negative eigenvalue of $\rho^{T_1}$, and $T_1$ denotes\
the partial transpose with respect to the first system. The negativity ${\cal N}$ is related to the trace norm of $\rho^{T_1}$ via $${\cal N(\rho)}=\frac{\|\rho^{T_1}\|_1-1}{2},$$ where the trace norm of $\rho^{T_1}$ is equal to the sum of the absolute values of the eigenvalues of $\rho^{T_1}$. In this paper, we will use the concept of negativity to study entanglement in (1/2,1) mixed-spin systems.

As shown in most previous works, models with the NN exchange interactions are considered and it is not easy to have pairwise entanglement between the NNN spins [@M_Osborne; @M_Osterloh]. It is true that there exist some quasi-one-dimension compounds offering us systems with NNN interactions. Bose and Chattopadhyay [@Ibose] and Gu et al. [@Gu] have investigated entanglement in spin-half Heisenberg chain with NNN interactions. In our paper here, we study entanglement properties not only in the (1/2,1) mixed-spin systems only with NN interactions, but also in the system with NNN interactions.

Entanglement in a system with a few spins displays general features of entanglement with more spins. For instance, in the anisotropic Heisenberg model with a large number of qubits, the pairwise entanglement shows a maximum at the isotropic point [@Gu]. This feature 