## 1 Introduction  
Aqueous two-phase system (ATPS) is an effective and promising liquid-liquid extraction technology, which was first introduced by [PERSON] [1]. The main systems were PEG/dextran and PEG/salt in the early period, then more and more ATPSs appeared, such as the alcohol/salt system [2], aqueous micellar system [3], and ionic liquid/salt system [4]. The aqueous micellar two-phase system (AMTPS) based on non-ionic surfactant was a process of temperature-induced phase separation, which can form two phases above the cloud point temperature of non-ionic surfactant. Thus, AMTPS can be also called cloud point extraction (CPE). Compared with the other liquid-liquid extraction, the AMTPS has the advantages of low toxicity of surfactants, the use of dilute solutions, no use of organic solvents, high preconcentration factor due to the small volume in surfactant-rich phase, and good biocompatibility [5; 6]. Likewise, the AMTPS has some disadvantages, such as the probable interference for analysis of target compounds caused by the co-existing hydrophobic species in the surfactant-rich phase, the high viscosity in surfactant-rich phase affecting the sample injection, and the long phase-separation time [7]. Up to now, the AMTPS was widely used in the extraction and separation field, such as the extraction of small molecule contaminants [8] or heavy metals [9] from aqueous solution, determination of pesticides in urine samples [10], determination of synthetic dyes [11] or heavy metals [12] in food samples, removal of dyes from wastewater [13], and extraction of bioactive compounds from natural plant resources [14].  
Magnetic solid phase extraction (MSPE) using MNPs as the solid absorbent has aroused great interest in the field of analytical chemistry, which has the advantages of simple operation, high selectivity and enrichment factor for analytes, free of organic solvent, versatile use by easy surface modification of MNPs, moreover, the easy dispersion of MNPs to the solution and simple recovery of MNPs by using a permanent magnetic field [15; 16; 17]. Thus, MSPE was widely used in the extraction, separation and enrichment of various samples, including the biological, environmental and food samples [16].  
This hybrid method of ATPS and magnetic separation was reported in other studies. For example, [PERSON] and coworkers combined the PEG/dextran ATPS with magnetic separation for the purification of polyclonal human immunoglobulin G (IgG), satisfactory recovery yield and purity were obtained by this method, and the phase separation time was shorten from 40 min to 25 min compared with individual ATPS without addition of MNPs [18]. [PERSON] and coworkers developed a combined method of magnetic separation using functionalized MNPs and AMTPS using a non-ionic surfactant for the continuous purification of proteins [19]. In this study, a hybrid method of AMTPS and MSPE named magnetic aqueous micellar two-phase system (MAMTPS) was developed for the extraction, enrichment and removal of dyes from aqueous solutions. Up to now, the similar methods were mainly reported for the purification of biomolecules, such as the protein [20], chymotrypsin [21], and antibody [18], but no relevant study hasbeen reported about their use in the extraction/isolation of small molecules contaminants from aqueous solution. Therefore, three common dyes (Congo red, methyl blue, and methyl violet) were chosen as the target compounds in this study, the influencing factors of type and amount of MNPs, surfactant concentration, vibration time, and extraction temperature were studied to obtain the optimal operation conditions.