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In a magnetic system, the spin orbit coupling can combine with the exchange interaction to generate an anisotropic exchange interaction that favors a chiral arrangement of the magnetization. This is known as the Dzyaloshinskii-Moriya interaction (DMI). Contrary to the Heisenberg exchange interaction, which leads to collinear alignment of lattice spins, the form of DMI is therefore very often to cant the spins by a small angle. If DMI is strong enough to compete with the Heisenberg exchange interaction and the magnetic anisotropy, it can stabilize chiral domain wall structure such as skyrmion. When a conduction electron passes through a chiral domain wall, the spin of the conduction electron will experience a fictitious magnetic field (Berry curvature) in real space, which deflects the conduction electrons perpendicular to the current direction. Therefore, it will cause an additional contribution to the observed Hall signal that is termed topological Hall effect (THE). The THE has attracted much attention since it is a promising tool for probing magnetic skyrmions. Recent extensive experiments have focused on the the THE in the ferromagnetic/non-ferromagnetic metal heterojunctions due to the inherent tunability of magnetic interactions in two dimensions. We firstly review the THE in ferromagnetic multilayers, in which the domain wall energy with interfacial DMI can be written as =4AK-D, where Dis the effective DMI energy constant, A the exchange constant, K the anisotropy constant. For the most favorable chirality, it lowers the energy. The limit of this situation is when goes to zero, which defines the critical DMI energy constant Dc=4AK/. Therefore, the domain wall energy would be negative and the chiral domain walls should proliferate if D Dc, and the methods that can modulate D and Dc to reduce have been explored. We have also reviewed the THE in MnGa/heavy metal bilayers. The largest THE signals have been found based on the MnGa films with smallest Dc, which correspondingly results in the smallest . The large topological portion of the Hall signal from the total Hall signal has been extracted in the whole temperature range from 5 to 300 K and the magnitude of fictitious magnetic field has been determined.
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Keywords:
- skyrmions /
- spin orbit coupling /
- spintronics
[1] Fert A, Cros V, Sampaio J 2013 Nat. Nano 8 152
[2] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[3] Moriya T 1960 Phys. Rev. 120 91
[4] Ye J, Kim Y B, Millis A J, Shraiman B I, Majumdar P, Teanovic Z 1999 Phys. Rev. Lett. 83 3737
[5] Bruno P, Dugaev V K, Taillefumier M 2004 Phys. Rev. Lett. 93 096806
[6] Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031
[7] Fert A 1990 Mater. Sci. Forum 59-60 439
[8] Soumyanarayanan A, Raju M, Oyarce A L G, Tan A K C, Im M Y, Petrovi A P, Ho P, Khoo K H, Tran M, Gan C K, Ernult F, Panagopoulos C 2017 Nat. Mater. 16 898
[9] Li Y, Kanazawa N, Yu X Z, Tsukazaki A, Kawasaki M, Ichikawa M, Jin X F, Kagawa F, Tokura Y 2013 Phys. Rev. Lett. 110 117202
[10] Kanazawa N, Onose Y, Arima T, Okuyama D, Ohoyama K, Wakimoto S, Kakurai K, Ishiwata S, Tokura Y 2011 Phys. Rev. Lett. 106 156603
[11] Moreau-Luchaire C, Moutas C, Reyren N, Sampaio J, Vaz C A F, van Horne N, Bouzehouane K, Garcia K, Deranlot C, Warnicke P, Wohlhter P, George J M, Weigand M, Raabe J, Cros V, Fert A 2016 Nat. Nano 11 444
[12] Woo S, Litzius K, Krger B, Im M Y, Caretta L, Richter K, Mann M, Krone A, Reeve R M, Weigand M, Agrawal P, Lemesh I, Mawass M A, Fischer P, Klui M, Beach G S D 2016 Nat. Mater. 15 501
[13] Boulle O, Vogel J, Yang H, Pizzini S, de Souza Chaves D, Locatelli A, Onur Menteș T, Sala A, Buda-Prejbeanu L D, Klein O, Belmeguenai M, Roussign Y, Stashkevich A, Chrif S M, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M, Gaudin G 2016 Nat. Nano 11 449
[14] Yang H, Thiaville A, Rohart S, Fert A, Chshiev M 2015 Phys. Rev. Lett. 115 267210
[15] Ueda K, Iguchi S, Suzuki T, Ishiwata S, Taguchi Y, Tokura Y 2012 Phys. Rev. Lett. 102 086601
[16] Shiomi Y, Mochizuki M, Kaneko Y, Tokura Y 2012 Phys. Rev. Lett. 108 056601
[17] Zhang S, Zhang S S L 2009 Phys. Rev. Lett. 102 086601
[18] Rohart S, Thiaville A 2013 Phys. Rev. B 88 184422
[19] Thiaville A, Rohart S, Ju E, Cros V, Fert A 2012 Europhys. Lett. 100 57002
[20] Maccariello D, Legrand W, Reyren N, Garcia K, Bouzehouane K, Collin S, Cros V, Fert, A 2018 Nat. Nano. 13 233
[21] Meng K K, Miao J, Xu X G, Xiao J X, Zhao J H, Jiang Y 2016 Phys. Rev. B 93 060406
[22] Meng K K, Miao J, Xu X G, Wu Y, Zhao X P, Zhao J H, Jiang Y 2016 Phys. Rev. B 94 214413
[23] Belabbes A, Bihlmayer G, Bechstedt F, Blgel S, Manchon A 2016 Phys. Rev. Lett. 117 247202
[24] Meng K K, Zhao X P, Liu P F, Liu Q, Wu Y, Li Z P, Chen J K, Miao J, Xu X G, Zhao J H, Jiang Y 2018 Phys. Rev. B 97 060407(R)
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[1] Fert A, Cros V, Sampaio J 2013 Nat. Nano 8 152
[2] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[3] Moriya T 1960 Phys. Rev. 120 91
[4] Ye J, Kim Y B, Millis A J, Shraiman B I, Majumdar P, Teanovic Z 1999 Phys. Rev. Lett. 83 3737
[5] Bruno P, Dugaev V K, Taillefumier M 2004 Phys. Rev. Lett. 93 096806
[6] Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031
[7] Fert A 1990 Mater. Sci. Forum 59-60 439
[8] Soumyanarayanan A, Raju M, Oyarce A L G, Tan A K C, Im M Y, Petrovi A P, Ho P, Khoo K H, Tran M, Gan C K, Ernult F, Panagopoulos C 2017 Nat. Mater. 16 898
[9] Li Y, Kanazawa N, Yu X Z, Tsukazaki A, Kawasaki M, Ichikawa M, Jin X F, Kagawa F, Tokura Y 2013 Phys. Rev. Lett. 110 117202
[10] Kanazawa N, Onose Y, Arima T, Okuyama D, Ohoyama K, Wakimoto S, Kakurai K, Ishiwata S, Tokura Y 2011 Phys. Rev. Lett. 106 156603
[11] Moreau-Luchaire C, Moutas C, Reyren N, Sampaio J, Vaz C A F, van Horne N, Bouzehouane K, Garcia K, Deranlot C, Warnicke P, Wohlhter P, George J M, Weigand M, Raabe J, Cros V, Fert A 2016 Nat. Nano 11 444
[12] Woo S, Litzius K, Krger B, Im M Y, Caretta L, Richter K, Mann M, Krone A, Reeve R M, Weigand M, Agrawal P, Lemesh I, Mawass M A, Fischer P, Klui M, Beach G S D 2016 Nat. Mater. 15 501
[13] Boulle O, Vogel J, Yang H, Pizzini S, de Souza Chaves D, Locatelli A, Onur Menteș T, Sala A, Buda-Prejbeanu L D, Klein O, Belmeguenai M, Roussign Y, Stashkevich A, Chrif S M, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M, Gaudin G 2016 Nat. Nano 11 449
[14] Yang H, Thiaville A, Rohart S, Fert A, Chshiev M 2015 Phys. Rev. Lett. 115 267210
[15] Ueda K, Iguchi S, Suzuki T, Ishiwata S, Taguchi Y, Tokura Y 2012 Phys. Rev. Lett. 102 086601
[16] Shiomi Y, Mochizuki M, Kaneko Y, Tokura Y 2012 Phys. Rev. Lett. 108 056601
[17] Zhang S, Zhang S S L 2009 Phys. Rev. Lett. 102 086601
[18] Rohart S, Thiaville A 2013 Phys. Rev. B 88 184422
[19] Thiaville A, Rohart S, Ju E, Cros V, Fert A 2012 Europhys. Lett. 100 57002
[20] Maccariello D, Legrand W, Reyren N, Garcia K, Bouzehouane K, Collin S, Cros V, Fert, A 2018 Nat. Nano. 13 233
[21] Meng K K, Miao J, Xu X G, Xiao J X, Zhao J H, Jiang Y 2016 Phys. Rev. B 93 060406
[22] Meng K K, Miao J, Xu X G, Wu Y, Zhao X P, Zhao J H, Jiang Y 2016 Phys. Rev. B 94 214413
[23] Belabbes A, Bihlmayer G, Bechstedt F, Blgel S, Manchon A 2016 Phys. Rev. Lett. 117 247202
[24] Meng K K, Zhao X P, Liu P F, Liu Q, Wu Y, Li Z P, Chen J K, Miao J, Xu X G, Zhao J H, Jiang Y 2018 Phys. Rev. B 97 060407(R)
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