Observation of the lock-in effect in Cu_xTiSe₂ single-crystals

    Our local magnetization measurements have shown the presence of an unexpected lock-in effect in the superconducting Cu_xTiSe₂ 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 (ξ_c<<d). Even though there are similarities between Cu_xTiSe₂ 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 Cu_xTiSe₂ 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 (B_ab>B_c~0) up to a certain value of the applied field H_k (inset of Fig.1a). The value of H_k depends on the angle θ_H of an applied field and can be scaled by sin θ_H 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 H_k and lock-in field value H_L which results from the fits. H_k and H_L 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 Cu_xTiSe₂ [Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in Cu_xTiSe₂; 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 Cu_xTiSe₂ 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 Cu_xTiSe₂ single crystals;
Physical Review B 93, 100501(R) 2016.

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