This research article examines how microscale size effects and exponential gradedness impact the properties of shear harmonic (SH) wave transmission in a cobalt ferrite (CoFe \(_2\) O \(_4\) ) piezomagnetic (PM) material. The layer is coupled with a substrate that exhibits microscale size effects. The article derives dispersion relations in determinant form for both open and short magnetic scenarios. Specific instances are derived and compared to existing results for validation purposes. The article incorporates graphical diagrams that illustrate how the phase velocity curve is affected by different factors, including characteristic length, layer thickness, exponential gradient, and PM material characteristics. The graphs also analyze the magnetomechanical coupling factor, magnetomechanical coupling coefficient, and group velocity.
