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Supervised deep learning needs a large amount of labeled data to achieve high performance. However, in medical imaging analysis, each site may only have a limited amount of data and labels, which makes learning ineffective. Federated learning (FL) can help in this regard by learning a shared model while keeping training data local for privacy. Traditional FL requires fully-labeled data for training, which is inconvenient or sometimes infeasible to obtain due to high labeling cost and the requirement of expertise. Contrastive learning (CL), as a self-supervised learning approach, can effectively learn from unlabeled data to pre-train a neural network encoder, followed by fine-tuning for downstream tasks with limited annotations. However, when adopting CL in FL, the limited data diversity on each client makes federated contrastive learning (FCL) ineffective. In this work, we propose an FCL framework for volumetric medical image segmentation with limited annotations. More specifically, we exchange the features in the FCL pre-training process such that diverse contrastive data are provided to each site for effective local CL while keeping raw data private. Based on the exchanged features, global structural matching further leverages the structural similarity to align local features to the remote ones such that a unified feature space can be learned among different sites. Experiments on a cardiac MRI dataset show the proposed framework substantially improves the segmentation performance compared with state-of-the-art techniques.