  Spin-orbit entangled magnetic dipoles, often referred to as pseudospins,
provide a new avenue to explore novel magnetism inconceivable in the weak
spin-orbit coupling limit, but the nature of their low-energy interactions
remains to be understood. We present a comprehensive study of the static
magnetism and low-energy pseudospin dynamics in the archetypal spin-orbit Mott
insulator Sr2IrO4. We find that in order to understand even basic magnetization
measurements, a formerly overlooked in-plane anisotropy is fundamental. In
addition to magnetometry, we use neutron diffraction, inelastic neutron
scattering and resonant elastic and inelastic x-ray scattering to identify and
quantify the interactions that determine the global symmetry of the system and
govern the linear responses of pseudospins to external magnetic felds and their
low-energy dynamics. We find that a pseudospin-only Hamiltonian is insufficient
for an accurate description of the magnetism in Sr2IrO4 and that
pseudospin-lattice coupling is essential. This finding should be generally
applicable to other pseudospin systems with sizable orbital moments sensitive
to anisotropic crystalline environments.
