## 1 Introduction  
A laser of around 3 \(\upmu\)m has attracted much attention in national defense and security, laser surgery, frequency conversion, greenhouse gas monitoring, and spectroscopy [1; 2; 3; 4; 5; 6]. Some applications, such as material processing, require high-power pulse laser sources to melt materials and tunable wavelengths to match the absorption peak of different materials. Additionally, for several spectroscopic and sensing applications, a tunable light source is needed. Q-switched erbium-doped ZBLAN fibers are a promising method to generate pulsed and tunable lasers around 3 \(\upmu\)m because erbium-doped ZBLAN fibers have made great progress in recent years in high-power output fields [7; 8; 9], and the emission band of erbium ion is relatively wide [10]. Compared to active Q-switching, passive schemes do not need any externally controlled modular. Instead, a saturable absorber (SA) is used to generate a pulse. The SA has an intensity-related absorption rate of the laser. The unsaturated SA absorbs light and forms a high Q-factor laser cavity. After saturation, the absorption rate of SA is greatly reduced, and the Q-factor of the cavity is declined. Passive Q-switching is more economical and more attractive. Recently, many passively Q-switched pulsed fiber lasers around 3 \(\upmu\)m were reported. Different kinds of SAs were used to modulate the cavity loss. Besides traditional bulk SA modulators, such as semiconductor saturable absorber mirrors (SESAM) [11; 12; 13; 14] and Fe\({}^{2+}\):ZnSe crystals [15], two-dimensional (2D) materials are widely investigated, including graphene [16; 17], black phosphorous [18], topological insulator [19; 20], magnetite (Fe\({}_{3}\)O\({}_{4}\)) [21; 22], antimonene [23], transmission metal dichalcogenides [24; 25], and gold nanorods [26].  
While SESAM is widely used for its mature manufacturing process and customized properties, the cost of production is high. Additionally, the operating wavelength is typically narrow, which is not suitable for wavelength-tunable applications. Thus far, many wavelength tunable Q-switched lasers around 2.8 um based on 2D SAs have been demonstrated, as shown in Table 1. However, demonstrations in the mid-infrared wavelength are seldom. Among reports in the near-infrared wavelength range, the majority of average output power is low, and the tunable bandwidth is below 48 nm. In 2020, a tunable Q-switched laser based on Fe\({}_{3}\)O\({}_{4}\)-nanoparticle SA was reported, and the wavelength was tunable from 2812.4 nm to 3031.6 nm, corresponding to a range of 219.2 nm [22]. Fe\({}_{3}\)O\({}_{4}\) is a suitable material to serve as a broadband mid-infrared Q-switcher. However, this report was demonstrated on a dysprovision (Dy\({}^{3+}\)) doped ZBLAN fiber. Dy\({}^{3+}\)-doped fiber can deliver a much longer wavelength tuning range [27]. However, the \({}^{6}\)H\({}_{13/2}\rightarrow{}^{6}\)H\({}_{15/2}\) transition of Dy\({}^{3+}\) ion has a significantly lower emission cross-section than the \({}^{4}\)I\({}_{11/2}\rightarrow{}^{4}\)I\({}_{13/2}\) transition of Er\({}^{3+}\) ion [28], which is detrimental to high power usage. For the typical usage of a Q-switched pulsed laser, a higher pulse energy is important.  
In this article, a broadband-tunable passively Q-switched erbium-doped ZBLAN fiber laser is demonstrated using a Fe\({}_{3}\)O\({}_{4}\) saturable absorber mirror (SAM). The SAM is fabricated via depositing Fe\({}_{3}\)O\({}_{4}\)-nanoparticles on a gold mirror. A refractive blazed grating is used to tune the wavelength. The wavelength tunable bandwidth is measured to be 100 nm. The Q-switched output power reaches a maximum of 188 mW at the wavelength of 2760 nm. The output characteristics with the varied pump power and wavelength are investigated.