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In the quest for novel, scalable and energy-efficient computing technologies, spin-based logic devices are being extensively explored due to their potential for nonvolatility, small cell area, and low operational power. Spin torque majority gate (STMG) is one of the most promising options for beyond CMOS nonvolatile logic circuits for normally-off computing. However, significant problems arose with cascade-ability, signal nonreciprocity, and complicated circuit configurations based on STMG. In this paper, a novel magnetic majority gate (MMG) logic has been proposed, utilizing both spin transfer torque and spin–orbit torque effects. A logic family including and/nand and or/nor functions can be achieved with an easy configuration and under a stable operation. Communication between logic units is realized by spin current injection through a nonferromagnetic metal wire to ensure its cascade-ability and nonreciprocity to design multiple logic-depth circuits. With all of these advantages, the proposed cascadable MMGs can be utilized to design logic functions such as the BUFFER/ NOT, XOR/ XNOR, and complicated logic gates, which pave the pathway for designing robust and comprehensive logic circuits using full spintronic devices. [ABSTRACT FROM AUTHOR]