The article reports the experimental observation of a spontaneous anomalous Hall effect (AHE) in epitaxial thin-film Mn5Si3 with a vanishingly small net magnetic moment, indicating a novel form of magnetic order known as d-wave alternarmagnetism. This phase exhibits strong time-reversal (T) symmetry breaking without a significant net magnetization, which is distinct from conventional ferromagnetic or antiferromagnetic orders. The AHE is attributed to the unconventional d-wave magnetic structure, which is supported by first-principles calculations and symmetry analysis. The observed AHE is comparable in strength to conventional s-wave ferromagnetism, suggesting that this phase could have significant implications for spintronics and magnetic topology. The study highlights the unique properties of Mn5Si3, including its hexagonal crystal structure and the absence of geometric frustration, which allows for the emergence of this novel magnetic phase. The AHE is found to be robust and not diminished by strong magnetic fields, and its spontaneous nature is consistent with the absence of a net magnetic moment. Theoretical analysis confirms that the observed AHE arises from the d-wave magnetic order, which is characterized by alternating spin polarization in both real and momentum space. The results suggest that Mn5Si3 is a promising candidate for exploring unconventional magnetic phases with potential applications in non-dissipative electronics, valleytronics, and spintronics. The study also compares Mn5Si3 with other materials and highlights its unique combination of high transition temperature and abundant elements, making it a valuable material for further research.The article reports the experimental observation of a spontaneous anomalous Hall effect (AHE) in epitaxial thin-film Mn5Si3 with a vanishingly small net magnetic moment, indicating a novel form of magnetic order known as d-wave alternarmagnetism. This phase exhibits strong time-reversal (T) symmetry breaking without a significant net magnetization, which is distinct from conventional ferromagnetic or antiferromagnetic orders. The AHE is attributed to the unconventional d-wave magnetic structure, which is supported by first-principles calculations and symmetry analysis. The observed AHE is comparable in strength to conventional s-wave ferromagnetism, suggesting that this phase could have significant implications for spintronics and magnetic topology. The study highlights the unique properties of Mn5Si3, including its hexagonal crystal structure and the absence of geometric frustration, which allows for the emergence of this novel magnetic phase. The AHE is found to be robust and not diminished by strong magnetic fields, and its spontaneous nature is consistent with the absence of a net magnetic moment. Theoretical analysis confirms that the observed AHE arises from the d-wave magnetic order, which is characterized by alternating spin polarization in both real and momentum space. The results suggest that Mn5Si3 is a promising candidate for exploring unconventional magnetic phases with potential applications in non-dissipative electronics, valleytronics, and spintronics. The study also compares Mn5Si3 with other materials and highlights its unique combination of high transition temperature and abundant elements, making it a valuable material for further research.