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We investigate a three component fermion mixture in the presence of weakattractive interactions. We use a combination of the equation of motion and theGaussian variational mean-field approaches, which both allow for simultaneoussuperfluid and magnetic ordering in an unbiased way, and capture the interplaybetween the two order parameters. This interplay significantly modifies thephase diagram, especially the superfluid-normal phase boundaries. In the closevicinity of the critical temperature and for small chemical potentialimbalances, strong particle-hole symmetry breaking leads to a phase diagramsimilar to the one predicted by Cherng et al. [Phys. Rev. Lett. 99, 130406(2007)], however, the overall phase diagram is markedly different: new chemicalpotential-driven first and second order transitions and triple points emerge aswell as more exotic second order multicritical points, and bicritical lineswith O(2,2) symmetry. We identify the terms which are necessary to capture thiscomplex phase diagram in a Ginzburg-Landau approach, and determine thecorresponding coefficients.

Global superfluid phase diagram of three component fermions with magnetic ordering