We introduce a minimal spin model for describing the magnetic properties of CuCrO 2 . Our Monte Carlo simulations of this model reveal a rich magnetic field induced phase diagram, which explains the measured field dependence of the electric polarization. The sequence of phase transitions between different mutiferroic states arises from a subtle interplay between spatial and spin anisotropy, magnetic frustration and thermal fluctuations. Our calculations are compared to new measurements up to 92 T. PACS numbers: 75.85.+t, 75.30.Kz, 75.50.Ee Triangular lattice antiferromagnets (TLA) are widely studied in the field of frustrated magnetism. Complex orderings and rich phase diagrams arise because three antiferromagnetic interactions within a triangle cannot be simultaneously satisfied. Delafossite CuCrO 2 is a particularly clean example of a TLA where quasi-classical Cr 3+ S = 3/2 spins form a triangular lattice in the ab plane. [1, 2] The spins have outof-plane anisotropy and weak interlayer coupling that is one to two orders of magnitude smaller than the in-plane interactions. [3][4][5] The three spins of each triangle form a nearly 120• structure and all three sublattices form proper-screw spirals that propagate along the same [110] axis with propagation vector q = 0.329 (the spins rotate in and out of the ab plane). [1,6,7] The spiral can propagate along any of six directions (three choices for the [110] axis and two choices for the helicity) leading to six possible domains.The proper-screw spiral induces an electric polarization P along the spiral propagation vector. [3,[6][7][8][9][10][11][12] This allows us to probe phase transitions between spiral states at high applied magnetic fields H a , while the magnetization is largely insensitive to these transitions. The non-zero P is consistent with Arima's mechanism for multiferroic behavior, [13] where the spiral magnetic structure slightly influences the hybridization between the Cr d-orbitals and the O p-orbitals via spin-orbit coupling, creating a net P q. Thus, a pattern of electromagnetic domains forms below the magnetic ordering temperature that can be influenced by small electric and magnetic fields relative to the dominant exchange interactions. [6,10] The triangular layers of CuCrO 2 stack along the c-axis such that a Cr 3+ ion from one layer lies at the center of a triangle of Cr 3+ ions in the next layer. [1, 2, 9] The triangular lattice distorts by about 0.01% as a result of the spiral magnetic ordering, leading to two different exchange interactions, J and J , along different bonds of the triangle [3,10,11,14,15] (Fig. 1). Thermodynamic measurements show two close-lying phase transitions. Elastic neutron diffraction measurements suggest that below T N = 24.2 K, the triangular plane develops collinear spin correlations. A spiral long-range order appears below T MF = 23.6 K and also induces net P, possibly via a first-order transition. [8,15,16] The H a dependence of this spiral ordering is only partially explored in experiments and theory. [8,9,17,1...