Non-reciprocal spin wave propagation in magnetic bilayer structures

One of the peculiar features of waves in general is their option of non-reciprocal dispersion relation, meaning the modification of the transport characteristics upon reversal of the waves’ propagation direction. Non-reciprocity in case of Magnetostatic Surface Spin Waves (MSSW) can be caused by various factors, such as surface anisotropy [1], interfacial Dzyaloshinskii-Moriya interaction [2] or inhomogeneous saturation magnetization across the film thickness [3]. Recently, it has been shown that a strong non-reciprocal propagation can be induced by the dynamic dipole-dipole interaction between two magnetic layers in spin-valve-like structures, for which the relative magnetization orientation in remanence is stabilized in antiparallel configuration [4]. In the present work we investigate the frequency non-reciprocity in ferromagnetic bilayer systems, where a nonmagnetic thin Ru interlayer is used to achieve antiferromagnetic alignment at zero field. Using conventional Brillouin light scattering, we perform systematic measurements of the frequency non-reciprocity as a function of an external magnetic field. As expected [4], for antiparallel alignment of the magnetic moments in the two layers we observe a large frequency non-reciprocity up to a few GHz, which vanishes when the relative magnetization orientation switches to the parallel configuration. Moreover, a non-monotonous dependence of the frequency non-reciprocity is found in the transition from the antiparallel to the parallel orientation, where the maximum of the frequency shift corresponds to the spin-flop phase. By varying the parameters of the bilayer structures, the non-reciprocal propagation at the spin-flop transition is studied. We demonstrate that by adjusting the strength of the exchange coupling between the two ferromagnetic layers via the appropriate choice of the stack parameters, one can precisely control the non-reciprocal propagation of spin waves via the field-driven magnetization reorientation.