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Abstract In this work we examine synthetic antiferromagnetic structures consisting of two, three, and four antiferromagnetic coupled layers, i.e. bilayers, trilayers, and tetralayers. We vary the thickness of the ferromagnetic layers across all structures and, using a macrospin formalism, find that the nearest neighbor exchange interaction between layers is consistent across all structures for a given thickness of the ferromagnetic layer. Our model and experimental results demonstrate significant differences in how the static equilibrium states of even and odd-layered structures evolve as a function of the external field. Even layered structures continuously evolve from a collinear antiferromagnetic state to a spin canted non-collinear magnetic configuration that is mirror-symmetric about the external field. In contrast, odd-layered structures begin with a ferrimagnetic ground state; at a critical field, the ferrimagnetic ground state evolves into a non-collinear state with broken symmetry. Specifically, the magnetic moments found in the odd-layered samples possess stable static equilibrium states that are no longer mirror-symmetric about the external field after a critical field is reached. 

In this work, we extract the temperature-dependent bilinear J1 and biquadratic J2 exchange energy densities in permalloy–ruthenium-based synthetic antiferromagnet bilayers, trilayers, and tetralayers. In our samples, the ruthenium interlayer thickness is fixed to be 1 nm across all structures, but we consider permalloy layers that are 3 and 9 nm thick. To the best of our knowledge, this work represents the first time that the influence of both the ferromagnetic layer thickness as well as the total number of ferromagnetic layers on biquadratic exchange interactions has been examined together. Across all samples, we observe a significant increase in the strength of J2 relative to J1 as the temperature is lowered. We also observe trends indicating that J2 is sensitive to both the thickness and the total number of permalloy layers. Our analysis suggests that in structures with thicker and more numerous ferromagnetic layers, J2 originates from interfacial roughness effects between the magnetic layer and the spacer layer. In samples with thinner and less numerous permalloy layers, multiple mechanisms must contribute to J2. These findings provide new insights into the complexity of interlayer exchange interactions in synthetic antiferromagnets, which will aid in interpreting ongoing magnonic and spintronic experimental studies of synthetic antiferromagnets.