## 1 Introduction  
Photonic crystals (PCs) can control the motion of photons because of their unique properties, such as photonic band-gap (PBG) and optical localization [1, 2]. PCs are considered to be the core of integrated optical communication in the future. PCs with PBG have many direct applications like mirror [3, 4], grating [5], and filters [6]. Based on optical localization, PCs with point or line defects have been extensively researched as the basis of high-quality resonator cavities [7, 8] and photonic crystals waveguide (PCW) [9, 10].  
Due to the emergence of PCW as a new transmission line, photonic integrated devices with PCW, such as circulators [11, 12, 13], optical distributors [14, 15], logical gates [16], all-optical adders [17], optical isolators [18, 19], encoders [20], and so on, are studied extensively. However, with the rapid development of photonic crystal integrated devices, more attention shall be paid to the problem of increased bit error rate because of nonlinear effect in large scale integrated optical path. Optical isolators have also been developed from the original one-dimensional photonic crystal isolator [18] to two-dimensional photonic crystal isolator [19], which can effectively isolate noise or reflections in the integrated optical path to reduce the bit error rate. Low-power transmission of the PCW can be used to avoid the occurrence of nonlinear effects in all-optical 8-to-3 encoder [20]. As we know, the 5G communication system is planned around 24 \(\sim\) 28 GHz by most nations and areas, which has broadband characteristic. Therefore, the research of broadband isolator based on low loss PCW has great significance to reduce the bit error rate and nonlinear effect of the communication system. In our previous work [21], based on Faraday rotation effect, a four-ports double Y-shaped magneto-photonic crystal circulator was designed by using an ultra-wideband PCW for 5G communication system.  
In this work, we focused on designing a broadband magneto-optical (MO) isolator by using the PCW and gyromagnetic materials, which is based on ferromagnetic resonance absorption effect. The MO isolator was formed by inserting two rectangular gyromagnetic ferrites into an ultra-wideband and high efficiency PCW that consisted of triangular lattice Al\({}_{2}\)O\({}_{3}\) dielectric posts. Based on the three-dimensional (3D) numerical simulation, it was found that the transmission efficiency of the PCW rises with its height and width. The optimal PCW structure with high transmission efficiency of 90.78% and relative bandwidth of 28.71% was achieved by numerical simulation and experimental verification, which was be used to design the MO isolator in 5G millimeter waveband here. By investigating the influence of the ferrite sheets' size and position in the PCW on the performance of the isolator, the structural and performance parameters of the MO isolator were optimized. The isolation of the MO isolator was optimized to be 49.49 dB at 26.30 GHz by finite element method (FEM) and kept above 15 dB between 24.85 to 27.15 GHz (the relative bandwidth is 8.85%) with the best ferrite sheets' length L of 20 mm and position \(d\) of 1 mm. The MO isolator also had an excellent forward transmission characteristic that the transmission efficiency kept above \(-\)3 dB in a wide frequency range from 22.00 to 27.40 GHz. The numerical results show that the MO isolator with broadband and high isolation can operate in the 24.85 to 27.15 GHz. If the photonic crystal devices are used to integrate 5G communication systems in the future, our design scheme will have potential application value.