Field-tuned incommensurate fan phase in an Ising-like triangular antiferromagnet

Using single-crystal neutron diffraction we report the observation of a field-tuned incommensurate phase in a field range just below magnetization saturation in the Ising-like triangular-lattice antiferromagnet Na${}_2$BaCo(PO${}_4$)${}_2$. This phase occurs for magnetic fields applied along the Ising axis and exhibits an in-plane incommensurate propagation vector that moves along the hexagonal Brillouin zone boundary upon varying field, challenging the simple $XXZ$ antiferromagnetic description of the system. Within a semiclassical framework, we successfully identify this pre-saturation phase as a coplanar fan phase and study the role of dipole-dipole interactions and bond-dependent exchange anisotropy in its stabilization mechanism. We additionally present a minimal exchange model including interlayer couplings, which reproduces the complex magnetic phase diagram in field including the observed field-dependence of the incommensurate propagation vector in the fan phase.