In this paper, we investigate the meromorphic solutions of the Fermat-type differential equations f’(z)<sup>n</sup> + f(z+c)<sup>m</sup> = e<sup>Az</sup><sup>+</sup>B ...In this paper, we investigate the meromorphic solutions of the Fermat-type differential equations f’(z)<sup>n</sup> + f(z+c)<sup>m</sup> = e<sup>Az</sup><sup>+</sup>B (c ≠ 0) over the complex plane C for positive integers m, n, and A, B, c are constants. Our results improve and extend some earlier results given by Liu et al. Moreover, some examples are presented to show the preciseness of our results.展开更多
Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last...Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last decade, while electrical detection compatible with semiconductor processes has not been achieved, and this is considered one of the most crucial gaps regarding the use of skyrmions in real applications. Here, we report the direct observation of nanoscale skyrmions in Co Fe B/Mg O-based magnetic tunnel junction devices at room temperature. High-resolution magnetic force microscopy imaging and tunneling magnetoresistance measurements are used to illustrate the electrical detection of skyrmions,which are stabilized under the cooperation of interfacial Dzyaloshinskii–Moriya interaction, perpendicular magnetic anisotropy, and dipolar stray field. This skyrmionic magnetic tunnel junction shows a stable nonlinear multilevel resistance thanks to its topological nature and tunable density of skyrmions under current pulse excitation. These features provide important perspectives for spintronics to realize highdensity memory and neuromorphic computing.展开更多
文摘In this paper, we investigate the meromorphic solutions of the Fermat-type differential equations f’(z)<sup>n</sup> + f(z+c)<sup>m</sup> = e<sup>Az</sup><sup>+</sup>B (c ≠ 0) over the complex plane C for positive integers m, n, and A, B, c are constants. Our results improve and extend some earlier results given by Liu et al. Moreover, some examples are presented to show the preciseness of our results.
基金financial support from the National Key R&D Program of China(2018YFB0407602,and 2020YFA0309300)National Natural Science Foundation of China(61627813,61871008,62001019,12004024,and 51901081)+5 种基金Beijing Natural Science Foundation(4202043)Beijing Nova Program from Beijing Municipal Science and Technology Commission(Z201100006820042)National Natural Science Foundation of China-German Research Foundation(52061135105)Outstanding Research Project of Shen Yuan Honors College,BUAA(230121102)the Science and Technology Program of Guangzhou(202002030052)Joint Research Key Fund for Guangzhou and Shen Zhen(2021B1515120047)。
文摘Chiral magnetic skyrmions are topological swirling spin textures that hold promise for future information technology. The electrical nucleation and motion of skyrmions have been experimentally demonstrated in the last decade, while electrical detection compatible with semiconductor processes has not been achieved, and this is considered one of the most crucial gaps regarding the use of skyrmions in real applications. Here, we report the direct observation of nanoscale skyrmions in Co Fe B/Mg O-based magnetic tunnel junction devices at room temperature. High-resolution magnetic force microscopy imaging and tunneling magnetoresistance measurements are used to illustrate the electrical detection of skyrmions,which are stabilized under the cooperation of interfacial Dzyaloshinskii–Moriya interaction, perpendicular magnetic anisotropy, and dipolar stray field. This skyrmionic magnetic tunnel junction shows a stable nonlinear multilevel resistance thanks to its topological nature and tunable density of skyrmions under current pulse excitation. These features provide important perspectives for spintronics to realize highdensity memory and neuromorphic computing.
