Paramagnetism on the temperature-magnetization dependences in a superconducting semiconductor solid solution (PbzSn1-z)1-xInxTe

In this work we studied magnetic properties of the semiconductor solid solution (PbzSn1-z)1-xInxTe in superconducting state. Peak-effect in magnetization vs magnetic field dependences was observed, and a paramagnetic response was obtained in superconducting state at certain magnetic fields and temperatures in a range of compounds. Possible relation between those effects is considered.


Introduction
Doping of a semiconductor solid solution of PbzSn1-zTe with In makes it possible to obtain materials with higher critical parameters of the superconducting (SC) transition (critical temperature Tc and critical magnetic field Hc2) compared to other SC semiconductors [1]. In addition, this material can exhibit properties of a topological crystalline insulator [2]. We studied magnetic properties of compounds in the region of maximum Tc based on previously obtained dependences of critical temperature on lead and indium content in the solid solution [1]: samples with indium content In (x) = 0.16, 0.2 and lead content Pb (z) = 0.3, 0.4, 0.5, 0.6 were used.

Experiment
Polycrystalline samples of (PbzSn1-z)1-xInxTe were obtained using the cermet method. The synthesis was carried out by fusion of the elementary In, Pb, Sn, Te materials taken in the appropriate proportions, in pumped and sealed quartz ampoules at a temperature of T ~ 900 -1000° C for 4 to 5 hours. Bulk samples have typical grain size d ≤ 300 μm. The homogeneity of the studied materials in terms of composition and concentration of dopants was monitored using an X-ray microanalyzer "Comеbax". The deviation from stoichiometry is about 1-2 at. %, and due to the fact that the content of In and Pb is high, it does not significantly affect the result. No noticeable traces of the second phase were detected in the studied samples. In addition to X-ray microanalysis, composition of the (PbzSn1-z)1-xInxTe thin films and the distribution of the components over the thickness was studied using the Auger method -electron spectroscopy with layer-by-layer etching with Ar + ions. The difference of values between the values of taken elemental composition and Auger profiles in the depth of the sample is about 1-2 at. % [3].
Measurements were carried out on a Quantum Design Physical Property Measurement System 14 using a vibrating sample magnetometer option. Magnetization data is obtained by oscillating the sample near a detection coil and synchronously detecting the induced voltage, which is subsequently converted IOP Publishing doi:10.1088/1742-6596/1697/1/012249 2 to magnetization. By using a compact gradiometer pickup coil configuration, a relatively large oscillation amplitude (1-3 mm peak) and sample oscillation frequency of 40 Hz, the system is able to resolve magnetization changes of less than 10 -6 emu.
When PbzSn1-zTe is doped with In impurity, a band of deep quasilocal impurity states with energy level EIn is formed in the energy spectrum of the compound. The band spectrum in the solid solution shifts from direct band structure in Pb1-xInxTe to reverse in Sn1-xInxTe, passing through a zero band gap state at a lead concentration z = 0.65( fig. 1). EIn also shifts from the conduction band of the material to its valence band with decreasing z. When the In level is located in the band gap, carriers in impurity states interact weakly with the band spectrum; at low temperatures (T < 20 K), long-term relaxation processes of nonequilibrium electrons are observed [4,5]; solid solutions with In level located in the valence band are characterized with an extremely high critical SC transition temperature Tc ≤ 4.2 K for semiconductors [1,6].

Results and discussion
Magnetization vs temperature m(T) and magnetization vs magnetic field m(H) dependences were obtained in the SC region of the materials at temperatures T > 2 K and in magnetic fields H < 30 kOe. An additional extremum is observed on the m(H) dependences in fields close to Hc2 and temperatures below Tc, which we interpret as peak-effect ( fig.2). This effect is observed in (Pb0.5Sn0.5)0.8In0.2Te, (Pb0.4Sn0.6)0.8In0.2Te, (Pb0.3Sn0.7)0.84In0.16Te and (Pb0.4Sn0.6)0.84In0.16Te compounds [7]. Peak amplitude increases with temperature decrease, and the secondary peak position on the m(H) dependence shifts to the region of lower magnetic fields.  3 m(T) dependences are characteristic for a type-II superconductor in most studied samples -an increase of the diamagnetic signal with a decrease in the magnetic field ( fig.3, 4). However, in (Pb0.4Sn0.6)0.8In0.2Te compound at H > 7 kOe and in (Pb0.4Sn0.6)0.84In0.16Te at H > 11kOe paramagnetic behavior can be observed on the curves obtained in zero field cooling (ZFC) regime ( fig.5). This is commonly referred to as the paramagnetic Meissner effect (PME, Wohlleben effect) and can be caused by inhomogenous superconducting transition [8]. If the outer regions of the sample become SC first, the flux becomes trapped in the sample, and is further compressed, creating a critical Bean region inside the superconductor. The magnetic moment of the sample in this case is a sum of the diamagnetic moment created by outer shielding currents and the paramagnetic moment of the inner pinning currents, which can lead to a paramagnetic total response. In our samples PME occurs in the same range of temperatures and magnetic fields as the peak effect on the m(H) dependences. We assume that both phenomena are caused by specific properties of the vortex lattice and its interaction with pinning centers at certain H and T.   It should be noted however that some samples that show peak effect on m(H) dependences do not exhibit PME on m(T) dependencies in any magnetic fields in studied range of T. Since magnetization of the studied compounds in SC state depends on history of H and T changes, the effects that occur in m(H) and m(T) dependencies at the same T and H can't be directly compared due to different history.

Conclusions
Magnetic properties of superconducting solid solution (PbzSn1-z)1-xInxTe with various concentrations of lead and indium were studied. In addition to the peak effect discovered earlier, paramagnetic Meissner effect was observed on the m(T) dependences obtained in the ZFC regime in (Pb0.4Sn0.6)0.8In0.2Te and (Pb0.4Sn0.6)0.84In0.16Te compounds. Since peak effect at m(H) and paramagnetism at m(T) appear in the same range of temperatures and magnetic fields, and since both effects are caused by features of vortex dynamics in the material, we can assume that those effects are related. Possible origins of both paramagnetism and peak-effect in (PbzSn1-z)1-xInxTe are still under discussion. We assume that PME in studied solid solutions is caused by flux capturing inside a superconducting sample and its consequent compression with lowering temperature due to inhomogeneities of SC transition.