## 1 Introduction  
Magnorheological fluids (MRFs) have become increasingly significant in smart materials research due to their unique ability to reversibly transition from a liquid to a semi-solid state under the influence of a magnetic field. This transformation largely affects the shear mechanical performance of MRFs, which is dependent on several factors including the type and distribution of magnetic particles, the carrier fluid, and the role of additives and surfactants. Recent studies have indicated that particle size distribution plays a crucial role in improving the magnetic and mechanical behavior of MRFs [1, 2, 3]. Specifically, a double-graded distribution involving various particle sizes can enhance the field-responsive behavior and mechanical properties of MRFs by optimizing particle packing density and magnetic field interactions [4,5]. Moreover, the choice of carrier fluid, whether involving silicone oil, polyalphaolefin, or other substances, substantially influences viscosity and thermal stability, thus affecting the shear response of MRFs under applied magnetic fields [6, 7, 8]. Additives such as oleic acid and surfactants such as Span 80 are often incorporated to further improve the dispersion stability and modulate rheological properties without inducing significant sedimentation issues [9, 10, 11].  
In parallel, magnetorheological (MR) dampers, which utilize these advanced MRFs, have exhibited significant advancements in dynamic mechanical performance, particularly in terms of damping force output. MR dampers capitalize on the tunable viscosity of MRFs to provide varying damping forces that can be precisely controlled by external magnetic fields [12, 13, 14]. This adaptability makes them ideal for applications in vibration control across different sectors, including the architectural [15], automotive, and aerospace fields [16, 17]. The enhancements in MR damper performance are typically assessed by evaluating the damping force range, response time, and energy dissipation efficiency [18, 19, 20]. The implementation of double-graded MRFs within these dampers has been found to significantly enhance these parameters, as these specially formulated fluids optimize the magnetic flux distribution and reduce the occurrence of phenomena such as particle clustering and chain breakage under stress [21, 22, 23].  
The development of a self-decoupling mechanism in MR dampers further augments their mechanical performance by minimizing the interference and interaction between the magnetic circuit and mechanical components. Through decoupling, the magnetic field effects are streamlined, allowing for more efficient force transmission and reduced energy losses [24, 25, 26, 27]. This innovation is pivotal in expanding the functional range of MR dampers, enabling them to be more resilient and responsive under variable load conditions. The combination of double-graded high-performance MRFs and self-decoupling mechanisms results in high-capacity MR dampers that are not only efficient at damping vibrations but also adaptive to the evolving demands of modern engineering systems [28, 29, 30, 31]. Hence, continuous research into optimizing the formulation of MRFs and the structural design of MR dampers is critical in advancing the application potential of these smart damping systems [32, 33, 34].  
This study demonstrates a high-performance magnetorheological fluid (HP-MRF) synthesized by dispersing single- and double-graded carbonyl iron particles (CIPs) in a composite carrier system combining a sol solution with methyl silicone oil. Furthermore, the optimized HP-MRF was subsequently implemented in a previously designed self-decoupling MR damper to investigate its dynamic hysteretic behavior. These studies establish that CIP grading optimization in MRFs enables exceptional damper performance for advanced vibration control applications.