Magnetic investigations of phase transitions, exchange interactions, and magnetic ground state in nanosheets of β -Co(OH)₂

Detailed investigations of the magnetic properties of the layered system β -Co(OH)₂ are presented. X-ray diffraction and scanning electron microscopy of the sample show it to consist of hexagonal nanosheets with thickness  ≈30 nm and width ∼100 nm–200 nm. Analysis of its measured magnetization (M) as a function of temperature ( T   =  2 K to 300 K) and magnetic field (H up to 90 kOe) yields a Neel temperature T_N  =  9.2 K. This lower T_N  =  9.2 K, compared to T _N  =  11.6 K reported for bulk β -Co(OH)₂, is due to finite-size effects. Analysis of the data for T   >   T_N shows that the M versus T data does not quite fit the Curie–Weiss law since both the Curie constant C and Weiss temperature θ have noticeable temperature dependence. This temperature dependence is interpreted to be due to the effect of spin–orbit coupling, yielding a low-temperature effective spin S   =  1/2 ground state with magnetic moment µ   =  4.745 µ_B and g   =  5.479. For T   <   T_N, M versus H data show two transitions, first at H_C1  ≃  15 kOe and second at H_C2  ≃  32 kOe. The transition at H_C1 is a spin-flop transition and H_C2 is due to forced alignment of the spins yielding saturation magnetization M _S  =  160 emu g⁻¹ at 2 K, in agreement with the calculated M_S  =  163 emu g⁻¹ for the complete alignment of the spins at T   =  0 K for the spin S   =  1/2 ground state with g   =  5.479. The fitting of the M versus T data for T   >   T_N to the high temperature series for S   =  1/2 XY model yields the in-plane ferromagnetic exchange constant J₁/ k _B  =  (1.8  ±  0.2) K for Co²⁺ ions, with the interplane exchange constant J₂/ k _B  ≃  −0.2 K determined from the magnitude of T_N. The temperature dependence of H _C1 and H_C2 is presented and discussed. (paper)