Title: Superconductor-altermagnet memory functionality without stray fields

Abstract: A novel class of antiferromagnets, dubbed altermagnets, exhibit a non-relativistically spin-split band structure reminiscent of $d$-wave superconductors, despite the absence of net magnetization. This unique characteristic enables utilization in cryogenic stray-field-free memory devices, offering the possibility of achieving high storage densities. In this Letter, we determine how a proximate altermagnet influences the critical temperature $T_c$ of a conventional $s$-wave singlet superconductor. Considering both a bilayer and trilayer, we show that such hybrid structures may serve as stray-field free memory devices where the critical temperature is controlled by rotating the N\'eel vector of one altermagnet, providing infinite magnetoresistance. Furthermore, our study reveals that altermagnetism can coexist with superconductivity up to a critical strength of the altermagnetic order as well as robustness of the altermagnetic influence on the conduction electrons against non-magnetic impurities, ensuring the persistence of the proximity effect under realistic experimental conditions.