This study present novel configurations for magnetically tunable AND/XOR logic gates, employing ring resonators, cross-shaped waveguides, and Terfenol-D cylinders integrated into a solid-solid phononic crystal. The proposed design provides the varying magnetic field intensities of Terfenol-D within the MHz frequency spectrum. These gates boast an ultra-compact design with a footprint measuring just 249× \(\:{10}^{-6}\) m² and 129× \(\:{10}^{-6}\) m², featuring two input waveguides and one output waveguide, each outfitted with two ring resonators. Each ring resonator integrates three utilized Terfenol-D cylinders that enable modulation of Young’s modulus. The symmetrical configuration of the structures facilitates the creation of unique resonant frequencies for the AND/XOR gates, adapting identically to variations in magnetic field intensities. These tunable AND/XOR gates are designed to be influenced by external magnetic fields, utilizing the variations in Young’s modulus that occur in magnetostrictive materials under various magnetic field intensities. The tunability and operational efficiency of these gates are greatly play a crucial role for enhancing the resonance frequency numbers of the ring resonators and the dynamic modulation of the Terfenol-D properties. Tunability experiments were conducted at several Young’s modulus values of Terfenol-Ds, corresponding to three varying magnetic field intensities, resulting in resonance frequencies of 1.5030 MHz, 1.5032 MHz, and 1.5033 MHz for the AND gate and 1.5040 MHz, 1.5044 MHz, 1.5047 MHz for the XOR gate. The performance of the gates was appraised using the finite element method, which yielded an average contrast ratio of 11.59 dB and 12.15 dB for AND logic gate and XOR logic gate, respectively. The suggested AND/XOR gates present a simple yet efficient solution for acoustic communication systems, networks, and digital acoustic computing circuits.
