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Second magnetization peak (SMP) in hole-doped cuprates and iron pnictide superconductors has been widely explored. However, similar feature in the family of electron-doped cuprates is not common. Here, we report the vortex dynamics study in the single crystal of an electron-doped cuprate Pr$_{0.87}$LaCe$_{0.13}$CuO$_4$ superconductor using dc magnetization measurements. A SMP feature in the isothermal $M(H)$ was observed for $H$$\parallel$$ab$-planes. On the other hand, no such feature was observed for $H$$\parallel$$c$-axis in the crystal. Using magnetic relaxation data, a detailed analysis of activation pinning energy via collective creep theory suggests an elastic to plastic creep crossover across the SMP. Moreover, for $H$$\parallel$$ab$, a peak in the temperature dependence of critical current density is also observed near 7 K, which is likely be related to a dimensional crossover (3D-2D) associated to the emergence of Josephson vortices at low temperatures. The anisotropy parameter obtained $\gamma$ $\approx$ 8-11 indicates the 3D nature of vortex lattice mainly for $H$$\parallel$$c$-axis. The $H$-$T$ phase diagrams for $H$$\parallel$$c$ and $H$$\parallel$$ab$ are presented., Comment: 10 Pages, 8 Figures

The cooling of solids by optical means only using anti-Stokes emission has a long history of research and achievements. Such cooling methods have many advantages ranging from no-moving parts or fluids through to operation in vacuum and may have applications to cryosurgery. However achieving large optical cryocooling powers has been difficult to achieve except in certain rare-earth crystals. Through study of the emission and absorption cross sections we find that diamond, containing either NV or SiV (Nitrogen or Silicon vacancy), defects shows potential for optical cryocooling and in particular, NV doping shows promise for optical refrigeration. We study the optical cooling of doped diamond microcrystals ranging 10-250 microns in diameter trapped either in vacuum or in water. For the vacuum case we find NV-doped microdiamond optical cooling below room temperature could exceed 10 Kelvin, for irradiation powers of P< 100 mW. We predict that such temperature changes should be easily observed via large alterations in the diffusion constant for optically cryocooled microdiamonds trapped in water in an optical tweezer or via spectroscopic signatures such as the ZPL width or Raman line., Comment: 8 pages, 6 figures