Title: Modeling Magnetic Anisotropy of Single Chain Magnets in $|d/J| \geq 1$ Regime,
Abstract: Single molecule magnets (SMMs) with single-ion anisotropies $\mathbf d$,
comparable to exchange interactions J, between spins have recently been
synthesized. In this paper, we provide theoretical insights into the magnetism
of such systems. We study spin chains with site spins, s=1, 3/2 and 2 and
on-site anisotropy $\mathbf d$ comparable to the exchange constants between the
spins. We find that large $\mathbf d$ leads to crossing of the states with
different $M_S$ values in the same spin manifold of the $\mathbf d = 0$ limit.
For very large $\mathbf d$'s we also find that the $M_S$ states of the higher
energy spin states descend below the $M_S$ states of the ground state spin
manifold. Total spin in this limit is no longer conserved and describing the
molecular anisotropy by the constants $D_M$ and $E_M$ is not possible. However,
the total spin of the low-lying large $M_S$ states is very nearly an integer
and using this spin value it is possible to construct an effective spin
Hamiltonian and compute the molecular magnetic anisotropy constants $D_M$ and
$E_M$. We report effect of finite sizes, rotations of site anisotropies and
chain dimerization on the effective anisotropy of the spin chains.