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Laser-triggered magnetization dynamics for diluted magnetic semiconductor (Ga, Mn)As has drawn great attention in recent years, aiming at studying the ultrafast manipulation of collective spin excitations towards spintronic information processing. In this work, different fitting methods for time-resolved magneto-optical Kerr (TR-MOKE) study of the laser-triggered magnetization dynamics in a diluted magnetic semiconductor (Ga, Mn)As are analyzed and compared. It is known that the exponentially damped cosine harmonic function and the numerical simulation based on Landau-Lifshitz-Gilbert (LLG) equation are usually applied to fit the laser-induced magnetization dynamics from TR-MOKE measurements. Under the specified experimental conditions, it is sometimes hard to fit the TR-MOKE response well with single-mode uniform precession by using the exponentially damped cosine harmonic function. Although the fitting with multiple precession frequencies may usually show much better fitting results, the numerical simulation based on LLG equation reveals that the multi-frequency precessional modes are caused by the superposition of three-dimensional trajectories of magnetization precession with different contributions from the in-plane and out-of-plane magneto-optical response in (Ga, Mn)As. Thus, the multi-frequency precessional modes obtained by adopting the fitting method with exponentially damped cosine harmonic function could be the fake ones. Meanwhile, it is important to note that though the LLG equation can be used to fit the macroscopic magnetization precession well with single frequency, the contribution of pulse-like background response from photo-generated polarized carriers at the above-bandgap excitation is strongly superimposed on the magnetization precession response, and the pulse-like background response cannot be described by LLG equation. Thus one should be cautious of applying LLG equation only to fit the entire TR-MOKE signal, especially when the excitation energy is above the band gap of (Ga, Mn)As. One may combine both fitting methods, namely, fitting with the exponentially damped cosine harmonic function and the LLG simulation by considering both the in-plane and out-of-plane magneto-optical response of (Ga, Mn)As film in order to properly fit the laser-triggered magnetization dynamic response from TR-MOKE measurements. The proper handling of fitting methods helps to extract the dynamic magnetic parameters correctly and to further understand the physical mechanisms for triggering the ultrafast manipulation of collective spin dynamics. This is fundamentally important for developing novel spintronics based on diluted magnetic semiconductor (Ga, Mn)As.
[1] Dietl T, Awschalom D D, Kaminska M, Ohno H 2008 Spintronics (Elsevier: Amsterdam) p 90-128
[2] Dietl T 2010 Nat. Mater. 9 965
[3] Kirilyuk A, Kimel A V, Rasing T 2010 Rev. Mod. Phys. 82 2731
[4] Hashimoto Y, Kobayashi S, Munekata H 2008 Phys. Rev. Lett. 100 067202
[5] Ji C J, Zhang C Q, Zhao G, Wang W J, Sun G, Yuan H M, Han Q F 2011 Chin. Phys. L 28 097101
[6] Liu X, Lim W L, Dobrowolska M, Furdyna J K, Wojtowicz T 2005 Phys. Rev. B 71 035307
[7] Luo X D, Ji C J, Wang Y Q, Wang J N 2008 Acta Phys. Sin. 57 5277 (in Chinese) [罗向东, 姬长建, 王玉琦, 王建农 2008 57 5277]
[8] Wang D M, Ren Y H, Liu X, Furdyna J K, Grimsditch M, Merlin R 2007 Phys. Rev. B 75 233308
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[10] Liu X D, Wang W Z, Gao R X, Zhao J H, Wen J H, Lin W Z, Lai T S 2008 Acta Phys. Sin. 57 3857 (in Chinese) [刘晓东, 王玮竹, 高瑞鑫, 赵建华, 文锦辉, 林位株, 赖天树 2008 57 3857]
[11] Hashimoto Y, Munekata H 2008 Appl. Phys. Lett. 93 202506
[12] Němec P, Rozkotová E, Tesařová N, Trojánek F, De Ranieri E, Olejník K, Zemen J, Novák V, Cukr M, Maly P, Jungwirth T 2012 Nat. Phys. 8 411
[13] Tesařová N, Němec P, Rozkotová E, Zemen J, Janda T, Butkovičová D, Trojánek F, Olejník K, Novák V, Maly P, Jungwirth T 2013 Nat. Photon. 7 492
[14] Oiwa A, Takechi H, Munekata H 2005 J. Supercond. Nov. Magn. 18 9
[15] Kobayashi S, Suda K, Aoyama J, Nakahara D, Munekata H 2010 IEEE Trans. Magn. 46 2470
[16] Takechi H, Oiwa A, Nomura K, Kondo T, Munekata H 2006 Phys. Status Solidi. 3 4267
[17] Wang J, Cotoros I, Dani K M, Liu X, Furdyna J K, Chemla D S 2007 Phys. Rev. Lett. 98 217401
[18] Qi J, Xu Y, Steigerwald A, Liu X, Furdyna J K, Perakis I E, Tolk N H 2009 Phys. Rev. B 79 085304
[19] Qi J, Xu Y, Tolk N H, Liu X, Furdyna J K, Perakis I E 2007 Appl. Phys. Lett. 91 112506
[20] Zemen J, Kučera J, Olejník K, Jungwirth T 2009 Phys. Rev. B 80 155203
[21] Kimel A V, Astakhov G V, Kirilyuk A, Schott G M, Karczewski G, Ossau W, Schmidt G, Molenkamp L W, Rasing T 2005 Phys. Rev. Lett. 94 227203
[22] Tesařová N, Němec P, Rozkotová E, Šubrt J, Reichlová H, Butkovičová D, Trojánek F, Maly P, Novák V, Jungwirth T 2012 Appl. Phys. Lett. 100 102403
[23] Tesařová N, Šubrt J, Maly P, Němec P, Ellis C T, Mukherjee A, Cerne J 2012 Rev. Sci. Instrum. 83 123108
[24] Rozkotová E, Němec P, Sprinzl D, Horodyská P, Trojánek F, Maly P, Novák V, Olejník K, Cukr M, Jungwirth T 2008 IEEE Tran. Magn. 44 2674
[25] Rozkotová E, Němec P, Horodyská P, Sprinzl D, Trojánek F, Maly P, Novák V, Olejník K, Cukr M, Jungwirth T 2008 Appl. Phys. Lett. 92 122507
[26] De Boer T, Gamouras A, March S, Novák V, Hall K C 2012 Phys. Rev. B 85 033202
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[1] Dietl T, Awschalom D D, Kaminska M, Ohno H 2008 Spintronics (Elsevier: Amsterdam) p 90-128
[2] Dietl T 2010 Nat. Mater. 9 965
[3] Kirilyuk A, Kimel A V, Rasing T 2010 Rev. Mod. Phys. 82 2731
[4] Hashimoto Y, Kobayashi S, Munekata H 2008 Phys. Rev. Lett. 100 067202
[5] Ji C J, Zhang C Q, Zhao G, Wang W J, Sun G, Yuan H M, Han Q F 2011 Chin. Phys. L 28 097101
[6] Liu X, Lim W L, Dobrowolska M, Furdyna J K, Wojtowicz T 2005 Phys. Rev. B 71 035307
[7] Luo X D, Ji C J, Wang Y Q, Wang J N 2008 Acta Phys. Sin. 57 5277 (in Chinese) [罗向东, 姬长建, 王玉琦, 王建农 2008 57 5277]
[8] Wang D M, Ren Y H, Liu X, Furdyna J K, Grimsditch M, Merlin R 2007 Phys. Rev. B 75 233308
[9] Yu Z, Li X, Long X, Cheng X W, Liu Y, Cao C B 2009 Chin. Phys. B 18 03040
[10] Liu X D, Wang W Z, Gao R X, Zhao J H, Wen J H, Lin W Z, Lai T S 2008 Acta Phys. Sin. 57 3857 (in Chinese) [刘晓东, 王玮竹, 高瑞鑫, 赵建华, 文锦辉, 林位株, 赖天树 2008 57 3857]
[11] Hashimoto Y, Munekata H 2008 Appl. Phys. Lett. 93 202506
[12] Němec P, Rozkotová E, Tesařová N, Trojánek F, De Ranieri E, Olejník K, Zemen J, Novák V, Cukr M, Maly P, Jungwirth T 2012 Nat. Phys. 8 411
[13] Tesařová N, Němec P, Rozkotová E, Zemen J, Janda T, Butkovičová D, Trojánek F, Olejník K, Novák V, Maly P, Jungwirth T 2013 Nat. Photon. 7 492
[14] Oiwa A, Takechi H, Munekata H 2005 J. Supercond. Nov. Magn. 18 9
[15] Kobayashi S, Suda K, Aoyama J, Nakahara D, Munekata H 2010 IEEE Trans. Magn. 46 2470
[16] Takechi H, Oiwa A, Nomura K, Kondo T, Munekata H 2006 Phys. Status Solidi. 3 4267
[17] Wang J, Cotoros I, Dani K M, Liu X, Furdyna J K, Chemla D S 2007 Phys. Rev. Lett. 98 217401
[18] Qi J, Xu Y, Steigerwald A, Liu X, Furdyna J K, Perakis I E, Tolk N H 2009 Phys. Rev. B 79 085304
[19] Qi J, Xu Y, Tolk N H, Liu X, Furdyna J K, Perakis I E 2007 Appl. Phys. Lett. 91 112506
[20] Zemen J, Kučera J, Olejník K, Jungwirth T 2009 Phys. Rev. B 80 155203
[21] Kimel A V, Astakhov G V, Kirilyuk A, Schott G M, Karczewski G, Ossau W, Schmidt G, Molenkamp L W, Rasing T 2005 Phys. Rev. Lett. 94 227203
[22] Tesařová N, Němec P, Rozkotová E, Šubrt J, Reichlová H, Butkovičová D, Trojánek F, Maly P, Novák V, Jungwirth T 2012 Appl. Phys. Lett. 100 102403
[23] Tesařová N, Šubrt J, Maly P, Němec P, Ellis C T, Mukherjee A, Cerne J 2012 Rev. Sci. Instrum. 83 123108
[24] Rozkotová E, Němec P, Sprinzl D, Horodyská P, Trojánek F, Maly P, Novák V, Olejník K, Cukr M, Jungwirth T 2008 IEEE Tran. Magn. 44 2674
[25] Rozkotová E, Němec P, Horodyská P, Sprinzl D, Trojánek F, Maly P, Novák V, Olejník K, Cukr M, Jungwirth T 2008 Appl. Phys. Lett. 92 122507
[26] De Boer T, Gamouras A, March S, Novák V, Hall K C 2012 Phys. Rev. B 85 033202
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