Europium (Eu)-cyclootetatrene (COT = C(8)H(8)) multidecker clusters (Eu(n)COT(n+1), n = 1-4) are studied by relativistic density functional theory calculations. These clusters are found to be thermodynamically stable with freely rotatable COT rings, and their total magnetic moments (MMs) increase linearly along with the number of Eu atoms. Each Eu atom contributes about 7 mu(B) to the cluster. Meanwhile, the internal COT rings have little MM contribution while the external COT rings have about 1 mu(B) MM aligned in opposite direction to that of the Eu atoms. The total MM of the Eu(n)COT(n+1) clusters can thus be generalized as 7n - 2 mu(B) where n is the number of Eu atoms. Besides, the ground states of these clusters are ferromagnetic and energetically competitive with the antiferromagnetic states, meaning that their spin states are very unstable, especially for larger clusters. More importantly, we uncover an interesting bonding characteristic of these clusters in which the interior ionic structure is capped by two hybrid covalent-ionic terminals. We suggest that such a characteristic makes the Eu(n)COT(n+1) clusters extremely stable. Finally, we reveal that for the positively charged clusters, the hybrid covalent-ionic terminals will tip further toward the interior part of the clusters to form deeper covalent-ionic caps. In contrast, the negatively charged clusters turn to pure ionic structures.