Anomalous finite-size effect on the magnetostructural transition in CrN

We report a systematic investigation of the finite-size effect on magnetostructural transition in CrN based on a series of nanoparticle samples with various sizes prepared by a high-pressure method, leading to the discovery of anomalous critical behaviors near transition, especially for spin correlation length. Such critical anomalies are presumably attributed to the strong spin-lattice coupling in this nitride, because the spin correlation of fluctuation can be greatly affected by the concurrent structural distortion. Using the conventional Gibbs-Thomson theorem and size-dependent effect, the scaling relationship between transition temperature and spin correlation length is deduced by involving a term of the transition-induced volume change that rationalizes the role that the lattice degree of freedom played during magnetic ordering. A phenomenological model is also established for understanding the kinetics and dynamics of magnetic fluctuation at transition in a finite-size system. In addition, our results also show that CrN nanoparticles possess a compressed surface shell, which can be described by Laplace pressure, obeying a unique $\frac{1}{{d}^1.8}$ finite-size scaling law.