磁性材料在微波及太赫兹波段的动力学研究
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摘要
磁性材料在微波及太赫兹波段的动力学的研究和应用已开展多年。由于近年来光子晶体和负折射系数材料的发展，微波传导的低能耗和谐振器件的小型化逐渐受到重视。在这些领域人们进行了多方面有益的探索，如磁性微波光子晶体和开口谐振环的磁响应。另一方面，随着信息技术的飞速发展，人们对磁性介质数据存储速度的要求越来越高，促使科研工作者不断探索新的磁化态操控技术。由激光脉冲激发的超快磁矩翻转现象的发现和研究，使人们意识到这一技术有可能成为下一代更快的磁存储技术的基础，该领域的工作逐渐成为凝聚态物理的研究热点之一。
本工作首先运用调节磁场的方法实现了对微波段磁性光子晶体带隙的调制，该系统由铁磁柱体材料组成的二维磁性光子晶体所构成。除了由光子晶体周期结构导致的布拉格散射带隙，我们在实验中还观测到了另外两种光子带隙：分别来自于磁性表面等离子体共振和自旋波共振。其中，磁性表面等离子体可视为金属表面等离子体在铁磁材料表面的类比物理量，其共振所引起的光子带隙具有外场可调的特殊性质。这一发现对于光子晶体波导理论和应用的研究都具有重要意义。
在上述磁性光子晶体带隙理论及实验研究的基础上，我们通过特定的实验方法制备了具有单向导波特性的磁性表面等离子体微波波导。当电磁波的频率处于磁性表面等离子体共振频率区域，由二维磁性光子晶体阵列构成的波导具有不对称的电磁波传输特性：即在由两个二维周期阵列（每个阵列外加方向相反的静磁场）所构成的导波通道中，电磁波只沿着一个方向传播，而在其反方向的传播被显著抑制。实验发现，该波导的单向传输特性不受金属障碍物和光子晶体周期性破坏的影响；更重要的是，其单向导波的工作频率可由外加磁场调制。理论研究表明：这一现象源自于磁性表面等离子体能带结构的时间反演对称破缺，类比于二维电子系统中的量子霍尔效应的手性边缘传输现象。
开口谐振环作为一种新型的电磁波谐振系统，其共振频率克服了传统散射波长的限制，尺寸可达到共振频率波长的1/10甚至更小。基于对开口谐振环的磁共振响应特性的研究，本工作运用溅射和光刻方法制备了一种新型的不共面开口谐振环。区别于传统的共面开口谐振环，实验发现不共面开口谐振环的共振频率与环-环间距具有线性关系。环-环间距越小，其共振频率越低。当环-环间距达到微米级别，发生磁共振时其几何尺寸可达到波长的1/120。这一实验结果可为天线的小型化研究提供有益参考。
本工作通过实验验证了铁磁薄膜的超快退磁效应可辐射出太赫兹波，并且发现了铁磁薄膜受激光脉冲激发后，其辐射出的太赫兹波的强度与薄膜本身的阻尼系数成明显的线性关系。实验采用磁控溅射方法制备铁磁薄膜，并利用自旋注入效应，改变与铁磁薄膜相邻的金属薄膜的厚度，从而获得具有不同阻尼系数的铁磁薄膜样品。使用抽运-探测技术观测到辐射的太赫兹波的强度与阻尼系数存在显著的正比关系：薄膜的阻尼系数越大，太赫兹波的辐射强度越大，表明磁矩的退磁过程更快。这一发现为进一步研究超快激光操控磁化态的动力学过程开辟了新的思路。实验中通过自旋注入效应改变薄膜的阻尼系数，表明了自旋注入理论也可能适用于太赫兹波范围。
The dynamics of magnetic materials in microwave and terahertz range have beenstudied and utilized for dacades. Most of attentions were focused on the insulatingmagnetic materials. Recently, due to the development of magnetic photonic crystals,negative refractive index materials and ultrafast laser pulse techniques, there have beenincreasing interests in the microwave guiding system such as magnetic surface plasmawaveguide and split ring resonator. On the other hand, the demands for theever-increasing speed of data storage in magnetic media have triggered intense searchesfor innovative methods to control magnetization, ultrafast magnetization switching bypulsed laser excitation can be viewed as one of the prospective technique.
We experimentally studied magnetically controllable photonic band gaps (PBGs)in two-dimensional magnetic photonic crystals (MPCs) consisting of ferrite rods.Besides the conventional PBG that relates to Bragg scattering, another two types ofPBGs, resulting from magnetic surface plasmon resonance and spin-wave resonance,respectively, are observed. The PBG due to magnetic surface plasmon resonance isparticularly interesting because of its analogy to surface plasmon in metal, furthermore,it is shown to be completely tunable by an external static magnetic field from bothexperimental and theoretical point of view.
We also have demonstrated experimentally a one-way magnetic surface plasmonelectromagnetic waveguide in the microwave range based on the MPCs The waveguideexhibits asymmetric transmission of electromagnetic waves in the frequency range nearthe magnetic surface plasmon resonance for an MPC, such that a significant one-waypropagation can be observed in the channel between the two MPC slabs, each in anexternal static magnetic field (ESMF) of opposite directions. The one-way waveguide isnot only immune to interstitial metal defects，but also robust against the disorder of rodposition. Furthermore, its working frequency can be flexibly tuned by an ESMF, whichmakes it more favorable for the design of electromagnetic devices. The physics isrelated to the broken time reversal symmetry of the magnetic surface plasmon bandstates and the excitation of a giant circulation of the energy flow, similar to the case in the quantized Hall Effect.
Based on the understanding of the magnetic resonance properties of split ringresonator no longer suffers from half-wavelength requirement for resonance, wedemonstrated that for coplanar split ring resonator, the wavelength of the resonancemode is about10times larger than geometrical size of the ring; for non-coplanar splitring resonator, the resonance frequency depends linearly on the ring-ring separation. Werealized the non-coplanar split ring system using sputtering and etching techniques, it’sgeormetrical size is only1/120of the wavelength at the lowest resonance mode. Thisdemonstration opens a door to miniaturization of resonator.
It is believed that ultrafast demagnetization process in ferromagnetic film canproduce terahertz (THz) emission. We present an experimental demonstration that,following ultrafast optical excitation, the magnitude of terahertz electromagnetic pulsesemitted from a ferromagnetic film is proportional to the Gilbert damping constant,which is conventionally used to describe the damping of magnetization precession.Different damping factors are obtained by varying the normal metal film adjacent to themagnetic film via spin pumping. It is shown that the larger the Gilbert damping, thelarger emitted THz signal and therefore, the faster demagnetizing process. On the otherhand, the nonlocally adjusted damping constant via spin pumping in this experimentalso indicates that the spin pumping theory may still be valid in THz regime. We expectthis study would lead to new perspectives of the ultrafast manipulation of magneticorder.
本工作首先运用调节磁场的方法实现了对微波段磁性光子晶体带隙的调制，该系统由铁磁柱体材料组成的二维磁性光子晶体所构成。除了由光子晶体周期结构导致的布拉格散射带隙，我们在实验中还观测到了另外两种光子带隙：分别来自于磁性表面等离子体共振和自旋波共振。其中，磁性表面等离子体可视为金属表面等离子体在铁磁材料表面的类比物理量，其共振所引起的光子带隙具有外场可调的特殊性质。这一发现对于光子晶体波导理论和应用的研究都具有重要意义。
在上述磁性光子晶体带隙理论及实验研究的基础上，我们通过特定的实验方法制备了具有单向导波特性的磁性表面等离子体微波波导。当电磁波的频率处于磁性表面等离子体共振频率区域，由二维磁性光子晶体阵列构成的波导具有不对称的电磁波传输特性：即在由两个二维周期阵列（每个阵列外加方向相反的静磁场）所构成的导波通道中，电磁波只沿着一个方向传播，而在其反方向的传播被显著抑制。实验发现，该波导的单向传输特性不受金属障碍物和光子晶体周期性破坏的影响；更重要的是，其单向导波的工作频率可由外加磁场调制。理论研究表明：这一现象源自于磁性表面等离子体能带结构的时间反演对称破缺，类比于二维电子系统中的量子霍尔效应的手性边缘传输现象。
开口谐振环作为一种新型的电磁波谐振系统，其共振频率克服了传统散射波长的限制，尺寸可达到共振频率波长的1/10甚至更小。基于对开口谐振环的磁共振响应特性的研究，本工作运用溅射和光刻方法制备了一种新型的不共面开口谐振环。区别于传统的共面开口谐振环，实验发现不共面开口谐振环的共振频率与环-环间距具有线性关系。环-环间距越小，其共振频率越低。当环-环间距达到微米级别，发生磁共振时其几何尺寸可达到波长的1/120。这一实验结果可为天线的小型化研究提供有益参考。
本工作通过实验验证了铁磁薄膜的超快退磁效应可辐射出太赫兹波，并且发现了铁磁薄膜受激光脉冲激发后，其辐射出的太赫兹波的强度与薄膜本身的阻尼系数成明显的线性关系。实验采用磁控溅射方法制备铁磁薄膜，并利用自旋注入效应，改变与铁磁薄膜相邻的金属薄膜的厚度，从而获得具有不同阻尼系数的铁磁薄膜样品。使用抽运-探测技术观测到辐射的太赫兹波的强度与阻尼系数存在显著的正比关系：薄膜的阻尼系数越大，太赫兹波的辐射强度越大，表明磁矩的退磁过程更快。这一发现为进一步研究超快激光操控磁化态的动力学过程开辟了新的思路。实验中通过自旋注入效应改变薄膜的阻尼系数，表明了自旋注入理论也可能适用于太赫兹波范围。
The dynamics of magnetic materials in microwave and terahertz range have beenstudied and utilized for dacades. Most of attentions were focused on the insulatingmagnetic materials. Recently, due to the development of magnetic photonic crystals,negative refractive index materials and ultrafast laser pulse techniques, there have beenincreasing interests in the microwave guiding system such as magnetic surface plasmawaveguide and split ring resonator. On the other hand, the demands for theever-increasing speed of data storage in magnetic media have triggered intense searchesfor innovative methods to control magnetization, ultrafast magnetization switching bypulsed laser excitation can be viewed as one of the prospective technique.
We experimentally studied magnetically controllable photonic band gaps (PBGs)in two-dimensional magnetic photonic crystals (MPCs) consisting of ferrite rods.Besides the conventional PBG that relates to Bragg scattering, another two types ofPBGs, resulting from magnetic surface plasmon resonance and spin-wave resonance,respectively, are observed. The PBG due to magnetic surface plasmon resonance isparticularly interesting because of its analogy to surface plasmon in metal, furthermore,it is shown to be completely tunable by an external static magnetic field from bothexperimental and theoretical point of view.
We also have demonstrated experimentally a one-way magnetic surface plasmonelectromagnetic waveguide in the microwave range based on the MPCs The waveguideexhibits asymmetric transmission of electromagnetic waves in the frequency range nearthe magnetic surface plasmon resonance for an MPC, such that a significant one-waypropagation can be observed in the channel between the two MPC slabs, each in anexternal static magnetic field (ESMF) of opposite directions. The one-way waveguide isnot only immune to interstitial metal defects，but also robust against the disorder of rodposition. Furthermore, its working frequency can be flexibly tuned by an ESMF, whichmakes it more favorable for the design of electromagnetic devices. The physics isrelated to the broken time reversal symmetry of the magnetic surface plasmon bandstates and the excitation of a giant circulation of the energy flow, similar to the case in the quantized Hall Effect.
Based on the understanding of the magnetic resonance properties of split ringresonator no longer suffers from half-wavelength requirement for resonance, wedemonstrated that for coplanar split ring resonator, the wavelength of the resonancemode is about10times larger than geometrical size of the ring; for non-coplanar splitring resonator, the resonance frequency depends linearly on the ring-ring separation. Werealized the non-coplanar split ring system using sputtering and etching techniques, it’sgeormetrical size is only1/120of the wavelength at the lowest resonance mode. Thisdemonstration opens a door to miniaturization of resonator.
It is believed that ultrafast demagnetization process in ferromagnetic film canproduce terahertz (THz) emission. We present an experimental demonstration that,following ultrafast optical excitation, the magnitude of terahertz electromagnetic pulsesemitted from a ferromagnetic film is proportional to the Gilbert damping constant,which is conventionally used to describe the damping of magnetization precession.Different damping factors are obtained by varying the normal metal film adjacent to themagnetic film via spin pumping. It is shown that the larger the Gilbert damping, thelarger emitted THz signal and therefore, the faster demagnetizing process. On the otherhand, the nonlocally adjusted damping constant via spin pumping in this experimentalso indicates that the spin pumping theory may still be valid in THz regime. We expectthis study would lead to new perspectives of the ultrafast manipulation of magneticorder.
引文
[1] J. C. Maxwell. On physical lines of force. Philosophical Magazine.1861,161-370
[2] S. John. Strong localization of photons in certain disordered dielectric superlattices. PhysicalReview Letters.1987,58(23):2486-2489
[3] E. Yablonovitch, T. J. Gmitter. Photonic band structure: The face-centered-cubic case. PhysicalReview Letters.1989,63:1950-1953
[4] J. B. Pendry, A. J. Holden, D. J. Robbins, et al. Magnetism from conductors and enhancednonlinear phenomena. Microwave Theory and Techniques, IEEE Transactions on.1999,47:2075-2084
[5] D. R. Smith, N. Kroll. Negative Refractive Index in Left-Handed Materials. Physical ReviewLetters.2000,85:2933-2936
[6] R. A. Shelby, D. R. Smith and S. Schultz. Experimental Verification of a Negative Index ofRefraction. Science.2001,292:77-79
[7] E. Yablonovitch. Inhibited Spontaneous Emission in Solid-State Physics and Electronics.Physical Review Letters.1987,58:2059-2062
[8] T. F. Krauss, R. M. DeLaRue and S. Brand. Two-dimensional photonic-bandgap structuresoperating at near infrared wavelengths. Nature.1996,383:699-702
[9] M. N. Baibich, J. M. Broto, A. Fert, et al. Giant magnetoresistance of (001)Fe/(001) Cr magneticsuperlattices. Physical Review Letters.1988,61:2472-2475
[10] T. J. Yen, W. J. Padilla, N. Fang, et al. Terahertz magnetic response from artificial materials.Science.2004,303:1494-1496
[11] S. Linden, C. Enkrich, M. Wegener, et al. Magnetic Response of Metamaterials at100Terahertz.Science.2004,306:1351-1353
[12] C. Enkrich, M. Wegener, S. Linden, et al. Magnetic Metamaterials at Telecommunication andVisible Frequencies. Physical Review Letters.2005,95:203901
[13] A. K. Azad, A. J. Taylor, E. Smirnova, et al. Characterization and analysis of terahertzmetamaterials based on rectangular split-ring resonators. Applied Physics Letters.2008,92:011119
[14] H. O. Moser, B. D. F. Casse, O. Wilhelmi, et al. Terahertz Response of a MicrofabricatedRod--Split-Ring-Resonator Electromagnetic Metamaterial. Physical Review Letters.2005,94:063901
[15] G. Binasch, P. Grunberg, F. Saurenbach, et al. Enhanced magnetoresistance in layeredmagnetic-structures with antiferromagnetic interlayer exchange. Physical Review B.1989,39:4828-4830
[16] S. S. P. Parkin, K. P. Roche, M. G. Samant, et al. Exchange-biased magnetic tunnel junctionsand application to nonvolatile magnetic random access memory (invited). Journal of AppliedPhysics.1999,85:5828-5833
[17] L. He, W. D. Doyle and H. Fujiwara. High-speed coherent switching below thestoner-wohlfarth limit. IEEE Transactions on Magnetics.1994,30:4086-4088
[18] J. A. Katine, F. J. Albert, R. A. Buhrman, et al. Current-driven magnetization reversal andspin-wave excitations in Co/Cu/Co pillars. Physical Review Letters.2000,84:3149-3152
[19] M. Tsoi, A. G. M. Jansen, J. Bass, et al. Excitation of a magnetic multilayer by an electriccurrent. Physical Review Letters.1998,80:4281-4284
[20] S. Urazhdin, N. O. Birge, W. P. Pratt, et al. Current-driven magnetic excitations inpermalloy-based multilayer nanopillars. Physical Review Letters.2003,91:146803
[21]E. Beaurepaire, J. C. Merle, A. Daunois, et al. Ultrafast Spin Dynamics in Ferromagnetic Nickel.Physical Review Letters.1996,76:4250
[22] M. Vomir, L. H. F. Andrade, L. Guidoni, et al. Real Space Trajectory of the UltrafastMagnetization Dynamics in Ferromagnetic Metals. Physical Review Letters.2005,94:237601
[23] J. Hohlfeld, E. Matthias, R. Knorren, et al. Nonequilibrium magnetization dynamics of nickel.Physical Review Letters.1997,78:4861-4864
[24] A. Scholl, L. Baumgarten, R. Jacquemin, et al. Ultrafast Spin Dynamics of Ferromagnetic ThinFilms Observed by fs Spin-Resolved Two-Photon Photoemission. Physical Review Letters.1997,79:5146-5149
[25] U. C. J. Güdde, V. J hnke, J. Hohlfeld, et al. Magnetization dynamics of Ni and Co films onCu(001) and of bulk nickel surfaces. Physical Review B.1999,59: R6608-R6611
[26] G. Ju, A. V. Nurmikko, R. F. C. Farrow, et al. Ultrafast Time Resolved PhotoinducedMagnetization Rotation in a Ferromagnetic/Antiferromagnetic Exchange Coupled System.Physical Review Letters.1999,82:3705-3708
[27] B. Koopmans, M. van Kampen, J. T. Kohlhepp, et al. Ultrafast Magneto-Optics in Nickel:Magnetism or Optics. Physical Review Letters.2000,85:844-847
[28] R. J. Hicken. Ultrafast nanomagnets: seeing data storage in a new light. PhilosophicalTransactions of the Royal Society of London Series a-Mathematical Physical and EngineeringSciences.2003,361:2827-2841
[29] H. S. Rhie, H. A. Dürr and W. Eberhardt. Femtosecond Electron and Spin Dynamics inNi/W(110) Films. Physical Review Letters.2003,90:247201
[30] J. Y. Bigot, L. Guidoni, E. Beaurepaire, et al. Femtosecond Spectrotemporal Magneto-optics.Physical Review Letters.2004,93:077401
[31] T. Ogasawara, K. Ohgushi, Y. Tomioka, et al. General Features of Photoinduced Spin Dynamicsin Ferromagnetic and Ferrimagnetic Compounds. Physical Review Letters.2005,94:087202
[32] A. V. Kimel, A. Kirilyuk, A. Tsvetkov, et al. Laser-induced ultrafast spin reorientation in theantiferromagnet TmFeO3. Nature.2004,429:850-853
[33] J. Y. Bigot, M. Vomir, L. H. F. Andrade, et al. Ultrafast magnetization dynamics inferromagnetic cobalt: The role of the anisotropy. Chemical Physics.2005,318:137-146
[34] G. Ju, J. Hohlfeld, B. Bergman, et al. Ultrafast Generation of Ferromagnetic Order via aLaser-Induced Phase Transformation in FeRh Thin Films. Physical Review Letters.2004,93:197403
[35] J. U. Thiele, M. Buess and C. H. Back. Spin dynamics of theantiferromagnetic-to-ferromagnetic phase transition in FeRh on a sub-picosecond time scale.Applied Physics Letters.2004,85:2857-2859
[36] A. Kirilyuk, A. V. Kimel and T. Rasing. Ultrafast optical manipulation of magnetic order.Reviews of Modern Physics.2010,82:2731-2784
[37] N. Kazantseva, U. Nowak, R. W. Chantrell, et al. Slow recovery of the magnetisation after asub-picosecond heat pulse. Europhysics Letters.2008,81:27004
[38] U. Atxitia, O. Chubykalo-Fesenko, R. W. Chantrell, et al. Ultrafast Spin Dynamics: The Effectof Colored Noise. Physical Review Letters.2009,102:057203
[39] T. Gerrits, H. A. M. van den Berg, J. Hohlfeld, et al. Ultrafast precessional magnetizationreversal by picosecond magnetic field pulse shaping. Nature.2002,418:509-512
[40] H. W. Schumacher, C. Chappert, R. C. Sousa, et al. Quasiballistic magnetization reversal.Physical Review Letters.2003,90:017204
[41] S. Franssila. Introduction to microfabrication. Wiley,2004
[42] B. D. Cullity. Elements of X-ray Diffraction,2nd edtion. Addison Wesley Publishing Company,Inc,1978
[43] S. Foner. Versatile and sensitive vibrating-sample magnetometer. Review of ScientificInstruments.1959,30:548-557
[44] S. Foner. Sensitivity of vibrating sample magnetometers-how to incresase sensitivity if needed.Review of Scientific Instruments.1974,45:1181-1183
[45] D. M. Pozar. Microwave Engineering. New York: Wiley,2004
[46] Y. Ding, T. J. Klemmer and T. M. Crawford. A coplanar waveguide permeameter for studyinghigh-frequency properties of soft magnetic materials. Journal of Applied Physics.2004,96:2969-2972
[47] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin. Nano-optics of surface plasmonpolaritons. Phys. Rep.2005,408:131-314
[48] S. A. Maier, P. G. Kik, H. A. Atwater, et al. Local detection of electromagnetic energy transportbelow the diffraction limit in metal nanoparticle plasmon waveguides. Nature Materials.2003,2:229-232
[49] S. Y. Liu, J. J. Du, Z. F. Lin, et al. Formation of robust and completely tunable resonantphotonic band gaps. Physical Review B.2008,78:155101
[50] S. T. Chui and Z. Lin. Long-wavelength behavior of two-dimensional photonic crystals.Physical Review E.2008,78:065601
[51] Z. F. Lin and S. T. Chui. Manipulating electromagnetic radiation with magnetic photoniccrystals. Optics Letters.2007,32:2288-2290
[52] S. T. Chui and Z. F. Lin. Probing states with macroscopic circulations in magnetic photoniccrystals. Journal of Physics-Condensed Matter.2007,19:406233
[53] S. T. Chui, S. Y. Liu and Z. F. Lin. Reflected wave of finite circulation from magnetic photoniccrystals. Journal of Physics-Condensed Matter.2010,22:182201
[54] S. Y. Liu, W. L. Lu, Z. F. Lin, et al. Magnetically controllable unidirectional electromagneticwaveguiding devices designed with metamaterials. Applied Physics Letters.2010,97:201113
[55]L. M. Li, Z. Q. Zhang. Muitiple-scattering approach to finite-sized photonic band-gap materials.Physical Review B.1998,58:9587-9590
[56] M. Sato, Y. Ishii, Simple and approximate expressions of demagnetizing factors of uniformitymagnetized rectangular rod and cylinder. Journal of Applied Physics,.1989,66:983-985
[57] S. Liu, Z. Lin. Opening up complete photonic bandgaps in three-dimensional photonic crystalsconsisting of biaxial dielectric spheres. Physical Review E.2006,73:066609
[58] S. Liu and Z. Lin. Modulation of photonic band structures with dielectric anisotropy. EuropeanPhysical Journal B.2006,53:301-306
[59] L. Shiyang, C. Weikang, D. Junjie, et al. Manipulating Negative-Refractive Behavior with aMagnetic Field. Physical Review Letters.2008,101:157407
[60] C. Enkrich, M. Wegener, S. Linden, et al. Magnetic metamaterials at telecommunication and visiblefrequencies. Physical Review Letters.2005,95:203901
[61] A. N. Grigorenko, A. K. Geim, H. F. Gleeson, et al. Nanofabricated media with negativepermeability at visible frequencies. Nature.2005,438:335-338
[62] S. Linden, M. Decker and M. Wegener. Model System for a One-Dimensional MagneticPhotonic Crystal. Physical Review Letters.2006,97:083902
[63] Z. Wang, Y. D. Chong, J. D. Joannopoulos, et al. Reflection-free one-way edge modes in agyromagnetic photonic crystal. Physical Review Letters.2008,100:013905
[64] E. Yablonovitch. Photonics One-way road for light. Nature.2009,461:744-744
[65] K. V. Klitzing, G. Dorda and M. Pepper. New Method for High-Accuracy Determination of theFine-Structure Constant Based on Quantized Hall Resistance. Physical Review Letters.1980,45:494-497
[66] F. D. M. Haldane and S. Raghu. Possible realization of directional optical waveguides inphotonic crystals with broken time-reversal symmetry. Physical Review Letters.2008,100:013904
[67]S. Raghu and F. D. M. Haldane. Analogs of quantum-Hall-effect edge states in photonic crystals.Physical Review A (Atomic, Molecular, and Optical Physics).2008,78:033834
[68] Z. Wang, Y. Chong, J. D. Joannopoulos, et al. Observation of unidirectionalbackscattering-immune topological electromagnetic states. Nature.2009,461:772-775
[69] W. Zheng, Y. D. Chong, D. J. John, et al. Reflection-Free One-Way Edge Modes in aGyromagnetic Photonic Crystal. Physical Review Letters.2008,100:013905
[70] Z. Yu, G. Veronis, Z. Wang, et al. One-Way Electromagnetic Waveguide Formed at the Interfacebetween a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal. PhysicalReview Letters.2008,100:023902
[71] V. G. Veselago. Elecrodynamics of substances with simultaneously negtive values of sigma andmu. Soviet Physics Uspekhi-Ussr.1968,10:509
[72] D. R. Smith, W. J. Padilla, D. C. Vier, et al. Composite Medium with Simultaneously NegativePermeability and Permittivity. Physical Review Letters.2000,84:4184-4187
[73] I. Bulu, H. Caglayan, K. Aydin, et al. Compact size highly directive antennas based on the SRRmetamaterial medium. New Journal of Physics.2005,7:10
[74] P. Gay-Balmaz and O. J. F. Martin. Efficient isotropic magnetic resonators. Applied PhysicsLetters.2002,81:939-941
[75] B. Sauviac, C. R. Simovski and S. A. Tretyakov. Double Split-Ring Resonators: AnalyticalModeling and Numerical Simulations. Electromagnetics.2004,24:317-338
[76] R. Marqués, J. Martel, F. Mesa, et al. Left-Handed-Media Simulation and Transmission of EMWaves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides. Physical ReviewLetters.2002,89:183901
[77] R. Marqués, F. Medina and R. Rafii-El-Idrissi. Role of bianisotropy in negative permeabilityand left-handed metamaterials. Physical Review B.2002,65:144440
[78] S. T. Chui, Y. Zhang and L. Zhou. Design and miniaturization of split ring structures based onan analytic solution of their resonance. Journal of Applied Physics.2008,104:034305
[79] L. Zhou and S. T. Chui. Magnetic resonances in metallic double split rings: Lower frequencylimit and bianisotropy. Applied Physics Letters.2007,90:041903
[80] L. Zhou and S. T. Chui. Eigenmodes of metallic ring systems: A rigorous approach. PhysicalReview B.2006,74:035419
[81] L. Zhou, X. Q. Huang, Y. Zhang, et al. Resonance properties of metallic ring systems. MaterialsToday.2009,12:52-59
[82] S. A. Ramakrishna. Physics of negative refractive index materials. Reports on Progress inPhysics.2005,68:449-521
[83] R. W. Ziolkowski and A. D. Kipple. Application of double negative materials to increase thepower radiated by electrically small antennas. IEEE Trans. Antennas Propag.2003,51:2626-2640
[84] J. Garcia-Garcia, F. Martin, F. Falcone, et al. Microwave filters with improved stopband basedon sub-wavelength resonators. IEEE Transactions on Microwave Theory and Techniques.2005,53:1997-2006
[85] K. Aydin and E. Ozbay. Capacitor-loaded split ring resonators as tunable metamaterialcomponents. Journal of Applied Physics.2007,101:024911
[86] J.-Y. Bigot, M. Vomir and E. Beaurepaire. Coherent ultrafast magnetism induced byfemtosecond laser pulses. Nat Phys.2009,5:515-520
[87] E. Beaurepaire, M. Maret, Halt, et al. Spin dynamics in CoPt_{3} alloy films: A magnetic phasetransition in the femtosecond time scale. Physical Review B.1998,58:12134
[88] E. Beaurepaire, M. Maret, Halt, et al. Spin dynamics in CoPt3alloy films: A magnetic phasetransition in the femtosecond time scale. Physical Review B.1998,58:12134
[89] P. M. Oppeneer and A. Liebsch. Ultrafast demagnetization in Ni: theory of magneto-optics fornon-equilibrium electron distributions. Journal of Physics-Condensed Matter.2004,16:5519-5530
[90]K. H. Bennemann. Ultrafast dynamics in solids. Journal of Physics-Condensed Matter.2004,16:R995-R1056
[91] U. Bovensiepen. Coherent and incoherent excitations of the Gd(0001) surface on ultrafasttimescales. Journal of Physics-Condensed Matter.2007,19:083201
[92] A. Vernes and P. Weinberger. Formally linear response theory of pump-probe experiments.Physical Review B.2005,71:165108
[93] J. G. Wang, C. J. Sun, Y. Hashimoto, et al. Ultrafast magneto-optics in ferromagnetic III-Vsemiconductors. Journal of Physics-Condensed Matter.2006,18: R501-R530
[94] G. P. Zhang, W. Hubner, G. Lefkidis, et al. Paradigm of the time-resolved magneto-optical Kerreffect for femtosecond magnetism. Nature Physics.2009,5:499-502
[95] A. Kirilyuk, A. Kimel, F. Hansteen, et al. Ultrafast all-optical control of the magnetization inmagnetic dielectrics. Low Temperature Physics.2006,32:748-767
[96] B. Koopmans, J. J. M. Ruigrok, F. D. Longa, et al. Unifying Ultrafast Magnetization Dynamics.Physical Review Letters.2005,95:267207
[97] E. Beaurepaire, G. M. Turner, S. M. Harrel, et al. Coherent terahertz emission fromferromagnetic films excited by femtosecond laser pulses. Applied Physics Letters.2004,84:3465-3467
[98] G. Malinowski, F. D. Longa, J. H. H. Rietjens, et al. Control of speed and efficiency of ultrafastdemagnetization by direct transfer of spin angular momentum. Nature Physics.2008,4:855-858
[99] S. Mizukami, Y. Ando and T. Miyazaki. Effect of spin diffusion on Gilbert damping for a verythin permalloy layer in Cu/permalloy/Cu/Pt films. Physical Review B.2002,66:104413
[100] Q. Wu and X. C. Zhang. Free-space electrooptic sampling of terahertz beams. Applied PhysicsLetters.1995,67:3523-3525
[101]A. Nahata, A. S. Weling and T. F. Heinz. A wideband coherent terahertz spectroscopy systemusing optical rectification and electro-optic sampling. Applied Physics Letters.1996,69:2321-2323
[102]D. M. Pozar. Microwave Engineering (3rd edition). India: Wiley2008
[2] S. John. Strong localization of photons in certain disordered dielectric superlattices. PhysicalReview Letters.1987,58(23):2486-2489
[3] E. Yablonovitch, T. J. Gmitter. Photonic band structure: The face-centered-cubic case. PhysicalReview Letters.1989,63:1950-1953
[4] J. B. Pendry, A. J. Holden, D. J. Robbins, et al. Magnetism from conductors and enhancednonlinear phenomena. Microwave Theory and Techniques, IEEE Transactions on.1999,47:2075-2084
[5] D. R. Smith, N. Kroll. Negative Refractive Index in Left-Handed Materials. Physical ReviewLetters.2000,85:2933-2936
[6] R. A. Shelby, D. R. Smith and S. Schultz. Experimental Verification of a Negative Index ofRefraction. Science.2001,292:77-79
[7] E. Yablonovitch. Inhibited Spontaneous Emission in Solid-State Physics and Electronics.Physical Review Letters.1987,58:2059-2062
[8] T. F. Krauss, R. M. DeLaRue and S. Brand. Two-dimensional photonic-bandgap structuresoperating at near infrared wavelengths. Nature.1996,383:699-702
[9] M. N. Baibich, J. M. Broto, A. Fert, et al. Giant magnetoresistance of (001)Fe/(001) Cr magneticsuperlattices. Physical Review Letters.1988,61:2472-2475
[10] T. J. Yen, W. J. Padilla, N. Fang, et al. Terahertz magnetic response from artificial materials.Science.2004,303:1494-1496
[11] S. Linden, C. Enkrich, M. Wegener, et al. Magnetic Response of Metamaterials at100Terahertz.Science.2004,306:1351-1353
[12] C. Enkrich, M. Wegener, S. Linden, et al. Magnetic Metamaterials at Telecommunication andVisible Frequencies. Physical Review Letters.2005,95:203901
[13] A. K. Azad, A. J. Taylor, E. Smirnova, et al. Characterization and analysis of terahertzmetamaterials based on rectangular split-ring resonators. Applied Physics Letters.2008,92:011119
[14] H. O. Moser, B. D. F. Casse, O. Wilhelmi, et al. Terahertz Response of a MicrofabricatedRod--Split-Ring-Resonator Electromagnetic Metamaterial. Physical Review Letters.2005,94:063901
[15] G. Binasch, P. Grunberg, F. Saurenbach, et al. Enhanced magnetoresistance in layeredmagnetic-structures with antiferromagnetic interlayer exchange. Physical Review B.1989,39:4828-4830
[16] S. S. P. Parkin, K. P. Roche, M. G. Samant, et al. Exchange-biased magnetic tunnel junctionsand application to nonvolatile magnetic random access memory (invited). Journal of AppliedPhysics.1999,85:5828-5833
[17] L. He, W. D. Doyle and H. Fujiwara. High-speed coherent switching below thestoner-wohlfarth limit. IEEE Transactions on Magnetics.1994,30:4086-4088
[18] J. A. Katine, F. J. Albert, R. A. Buhrman, et al. Current-driven magnetization reversal andspin-wave excitations in Co/Cu/Co pillars. Physical Review Letters.2000,84:3149-3152
[19] M. Tsoi, A. G. M. Jansen, J. Bass, et al. Excitation of a magnetic multilayer by an electriccurrent. Physical Review Letters.1998,80:4281-4284
[20] S. Urazhdin, N. O. Birge, W. P. Pratt, et al. Current-driven magnetic excitations inpermalloy-based multilayer nanopillars. Physical Review Letters.2003,91:146803
[21]E. Beaurepaire, J. C. Merle, A. Daunois, et al. Ultrafast Spin Dynamics in Ferromagnetic Nickel.Physical Review Letters.1996,76:4250
[22] M. Vomir, L. H. F. Andrade, L. Guidoni, et al. Real Space Trajectory of the UltrafastMagnetization Dynamics in Ferromagnetic Metals. Physical Review Letters.2005,94:237601
[23] J. Hohlfeld, E. Matthias, R. Knorren, et al. Nonequilibrium magnetization dynamics of nickel.Physical Review Letters.1997,78:4861-4864
[24] A. Scholl, L. Baumgarten, R. Jacquemin, et al. Ultrafast Spin Dynamics of Ferromagnetic ThinFilms Observed by fs Spin-Resolved Two-Photon Photoemission. Physical Review Letters.1997,79:5146-5149
[25] U. C. J. Güdde, V. J hnke, J. Hohlfeld, et al. Magnetization dynamics of Ni and Co films onCu(001) and of bulk nickel surfaces. Physical Review B.1999,59: R6608-R6611
[26] G. Ju, A. V. Nurmikko, R. F. C. Farrow, et al. Ultrafast Time Resolved PhotoinducedMagnetization Rotation in a Ferromagnetic/Antiferromagnetic Exchange Coupled System.Physical Review Letters.1999,82:3705-3708
[27] B. Koopmans, M. van Kampen, J. T. Kohlhepp, et al. Ultrafast Magneto-Optics in Nickel:Magnetism or Optics. Physical Review Letters.2000,85:844-847
[28] R. J. Hicken. Ultrafast nanomagnets: seeing data storage in a new light. PhilosophicalTransactions of the Royal Society of London Series a-Mathematical Physical and EngineeringSciences.2003,361:2827-2841
[29] H. S. Rhie, H. A. Dürr and W. Eberhardt. Femtosecond Electron and Spin Dynamics inNi/W(110) Films. Physical Review Letters.2003,90:247201
[30] J. Y. Bigot, L. Guidoni, E. Beaurepaire, et al. Femtosecond Spectrotemporal Magneto-optics.Physical Review Letters.2004,93:077401
[31] T. Ogasawara, K. Ohgushi, Y. Tomioka, et al. General Features of Photoinduced Spin Dynamicsin Ferromagnetic and Ferrimagnetic Compounds. Physical Review Letters.2005,94:087202
[32] A. V. Kimel, A. Kirilyuk, A. Tsvetkov, et al. Laser-induced ultrafast spin reorientation in theantiferromagnet TmFeO3. Nature.2004,429:850-853
[33] J. Y. Bigot, M. Vomir, L. H. F. Andrade, et al. Ultrafast magnetization dynamics inferromagnetic cobalt: The role of the anisotropy. Chemical Physics.2005,318:137-146
[34] G. Ju, J. Hohlfeld, B. Bergman, et al. Ultrafast Generation of Ferromagnetic Order via aLaser-Induced Phase Transformation in FeRh Thin Films. Physical Review Letters.2004,93:197403
[35] J. U. Thiele, M. Buess and C. H. Back. Spin dynamics of theantiferromagnetic-to-ferromagnetic phase transition in FeRh on a sub-picosecond time scale.Applied Physics Letters.2004,85:2857-2859
[36] A. Kirilyuk, A. V. Kimel and T. Rasing. Ultrafast optical manipulation of magnetic order.Reviews of Modern Physics.2010,82:2731-2784
[37] N. Kazantseva, U. Nowak, R. W. Chantrell, et al. Slow recovery of the magnetisation after asub-picosecond heat pulse. Europhysics Letters.2008,81:27004
[38] U. Atxitia, O. Chubykalo-Fesenko, R. W. Chantrell, et al. Ultrafast Spin Dynamics: The Effectof Colored Noise. Physical Review Letters.2009,102:057203
[39] T. Gerrits, H. A. M. van den Berg, J. Hohlfeld, et al. Ultrafast precessional magnetizationreversal by picosecond magnetic field pulse shaping. Nature.2002,418:509-512
[40] H. W. Schumacher, C. Chappert, R. C. Sousa, et al. Quasiballistic magnetization reversal.Physical Review Letters.2003,90:017204
[41] S. Franssila. Introduction to microfabrication. Wiley,2004
[42] B. D. Cullity. Elements of X-ray Diffraction,2nd edtion. Addison Wesley Publishing Company,Inc,1978
[43] S. Foner. Versatile and sensitive vibrating-sample magnetometer. Review of ScientificInstruments.1959,30:548-557
[44] S. Foner. Sensitivity of vibrating sample magnetometers-how to incresase sensitivity if needed.Review of Scientific Instruments.1974,45:1181-1183
[45] D. M. Pozar. Microwave Engineering. New York: Wiley,2004
[46] Y. Ding, T. J. Klemmer and T. M. Crawford. A coplanar waveguide permeameter for studyinghigh-frequency properties of soft magnetic materials. Journal of Applied Physics.2004,96:2969-2972
[47] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin. Nano-optics of surface plasmonpolaritons. Phys. Rep.2005,408:131-314
[48] S. A. Maier, P. G. Kik, H. A. Atwater, et al. Local detection of electromagnetic energy transportbelow the diffraction limit in metal nanoparticle plasmon waveguides. Nature Materials.2003,2:229-232
[49] S. Y. Liu, J. J. Du, Z. F. Lin, et al. Formation of robust and completely tunable resonantphotonic band gaps. Physical Review B.2008,78:155101
[50] S. T. Chui and Z. Lin. Long-wavelength behavior of two-dimensional photonic crystals.Physical Review E.2008,78:065601
[51] Z. F. Lin and S. T. Chui. Manipulating electromagnetic radiation with magnetic photoniccrystals. Optics Letters.2007,32:2288-2290
[52] S. T. Chui and Z. F. Lin. Probing states with macroscopic circulations in magnetic photoniccrystals. Journal of Physics-Condensed Matter.2007,19:406233
[53] S. T. Chui, S. Y. Liu and Z. F. Lin. Reflected wave of finite circulation from magnetic photoniccrystals. Journal of Physics-Condensed Matter.2010,22:182201
[54] S. Y. Liu, W. L. Lu, Z. F. Lin, et al. Magnetically controllable unidirectional electromagneticwaveguiding devices designed with metamaterials. Applied Physics Letters.2010,97:201113
[55]L. M. Li, Z. Q. Zhang. Muitiple-scattering approach to finite-sized photonic band-gap materials.Physical Review B.1998,58:9587-9590
[56] M. Sato, Y. Ishii, Simple and approximate expressions of demagnetizing factors of uniformitymagnetized rectangular rod and cylinder. Journal of Applied Physics,.1989,66:983-985
[57] S. Liu, Z. Lin. Opening up complete photonic bandgaps in three-dimensional photonic crystalsconsisting of biaxial dielectric spheres. Physical Review E.2006,73:066609
[58] S. Liu and Z. Lin. Modulation of photonic band structures with dielectric anisotropy. EuropeanPhysical Journal B.2006,53:301-306
[59] L. Shiyang, C. Weikang, D. Junjie, et al. Manipulating Negative-Refractive Behavior with aMagnetic Field. Physical Review Letters.2008,101:157407
[60] C. Enkrich, M. Wegener, S. Linden, et al. Magnetic metamaterials at telecommunication and visiblefrequencies. Physical Review Letters.2005,95:203901
[61] A. N. Grigorenko, A. K. Geim, H. F. Gleeson, et al. Nanofabricated media with negativepermeability at visible frequencies. Nature.2005,438:335-338
[62] S. Linden, M. Decker and M. Wegener. Model System for a One-Dimensional MagneticPhotonic Crystal. Physical Review Letters.2006,97:083902
[63] Z. Wang, Y. D. Chong, J. D. Joannopoulos, et al. Reflection-free one-way edge modes in agyromagnetic photonic crystal. Physical Review Letters.2008,100:013905
[64] E. Yablonovitch. Photonics One-way road for light. Nature.2009,461:744-744
[65] K. V. Klitzing, G. Dorda and M. Pepper. New Method for High-Accuracy Determination of theFine-Structure Constant Based on Quantized Hall Resistance. Physical Review Letters.1980,45:494-497
[66] F. D. M. Haldane and S. Raghu. Possible realization of directional optical waveguides inphotonic crystals with broken time-reversal symmetry. Physical Review Letters.2008,100:013904
[67]S. Raghu and F. D. M. Haldane. Analogs of quantum-Hall-effect edge states in photonic crystals.Physical Review A (Atomic, Molecular, and Optical Physics).2008,78:033834
[68] Z. Wang, Y. Chong, J. D. Joannopoulos, et al. Observation of unidirectionalbackscattering-immune topological electromagnetic states. Nature.2009,461:772-775
[69] W. Zheng, Y. D. Chong, D. J. John, et al. Reflection-Free One-Way Edge Modes in aGyromagnetic Photonic Crystal. Physical Review Letters.2008,100:013905
[70] Z. Yu, G. Veronis, Z. Wang, et al. One-Way Electromagnetic Waveguide Formed at the Interfacebetween a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal. PhysicalReview Letters.2008,100:023902
[71] V. G. Veselago. Elecrodynamics of substances with simultaneously negtive values of sigma andmu. Soviet Physics Uspekhi-Ussr.1968,10:509
[72] D. R. Smith, W. J. Padilla, D. C. Vier, et al. Composite Medium with Simultaneously NegativePermeability and Permittivity. Physical Review Letters.2000,84:4184-4187
[73] I. Bulu, H. Caglayan, K. Aydin, et al. Compact size highly directive antennas based on the SRRmetamaterial medium. New Journal of Physics.2005,7:10
[74] P. Gay-Balmaz and O. J. F. Martin. Efficient isotropic magnetic resonators. Applied PhysicsLetters.2002,81:939-941
[75] B. Sauviac, C. R. Simovski and S. A. Tretyakov. Double Split-Ring Resonators: AnalyticalModeling and Numerical Simulations. Electromagnetics.2004,24:317-338
[76] R. Marqués, J. Martel, F. Mesa, et al. Left-Handed-Media Simulation and Transmission of EMWaves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides. Physical ReviewLetters.2002,89:183901
[77] R. Marqués, F. Medina and R. Rafii-El-Idrissi. Role of bianisotropy in negative permeabilityand left-handed metamaterials. Physical Review B.2002,65:144440
[78] S. T. Chui, Y. Zhang and L. Zhou. Design and miniaturization of split ring structures based onan analytic solution of their resonance. Journal of Applied Physics.2008,104:034305
[79] L. Zhou and S. T. Chui. Magnetic resonances in metallic double split rings: Lower frequencylimit and bianisotropy. Applied Physics Letters.2007,90:041903
[80] L. Zhou and S. T. Chui. Eigenmodes of metallic ring systems: A rigorous approach. PhysicalReview B.2006,74:035419
[81] L. Zhou, X. Q. Huang, Y. Zhang, et al. Resonance properties of metallic ring systems. MaterialsToday.2009,12:52-59
[82] S. A. Ramakrishna. Physics of negative refractive index materials. Reports on Progress inPhysics.2005,68:449-521
[83] R. W. Ziolkowski and A. D. Kipple. Application of double negative materials to increase thepower radiated by electrically small antennas. IEEE Trans. Antennas Propag.2003,51:2626-2640
[84] J. Garcia-Garcia, F. Martin, F. Falcone, et al. Microwave filters with improved stopband basedon sub-wavelength resonators. IEEE Transactions on Microwave Theory and Techniques.2005,53:1997-2006
[85] K. Aydin and E. Ozbay. Capacitor-loaded split ring resonators as tunable metamaterialcomponents. Journal of Applied Physics.2007,101:024911
[86] J.-Y. Bigot, M. Vomir and E. Beaurepaire. Coherent ultrafast magnetism induced byfemtosecond laser pulses. Nat Phys.2009,5:515-520
[87] E. Beaurepaire, M. Maret, Halt, et al. Spin dynamics in CoPt_{3} alloy films: A magnetic phasetransition in the femtosecond time scale. Physical Review B.1998,58:12134
[88] E. Beaurepaire, M. Maret, Halt, et al. Spin dynamics in CoPt3alloy films: A magnetic phasetransition in the femtosecond time scale. Physical Review B.1998,58:12134
[89] P. M. Oppeneer and A. Liebsch. Ultrafast demagnetization in Ni: theory of magneto-optics fornon-equilibrium electron distributions. Journal of Physics-Condensed Matter.2004,16:5519-5530
[90]K. H. Bennemann. Ultrafast dynamics in solids. Journal of Physics-Condensed Matter.2004,16:R995-R1056
[91] U. Bovensiepen. Coherent and incoherent excitations of the Gd(0001) surface on ultrafasttimescales. Journal of Physics-Condensed Matter.2007,19:083201
[92] A. Vernes and P. Weinberger. Formally linear response theory of pump-probe experiments.Physical Review B.2005,71:165108
[93] J. G. Wang, C. J. Sun, Y. Hashimoto, et al. Ultrafast magneto-optics in ferromagnetic III-Vsemiconductors. Journal of Physics-Condensed Matter.2006,18: R501-R530
[94] G. P. Zhang, W. Hubner, G. Lefkidis, et al. Paradigm of the time-resolved magneto-optical Kerreffect for femtosecond magnetism. Nature Physics.2009,5:499-502
[95] A. Kirilyuk, A. Kimel, F. Hansteen, et al. Ultrafast all-optical control of the magnetization inmagnetic dielectrics. Low Temperature Physics.2006,32:748-767
[96] B. Koopmans, J. J. M. Ruigrok, F. D. Longa, et al. Unifying Ultrafast Magnetization Dynamics.Physical Review Letters.2005,95:267207
[97] E. Beaurepaire, G. M. Turner, S. M. Harrel, et al. Coherent terahertz emission fromferromagnetic films excited by femtosecond laser pulses. Applied Physics Letters.2004,84:3465-3467
[98] G. Malinowski, F. D. Longa, J. H. H. Rietjens, et al. Control of speed and efficiency of ultrafastdemagnetization by direct transfer of spin angular momentum. Nature Physics.2008,4:855-858
[99] S. Mizukami, Y. Ando and T. Miyazaki. Effect of spin diffusion on Gilbert damping for a verythin permalloy layer in Cu/permalloy/Cu/Pt films. Physical Review B.2002,66:104413
[100] Q. Wu and X. C. Zhang. Free-space electrooptic sampling of terahertz beams. Applied PhysicsLetters.1995,67:3523-3525
[101]A. Nahata, A. S. Weling and T. F. Heinz. A wideband coherent terahertz spectroscopy systemusing optical rectification and electro-optic sampling. Applied Physics Letters.1996,69:2321-2323
[102]D. M. Pozar. Microwave Engineering (3rd edition). India: Wiley2008