Negative refraction in ferromagnetic materials under external magnetic field: a theoretical analysis

doi:10.1088/1674-1056/19/5/057801

Abstract We present a detailed theoretical analysis on the possibilities and conditions for negative permeability and negative refraction occuring in the magnetic materials with both pronounced magnetic and dielectric responses to electromagnetic waves. The results indicate that the permeability is always positive for $\delta=(2q+0.5)\pi$ ($\delta$ is the initial phase difference of magnetic components $h_{x}$ and $h_{y }$ of incident electromagnetic wave, $q$ is integer), which means that it is difficult to realize negative refraction. However, for $\delta=2q\pi$, $\delta=(2q+1)\pi$, or $\delta=(2q-0.5)\pi$, the negative permeability occurs at some range of free procession frequency, which means that the refraction can become negative under certain conditions. Further analysis reveals that for general positive permittivity there are various opportunities for realizing the negative refraction provided that some requirements are met. One concludes also that the refractive index for $\delta=2q\pi$ case is similar to $\delta=(2q+1)\pi$. The only difference between two cases of $\delta=2q\pi$ and $\delta=(2q+1)\pi$ is that the $x$-direction for $\delta=2q\pi$ corresponds to the $y$-direction for $\delta=(2q+1)\pi$, and the $y$-direction for $\delta=2q\pi$ corresponds to the $x$-direction for $\delta=(2q+1)\pi$. The results are valuable for designing and analysing the complex negative refraction of magnetic materials.

Keywords: negative refraction ferromagnetic materials

Received: 15 July 2009
Revised: 21 November 2009
Accepted manuscript online:

PACS:	75.30.Cr	(Saturation moments and magnetic susceptibilities)
	77.22.Ch	(Permittivity (dielectric function))
	75.50.Dd	(Nonmetallic ferromagnetic materials)
	75.60.Ej	(Magnetization curves, hysteresis, Barkhausen and related effects)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~50772120 and 60977004), and Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering (Grant No.~KJCXZYW.NANO.06), Shanghai Rising Star Tracking Program (Grant No.~10QH1402700) and UNAM-DGAPA Mexico IN120406-3.

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Wei Jing-Song(魏劲松) and Xiao Mu-Fei(肖暮霏) Negative refraction in ferromagnetic materials under external magnetic field: a theoretical analysis 2010 Chin. Phys. B 19 057801

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Negative refraction in ferromagnetic materials under external magnetic field: a theoretical analysis

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