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Chin. Phys. B, 2010, Vol. 19(5): 057801    DOI: 10.1088/1674-1056/19/5/057801
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

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

Wei Jing-Song(魏劲松)a) and Xiao Mu-Fei(肖暮霏)b)
a Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China; b Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, Apartado Postal 365, CP 22800 Ensenada, Baja California, México
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.

Cite this article: 

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

[1] Wood J 2007 Materials Today 10 9
[2] Veselago G 1968 Sov. Phys. Usp. 10 509
[3] Parazzoli C G, Greegor R B, Nielsen J A, Thompson M A, Li K, Vetter A M, Tanielian M H and Vier D C 2004 Appl. Phys. Lett. 84 3232
[4] Foteinopoulou S, Economou E N and Soukoulis C M 2003 Phys. Rev. Lett. 90 107402
[5] Zhou J, Koschny T, Zhang L and Tuttle G 2006 Appl. Phys. Lett. 88 221103
[6] Hu L and Chui S T 2002 Phys. Rev. B 66 085108
[7] Pendry J B 2000 Phys. Rev. Lett. 85 3966
[8] Lu Z, Chen C, Schuetz C A, Shi S, Murakowski J A, Schneider G J and Prather D W 2005 Appl. Phys. Lett. 87 091907
[9] Aguanno M S, Mattiucci G N, Bloemer M J, de Ceglia D, Centini M, Mandatori A, Sibilia C, Akozbek N, Cappeddu M G, Fowler M and Haus J W 2007 Opt. Express 15 508
[10] Ruan Z and Qiu M 2006 Opt. Express 14 6172
[11] Yannopapas V 2007 Phys. Rev. B 75 035112
[12] Khoo I C, Werner D H, Liang X, Diaz A and Weiner B 2006 Opt. Lett. 31 2592
[13] Al\`{U A and Engheta N 2007 Phys. Rev. B 75 024304
[14] Feng L, Liu X, Tang Y, Chen Y, Zi J, Zhu S and Zhu Y 2005 Phys. Rev. B 71 195106
[15] Decoopman T, Tayeb G, Enoch S, Maystre D and Gralak B 2006 Phys. Rev. Lett. 97 073905
[16] Chui S, Chan C T and Lin Z F 2006 J. Phys.: Condens. Matter 18 L89
[17] Huang Y and Gao L 2009 J. Appl. Phys. 105 013532
[18] Wheeler M S, Aitchison J S and Mojahedi M 2006 Phys. Rev. B 73 045105
[19] Chen Y, Fischer P and Wise F W 2005 Phys. Rev. Lett. 95 067402
[20] Tomita S, Yashiro H, Kashiwagi T, Hagiwara M, Mitsumata C, Nawafune H and Akamatsu K 2006 Technical Digest (CD) (Optical Society of America) paper WD13
[21] Tomita S, Akamatsu K, Shinkai H, Ikeda S, Nawafune H, Mitsumata C, Kashiwag T and Hagiwara M 2005 Phys. Rev. B 71 180414R
[22] Wei J and Xiao M 2007 J. Phys.: Condens. Matters 19 072203
[23] Kasagi T, Tsutaoka T and Hatakeyama K 2006 Appl. Phys. Lett. 88 172502
[24] Garc\'{\hia-Miquel H, Carbonell J, Boria V E and S\'{anchez-Dehesa J 2009 Appl. Phys. Lett. 94 054103
[25] Chui S T and Hu L 2002 Phys. Rev. B 65 144407
[26] Chen P, Wu R, Zhao T, Yang F and Xiao J Q 2005 J. Phys. { D: Appl. Phys. 38 2302
[27] Wu R, Zhang X, Lin Z, Chui S and Xiao J Q 2004 J. Mag. Mag. Mater. 271 180
[28] Chui S T, Lin Z F and Hu L B 2003 Phys. Lett. A 319 85
[29] Pimenov A, Loidl A, Przyslupski P and Dabrowski B 2005 Phys. Rev. Lett. 95 247009
[30] Pimenov A, Loidl A, Gehrke K, Moshnyaga V and Samwer K 2007 Phys. Rev. Lett. 98 197401
[31] Bai Y, Xu F and Qiao L J 2009 Appl. Phys. Lett. 94 094101
[32] Xu F, Bai Y, Qiao L J, Zhao H J and Zhou J 2009 Chin. Phys. B 18 1653
[33] Zhao H, Zhou J, Zhao Q, Li B, Kang L and Bai Y 2007 Appl. Phys. Lett. 91 131107
[34] Zhao H, Zhou J, Kang L and Zhao Q 2009 Opt. Express 17 13373
[35] Liao S 2000 Ferromagnetism (Beijing: Science Press) p1--88 (in Chinese)
[36] Wei J and Xiao M 2007 Opt. Commun. 270 455
[37] Singh P, Babbar V K, Razdan A, Puri R K and Goel T 2000 J. Appl. Phys. 87 4362
[38] Verma A, Saxena A and Dube D 2003 J. Magnetism and Magnetic Materials 263 228
[39] Li Z W, Wu Y P and Lin G Q 2007 J. Appl. Phys. 102 083908
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