AC magnetic response of superconducting single crystals exhibiting a second peak on the DC magnetization curves
Introduction
The AC magnetic response registered at usual frequencies f (roughly, from ∼1 Hz up to several kHz) and amplitudes hAC (below 15 Oe) in the presence of a DC magnetic field H is often considered to investigate the vortex pinning properties of superconductors, the vortex phase diagram, and the dynamics of vortices [1], [2], [3], [4], [5], [6], [7], [8]. Moreover, in the framework of the strong pinning theory, a spectroscopy of the pinning landscape based on the linear AC magnetic response has been proposed [9].
One of the most relevant features for the vortex phase diagram of superconductors in the presence of relevant vortex pinning is the peak occurring in the H variation of the absolute value of the DC magnetization of single crystal specimens with randomly distributed vortex pinning centres. In the case of weakly pinned low- and high-temperature superconductors, the onset field Hon for the enhancement of the effective critical current density Jc with increasing H corresponding to this peak is located in the vicinity of the DC irreversibility line IL (defined by a vanishing irreversible magnetization). This is called the peak effect (PE) [10], [11], [12], [13], [14], [15], [16], where the strong thermally induced vortex fluctuations close to the IL generate dynamic history effects.
By increasing pinning, the PE is substituted by the so called second magnetization peak (SMP) [17], with Hon and the peak field Hp located well below the IL, leading to fishtail shaped DC magnetic hysteresis curves. In the last years, several SMP models have been more often considered, such as those based on a crossover in the collective pinning regime [18], the presence of twin boundaries [19], the square-to-rhombic structural vortex-lattice transition [20], an order-disorder transition [21], or a continuous pinning-induced disordering of the low-H quasi-ordered vortex solid (the Bragg vortex glass [22], stable against dislocation formation) between Hon and Hp [23], [24], [25]. The latter is supported by a crossover elastic vortex creep-plastic creep accompanying the SMP (see [26], for example), and offers a simple explanation for the increase of the effective pinning, through a better accommodation of vortices to the pinning landscape in a disordered vortex system.
A large, specific, nonmonotonic distortion of the critical-state related (nonlinear, dissipative) AC magnetic signal [27] in the temperature T range of a PE is expected [28], [29], since both are fully generated close to the IL. However, the conditions in which the presence of a DC SMP leads to a nonmonotonic AC magnetic response are not clear. For example, the DC and AC magnetic results obtained for 2H–NbSe2 single crystals [30] revealed a crossover from weak collective pinning to a strong pinning regime across a DC SMP which is not associated with a peak in the AC signal. On the other hand, the observation of the SMP in (Tl, Bi)-1212 single crystals by AC susceptibility measurements was reported in Ref. [31], with no change in the vortex dynamics across the SMP. At the same time, the complex, nonmonotonic temperature variation of the AC signal of Ba0.5K0.5Fe2As2 single crystals in applied H has been attributed to a peculiar superposition of an SMP with a PE [32].
In this work, we analyze the AC magnetic behaviour of La2−xSrxCuO4 and BaFe2(As1−xPx)2 (122-type) single crystals [33], [34] exhibiting a well developed DC SMP, to elucidate the conditions in which the AC magnetic response at usual frequencies and amplitudes is significantly affected by the presence of a DC SMP. It was found that the linear AC signal remains undistorted across the SMP, suggesting low values of the Campbell penetration depth. The nonlinear (Bean) AC regime (i. e., a finite penetration of the AC critical state) has been attained in the SMP domain for specimens with strong demagnetization effects. In these conditions, one can observe an SMP-related nonmonotonic AC signal behaviour, but only for the DC field dependence of the out of phase component of the AC magnetic moment. This is simply generated by the modulation of the penetration distance of the AC critical state due to the increase of the effective pinning between Hon and Hp.
Section snippets
Samples and experiments
We performed detailed DC and AC magnetic measurements for an overdoped La2−xSrxCuO4 single crystal [33] (x = 0.2, denoted LaSrCuO), having the critical temperature Tc ∼30.5 K (determined at the onset of the diamagnetic DC signal in H = 10 Oe), and for two BaFe2(As1−xPx)2 (P-Ba122) specimens [34]: an underdoped sample (P-Ba122ud, nominal x = 0.28, Tc ∼28 K), and an optimally doped one (P-Ba122op, x = 0.30, Tc ∼29 K). The in-plane characteristic size of all specimens is of the order of 1 mm,
Results and discussion
The analysis below refers first to the case of negligible demagnetization effects (La2−xSrxCuO4). It is known that the single crystals from this superconducting system exhibit an SMP for a wide doping range and in a large temperature interval. With H oriented along the c axis, the SMP is missing only in a relatively narrow doping interval around x ∼ 1/8, where a static stripe structure develops [36], [37].
Fig. 1(a) illustrates the m(H) curves for LaSrCuO at several temperatures, with a
Conclusions
In summary, the analysis of the DC magnetic hysteresis curves and of the AC magnetic response at usual frequencies and amplitudes registered for several superconducting single crystals (cuprates and pnictides) exhibiting a well developed DC SMP leads to the following conclusions:
- (i)
In the absence of strong demagnetization effects, the linear regime the of the AC magnetic response extends above the Hp(T) line.
- (ii)
No distortion of the linear AC signal in the SMP domain can be detected within the high
Acknowledgements
Work supported by the Romanian Ministry of Research and Innovation through POC (European Regional Development Fund, Operational Fund Competitiveness), Project P-37_697 number 28/01.09.2016, PED88/2016, and Core Programme PN18-110101. The kind assistance of the Alexander von Humboldt Foundation is gratefully acknowledged.
References (50)
- et al.
Physica C
(2015) - et al.
Supercond. Sci. Technol.
(2017) - et al.
Phys. Rev. B
(2010) - et al.
AIP Adv.
(2016) - et al.
Supercond. Sci. Technol.
(2016) - et al.
Phys. Rev. Lett.
(2001) - et al.
Phys. Rev. Lett.
(2008) - et al.
Supercond. Sci. Technol.
(2017) - et al.
Appl. Phys. Lett.
(2014) - et al.
Phys. Rev. Lett.
(2015)