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Local field distribution and NMR line shape in YNi2B2C
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 169–170
Local field distribution and NMR line shape in YNi2B2 C K.H. Leea, K.H. Kanga, B.J. Meana, C.Y. Kwaka, Moohee Leea,*, J.S. Chob b
a Department of Physics, Konkuk University, 93-1 Mojin-dong Kwangjin-ku, Seoul 143-701, South Korea Department of Information and Communication, Suwon Science College, Wha-sung Kyong-gi 445-960, South Korea
Abstract Local field distribution in the mixed state of type II superconductors is numerically calculated and compared with 11 B NMR spectrum of YNi2 B2 C single crystal. We find that just small distortion of vortex positions severely distorts and broadens the line shape. Thus the NMR linewidth is susceptible to a small degree of vortex distortion. Also, since NMR signals are usually very weak due to significant line broadening in the vortex state, only a limited range of the full distribution around the saddle-point tends to be observed. Therefore, unless the characteristic edges of field distribution at the minimum field and the maximum field values are observed confirming that the full NMR line in the vortex state is securely measured, then analysis based only on the limited part of the full spectrum may lead to erroneous conclusions regarding vortex structure and dynamics. r 2004 Elsevier B.V. All rights reserved. PACS: 74.70.Dd; 74.25.Qt; 76.60. k Keywords: YNi2 B2 C; Vortex state; Local field distribution;
11
B NMR line shape
Recently, NMR measurements have played a great role in unveiling vortex dynamics in borocarbides as well as cuprates [1,2]. NMR is sensitive to the local field distribution and fluctuation in the precession period of a nuclear spin. Static information is the peak position and the linewidth of NMR resonance peak, which are proportional to, respectively, a saddle-point field and local field inhomogeneity. Since nuclear sites form a really find grid probing local magnetic field in the vortex state, NMR is a sensitive tool for understanding of vortex structures and dynamics. In this paper, we report numerical calculation of local field distribution in the mixed state of YNi2 B2 C single crystal and compare results with a line shape of 11 B NMR. Assuming that the local magnetic field for a single vortex decreases as the modified Bessel function, [3] we sum up the respective local fields of 300 300 vortices in a unit cell of 300 300 pixels for a square lattice at 1:8 T [4]. The calculated field distribution in Fig. 1 exhibits an asymmetric shape with a long tail in the high-frequency side, which is characteristic of local field distribution in a *Corresponding author. Fax: +82-2-455-4863. E-mail address: [email protected] (M. Lee).
Abrikosov vortex lattice. It clearly shows a peak at the saddle-point field HS ; a low-frequency shoulder at the minimum field Hm ; and a high-frequency edge at HM : In order to understand how this field distribution changes as the vortex positions deviate from the square lattice points, we introduce a random distortion of vortex position. As soon as vortices are free to move by 1.25% of vortex spacing, the low-frequency shoulder at Hm smears out and the line shape substantially broadens. Even for the small distortion of 2.5%, the left shoulder is completely washed out and the edge at HM disappears. Furthermore, the peak at Hs significantly broadens and the distribution shape changes to a broad symmetric line like Gaussian centered at HS : Since a NMR frequency is exactly proportional to local magnetic field, these field distributions should be measured by NMR line shapes. However, the characteristic line shape of the perfect vortex lattice is never observed from NMR on cuprates. Most NMR results for cuprates report rather a symmetric Gaussian shape near Hs : However, 11 B NMR spectrum of YNi2 B2 C shows an asymmetric shape with a long tail in the highfrequency side (Fig. 2). In addition, the left shoulder at Hm and the high-frequency edge at HM are also
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.070
ARTICLE IN PRESS 170
K.H. Lee et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 169–170
1.25% Distortion
Intensity
Intensity
No Distortion
Hm
HS HM
2.5% Distortion
-100
Magnetic Field Fig. 1. Local field distribution calculated for a distorted square lattice.
observed. This shape is characteristic of the Abrikosov lattice with small distortion and consequently guarantees that a full range of the field distribution is observed. Fig. 1 shows that NMR linewidth is very susceptible to a small degree of vortex distortion. Since the local field inhomogeneity is related to the penetration depth, NMR linewidth analysis is utilized to measure the penetration depth at high field, where the principle is exactly same for mSR measurement. Therefore, this finding provides an important meaning for NMR linewidth analysis. On the other hand, the saddle-point field position is robust over even large distortion of vortices. Although NMR is very sensitive to local field, the signal is extremely weak especially for broad lines in the mixed state and then the very broad lines in Fig. 1 are hardly measured over the full range. One problem with NMR measurements in the mixed state is that it is hardly guaranteed that an observed NMR spectrum reflects the full range of field distribution. Since NMR spectrum broadens and the signal becomes very weak in the mixed state, it is most likely that only a limited range of field distribution around Hs (usually narrow and symmetric) is observed. Then the linewidth is measured to be smaller than the correct linewidth
-50
0
50
∆ f (kHz)
100
Fig. 2. 11 B NMR spectrum for YNi2 B2 C single crystal at 3:8 K and 3:0 T parallel to the c-axis.
of full distribution. This incorrect linewidth can lead to misinterpretation of motional narrowing due to vortex motion. Unless the characteristic edges at Hm and HM are observed, we cannot guarantee whether or not an observed NMR spectrum reflects the full range of field distribution. In this case, it is highly likely that only a limited range of full spectrum is observed due to the weak signal and consequently analysis based on the partial spectrum may lead to erroneous conclusions. This work was supported by Grant No. R01-2002000-00326-0 from the Korea Science & Engineering Foundation. This measurement was carried out utilizing the Shared Research Equipment Assistance Program (R23-2000-000-00003-0).
References [1] H.N. Bachman, et al., Phys. Rev. Lett. 80 (1998) 1726. [2] K.H. Lee, et al., Physica B 284–288 (2000) 709. [3] E.H. Brandt, Rep. Prog. Phys. 58 (1995) 1465. [4] M. Yethiraj, et al., Phys. Rev. Lett. 78 (1997) 4849.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 169–170
Local field distribution and NMR line shape in YNi2B2 C K.H. Leea, K.H. Kanga, B.J. Meana, C.Y. Kwaka, Moohee Leea,*, J.S. Chob b
a Department of Physics, Konkuk University, 93-1 Mojin-dong Kwangjin-ku, Seoul 143-701, South Korea Department of Information and Communication, Suwon Science College, Wha-sung Kyong-gi 445-960, South Korea
Abstract Local field distribution in the mixed state of type II superconductors is numerically calculated and compared with 11 B NMR spectrum of YNi2 B2 C single crystal. We find that just small distortion of vortex positions severely distorts and broadens the line shape. Thus the NMR linewidth is susceptible to a small degree of vortex distortion. Also, since NMR signals are usually very weak due to significant line broadening in the vortex state, only a limited range of the full distribution around the saddle-point tends to be observed. Therefore, unless the characteristic edges of field distribution at the minimum field and the maximum field values are observed confirming that the full NMR line in the vortex state is securely measured, then analysis based only on the limited part of the full spectrum may lead to erroneous conclusions regarding vortex structure and dynamics. r 2004 Elsevier B.V. All rights reserved. PACS: 74.70.Dd; 74.25.Qt; 76.60. k Keywords: YNi2 B2 C; Vortex state; Local field distribution;
11
B NMR line shape
Recently, NMR measurements have played a great role in unveiling vortex dynamics in borocarbides as well as cuprates [1,2]. NMR is sensitive to the local field distribution and fluctuation in the precession period of a nuclear spin. Static information is the peak position and the linewidth of NMR resonance peak, which are proportional to, respectively, a saddle-point field and local field inhomogeneity. Since nuclear sites form a really find grid probing local magnetic field in the vortex state, NMR is a sensitive tool for understanding of vortex structures and dynamics. In this paper, we report numerical calculation of local field distribution in the mixed state of YNi2 B2 C single crystal and compare results with a line shape of 11 B NMR. Assuming that the local magnetic field for a single vortex decreases as the modified Bessel function, [3] we sum up the respective local fields of 300 300 vortices in a unit cell of 300 300 pixels for a square lattice at 1:8 T [4]. The calculated field distribution in Fig. 1 exhibits an asymmetric shape with a long tail in the high-frequency side, which is characteristic of local field distribution in a *Corresponding author. Fax: +82-2-455-4863. E-mail address: [email protected] (M. Lee).
Abrikosov vortex lattice. It clearly shows a peak at the saddle-point field HS ; a low-frequency shoulder at the minimum field Hm ; and a high-frequency edge at HM : In order to understand how this field distribution changes as the vortex positions deviate from the square lattice points, we introduce a random distortion of vortex position. As soon as vortices are free to move by 1.25% of vortex spacing, the low-frequency shoulder at Hm smears out and the line shape substantially broadens. Even for the small distortion of 2.5%, the left shoulder is completely washed out and the edge at HM disappears. Furthermore, the peak at Hs significantly broadens and the distribution shape changes to a broad symmetric line like Gaussian centered at HS : Since a NMR frequency is exactly proportional to local magnetic field, these field distributions should be measured by NMR line shapes. However, the characteristic line shape of the perfect vortex lattice is never observed from NMR on cuprates. Most NMR results for cuprates report rather a symmetric Gaussian shape near Hs : However, 11 B NMR spectrum of YNi2 B2 C shows an asymmetric shape with a long tail in the highfrequency side (Fig. 2). In addition, the left shoulder at Hm and the high-frequency edge at HM are also
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.070
ARTICLE IN PRESS 170
K.H. Lee et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 169–170
1.25% Distortion
Intensity
Intensity
No Distortion
Hm
HS HM
2.5% Distortion
-100
Magnetic Field Fig. 1. Local field distribution calculated for a distorted square lattice.
observed. This shape is characteristic of the Abrikosov lattice with small distortion and consequently guarantees that a full range of the field distribution is observed. Fig. 1 shows that NMR linewidth is very susceptible to a small degree of vortex distortion. Since the local field inhomogeneity is related to the penetration depth, NMR linewidth analysis is utilized to measure the penetration depth at high field, where the principle is exactly same for mSR measurement. Therefore, this finding provides an important meaning for NMR linewidth analysis. On the other hand, the saddle-point field position is robust over even large distortion of vortices. Although NMR is very sensitive to local field, the signal is extremely weak especially for broad lines in the mixed state and then the very broad lines in Fig. 1 are hardly measured over the full range. One problem with NMR measurements in the mixed state is that it is hardly guaranteed that an observed NMR spectrum reflects the full range of field distribution. Since NMR spectrum broadens and the signal becomes very weak in the mixed state, it is most likely that only a limited range of field distribution around Hs (usually narrow and symmetric) is observed. Then the linewidth is measured to be smaller than the correct linewidth
-50
0
50
∆ f (kHz)
100
Fig. 2. 11 B NMR spectrum for YNi2 B2 C single crystal at 3:8 K and 3:0 T parallel to the c-axis.
of full distribution. This incorrect linewidth can lead to misinterpretation of motional narrowing due to vortex motion. Unless the characteristic edges at Hm and HM are observed, we cannot guarantee whether or not an observed NMR spectrum reflects the full range of field distribution. In this case, it is highly likely that only a limited range of full spectrum is observed due to the weak signal and consequently analysis based on the partial spectrum may lead to erroneous conclusions. This work was supported by Grant No. R01-2002000-00326-0 from the Korea Science & Engineering Foundation. This measurement was carried out utilizing the Shared Research Equipment Assistance Program (R23-2000-000-00003-0).
References [1] H.N. Bachman, et al., Phys. Rev. Lett. 80 (1998) 1726. [2] K.H. Lee, et al., Physica B 284–288 (2000) 709. [3] E.H. Brandt, Rep. Prog. Phys. 58 (1995) 1465. [4] M. Yethiraj, et al., Phys. Rev. Lett. 78 (1997) 4849.