圆盘形双层膜系统中的交变逆自旋霍尔效应
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摘要
以铁磁体Py与顺磁金属Pt构成的圆盘形双层膜系统为研究对象,在垂直于界面的磁化建立后,沿盘面的激发场可以泵浦自旋流从铁磁体进入顺磁金属,由于逆自旋霍尔效应,发现系统中不存在直流电压,只存在交流电压。通过沿不同方向的测量可以区分逆自旋霍尔效应诱致的交流电压和激发磁场自身诱致的交流电压。计算了逆自旋霍尔效应诱致的交流电压大小和激发磁场自身诱致的交流电压大小对外磁场的依赖性,发现在铁磁共振时,逆自旋霍尔效应诱致的交流电压大小达到最大,而偏离共振磁场后,交流电压大小很快衰减;而激发磁场自身诱致的交流电压大小随外磁场的增大而增加。其次,研究了在不同位相差下,在垂直于激发场方向总的交流电压大小对外磁场的依赖性,发现交流电压大小随着两者之间相位差的变化在共振点附近变化很明显;进一步在共振点附近,计算了总的交流电压大小对相位差的依赖性,发现相位为0时,交流电压达到最大;而相位为π时,交流电压达到最小。最后,文章还计算了交流电压大小对激发功率的依赖性,发现不同于直流电压与激发功率P成正比的情况,两种类型的交流电压都与P~(1/2)成正比。
The spin current pumped by an in-plane excitation magnetic field into an adjacent normal metal only can give rise to an AC voltage(current)observed due to the inverse spin Hall effect when the magnetization in the ferromagnet perpendicular to the interface has been constructed.We can discriminate the AC voltages(currents)induced by the inverse Hall effect and the excitation field by measuring the voltages along different directions.We firstly calculate the dependence of the magnitude of the AC voltages induced by the inverse Hall effect and the excitation field on the external magnetic field and find that the former attains the maximum at the ferromagnetic resonance(FMR)and decay quickly away from the FMR,and that the latter always increase with the external magnetic field.Secondly,the magnitude of the total AC voltage perpendicular to the excitation field as a function of the field is investigated for different phase difference between two AC voltages.We obtain that the magnitude of the total AC voltage changes obviously near the FMR and its magnitude attains the maximum at the phase difference 0 and the minimum at the phase differenceπ.Finally,the dependence of the AC voltage on the excitation power is studied and the AC voltages are in scale with P~(1/2),different from the DC voltages proportional to P.
The spin current pumped by an in-plane excitation magnetic field into an adjacent normal metal only can give rise to an AC voltage(current)observed due to the inverse spin Hall effect when the magnetization in the ferromagnet perpendicular to the interface has been constructed.We can discriminate the AC voltages(currents)induced by the inverse Hall effect and the excitation field by measuring the voltages along different directions.We firstly calculate the dependence of the magnitude of the AC voltages induced by the inverse Hall effect and the excitation field on the external magnetic field and find that the former attains the maximum at the ferromagnetic resonance(FMR)and decay quickly away from the FMR,and that the latter always increase with the external magnetic field.Secondly,the magnitude of the total AC voltage perpendicular to the excitation field as a function of the field is investigated for different phase difference between two AC voltages.We obtain that the magnitude of the total AC voltage changes obviously near the FMR and its magnitude attains the maximum at the phase difference 0 and the minimum at the phase differenceπ.Finally,the dependence of the AC voltage on the excitation power is studied and the AC voltages are in scale with P~(1/2),different from the DC voltages proportional to P.
引文
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[31] Liu L,Buhrman R A,Ralph D C.Review and Analysis of Measurements of the Spin Hall Effect in Platinum[Z/OL].2011,arXiv:1111.3702.
[2] Hirsch J E.Spin Hall Effect[J].Physical Review Letters,1999,83(9):1834-1837.DOI:10.1103/PhysRevLett.83.1834.
[3] Zhang S.Spin Hall Effect in the Presence of Spin Diffusion[J].Physical Review Letters,2000,85(2):393-396.DOI:10.1103/PhysRevLett.85.393.
[4] Murakami S,Nagaosa N,Zhang S C.Dissipationless Quantum Spin Current at Room Temperature[J].Science,2003,301(5638):1348-1351.DOI:10.1126/science.1087128.
[5] Sinova J,Culcer D,Niu Q,et al.Universal Intrinsic Spin Hall Effect[J].Physical Review Letters,2004,92(12):126603.DOI:10.1103/PhysRevLett.95.126603.
[6] Kato Y K,Myers R C,Gossard A C,et al.Current-induced Spin Polarization in Strained Semiconductors[J].Physical Review Letters,2004,93(17):176601.DOI:10.1103/PhysRevLett.93.176601.
[7] Wunderlich J,Kaestner B,Sinova J,et al.Experimental Observation of the Spin-Hall Effect in a Two-dimensional Spin-orbit Coupled Semiconductor System[J].Physical Review Letters,2005,94(4):047204.DOI:10.1103/PhysRevLett.94.047204.
[8] Saitoh E,Ueda M,Miyajima H,et al.Conversion of Spin Current into Charge Current at Room Temperature:Inverse SpinHall effect[J].Applied Physics Letters,2006,88(18):345-353.DOI:10.1063/1.2199473.
[9] Valenzuela S O,Tinkham M.Direct Electronic Measurement of the Spin Hall Effect[J].Nature,2006,442(7099):176-179.DOI:10.1038/nature04937.
[10] Kimura T,Otani Y,Sato T,et al.Room-temperature Reversible Spin Hall Effect[J].Physical Review Letters,2007,98(15):156601.DOI:10.1103/PhysRevLett.98.156601.
[11] Tserkovnyak Y,Brataas A,Bauer G E W.Enhanced Gilbert Damping in Thin Ferromagnetic Films[J].Physical Review Letters,2002,88(11):117601.DOI:10.1103/PhysRevLett.88.117601.
[12] Tserkovnyak Y,Brataas A,Bauer G E W,et al.Nonlocal Magnetization Dynamics in Ferromagnetic Heterostructures[J].Reviews of Modern Physics,2005,77:1375-4.DOI:10.1103/RevModPhys.77.1375.
[13] Guimaraes F S M,Costa A T,Muniz R B,et al.Spin Currents in Metallic Nanostructures:Explicit Calculations[J].Physical Review B,2011,84(5):3337-3344.DOI:10.1103/PhysRevB.84.054403.
[14] Mosendz O,Pearson J E,Fradin F Y,et al.Quantifying Spin Hall Angles from Spin Pumping:Experiments and Theory[J].Physical Review Letters,2010,104(4):046601.DOI:10.1103/PhysRevLett.104.046601.
[15] Azevedo A,Vilelale2o L H,Rodríguezsurez R L,et al.Spin Pumping and Anisotropic Magnetoresistance Voltages in Magnetic Bilayers:Theory and Experiment[J].Physical Review B Condensed Matter,2011,83(14):970-978.DOI:10.1103/PhysRevB.83.144402.
[16] Ando K,Takahashi S,Ieda J,et al.Electrically Tunable Spin Injector Free from the Impedance Mismatch Problem[J].Nature Materials,2011,10(9):655-659.DOI:10.1038/nmat3052.
[17] Lin C,Matsukura F,Ohno H.Direct-current Voltages in(Ga,Mn)As Structures Induced by Ferromagnetic Resonance[J].Nature Communications,2013,4(3):2055.DOI:10.1038/ncomms3055.
[18] Tang Z,Shikoh E,Ago H,et al.Dynamically-generated Pure Spin Current in Single-layer Graphene[J].Physical Review B,2012,87(14):1948-1954.DOI:10.1103/PhysRevB.87.14041.
[19] Ando K,Watanabe S,Mooser S,et al.Solution-processed Organic Spin-charge Converter[J].Nature Materials,2013,12(7):622-7.DOI:10.1038/nmat3634.
[20] Jiao H,Bauer G E.Spin Backflow and a.c.Voltage Generation by Spin Pumping and the Inverse Spin Hall Effect[J].Physical Review Letters,2013,110(21):217602.DOI:10.1103/PhysRevLett.110.217602.
[21] Hahn C,De L G,Viret M,et al.Detection of Microwave Spin Pumping Using the Inverse Spin Hall Effect[J].Physical Review Letters,2013,111(21):217204.DOI:10.1103/PhysRevLett.111.217204.
[22] Wei D,Obstbaum M,Ribow M,et al.Spin Hall Voltages from a.c.and d.c.Spin Currents[J].Nature Communications,2014,5(5):3768-3774.DOI:10.1038/ncomms4768.
[23] Brataas A,Nazarov Y V,Bauer G E.Finite-element Theory of Transport in Ferromagnet-normal Metal Systems[J].Physical Review Letters,2000,84(11):2481-2484.DOI:10.1103/PhysRevLett.84.2481.
[24] Johnson M,Silsbee R H.Coupling of Electronic Charge and Spin at a Ferromagnetic-paramagnetic Metal Interface[J].Physical Review B Condensed Matter,1988,37(10):5312.DOI:10.1103/PhysRevB.37.5312.
[25] Azevedo A,Vilela Leao L H,Rodriguez-Suarez R L,et al.Dc Effect in Ferromagnetic Resonance:Evidence of the Spinpumping Effect?[J].Journal of Applied Physics,2005,97(10):11465.DOI:10.1063/1.1855251.
[26] Mosendz O,Vlaminck V,Pearson J E,et al.Detection and Quantification of Inverse Spin Hall Effect from Spin Pumping in Permalloy/Normal Metal Bilayers[J].Physical Review B,2010,82(21):374-376.DOI:10.1103/PhysRevB.82.214403.
[27] Feng Z,Hu J,Sun L,et al.Spin Hall Angle Quantification from Spin Pumping and Microwave Photoresistance[J].Physical Review B Condensed Matter,2012,85(21):35-40.DOI:10.1103/PhysRevB.85.214423.
[28] Czeschka F D,Dreher L,Brandt M S,et al.Scaling Behavior of the Spin Pumping Effect in Ferromagnet-platinum Bilayers[J].Physical Review Letters,2011,107(4):046601.DOI:10.1103/PhysRevLett.107.046601.
[29]yvind Johansen,Brataas A.Spin Pumping and Inverse Spin Hall Voltages from Dynamical Antiferromagnets[J].Physical Review B,2017,95(22):1-14.DOI:10.1103/PhysRevB.95.220408.
[30] Roy K.Estimating the Spin Diffusion Length and the Spin Hall Angle from Spin Pumping Induced Inverse Spin Hall Voltages[J].Physical Review B,2017,96(17):1-8.DOI:10.1103/PhysRevB.96.174432.
[31] Liu L,Buhrman R A,Ralph D C.Review and Analysis of Measurements of the Spin Hall Effect in Platinum[Z/OL].2011,arXiv:1111.3702.