The channel knowledge map (CKM) enables efficient construction of high-fidelity mapping between spatial environments and channel parameters via electromagnetic information analysis. Nevertheless, existing studies are largely confined to single-antenna systems, failing to offer dedicated guidance for multi-antenna communication scenarios. To address the inherent conflict between traditional real-value pathloss map and multi-degree-of-freedom (DoF) coherent beamforming in B5G/6G systems, this paper proposes a novel concept of BeamCKM and CKMTransUNet architecture. The CKMTransUNet approach combines a UNet backbone for multi-scale feature extraction with a vision transformer (ViT) module to capture global dependencies among encoded linear vectors, utilizing a composite loss function to characterize the beam propagation characteristics. Furthermore, based on the CKMTransUNet backbone, this paper presents a methodology named M3ChanNet. It leverages the multi-modal learning technique and cross-attention mechanisms to extract intrinsic side information from environmental profiles and real-time multi-beam observations, thereby further improving the map construction accuracy. Simulation results demonstrate that the proposed method consistently outperforms state-of-the-art (SOTA) interpolation methods and deep learning (DL) approaches, delivering superior performance even when environmental contours are inaccurate. For reproducibility, the code is publicly accessible at https://github.com/github-whh/BeamCKM.