**1. Introduction**

Magnetorheological elastomer (MRE) is one of the smart materials consisting of micron size magnetic particles embedded in rubber matrix. The rheological properties of MRE can be tuned continuously and reversibly by the external magnetic field. This kind of smart material has potential applications including dampers, sensors, and actuators for vibration systems [1–4]. Currently, researchers in the field of MRE are mainly focused on the e ffect of di fferent elastomer matrices [5–7], types of magnetic particles [8–10], the e ffect of the particle sizes [11], and the shapes of the magnetic particles [12]. Silicon rubber (SR) has been widely used in MRE fabrication as the matrix due to its softness which can lead to a high MR e ffect [13–17]. Meanwhile, carbonyl iron particles (CIPs) have been widely used in MRE fabrication due to their high magnetic saturation, high permeability, and low remanence. In addition, additives and fillers also have been introduced in MRE fabrication to strengthen the interaction between the matrix and the CIP and hence improve mechanical, rheological, and electrical properties. On the other hand, a few researchers endeavored to fabricate MRE using the nanoparticles as magnetic particles to achieve large surface area, stable chemical reaction, and easy surface modifications [18–20]. Mordina et al. [21] introduced two types of di fferent shapes of CoFe2O4, spherical and fiber in silicon-based nanocomposites, and found that the nanofibers enhanced the magnetic saturation as low as 5 wt.%, but the saturation tended to decrease at a higher loading of 10 wt.% due to the low formation of interconnected network of nanofibers. Despite this, by implementing the nanoparticles as an additive or filler in MRE, the magnetic and rheological properties of MRE can be appropriately tuned. Commercially available additives such as carbon black [22,23], graphite [4,24], ester [25,26], oils [27], and carbon nanotubes [28–30] have been used in MRE fabrication and have proven to enhance various performances of MRE as compared to the original MRE without these additives. Aziz et al. [31] introduced a few types of multiwall carbon nanotube (MWCNTs) as an additive in MRE fabrication. The results demonstrated that with the addition of 0.1 wt.% of MWCNTs, the magnetic saturation of MRE is slightly changed, as the saturation of MRE is increased up to 4%. In a similar work, Poojary et al. [28] fabricated MRE with di fferent percentages of carbon nanotube (CNT), 0.1 wt.% to 0.5 wt.%, as additives and found that the sti ffness and loss factor was the highest with the addition of 0.25 wt.% CNT, whereas MRE without CNT exhibited the highest MR e ffect of 48%. Padalka et al. [32] synthesized Fe, Co, and Ni nanowires and fabricated 10 wt.% of each in MRE composite. Their study focused on the strain and frequency with compression mode showing that MRE with Fe and Co exhibited the highest MR e ffect at 1% strain and tended to drop at 2% strain. Meanwhile, Yu et al. [33] used the nanoparticles for MRE fabrication as a coating material for the damping applications. They synthesized CIPs which were coated with Fe nanoflakes and demonstrated that the MR e ffect and damping properties increased up to 162% and 65%, respectively, with the incorporation of 6% CIP-Nano-Fe.

Generally, neat MRE is considered to be an insulator, and thus electrical property can be changed by adding the proper filling material for the development of long-lasting products for sensor applications. Thus far, a few researchers have attempted to synthesize MREs associated with the nanoparticles of additives or fillers to enhance various properties such as magnetic, electrical, optical, and catalytic properties, which are known to be useful in science and technological applications [21–23]. For instance, cobalt ferrites nanoparticles have been extensively studied due to their variety of applications including electrical and magnetic applications. Generally, the properties of cobalt ferrite can be altered by adding dopants and metal ions, adopting a variety of synthesis methods, and varying calcination temperature and other reaction conditions. Hossain et al. [22] synthesized various Ni substituted Zn1-xNixFe2O4 by solid-state reaction technique from stoichiometric amounts of Fe2O3, ZnO, and NiO of 99.99% purity and showed that the magnetoresistance (MR) was increased with the increment of Ni-substituted Zn-Ni ferrites due to spin-dependent scattering. Berchmans et al. [23] investigated

the structural and electrical properties of the magnesium-substituted nickel ferrite and found that all samples exhibited semiconductor behavior as the dielectric constantly was decreased with the frequency increment. Notably, during the last several years, the role of nanoparticles as an additive or filler has received significant research interest as sensing applications of MR-based detection methods. Nevertheless, study on this issue is considerably rare. Shabdin et al. [4] found that the application of 33 wt.% of 16 μm graphite particle size in MRE could alter the conductivity and resistivity of MRE subjected to an external applied force. Li et al. [34] fabricated MRE with di fferent concentrations of 5.88 wt.% to 23.81 wt.% graphite and found that samples with higher graphite weight fraction showed higher electrical conductivity and lower decline in resistance. In fact, in previously published data [24,35,36], electrical properties of MRE mainly focused on the resistivity or resistance and contents of fillers. Less consideration has been given to the mechanism of particle interaction with respect to both rheological and electrical properties which are the main concern in practical applications. Although the conductivity of MRE can be improved by increasing the weight fraction of graphite, excessive implementation of particles or fillers in MRE often leads to the decrement of some other properties such as elasticity. Moreover, this makes the processing and dispersion of particles more di fficult, which leads to a brittle phase and decrement of the field-dependent modulus of MRE.

The main technical contribution of this work is to fabricate a new MRE associated with the nanosized Ni-Mg cobalt ferrites with di fferent concentrations of Mg, and to experimentally investigate various properties of the proposed MRE including the field-dependent viscoelastic properties and electrical resistance. The nanosized Ni-Mg cobalt ferrites are introduced as a filler in MRE fabrication to enhance magnetic and electric properties of MRE with the least brittleness. It should be noted that to the best of our knowledge, MRE with the nanosized Ni-Mg cobalt ferrites as a filler has never been reported, despite several benefits of the proposed filler. For example, the nanosized Ni-Mg cobalt ferrites exhibit high magnetic remanence and large surface activities [37]. Their properties are believed to demonstrate better magnetic, rheological, as well as electrical properties of MRE. In order to validate the enhanced properties of the proposed MRE, first, three MRE samples are prepared and their morphological observations are recorded. Subsequently, magnetic, field-dependent rheological, and electrical properties are investigated and compared with respect to the di fferent compositions of Mg. It is identified that MRE with the proposed filler can enhance the saturation of magnetization by 3% and the storage modulus and loss factor by 66%. In addition, evaluations show that MRE with a higher content Mg exhibits higher electrical resistance, in the range of 1% to almost 400% in o ff- and on-state conditions, due to the easier movement of the particles.
