双层铁磁系统中交换耦合式自旋动力学研究
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摘要
目前,铁磁薄膜系统在现代信息技术领域处于非常重要的地位,在磁性数据存储到传感器或磁随机存储器方面都得到了广泛的应用.对于器件而言,材料的低激发态性质非常重要,当外场感应或进行读取数据,材料内部就会产生激发.而且已经发现现代磁性材料中的自旋翻转速度由材料的本征激发决定.所以,对层状磁性材料中的自旋激发的研究有助于理解系统的磁学性质.本文应用界面重方法,采用非周期性边界条件讨论了两层铁磁薄膜中自旋波及其共振.
首先,我们建立了层状体系中的统一微观理论,具体将此理论应用于两层对称的体系详细研究了这种体系中的本征激发,给出了体系中本征值存在的判据.研究结果发现,当界面是铁磁耦合时,体系的奇数支本征模(对称模)与界面性质无关,而偶数支本征模(反对称模)的能量随界面交换作用参数的增加而增大；当界面反铁磁耦合时,奇数支本征模(对称模)的能量随界面耦合参数的减小而减小,而偶数支本征模(反对称模)的性质与界面耦合无关,并将计算结果与已有的结论进行了对比,结果符合得很好.在此基础上,我们进一步研究了界面交换作用对自旋波共振的影响,结果发现,界面铁磁耦合体系中只有第一支本征模存在共振,其余所有的本征模都不存在共振；对于界面反铁磁耦合体系,所有关于界面对称的本征模都存在共振,除第一支本征模外,每支模的共振随着界面交换作用参数的减小每支模的共振增强.
之后,我们又将理论应用于两层非对称界面铁磁耦合薄膜体系,详尽地讨论了体系的第一布里渊区的能带精细结构.结果发现,这种体系的能带结构可以看成是每一子层独立存在时能带的“交叠”,实质上并没有完全交叠,而是因为两层的体交换作用和自旋的乘积不同以及两层间又存在界面耦合而导致的结果.对于这样的体系可能存在两种能带结构,一种是有带隙(β<2/3,其中β=JBSB/JASA),一种是没有带隙(β>2/3).在此基础上我们又进—步讨论了各种本征模在第一布里渊区的演化条件,主要包括光学界面模转化为A层中的禁闭模,体模转化为A层中的禁闭模,体模转化为B层中的禁闭模和B层中的禁闭模转化为带隙中的界面模.
我们还进一步讨论了第一布里渊区的自旋波共振的演化,结果发现,在体模存在区域会存在多重共振峰,但峰值相对较弱,较强的共振尖峰可能出现在不同性质的本征模转化的临界点.
对于两层非对称体系,我们进一步研究了各向异性对本征值的影响.结果发现,易轴型各向异性使得能量相对较高的能带整体上移,而能量较低的能带不动,这样就使得两带的交叠区域变小,体模和光学界面模存在的区域变小,而使得禁闭模和带隙中的界面模存在的区域变大,进而给出了在整个布里渊区存在带隙的条件；对于给定参数的体系,自旋波的演化条件是不变的,自旋波共振的演化会发生改变.对于异面型各向异性,在我们讨论的条件下,异面型各向异性使得能量相对高的能带整体下移,而能量较低的能带不动,这样就使得两带的交叠区域变大,体模和光学界面模存在的区域变大,而使得原来禁闭模和带隙中的界面模存在的区域变小,出现了两种新的禁闭模；在此基础上我们也给出了在整个布里渊区存在带隙的条件；通过进一步对自旋波共振的研究发现,由于特殊能带结构的出现,在整个布里渊区会存在双共振尖峰.
最后,我们建立了考虑表面各向异性的自旋波理论,并把理论应用于最简单的对称体系进行讨论表面各向异性对体系本征值和自旋波共振的影响.结果发现,当表面各向异性参数为正值时,表面各向异性不影响每支本征模的传播性质,当表面各向异性参数为负值时,能量最低的两支体模转化为声学界面模；而且表面各向异性参数为正值时,体模波长变短,而表面各向异性参数为负值时,体模波长变长.此外,当界面为铁磁耦合时,第一支本征模的共振会出现最大共振峰,其它本征模的共振规律完全相同,都出现最小共振峰,出现在没有各向异性的位置；当界面反铁磁耦合时,第一支本征模共振出现最大共振峰,其它本征模出现最小共振峰,但出现的位置有两个,即界面反铁磁耦合时,体模的共振存在两种规律.
Currently, the ferromagnetic film systems play important roles in modern information technology ranging from magnetic data storage to sensors or magnetic random access memory. For a functioning device, when a field is sensed or data are written, the magnetic system is excited. Moreover, an important role for the speed of magnetization reversal is played by confined spin waves. Therefore, studying spin excitations in magnetic multilayers will improve understanding their magnetic properties. Under the aperiodic boundary condition, eigenmodes and resonance of spin waves in a ferromagnetic bilayer system are explored by using the interface rescaling approach in this paper.
Firstly, we have deduced the uniform micro-spin-wave theory of magnetic multilayer systems and applied it to the symmetrical magnetic bilayer systems. The eigenproblems are examined in this system and the criteria of conditions for the existence of eigenmodes are given. The results show that if the interface coupling is ferromagnetic, all modes non-affected by the interface coupling are symmetrical modes, while all those affected are antisymmetrical modes. For antiferromagnetic interface coupling, the reverse holds. We compare the results with those H. Puszkarski had discussed and found that they are consistent. Furthermore, we have discussed the spin-wave resonance. It is shown that only the single-line intensity is non-zero when k=0 and this is the case of ordinary ferromagnetic resonance when the spectrum presents but one resonance line. Multi-peak bilayer spin-wave resonance therefore requires antiferromagnetic interface coupling.
Secondly, we applied this theory to the unsymmetrical magnetic bilayer systems, we turn to analyze numerically in detail the energy-band configuration of the longitudinal spin waves with the transverse wave vectorΓ// varying along the high-symmetry paths of two dimensional (2D) Brillouin zone. There are two types of the energy-band structure. Whenβ< 2/3, an energy gap between the two subbands exists (see FIG.1), otherwise the energy gap will disappear forβ> 2/3. In the regions of the bulk modes, the phenomenon of hybridization between subbands can be observed due to the distinction of JASA and JBSB. When the magnitude ofβincreases, the hybridization regions become larger, and vice versa. We also detailed the evolutive conditions of different spin waves and the evolution of spin-wave resonance. It is shown that the sharp intensity may exists critical point where different eigenmodes transform each other.
Thirdly, we discussed the effects of the bulk anisotropy for the eigenmodes in the bilayer system. The results show that the higher subband moves up globally with increasing DA or drops globally with the declining DA. However, the lower subband is fixed; the hybridized (or seem overlap) branches reduces with the increasing DA or the hybridized (or seem overlap) branches enhances with the decreasing DA Moreover, we deduced conditions for the existence of energy-band gap in the whole first Brillouin zone. Because there are the complicated energy band fine structure, double Sharp intensity maybe exist.
At last, the effects of the surface anisotropy for the eigenmodes in the symmetrical bilayer system are investigated. It is shown that when the anisotropy is easy-axis type the eigenmodes are pinned. While the two energetically lowest eigenmodes evolve into surface modes. when the anisotropy is easy-plane type. Moreover, whether the exchange coupling of interface is ferromagnetic or antiferromagnetic, multi-peak bilayer spin-wave resonance will appear.
首先,我们建立了层状体系中的统一微观理论,具体将此理论应用于两层对称的体系详细研究了这种体系中的本征激发,给出了体系中本征值存在的判据.研究结果发现,当界面是铁磁耦合时,体系的奇数支本征模(对称模)与界面性质无关,而偶数支本征模(反对称模)的能量随界面交换作用参数的增加而增大；当界面反铁磁耦合时,奇数支本征模(对称模)的能量随界面耦合参数的减小而减小,而偶数支本征模(反对称模)的性质与界面耦合无关,并将计算结果与已有的结论进行了对比,结果符合得很好.在此基础上,我们进一步研究了界面交换作用对自旋波共振的影响,结果发现,界面铁磁耦合体系中只有第一支本征模存在共振,其余所有的本征模都不存在共振；对于界面反铁磁耦合体系,所有关于界面对称的本征模都存在共振,除第一支本征模外,每支模的共振随着界面交换作用参数的减小每支模的共振增强.
之后,我们又将理论应用于两层非对称界面铁磁耦合薄膜体系,详尽地讨论了体系的第一布里渊区的能带精细结构.结果发现,这种体系的能带结构可以看成是每一子层独立存在时能带的“交叠”,实质上并没有完全交叠,而是因为两层的体交换作用和自旋的乘积不同以及两层间又存在界面耦合而导致的结果.对于这样的体系可能存在两种能带结构,一种是有带隙(β<2/3,其中β=JBSB/JASA),一种是没有带隙(β>2/3).在此基础上我们又进—步讨论了各种本征模在第一布里渊区的演化条件,主要包括光学界面模转化为A层中的禁闭模,体模转化为A层中的禁闭模,体模转化为B层中的禁闭模和B层中的禁闭模转化为带隙中的界面模.
我们还进一步讨论了第一布里渊区的自旋波共振的演化,结果发现,在体模存在区域会存在多重共振峰,但峰值相对较弱,较强的共振尖峰可能出现在不同性质的本征模转化的临界点.
对于两层非对称体系,我们进一步研究了各向异性对本征值的影响.结果发现,易轴型各向异性使得能量相对较高的能带整体上移,而能量较低的能带不动,这样就使得两带的交叠区域变小,体模和光学界面模存在的区域变小,而使得禁闭模和带隙中的界面模存在的区域变大,进而给出了在整个布里渊区存在带隙的条件；对于给定参数的体系,自旋波的演化条件是不变的,自旋波共振的演化会发生改变.对于异面型各向异性,在我们讨论的条件下,异面型各向异性使得能量相对高的能带整体下移,而能量较低的能带不动,这样就使得两带的交叠区域变大,体模和光学界面模存在的区域变大,而使得原来禁闭模和带隙中的界面模存在的区域变小,出现了两种新的禁闭模；在此基础上我们也给出了在整个布里渊区存在带隙的条件；通过进一步对自旋波共振的研究发现,由于特殊能带结构的出现,在整个布里渊区会存在双共振尖峰.
最后,我们建立了考虑表面各向异性的自旋波理论,并把理论应用于最简单的对称体系进行讨论表面各向异性对体系本征值和自旋波共振的影响.结果发现,当表面各向异性参数为正值时,表面各向异性不影响每支本征模的传播性质,当表面各向异性参数为负值时,能量最低的两支体模转化为声学界面模；而且表面各向异性参数为正值时,体模波长变短,而表面各向异性参数为负值时,体模波长变长.此外,当界面为铁磁耦合时,第一支本征模的共振会出现最大共振峰,其它本征模的共振规律完全相同,都出现最小共振峰,出现在没有各向异性的位置；当界面反铁磁耦合时,第一支本征模共振出现最大共振峰,其它本征模出现最小共振峰,但出现的位置有两个,即界面反铁磁耦合时,体模的共振存在两种规律.
Currently, the ferromagnetic film systems play important roles in modern information technology ranging from magnetic data storage to sensors or magnetic random access memory. For a functioning device, when a field is sensed or data are written, the magnetic system is excited. Moreover, an important role for the speed of magnetization reversal is played by confined spin waves. Therefore, studying spin excitations in magnetic multilayers will improve understanding their magnetic properties. Under the aperiodic boundary condition, eigenmodes and resonance of spin waves in a ferromagnetic bilayer system are explored by using the interface rescaling approach in this paper.
Firstly, we have deduced the uniform micro-spin-wave theory of magnetic multilayer systems and applied it to the symmetrical magnetic bilayer systems. The eigenproblems are examined in this system and the criteria of conditions for the existence of eigenmodes are given. The results show that if the interface coupling is ferromagnetic, all modes non-affected by the interface coupling are symmetrical modes, while all those affected are antisymmetrical modes. For antiferromagnetic interface coupling, the reverse holds. We compare the results with those H. Puszkarski had discussed and found that they are consistent. Furthermore, we have discussed the spin-wave resonance. It is shown that only the single-line intensity is non-zero when k=0 and this is the case of ordinary ferromagnetic resonance when the spectrum presents but one resonance line. Multi-peak bilayer spin-wave resonance therefore requires antiferromagnetic interface coupling.
Secondly, we applied this theory to the unsymmetrical magnetic bilayer systems, we turn to analyze numerically in detail the energy-band configuration of the longitudinal spin waves with the transverse wave vectorΓ// varying along the high-symmetry paths of two dimensional (2D) Brillouin zone. There are two types of the energy-band structure. Whenβ< 2/3, an energy gap between the two subbands exists (see FIG.1), otherwise the energy gap will disappear forβ> 2/3. In the regions of the bulk modes, the phenomenon of hybridization between subbands can be observed due to the distinction of JASA and JBSB. When the magnitude ofβincreases, the hybridization regions become larger, and vice versa. We also detailed the evolutive conditions of different spin waves and the evolution of spin-wave resonance. It is shown that the sharp intensity may exists critical point where different eigenmodes transform each other.
Thirdly, we discussed the effects of the bulk anisotropy for the eigenmodes in the bilayer system. The results show that the higher subband moves up globally with increasing DA or drops globally with the declining DA. However, the lower subband is fixed; the hybridized (or seem overlap) branches reduces with the increasing DA or the hybridized (or seem overlap) branches enhances with the decreasing DA Moreover, we deduced conditions for the existence of energy-band gap in the whole first Brillouin zone. Because there are the complicated energy band fine structure, double Sharp intensity maybe exist.
At last, the effects of the surface anisotropy for the eigenmodes in the symmetrical bilayer system are investigated. It is shown that when the anisotropy is easy-axis type the eigenmodes are pinned. While the two energetically lowest eigenmodes evolve into surface modes. when the anisotropy is easy-plane type. Moreover, whether the exchange coupling of interface is ferromagnetic or antiferromagnetic, multi-peak bilayer spin-wave resonance will appear.
引文
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