dHvA effect and superconductivity of MgB2 detected by AC torque method down to the fields below Hc2

doi:10.1016/j.physc.2004.10.010

Physica C: Superconductivity

Volume 417, Issues 3–4, 1 January 2005, Pages 110-118

https://doi.org/10.1016/j.physc.2004.10.010 Get rights and content

Abstract

We have grown high quality single crystals of MgB₂ by the encapsulation method. A new method which combines the magnetic torque method and the field modulation method is successfully employed to detect the dHvA oscillation and the AC response of the superconductor down to the fields below H_c2. The AC torque signal indicates that the surface superconductivity develops well above H_c2 and it evolves into the bulk superconductivity with decreasing field. The irreversible torque curve is observed at much higher fields than H_c2 and can be attributed to a pinning effect of the surface vortices. The superconducting transition detected by the AC torque method significantly broadens indicating that the supercondcuting fluctuation is not negligible. It is suggested that both the surface superconductivity and the fluctuation contribute considerably to the broadening of the resistive transition. We have found that the damping of the dHvA signal from the π band is very large around H_c2 due to the superconducting fluctuation and the pinning effect, but the damping rate becomes moderate with further decreasing field, implying that the superconducting gap may be small for the π band near H_c2.

Introduction

Since the discovery of high-T_c superconductor MgB₂ [1], extensive studies have been performed to reveal the interesting properties. It is now established that there are two kinds of bands which come from the boron σ and π bands, respectively [2], [3]. The electron–phonon interaction is considerably different for the two bands and accordingly there are almost two distinct superconducting gaps [4], [5], [6], [7], [8], [9].

However, under magnetic fields there are still several unsettled problems related with the peculiar feature of superconductivity. The transport measurements give larger H_c2’s than bulk measurements like magnetic, specific heat and thermal conductivity measurements [10], [11], [12], [13], [14], [15], [16]. Moreover, it is still controversial why the resistive superconducting transition broadens under magnetic fields. Several mechanisms like two superconducting gaps [17], a continuous vortex phase transition [18], superconducting fluctuations [14] and surface superconductivity [12], [13], [19] have been proposed for the broadening or the larger H_c2’s. The behavior of the two superconducting gaps under magnetic fields has been studied by point contact spectroscopy measurements, but seems to be still controversial. Some groups [20], [21], [22] report that the superconducting gap of the σ band closes at approximately the same H_c2 determined by the bulk measurements, while that of π band collapses at a much smaller field. On the other hand, other recent measurements on single crystals [23] and thin films [24] report that the both gaps survive up to a larger field than H_c2’s determined by the bulk measurements. Moreover, it is reported that an irreversible behavior in the magnetic torque extends well above H_c2 [25]. It has not been clarified whether these observations as well as the discrepancy arise from superconducting fluctuation, surface superconductivity, some unknown effects due to the two gaps or a combined effect of these.

It is therefore interesting and useful to gain more pieces of experimental evidence on superconducting fluctuation, surface superconductivity and supercondcuting gaps under magnetic fields. The AC magnetic measurement is useful to study these superconducting properties as well as to detect the dHvA effect. Particularly, the dHvA effect measuements below H_c2 can give information of the supercondcuting gap under magnetic fields [26]. However, since MgB₂ single crystals are very tiny, it is difficult to apply the conventional AC method which uses a modulation field and a pick up coil. In the present paper, we report the measurements of the AC magnetic torque to reveal the surface superconductivity, supercondcuting fluctuation, irreversibility due to the vortex pinning in the surface sheath as well as in the bulk, and the dHvA oscillations below and above H_c2 [27].

Section snippets

Experimental

Single crystals of MgB₂ were grown by the encapsulation technique. At the early stage of the crystal growth, we followed the procedure reported in Ref. [28]. Mg (4N purity) and B (3N purity) chunks with sizes of several mm were directly sealed in an evacuated Mo crucible using an electron beam welder. Various temperatures and durations of the heat treatment were tried to reveal appropriate conditions for the crystal growth. The crystal size and morphology are always almost the same although we

Results and discussion

Fig. 1 shows a typical dHvA oscillation detected by the AC torque method. A clear signal can be observed down to the low fields. Fig. 2 shows the angular dependence of the dHvA frequency in the [0 0 0 1]–[ $1 1 \bar{2} 0$ ] and [0 0 0 1]–[ $1 0 \bar{1} 0$ ] planes. Since the sample is very tiny and an accurate setting of the sample is difficult, the angle is determined considering the angular dependence of physical properties, particularly the dHvA frequency, after all the measurements have been completed. The original

Summary

We have observed the dHvA oscillation of MgB₂ down to the fields below H_c2 by the AC torque method. The dHvA signal or AC torque signal indicates that the surface superconductivity develops well above H_c2 and it evolves into the bulk superconductivity with decreasing field. It is likely that an appreciable pinning of the surface vortices takes place at fields above H_c2 where the irreversible torque curve is observed. Both the surface superconductivity and the surface pinning affect the dHvA

Acknowledgments

We thank Mr. M. Suzuki and Mr. M. Kikuchi for help in the low temperature experiments. This work is supported by grants from the MEXT of Japan and JSPS.

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Citation Excerpt :
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