11 B NMR measurements of vortex dynamics for YNi2B2C superconductor

Physica C 364±365 (2001) 507±510

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B NMR measurements of vortex dynamics for YNi2B2C superconductor

K.H. Lee a, K.H. Kang a, H.S. Seo a, B.J. Mean a, Moohee Lee a,*, B.K. Cho b b

a Department of Physics, Konkuk University, Seoul 143-701, South Korea Department of Material Science and Technology, KJ-IST, Kwangju 500-712, South Korea

Abstract 11

B Pulsed nuclear magnetic resonance (NMR) measurements have been performed on a single crystal of YNi2 B2 C superconductor to investigate the vortex structure and dynamical behavior. Spectrum, line width and transverse relaxation rate of 11 B NMR are measured at 1.8 and 3.0 T. The spectrum below 4 K exhibits a typical local ®eld distribution for a square lattice at 3.0 T parallel to the c-axis. However, the shape of the spectrum at higher temperature changes to a symmetric narrow line, which indicates signi®cant motion of vortices. Furthermore, thermal hysteresis of the saddle-point ®eld, motional narrowing of line width, and enhancement of transverse relaxation rate also con®rm substantial distortion and ¯uctuation of vortices in this low Tc and nearly isotropic 3D superconductor. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: YNi2 B2 C; Vortex dynamics;

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B NMR; Shift and transverse relaxation rate

1. Introduction Numerous important research results have been reported on unusual vortex motions including vortex lattice melting in cuprate superconductors [1±8]. These features are attributed to the high transition temperature Tc , the short coherence length n, and the high anisotropy. Despite that Tc is low, n is relatively large, and superconducting properties are nearly isotropic, unique results, however, have been recently reported for RNi2 B2 C superconductors [9±13] showing exotic vortex structures as well as vortex motions. These include

* Corresponding author. Tel.: +82-2-450-4084; fax: +82-23436-5361. E-mail address: [email protected] (M. Lee).

the vortex melting [9] and a transition from triangular to square vortex lattices [10]. Vortex dynamics for RNi2 B2 C are probed by transport measurements [9], STM [11], and small angle neutron scattering experiments [12±14]. Recently, NMR experiments have played a great role not only in clarifying the importance of antiferromagnetic ¯uctuation [15] but also in understanding vortex dynamics in cuprate superconductors [16±24]. NMR is sensitive to the local ®eld distribution and ¯uctuation in the precession period of a nuclear spin. The static information is the peak position and the line width of NMR resonance signal, which re¯ect, respectively, the saddle-point ®eld and the local ®eld inhomogeneity in the mixed state. In the mixed state of type II superconductors, vortices generate spatial ®eld modulation. The

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K.H. Lee et al. / Physica C 364±365 (2001) 507±510

vortex spacing d for the square lattice is d ˆ …/0 = 1=2 Hext † , where /0 is the ¯ux quantum and Hext is the external ®eld. Then NMR spectrum just re¯ects local ®eld distribution at the probing nuclear sites. Since d is 33.3 nm at 1.8 T and the boron nuclei are 0.375 nm apart, the boron nuclei form a ®ne grid probing local magnetic ®eld in the vortex state. In this paper, we report vortex dynamics for YNi2 B2 C single crystal measured by 11 B NMR at various magnetic ®elds. 2. Experiment YNi2 B2 C single crystal was grown by the Ni2 B high-temperature ¯ux growth method. The sample was roughly 11  7  2 mm3 . The pulsed 11 B NMR measurements were carried out at 1.0±4.0 T parallel to the c-axis. The phase-alternating pulse sequences were employed to signi®cantly reduce the electromechanical vibration (ring-down) after pulses. The cryogenic measurements were performed in the Oxford continuous ¯ow cryostat (CF1200N). 3. Results and discussion Fig. 1 shows 11 B NMR spectrum at 1.8 T and 3.8 K. This line shape exhibits a typical asym-

metric shape with a long tail in the high frequency side, which reminds us of the characteristic ®eld distribution for Abrikosov vortex lattice. 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 ®eld distribution in the mixed state of YNi2 B2 C superconductor. Assuming that the local magnetic ®eld for a single vortex decreases as the modi®ed Bessel function [2], we sum up the respective local ®elds of 300  300 vortices in a unit cell of 300  300 pixels. Since we think that the absence of the shoulder may originate from distortion of vortex lattice due to pinning centers, we calculate local ®eld distribution accounting for random distortion of vortices from the regular lattice positions. Then, the core ®nding from our numerical calculation is that a small amplitude (2%) of random distortion is enough to wash out the left shoulder, as shown in Fig. 2. Furthermore, the line shape for larger distortion becomes much broader approaching a symmetric Gaussian shape. Indeed, at higher magnetic ®eld of 3.0 T for a stronger NMR signal, we have ®nally observed a typical NMR line shape, as shown in Fig. 3. From the line shape, we can unambiguously identify minimum ®eld Hm , saddlepoint ®eld Hs , and maximum ®eld HM at the vortex core. This line shape con®rms that vortices form a vortex lattice. The formation of vortex lattice at

Intensity (A.U.)

H=1.8 T, T=3.8 K

-0.2

-0.1

0.0

0.1

0..2

0..3

∆ f (MHz) Fig. 1. 11 B NMR spectrum of YNi2 B2 C at 1.8 T for ®eld parallel to the c-axis.

Fig. 2. Calculated 11 B NMR spectrum of YNi2 B2 C for the 1.23% randomly distorted vortex lattice of square type.

K.H. Lee et al. / Physica C 364±365 (2001) 507±510

509

Intensity (A.U.)

H=3.0 T, T=3.8 K

-0.10

-0.05

0.00

0.05

0.10

0.15

∆ f (MHz) Fig. 3. 11 B NMR spectrum of YNi2 B2 C at 3.0 T for ®eld parallel to the c-axis.

low temperature is due to dominance of the elastic energy. De®ning b ˆ …Hs Hm †=…HM Hm † as an aspect of the ®eld distribution, we can distinguish triangular and square lattices; b ˆ 0:07 for the triangular lattice and b ˆ 0:29 for the square lattice [25]. For YNi2 B2 C, b is measured to be 0:26  0:05, suggesting that the vortex lattice at 1.8 and 3.0 T parallel to the c-axis is a square type, consistent with the published reports [12±14]. It should be noted that this line shape has been rarely observed in the NMR measurements on the aligned powder samples of cuprate superconductors. Figs. 4 and 5 show all 11 B NMR data at 1.8 and 3.0 T parallel to the c-axis. Two ®gures show a

Fig. 4.

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B NMR data of YNi2 B2 C at 1.8 T.

Fig. 5.

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B NMR data of YNi2 B2 C at 3.0 T.

similar behavior. NMR shift in the mixed state is often dominated by a diamagnetic shift due to incomplete ®eld penetration into superconductors. Since local ®eld distribution in the mixed state has a logarithmic singularity at the saddle point, NMR shift mainly re¯ects a local magnetic ®eld at the point. Therefore, the shift re¯ects a static averaged ®eld value probed at the saddle point. Figs. 4 and 5 clearly exhibit a hysteresis of 11 B NMR shifts when the sample temperature is slowly warmed up and rapidly cooled down. The hysteresis con®rms that vortices do not come back to equilibrium positions due to pinning centers. The size of hysteresis is related to the amplitude of vortex distortion from regular lattice points. Line width measures static ®eld inhomogeneity seen by probing nuclei, which is related to the vortex distortion from the regular lattice points. Then, line width in Figs. 4 and 5 displays peculiar plateau behavior. Furthermore, the magnitude of line width is much smaller than a calculated value for triangular or square lattices of stationary vortex lattices. This deviation is more prominent at high temperature. This reduction of line width comes from vortex motion; namely, the large inhomogeneity of local ®eld for a rigid vortex lattice is averaged and the line width is narrowed down by rapid vortex ¯uctuation. Then, the time scale of vortex ¯uctuation can be estimated from the reduction ratio of line width from a calculated value for the rigid vortex lattices. Contrary to the shift and line width sensitive to the static or averaged ®eld distribution and

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inhomogeneity, the transverse relaxation rate 1=T2 is sensitive to vortex motion in a time scale of echo formation time, which is order of few tens microsecond. The transverse relaxation rate is also shown in Figs. 4 and 5. 1=T2 is temperature-independent in the normal state, which is determined by the homonuclear dipole±dipole interaction between boron nuclei. In the superconducting state, on the other hand, 1=T2 usually decreases since the local ®eld inhomogeneity blocks the nuclear dipole-dipole interaction between neighboring nuclei, and consequently 1=T2 is suppressed if vortices are stationary. This reduction is commonly observed for most conventional superconductors, where vortex motion is negligible due to low transition temperature, small penetration depth, and large coherence length. On the contrary, Figs. 4 and 5 highlight a double-peak behavior of 1=T2 , which is also a signature of signi®cant vortex motion. Since 1=T2 is sensitive to local ®eld ¯uctuation in a time scale of the echo formation time, these peaks prove that vortices ¯uctuate in the time scale of 10 ls. The peaks of 1=T2 and the reduction of line width con®rm that signi®cant vortex motion and ¯uctuation exist even for this low Tc and isotropic 3D superconductor. 4. Summary We have performed 11 B NMR measurements on YNi2 B2 C single crystal to investigate the vortex lattice dynamics. 11 B NMR shift shows a peculiar decrease and hysteresis at low temperature and the line width is signi®cantly reduced from the expected value for the rigid vortices. Furthermore, the transverse relaxation rate clearly shows double peaks. The temperature dependence of shift, line width, and transverse relaxation rate con®rm that

¯ux lines ¯uctuate signi®cantly in this low Tc and isotropic superconductor. Acknowledgements This work is supported by Korean Science and Engineering Foundation through Electron Spin Science Center at POSTECH. One of the authors (M. Lee) also acknowledges ®nancial support from Korea Research Foundation though grant no. 2000-015-DP0118 and from Korea Basic Science Institute through shared research equipment assistance program. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

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