Structural, Optical and Single-domain Magnetic Features of the Noncollinear Ferrimagnetic Nano-spinel Chromites ACr$_2$O$_4$ (A = Ni, Co, and Mn)

Spinel chromites ACr$_2$O$_4$ with inherent magnetic geometrical frustration usually exhibit a noncollinear ferrimagnetic ground state when A are magnetic ions, with possibly crystallite-size dependent intriguing magnetic features. Here, we report single-domain magnetic properties of ACr$_2$O$_4$ (A = Ni, Co, and Mn) nanocrystals, with an average crystallite size of 18, 15 and 10 nm, exhibiting an optical energy gap of 2.87, 3.05 and 2.9 eV, respectively. The temperature dependence of magnetization indicates the main bulk magnetic transitions with a commonly coexisting spin-glass-like state and finite-size effects on the noncolinear ferrimagnetic transitions. An anomaly observed at Ts = 15, 24 and 10 K is attributed to the bulk magnetic transition to a canted antiferromagnetic state in NiCr$_2$O$_4$ and incommensurate spiral orders in CoCr$_2$O$_4$ and MnCr$_2$O$_4$ NCs, respectively. A further bulk magnetic transition to a commensurate spiral order is observed for CoCr$_2$O$_4$ NCs at a lock-in temperature Tl = 5 K much lower than that reported using bulk samples, while it is completely suppressed in the MnCr$_2$O$_4$ NCs. Finite-size effects and single-domain magnetic behaviors indicated by anomalous temperature-dependences of the coercive field and the hysteresis-loop squareness, mainly driven by a magnetocrystalline anisotropy, are discussed in comparison to results reported using bulk counterparts.