Phase Diagram of a Geometrically-Frustrated Triangular-Lattice Antiferromagnet in a Magnetic Field*

The magnetic phase diagram of a geometrically-frustrated triangular-lattice antiferromagnet is evaluated as a function of magnetic field and anisotropy using a trial spin state built from harmonics of a fundamental ordering wavevector. A non-collinear incommensurate state, observed to be chiral and ferroelectric in CuFeO$_2$, appears above a collinear state with 4 sublattices (SLs). A previously unobserved collinear 5-SL phase may be accessible in a magnetic field for a non-stoichiometric compound with excess or deficient oxygen. The apparent absence of multiferroic behavior for predicted chiral, non-collinear 5-SL states poses a challenge to theories of the ferroelectric coupling in CuFeO$_2$.