We address the fundamental task of inferring cross-document coreference and hierarchy in scientific texts, which has important applications in knowledge graph construction, search, recommendation and discovery. Large Language Models (LLMs) can struggle when faced with many long-tail technical concepts with nuanced variations. We present a novel method which generates context-dependent definitions of concept mentions by retrieving full-text literature, and uses the definitions to enhance detection of cross-document relations. We further generate relational definitions, which describe how two concept mentions are related or different, and design an efficient re-ranking approach to address the combinatorial explosion involved in inferring links across papers. In both fine-tuning and in-context learning settings, we achieve large gains in performance on data subsets with high amount of different surfaces forms and ambiguity, that are challenging for models. We provide analysis of generated definitions, shedding light on the relational reasoning ability of LLMs over fine-grained scientific concepts.