Memorizing vocabulary is a key part of second language acquisition; however, many people rely on rote memorization. Despite the proven effectiveness of the mnemonic keyword method for learning vocabulary, its usage remains limited because coming up with keywords can be time-consuming and creatively demanding. Previous solutions for automatically generating mnemonic keywords are inflexible and outdated, given the advancements in the field of Natural Language Processing driven by large language models (LLMs) in recent years. This study's research questions focus on how LLMs can be used to generate personalized mnemonic keywords and how these personalized mnemonics impact the learning experience and outcome compared to non-personalized approaches. By designing Keymagine, an LLM-powered system for keyword generation, we show that LLMs can effectively generate keywords through In-Context Learning and be personalized through user feedback. In an experimental evaluation, students (N = 22) used both Keymagine-generated and other automatically generated keywords to learn 36 German words. Results demonstrated a significantly higher perceived helpfulness of Keymagine-generated keywords and a significantly higher rate of recall.