Dominant surface barriers and marginal bulk pinning in molybdenum nitride microcrystals

We report on the superconducting properties and vortex pinning in micron-sized molybdenum nitride microcrystals. These hexagonally shaped crystals, with ∼16 μm lateral size and ∼2 μm thickness, were characterized using electrical transport measurements and local magnetization measurements with Hall sensors. The results show that the samples are predominantly in the cubic γ-Mo₂N phase with T_c ≈ 5.2 K, along with a minor fraction of the hexagonal δ-MoN phase (T_c ≈ 11 K). Electrical transport measurements reveal isotropic upper critical fields (H_c2), consistent with the cubic structure, with an estimated μ₀H_c2(0) ≈ 10 T corresponding to a short coherence length (ξ) of ∼5.8 nm. Local magnetization measurements confirm the coexistence of Mo₂N and MoN phases, affecting both magnetic field screening and reversible magnetization loops. Based on magnetic hysteresis loops and considering the critical state model, we find that the irreversible magnetization is dominated by surface barriers controlling vortex entry and exit, while bulk pinning is marginal, as evidenced by the rapid decay of the critical current with increasing field. This analysis reveals that vortex entry and exit in these microcrystals are dominated by size effects and surface barriers imposed by their well-defined geometry.