We observe a spontaneous parity breaking bifurcation to a ferromagnetic state in a spatiallytrapped exciton-polariton condensate. At a critical bifurcation density under nonresonant excitation, the whole condensate spontaneously magnetizes and randomly adopts one of two ellipticallypolarized (up to 95% circularly-polarized) states with opposite handedness of polarization. The magnetized condensate remains stable for many seconds at 5 K, but at higher temperatures it can flip from one magnetic orientation to another. We optically address these states and demonstrate the inversion of the magnetic state by resonantly injecting 100-fold weaker pulses of opposite spin. Theoretically, these phenomena can be well described as spontaneous symmetry breaking of the spin degree of freedom induced by different loss rates of the linear polarizations.Condensation of exciton-polaritons (polaritons) spontaneously breaks the global phase symmetry [1][2][3][4][5]. Owing to their easy optical interrogation, high-speed (ps) interactions, and macroscopic coherence (over hundreds of microns) [6], polariton condensates are excellent candidates to probe and exploit for sensing [7,8], spinoptronics [9][10][11], new optoelectronic devices [12][13][14], and quantum simulators [15]. The driven-dissipative multicomponent polariton system can undergo additional bifurcations and condense into states which are not eigenstates of the single-particle Hamiltonian, but many-body states with reduced symmetry [16,17]. Thus, we should expect that two-component exciton-polariton condensates can also show spontaneous symmetry breaking bifurcations in their polarization state. Spin studies of microcavity polaritons have been of great interest in recent years [18][19][20][21][22][23][24][25][26][27][28][29]. However, spontaneous symmetry-breaking bifurcation of spin has not been observed before.Here, we demonstrate spontaneous magnetization in an exciton-polariton condensate, as a direct result of bifurcations in the spin degree of freedom. Utilizing an optically trapped geometry, condensates spontaneously emerge in either of two discrete spin-polarized states that are stable for many seconds, > 10 10 longer than their formation time. These states emit highly circularly-polarized coherent light (up to 95%) and have opposite circular polarizations. The condensate stochastically condenses in a left-or right-circularly polarized state, with an occurrence likelihood that can be controlled by the ellipticity * ho278@cam.ac.uk † jjb12@cam.ac.uk of the nonresonant pump. The two spin-polarized states can be initialized and switched from one state to another with weak resonant optical pulses. Our system has potential applications in sensing, optical spin memories and spin switches, and it can be implemented for studying long-range spin interactions in polariton condensate lattices. This article is structured as follows: in Section I we review trapped polariton condensates and the current understanding of polarization in untrapped polariton condensates. In Section ...