双层超晶格的磁性质
摘要
磁性材料是应用越来越广泛一种功能材料。随着镀膜技术的发展,电子器件的尺寸已进入到微/纳米尺度。当薄膜厚度减小至超薄膜时,其结构、微结构、热力学性质和磁性质均与大块材料有很大不同。在基础磁性理论和应用技术上,磁性超品格的研究具有重大的意义。特别是,磁性超晶格为我们提供了一个人造新材料的途径,通过人工调制超晶格的组成和几何特征,就能得到我们所需要的磁性材料。同时,理论上对磁性超晶格的磁学性质进行分析,对新的功能材料的研究有指导意义。
本文采用Heisenberg模型为基础,对双层亚铁磁和铁磁超品格的磁性质进行理论研究。利用线性自旋波近似、付立叶变换和格林函数技术分别计算出双层亚铁磁和铁磁超晶格的各种磁性质,分析系统参数(自旋量子数、层间交换耦合系数、层内交换耦合系数、各向异性参数、外磁场)对磁性质的影响。结果表明:系统参数对此系统的磁性质有着重要的影响。双层亚铁磁性超晶格和双层铁磁性超晶格系统都存在两支能谱,且系统的各个参数都对这两支能谱有着重要的影响。系统的自旋量子数S_1(层间交换耦合系数J_(12))和S_2(J_(21))对能隙的影响相同,能隙随着S_1(J_(12))和S_2(J_(21))的差值的增加而增大。对于亚铁磁超晶格来说,两层的各向异性参数D_1和D_2对能隙的影响不同,外磁场对能隙有一定的影响。而对于铁磁性超晶格而言,两层的各向异性参数对能隙的影响相同,能隙随着D_1和D_2差值的增加而增大,外磁场对能隙没有影响。对于双层亚铁磁性超晶格和双层铁磁性超晶格,低温磁矩随着温度的升高而减小,随着自旋量子数、层内耦合系数、各向异性参数的增大而增大。内能和比热随着自旋量子数、层间耦合系数的绝对值、层内耦系数以及各向异性参数的增加而减小。对于亚铁磁性超晶格来说,内能随着磁场的增强而减小,磁场对比热几乎没有影响。对于铁磁性超晶格来说,内能和比热随着外磁场的增加而减小。
Magnetic material as one kind of functional material is applied more and more widely. With the rapid development of technique of plating, the dimensions of electronic devices are extended to the scale of micro/nano. When films are diminished to extra thin films, all the structure, micro-structure, thermodynamic and magnetic properties are very different from those of the bulk ones. To the basic magnetic theories and applied technologies, it is very significant to research magnetic superlattices. Especially, a method to make artificial materials is obtained from magnetic superlattices theories, and the needful materials can be obtained by changing its ingredients and geometric structure. At the same time, the analysis of magnetic properties of magnetic superlattice in theories gives some significant guidances to the study of new functional materials.
Magnetic properties of double-layer ferromagnetic/ferromagnetic superlattices are researched on the basis of Heisenberg model. By linear spin wave approximation, Fourier transformation and Green's function technology, the magnetic properties of ferrimagnetic superlattices and ferromagnetic superlattices are calculated and the effects of the system parameters on their magnetic properties are also analyzed, such as: spin quantum number, interlayer exchange couplings, intralayer exchange couplings, anisotropy constant and external magnetic field. The result shows that system parameters have an important effect on its magnetic properties. Two branches of energy spectra exist in both ferrimagnetic/ ferromagnetic superlattices, and the parameters of the system have important effect on these two branches. S_1(J_(12)) and S_2(J_(21)) have the same effect on the energy gap, and the energy gap increases with increasing the difference between S_1(J_(12)) and S_2(J_(21)). For the ferrimagnetic superlattice, the anisotropy constants D_1 and D_2 have the different effect on the energy gap, and external magnetic field has an effect on it. For the ferromagnetic superlattice, the anisotropy constants D_1 and D_2 have the same effect on the energy gap, and external magnetic field has no effect on it. For double-layer ferromagnetic and ferromagnetic superlattices, the magnetization decreases with increasing temperature, and increases with increasing spin quantum number, intralayer exchange couplings and anisotropy constant. The Internal energy and the specific heat decrease with increasing spin quantum numbers, absolute values of interlayer exchange couplings, intralayer exchange couplings and anisotropy constants. For ferrimagnetic superlattice, the internal energy decreases with increasing external magnetic field, and external magnetic field has no effect on the specific heat. For ferromagnetic superlattice, the internal energy and the specific heat decrease with increasing external magnetic field.
本文采用Heisenberg模型为基础,对双层亚铁磁和铁磁超品格的磁性质进行理论研究。利用线性自旋波近似、付立叶变换和格林函数技术分别计算出双层亚铁磁和铁磁超晶格的各种磁性质,分析系统参数(自旋量子数、层间交换耦合系数、层内交换耦合系数、各向异性参数、外磁场)对磁性质的影响。结果表明:系统参数对此系统的磁性质有着重要的影响。双层亚铁磁性超晶格和双层铁磁性超晶格系统都存在两支能谱,且系统的各个参数都对这两支能谱有着重要的影响。系统的自旋量子数S_1(层间交换耦合系数J_(12))和S_2(J_(21))对能隙的影响相同,能隙随着S_1(J_(12))和S_2(J_(21))的差值的增加而增大。对于亚铁磁超晶格来说,两层的各向异性参数D_1和D_2对能隙的影响不同,外磁场对能隙有一定的影响。而对于铁磁性超晶格而言,两层的各向异性参数对能隙的影响相同,能隙随着D_1和D_2差值的增加而增大,外磁场对能隙没有影响。对于双层亚铁磁性超晶格和双层铁磁性超晶格,低温磁矩随着温度的升高而减小,随着自旋量子数、层内耦合系数、各向异性参数的增大而增大。内能和比热随着自旋量子数、层间耦合系数的绝对值、层内耦系数以及各向异性参数的增加而减小。对于亚铁磁性超晶格来说,内能随着磁场的增强而减小,磁场对比热几乎没有影响。对于铁磁性超晶格来说,内能和比热随着外磁场的增加而减小。
Magnetic material as one kind of functional material is applied more and more widely. With the rapid development of technique of plating, the dimensions of electronic devices are extended to the scale of micro/nano. When films are diminished to extra thin films, all the structure, micro-structure, thermodynamic and magnetic properties are very different from those of the bulk ones. To the basic magnetic theories and applied technologies, it is very significant to research magnetic superlattices. Especially, a method to make artificial materials is obtained from magnetic superlattices theories, and the needful materials can be obtained by changing its ingredients and geometric structure. At the same time, the analysis of magnetic properties of magnetic superlattice in theories gives some significant guidances to the study of new functional materials.
Magnetic properties of double-layer ferromagnetic/ferromagnetic superlattices are researched on the basis of Heisenberg model. By linear spin wave approximation, Fourier transformation and Green's function technology, the magnetic properties of ferrimagnetic superlattices and ferromagnetic superlattices are calculated and the effects of the system parameters on their magnetic properties are also analyzed, such as: spin quantum number, interlayer exchange couplings, intralayer exchange couplings, anisotropy constant and external magnetic field. The result shows that system parameters have an important effect on its magnetic properties. Two branches of energy spectra exist in both ferrimagnetic/ ferromagnetic superlattices, and the parameters of the system have important effect on these two branches. S_1(J_(12)) and S_2(J_(21)) have the same effect on the energy gap, and the energy gap increases with increasing the difference between S_1(J_(12)) and S_2(J_(21)). For the ferrimagnetic superlattice, the anisotropy constants D_1 and D_2 have the different effect on the energy gap, and external magnetic field has an effect on it. For the ferromagnetic superlattice, the anisotropy constants D_1 and D_2 have the same effect on the energy gap, and external magnetic field has no effect on it. For double-layer ferromagnetic and ferromagnetic superlattices, the magnetization decreases with increasing temperature, and increases with increasing spin quantum number, intralayer exchange couplings and anisotropy constant. The Internal energy and the specific heat decrease with increasing spin quantum numbers, absolute values of interlayer exchange couplings, intralayer exchange couplings and anisotropy constants. For ferrimagnetic superlattice, the internal energy decreases with increasing external magnetic field, and external magnetic field has no effect on the specific heat. For ferromagnetic superlattice, the internal energy and the specific heat decrease with increasing external magnetic field.
引文
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[2]K.Mohri,F.B.Humphrey,J.Yamosaki,et al.Jitter-lesspulse generator elements using amorphous bistable wires.IEEE Trans.Mag.,1984,20(5):1409-1411.
[3]K.Mohri,F.B.Humphrey,K.Kawashima,et al.Large Barkhausen and Matt-eucci effects in FeCoSiB,FeCrSiB,and FeNiSiB amorphous wires.IEEE Trans.Mag.,1990,26(5):1789-1791.
[4]P.Poddar,J.L.Wilson,H.Srikanth,et al.Grain size influence on soft ferromagnetic properties in Fe-Co nanoparticles.Mater Sci.Engin.B,2004,106(1):95-100.
[5]E.F.Kneller,R.Hawig.The exchange-spring magnet:a new material principle for permanent magnets.IEEE Trans.Mag.,1991,27(4):3588-3600.
[6]K.Ullakko,J.K.Huang,C.Kantner,et al.Large magnetic-field-induced strains in Ni_2MnGa single crystals.Appl.Phys.Lett.,1996,69(13):1966-1968.
[7]F.Sauerenback,J.Barnas,G.Binasch,et al.Spin waves and magnetoresistance in exchange coupled layered magnetic structures.Thin Solid Films,1989,175:317-324.
[8]都有为.磁性材料新近进展.物理.2006,35(9):730-739.
[9]T.Oguchi.Theory of spin-wave interactions in ferro- and antiferro-magnetism.Phys.Rev.,1960,117(1):117-123.
[10]D.L.Mills,A.A.Maradudin.Some thermodynamic properties of a semi-infinite Heisenberg ferromagnet.J.Phys.Chem.Solids,1967,28(10):1855-1874.
[11]Ze Nong Ding,Yu Xia,Li-Bin Lin,et al.Spin wave spectra of two-sublattice Heisenberg ferrimagnetic thin films.Solid State Communications,1991,79(3):273-276.
[12]D.L.Lin,Hang Zheng.Spin waves of two-sublattice Heisenberg ferrimagnets.Phys.Rev.B,1998,37(10):5394-5400.
[13]Hang Zheng,D.L.Lin.Surface spin waves of semi-infinite two-sublattice ferrimagnets.Phys.Rev.B,1988,37(16):9615-9624.
[14]L.L.Hinchey,D.L.Mills.Magnetic properties of superlattices formed from ferromagnetic and antiferromagnetic materials.Phys.Rev.B,1986,33(5):3329-3343.
[15]R.P.van Stapele,F.J.A.M.Gredanus,J.W.Smits.The spin-wave spectrum of layered magnetic thin films.J.Appl.Phys.,1985,57(4):1282-1290.
[16] M.Vohl, J.Barnas, P.Grunberg. Effect of interlayer exchange coupling on spin-wave spectra in magnetic double layers: Theory and experiment. Phys. Rev. B, 1989, 39(16): 12003-12012.
[17] Yu.A. Fridman, D.V. Spirin. Spin waves in two-dimensional ferromagnet with large easy-plane anisotropy. Journal of Magnetism and Magnetic Materials, 2002, 253(3): 111-117.
[18] Antoine Praz, Christopher Mudry, M. B. Hastings. Scaling relations in the quasi-two-dimensional Heisenberg antiferromagnet. Phys. Rev. B, 2006, 74:184407.
[19] L.Dobrzynski, B.D.Rouhani. Theory of bulk and surface magnons in Heisenberg ferromagnetic superlattices. Phys. Rev. B, 1986, 33(5): 3251-3256.
[20] E. Meloche, C. M. Pinciuc, M. L. Plumer. Theory of surface spin waves in a stacked triangular antiferromagnet with ferromagnetic interlayer coupling. Phys. Rev. B, 2006, 74:094424.
[21] P. N. Timonin, V. B. Shirokov. Phase transitions in random magnetic bilayer with the mean-field approximation. Phys. Rev. B, 2006, 74: 094401.
[22] Yu.A. Fridman, D.V. Spirin, C.N. Alexeyev. Reorientation phase transition in temperature in a two and three-dimensional ferromagnet with the account of magnetoelastic coupling. Journal of Magnetism and Magnetic Materials, 2001, 234(1): 174-183.
[23] Yu. A. Fridman, D.V. Spirin, P. N. Klevets. Reorientation of magnetization with temperature in 2D ferromagnets. Journal of Magnetism and Magnetic Materials, 2002, 253(3): 105-110.
[24] M. B. Silva Neto, L. Benfatto, V. Juricic, et al. Magnetic susceptibility anisotropies in a two-dimensional quantum Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. Phys. Rev. B, 2006, 73:045132.
[25] K.S.Khizriev, A.K.Murtazaev, V.M.Uzdin. Magnetic and critical properties of models of magnetic superlattices. Journal of Magnetism and Magnetic Materials, 2006, 300: e546-e549.
[26] Guo-zhu Wei, Rong-ke Qiu, An Du. Spin-wave theory of layered Heisenberg ferrimagnets. Physics Letters A, 1995, 205(4):335-339.
[27] Guo-Zhu Wei, Wei Jiang, An Du. Spin-wave theory of ferromagnetic-antiferromagnetic double layers. Physics Letters A, 1996, 224(1): 137-141.
[28] A.Moschel, K.D.Usadel, A.Hucht. Magnetization of ferromagnetic- antiferromagnetic double layers. Phys. Rev. B, 1993, 47(14):8676-8680.
[29] G.J.Mata, E.Pestana. Quantum fluctuations and the exchange bias field. Phys. Rev. B, 2006, 74:144407.
[30] L.Esaki, R.Tsu. Superlattice and negative differential conductivity in semiconductors. IBM J Res. Dev., 1970, 14(28): 61-62.
[31] D.J.Webb, A.F.Marshall, A.M.Toxen, et al. Observation of giant exchange anisotropy. IEEE Trans. Magn., 1988, 24(3): 2013-2015.
[32] D.J.Webb, R.G.Walmsley, K.Parvin, et al. Sequential deposition and metastable states in rare-earth/Co films. Phys. Rev. B, 1985, 32(7): 4667-4675.
[33] C.Carbone, S.F.Alvarado. Antiparallel coupling between Fe layers separated by a Cr interlayer: Dependence of the magnetization on the film thickness. Phys. Rev. B, 1987, 36(4): 2433-2435.
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