The control of magnetic fields, essential for our science and technology, is currently achieved by magnetic materials with positive permeability, including ferromagnetic, paramagnetic, and diamagnetic types. Here we introduce materials with negative static permeability as a new paradigm for manipulating magnetic fields. As a first step, we extend the solutions of Maxwell magnetostatic equations to include negative-permeability values. The understanding of these new solutions allow us to devise a negative-permeability material as a suitably tailored set of currents arranged in space, overcoming the fact that passive materials with negative permeability do no exist in magnetostatics. We confirm the theory by experimentally creating a spherical shell that emulates a negative-permeability material in a uniform magnetic field. Our results open new possibilities for creating and manipulating magnetic fields, which can be useful for practical applications.

中文翻译：

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静磁率的负磁导率及其实验证明

对我们的科学和技术必不可少的磁场控制，目前是通过具有正磁导率的磁性材料实现的，包括铁磁，顺磁和抗磁类型。在这里，我们介绍具有负静磁导率的材料作为操纵磁场的新范例。第一步，我们扩展麦克斯韦静磁方程的解，使其包含负磁导率值。对这些新解决方案的理解使我们能够将负磁导率材料设计为在空间中适当定制的一组电流，从而克服了静磁率中不存在具有负磁导率的无源材料这一事实。我们通过实验创建一个球形壳来证实该理论，该球形壳在均匀磁场中模拟负磁导率材料。