We propose a spatial loss for unsupervised multi-channel source separation. The proposed loss exploits the duality of direction of arrival (DOA) and beamforming: the steering and beamforming vectors should be aligned for the target source, but orthogonal for interfering ones. The spatial loss encourages consistency between the mixing and demixing systems from a classic DOA estimator and a neural separator, respectively. With the proposed loss, we train the neural separators based on minimum variance distortionless response (MVDR) beamforming and independent vector analysis (IVA). We also investigate the effectiveness of combining our spatial loss and a signal loss, which uses the outputs of blind source separation as the reference. We evaluate our proposed method on synthetic and recorded (LibriCSS) mixtures. We find that the spatial loss is most effective to train IVA-based separators. For the neural MVDR beamformer, it performs best when combined with a signal loss. On synthetic mixtures, the proposed unsupervised loss leads to the same performance as a supervised loss in terms of word error rate. On LibriCSS, we obtain close to state-of-the-art performance without any labeled training data.