  Laser cooled lanthanide atoms are ideal candidates with which to study strong
and unconventional quantum magnetism with exotic phases. Here, we use
state-of-the-art closed-coupling simulations to model quantum magnetism for
pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical
lattice. In contrast to the widely used single-channel Hubbard model
description of atoms and molecules in an optical lattice, we focus on the
single-site multi-channel spin evolution due to spin-dependent contact,
anisotropic van der Waals, and dipolar forces. This has allowed us to identify
the leading mechanism, orbital anisotropy, that governs molecular spin dynamics
among erbium atoms. The large magnetic moment and combined orbital angular
momentum of the 4f-shell electrons are responsible for these strong anisotropic
interactions and unconventional quantum magnetism. Multi-channel simulations of
magnetic Cr atoms under similar trapping conditions show that their
spin-evolution is controlled by spin-dependent contact interactions that are
distinct in nature from the orbital anisotropy in Er. The role of an external
magnetic field and the aspect ratio of the lattice site on spin dynamics is
also investigated.
