics, Kon-Kuk University, Seoul 143-701, Korea bDepartment of Material Science and Technology, KJ-IST, Kwangju 500-712, Korea CNational Creative Initiative Center for Superconductivity, POSTECH, Pohang 790-784, Korea Local field distribution in the mixed state of type II superconductors has been numerically calculated and compared with tlB NMR spectra for YNi2B2C single crystals. We find that only small distortion of vortex positions from the perfect lattice points is enough to smear out the low frequency shoulder. It is found that the second moment of the field distribution has a major contribution from the high frequency tall. Consequently, a linewidth calculated from the .second moment assuming for a Gaussian line shape is overestimated.
1. I n t r o d u c t i o n Recently, NMR experiments have played a great role in understanding vortex dynamics in cuprate superconductors. NMR is sensitive to the local field distribution and fluctuation in the precession period of a nuclear spin. The static information is the peak position and the linewidth of NMR resonance signal, which reflect, respectively, the saddle-point field and the local field inhomogeneity in the mixed state. In this paper, we report numerical calculation of local field distribution in the mixed state of YNi2B2C superconductor and compare the results with 11B NMR data.
=
-0.2
Experiment
YNi2B2C single crystal was grown by the Ni2B high-temperature flux growth method. The sample was roughly 11 x 7 × 2mm 3. The pulsed 11B NMR measurements were carried out at 1.8 - 4.0 T parallel to the c-axis. * Corresponding author: mhlee~kkucc.konkuk.ac.kr. M.L. acknowledges financial support from the Korea Science & Engineering Foundation through the Grant No. 1999-2-114-005-5 and through Center for Strongly Correlated Materials Research at Seoul National University in 1999.
-0'.1 '
010
,
=
.
• 011 0 1 2
00
~af (MHz)
Figure 1. l i b NMR spectrum for YNi2B2C single crystal at 1.8 T and 3.8 K.
3. 2.
•"
.
Results
and
Discussion
Figure 1 shows 11B NMR spectrum at 1.8 T and 3.8 K. This line shape exhibits a typical asymmetric shape with a long tall in the high frequency side, which is similar to the characteristic field distribution for Abrikosov vortex lattice of square type, as calculated and shown in Fig. 2. However, a shoulder in the low frequency side is missing in Fig. 1. To understand absence of the shoulder, we have carried out numerical calculation of the local field distribution in the mixed state of YNi2B2C superconductor. Assuming that the local magnetic field for a single vortex decreases as the modified Bessel function,
0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)01064-9
D.H. Kim et aL/Physica C 341-348 (2000) 2137-2138
2138
0.10 ...... H=1.8 T ice
0.08
Analytic Calculation- Ref. 3 Numerical Calculation - This Work AH(T) ffi Ic %l'kZ(T)
0.06 Square Lattice YNi2B2C He= 360 Oe Ho~ =I 0,5 T
0.04
I
.
.
.
.
.
.
.
.
Magnetic Field (A.U.)
0.02
0.00
Figure 2. Calculated 11B NMR spectrum of YNi2B2C for the perfect square lattice.
I
I
I
4
6
8
",'"'-,-
10
H(T) Figure 3. The second moment calculation of 11B NMR linewidth in the mixed state of YNi2B2C.
H(r) ~, 2=-~ Ko[(r 2 + 2~2)1/2/A] [1], we sum up the respective local fields of 300 x 300 vortices in a unit cell of 300 x 300 pixels for a square lattice. The square lattice has been observed in this field range [2]. Since we think that the absence of the shoulder may originate from distortion of vortex lattice due to pinning centers, we calculate local field distribution accounting for random distortion of vortices from the regular lattice positions. Then, core finding from our numerical calculation is that a small amplitude (-,,2%) of random distortion is enough to wash out the left shoulder. Furthermore, the line shape for larger distortion becomes much broader approaching a symmetric Gaussian shape. Indeed, at higher magnetic field of 3.0 T for a stronger NMR signal, we have finally observed a NMR line shape, which is very close to the calculated line shape in Fig. 2 . The field inhomogeneity of the perfect vortex lattice can be calculated by taking account of the spatial modulation of the local field in the mixed state. The second moment of the field variation is given as < AH2(T) >1/2= ~@o/A(T)2 where @o is the flux quantum, A(T) is the penetration depth, and ~ is a numerical factor. The formula for ~ has been calculated for Hcz << H << He2 and 0.5Hcl < H < He2 [3]. However, for the intermediate field value as for our magnetic field of 1.8 and 3.0 T, ~ can be only numerically calculated. Using X(0) = 1207 A [4] and the coherence length ~(0) = 55/~ from Hc2(0)--10.5 W [5], we have carried out the numerical calculation and obtained ~ for several values of magnetic field,
which is shown in Fig. 3. Numerical results are compared with the results of analytic calculation [3]. Two results are fairly close. We find that the second moment of local field distribution is dominated mostly by the long tail in the high frequency side. To compare NMR data with calculation, we usually take a linewidth of NMR spectrum as a measure of field inhomogeneity. Then, assuming a Ganssian line shape, the full-width-at-halfmaximum (FWHM) is given by A f = 2.367AH where 7 is the nuclear gyromagnetic ratio of 11B nucleus, 13.67 kHz/Oe. We find this analysis is erroneous since contribution to the second moment of the line shape comes mostly from the long tail in the high frequency side and the line shape is not a Gaussian line shape unless the samples are dirty with many pinning centers. REFERENCES 1. E.H. Brandt, Rep. Prog. Phys. 58 (1995) 1465. 2. M. Yethiraj et aL, Phys. Rev. Lett. 78 (1997) 4849. 3. E.H. Brandt, Phys. l~v. Lett. 66 (1991) 3213. 4. K.D.D. Rathnayaka et al., Phys. Rev. B 55 (1997) 8506. 5. S.V. Shulga et aL, Phys. Rev. Lett. 80 (1998) 1730.