Observation of the lock-in effect in CuxTiSe2 single-crystals

    Our local magnetization measurements have shown the presence of an unexpected lock-in effect in the superconducting CuxTiSe2 single crystals. Lock-in effect develops in superconductors when vortices penetrating into the sample remain locked along the planes even though magnetic field is not parallel with the planes. This effect is usually observed in high temperature superconductors (HTS) with layered structure characterized by large mass anisotropy (Γ>7), large Ginzburg-Landau parameter (κ>10) or coherence length smaller than the interlayer distance (ξc<<d). Even though there are similarities between CuxTiSe2 and HTS (e.g. the phase diagram), with the small anisotropy and Ginzburg-Landau parameter values (Γ=1.7, κ<10) no intrinsic lock-in is expected in this compound. Despite that, we could observe its signatures in CuxTiSe2 through the local Hall probe measurements of a magnetic induction B. Comparison of the in-plane and out-of-plane components of magnetic field B induced in the sample showed that for tilted magnetic fields most of the vortices remain aligned with the ab-planes (Bab>Bc~0) up to a certain value of the applied field Hk (inset of Fig.1a). The value of Hk depends on the angle θH of an applied field and can be scaled by sin θH to a single value which is one of the lock-in effect signatures (Fig.1b). For higher magnetic fields the field dependence of the vortex direction could be well described assuming that vortices remain partially locked in the planes forming a staircase structure (Fig.2 - red curves calculated from a model shown in the inset). From experimental data and parameters deduced from the fits we constructed the vortex phase diagram shown in the Fig.3. A good agreement between the model and the data is proved by a good agreement of the experimentally obtained Hk and lock-in field value HL which results from the fits. Hk and HL points form a boundary with lock-in vortex state below and the vortex staircase structure above. For the highest angles and magnetic fields vortices finally align with the applied field. Since the lock-in effect in this compound cannot be intrinsic, our results indicate the existence of a strong modulation of the vortex core energy along the c-axis of unclear origin. Light to this problem might be brought by the recent X-ray experiments on CuxTiSe2 [Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in CuxTiSe2; A. Kogar, G.A. de la Pena, S. Lee, Y. Fang, S.X.-L. Sun, D.B. Lioi, G. Karapetrov, K.D. Finkelstein, J.P.C. Ruff, P. Abbamonte, S. Rosenkranz: arXiv:1608.05957 (2016)] which revealed the presence of charge density waves domain walls in the sample. These domain walls could play a role in the emergence of superconductivity in CuxTiSe2 and might be also responsible for the lock-in effect in this compound.

Z. Medvecká, T. Klein, V. Cambel, J. Šoltýs, G. Karapetrov, F. Levy-Bertrand, B. Michon, C. Marcenat, Z. Pribulová and P. Samuely:
Observation of a transverse Meissner effect in CuxTiSe2 single crystals;
Physical Review B 93, 100501(R) 2016.

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