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2022 | OriginalPaper | Chapter

2. Fundamentals of Spin Dynamics in Two-Dimensional Materials

Author : Dr. Marc Vila Tusell

Published in: Spin Dynamics in Two-Dimensional Quantum Materials

Publisher: Springer International Publishing

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Abstract

In this section, I review some of the principal physical phenomena involved in spin dynamics.

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previous chapter Introduction
next chapter Quantum Transport Methodologies for Spin Transport
Footnotes
1
These broadenings can also have physical meaning. For example, the derivative of the Fermi-Dirac distribution is used to account for thermal broadening at a finite temperature.
 
2
Contacts can also be called electrodes or leads.
 
3
Sometimes a factor of 1/2 is used when defining the spin ECP, \(\mu _s = \frac{\mu _\uparrow - \mu _\downarrow }{2}\). It is just a convention and both choices are widely used in the literature [3, 4, 12].
 
4
The spin current (density) is in fact a tensor including both the direction of the spin polarization and the direction of propagation. See List of Acronyms and useful Symbols for the different definitions used in this thesis.
 
5
This nonlocal resistance is not a resistance in the usual sense. It can take positive and negative values and normalizes the output voltage by the input current.
 
6
Although the nontrivial topological phase can remain even without spin conservation [58, 59].
 
Literature
1.
Dresselhaus G (1955) Spin-orbit coupling effects in zinc blende structures. Phys Rev 100:580–586CrossRef
2.
Bychkov YA, Rashba ÉI (1984) Properties of a 2D electron gas with lifted spectral degeneracy. Soviet J Exp Theor Phys Lett 39:78
3.
Žutić I, Fabian J, Das Sarma S (2004) Spintronics: fundamentals and applications. Rev Mod Phys 76:323–410CrossRef
4.
Fabian J, Matos-Abiaguea A, Ertler P, snd Stano C, Žutić I (2007) Semiconductor spintronics. Acta Phys Slovaca 57:565–907 (2007)
5.
Wu M, Jiang J, Weng M (2010) Spin dynamics in semiconductors. Phys Rep 493:61–236CrossRef
6.
Elliott RJ (1954) Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors. Phys Rev 96:266–279CrossRef
7.
Yafet Y (1963) g factors and spin-lattice relaxation of conduction electrons. In: Solid state physics, vol 14. Academic Press, pp 1–98
8.
D’Yakonov MI, Perel’ VI (1971) Spin orientation of electrons associated with the interband absorption of light in semiconductors. Soviet J Exp Theo Phys 33:1053
9.
Hanle W (1924) Über magnetische beeinflussung der polarisation der resonanzfluoreszenz. Zeitschrift für Physik 30:93–105CrossRef
10.
Johnson M, Silsbee RH (1985) Interfacial charge-spin coupling: Injection and detection of spin magnetization in metals. Phys Rev Lett 55:1790–1793CrossRef
11.
Takahashi S, Maekawa S (2008) Spin current, spin accumulation and spin Hall effect. Sci Technol Adv Mater 9:014105
12.
Valenzuela SO (2009) Nonlocal electronic spin detection, spin accumulation and the spin Hall effect. Int J Mod Phys B 23:2413–2438CrossRef
13.
Silsbee RH (1980) Novel method for the study of spin transport in conductors. Bull Magn Reson 2:284–285
14.
Rashba EI (2000) Theory of electrical spin injection: tunnel contacts as a solution of the conductivity mismatch problem. Phys Rev B 62:R16267–R16270CrossRef
15.
Fert A, Jaffrès H (2001) Conditions for efficient spin injection from a ferromagnetic metal into a semiconductor. Phys Rev B 64:184420
16.
Takahashi S, Maekawa S (2003) Spin injection and detection in magnetic nanostructures. Phys Rev B 67:052409
17.
Jedema FJ, Nijboer MS, Filip AT, van Wees BJ (2003) Spin injection and spin accumulation in all-metal mesoscopic spin valves. Phys Rev B 67:085319
18.
Han W, Kawakami RK, Gmitra M, Fabian J (2014) Graphene spintronics. Nat Nanotechnol 9:794–807CrossRef
19.
Avsar A, Ochoa H, Guinea F, Özyilmaz B, van Wees BJ, Vera-Marun IJ (2020) Colloquium: spintronics in graphene and other two-dimensional materials. Rev Mod Phys 92:021003
20.
Johnson M, Silsbee RH (1988) Coupling of electronic charge and spin at a ferromagnetic-paramagnetic metal interface. Phys Rev B 37:5312–5325CrossRef
21.
Jedema F, Heersche H, Filip A, Baselmans J, Van Wees B (2002) Electrical detection of spin precession in a metallic mesoscopic spin valve. Nature 416:713–716CrossRef
22.
Bandyopadhyay S, Cahay M (2008) Introduction to spintronics. CRC Press
23.
Józsa C, Maassen T, Popinciuc M, Zomer PJ, Veligura A, Jonkman HT, van Wees BJ (2009) Linear scaling between momentum and spin scattering in graphene. Phys Rev B 80:241403
24.
Garcia JH, Vila M, Cummings AW, Roche S (2018) Spin transport in graphene/transition metal dichalcogenide heterostructures. Chem Soc Rev 47:3359–3379CrossRef
25.
Raes B, Scheerder JE, Costache MV, Bonell F, Sierra JF, Cuppens J, Van de Vondel J, Valenzuela SO (2016) Determination of the spin-lifetime anisotropy in graphene using oblique spin precession. Nat Commun 7
26.
D’Yakonov MI, Perel’ VI (1971) Possibility of orienting electron spins with current. Soviet J Exp Theor Phys Lett 13:467
27.
D’Yakonov M, Perel’ V (1971) Current-induced spin orientation of electrons in semiconductors. Phys Lett A 35:459–460CrossRef
28.
29.
Zhang S (2000) Spin Hall effect in the presence of spin diffusion. Phys Rev Lett 85:393–396CrossRef
30.
Sinova J, Culcer D, Niu Q, Sinitsyn NA, Jungwirth T, MacDonald AH (2004) Universal intrinsic spin Hall effect. Phys Rev Lett 92:126603
31.
Kato YK, Myers RC, Gossard AC, Awschalom DD (2004) Observation of the spin Hall effect in semiconductors. Science 306:1910–1913CrossRef
32.
Wunderlich J, Kaestner B, Sinova J, Jungwirth T (2005) Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys Rev Lett 94:047204
33.
Sih V, Myers RC, Kato YK, Lau WH, Gossard AC, Awschalom DD (2005) Spatial imaging of the spin Hall effect and current-induced polarization in two-dimensional electron gases. Nat Phys 1:31–35CrossRef
34.
Valenzuela SO, Tinkham M (2006) Direct electronic measurement of the spin Hall effect. Nature 442:176–179CrossRef
35.
Edelstein V (1990) Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun 73:233–235CrossRef
36.
Ganichev SD, Ivchenko EL, Bel’kov VV, Tarasenko SA, Sollinger M, Weiss D, Wegscheider W, Prettl W (2002) Spin-galvanic effect. Nature 417:153–156CrossRef
37.
Kato YK, Myers RC, Gossard AC, Awschalom DD (2004) Current-induced spin polarization in strained semiconductors. Phys Rev Lett 93:176601
38.
Silov AY, Blajnov PA, Wolter JH, Hey R, Ploog KH, Averkiev NS (2004) Current-induced spin polarization at a single heterojunction. Appl Phys Lett 85:5929–5931CrossRef
39.
Fert A, Cros V, Sampaio J (2013) Skyrmions on the track. Nat Nanotechnol 8:152–156CrossRef
40.
Nagaosa N, Tokura Y (2013) Topological properties and dynamics of magnetic skyrmions. Nat Nanotechnol 8:899–911CrossRef
41.
Yamaguchi A, Ono T, Nasu S, Miyake K, Mibu K, Shinjo T (2004) Real-space observation of current-driven domain wall motion in submicron magnetic wires. Phys Rev Lett 92:077205
42.
Tatara G, Kohno H, Shibata J (2008) Microscopic approach to current-driven domain wall dynamics. Phys Rep 468:213–301CrossRef
43.
Petrović MD, Popescu BS, Bajpai U, Plecháč P, Nikolić BK (2018) Spin and charge pumping by a steady or pulse-current-driven magnetic domain wall: a self-consistent multiscale time-dependent quantum-classical hybrid approach. Phys Rev Appl 10:054038
44.
Kajiwara Y, Harii K, Takahashi S, Ohe J, Uchida K, Mizuguchi M, Umezawa H, Kawai H, Ando K, Takanashi K, Maekawa S, Saitoh E (2010) Transmission of electrical signals by spin-wave interconversion in a magnetic insulator. Nature 464:262–266CrossRef
45.
Ciccarelli C, Hals KMD, Irvine A, Novak V, Tserkovnyak Y, Kurebayashi H, Brataas A, Ferguson A (2015) Magnonic charge pumping via spin-orbit coupling. Nat Nanotechnol 10:50–54CrossRef
46.
Cornelissen LJ, Liu J, Duine RA, Youssef JB, van Wees BJ (2015) Long-distance transport of magnon spin information in a magnetic insulator at room temperature. Nat Phys 11:1022–1026CrossRef
47.
Xiao D, Chang M-C, Niu Q (2010) Berry phase effects on electronic properties. Rev Mod Phys 82:1959–2007CrossRef
48.
Sinova J, Valenzuela SO, Wunderlich J, Back CH, Jungwirth T (2015) Spin Hall effects. Rev Mod Phys 87:1213–1260CrossRef
49.
Klitzing KV, Dorda G, Pepper M (1980) New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys Rev Lett 45:494–497
50.
Hasan MZ, Kane CL (2010) Colloquium: topological insulators. Rev Mod Phys 82:3045–3067CrossRef
51.
Halperin BI (1982) Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys Rev B 25:2185–2190CrossRef
52.
Hatsugai Y (1993) Chern number and edge states in the integer quantum Hall effect. Phys Rev Lett 71:3697–3700CrossRef
53.
Thouless DJ, Kohmoto M, Nightingale MP, den Nijs M (1982) Quantized Hall conductance in a two-dimensional periodic potential. Phys Rev Lett 49:405–408CrossRef
54.
Yao Y, Kleinman L, MacDonald AH, Sinova J, Jungwirth T, Wang D-S, Wang E, Niu Q (2004) First principles calculation of anomalous Hall conductivity in ferromagnetic bcc Fe. Phys Rev Lett 92:037204
55.
Qiao Z, Ren W, Chen H, Bellaiche L, Zhang Z, MacDonald AH, Niu Q (2014) Quantum anomalous Hall effect in graphene proximity coupled to an antiferromagnetic insulator. Phys Rev Lett 112:116404
56.
Fan Z, Garcia J, Cummings A, Barrios-Vargas J, Panhans M, Harju A, Ortmann F, Roche S (2020) Linear scaling quantum transport methodologies. Phys Rep (in press)
57.
Kohmoto M (1985) Topological invariant and the quantization of the Hall conductance. Ann Phys 160:343–354CrossRef
58.
Kane CL, Mele EJ (2005) \({Z}_{2}\) topological order and the quantum spin Hall effect. Phys Rev Lett 95:146802
59.
Sheng DN, Weng ZY, Sheng L, Haldane FD (2006) Quantum spin-Hall effect and topologically invariant Chern numbers. Phy. Rev Lett 97:1–4CrossRef
60.
Murakami S, Nagaosa N, Zhang S-C (2003) Dissipationless quantum spin current at room temperature. Science 301:1348–1351CrossRef
61.
Kane CL, Mele EJ (2005) Quantum spin Hall effect in graphene. Phys Rev Lett 95:226801
62.
Bernevig BA, Zhang S-C (2006) Quantum spin Hall effect. Phys Rev Lett 96:106802
63.
Sheng L, Sheng DN, Ting CS, Haldane FD (2005) Nondissipative spin Hall effect via quantized edge transport. Phys Rev Lett 95:95–98CrossRef
64.
Haldane FDM (1988) Model for a quantum Hall effect without Landau levels: condensed-matter realization of the parity anomaly. Phys Rev Lett 61:2015–2018
65.
Murakami S (2006) Quantum spin Hall effect and enhanced magnetic response by spin-orbit coupling. Phys Rev Lett 97:236805
66.
Roth A, Brüne C, Buhmann H, Molenkamp LW, Maciejko J, Qi X-L, Zhang S-C (2009) Nonlocal transport in the quantum spin Hall state. Science 325:294–297CrossRef
67.
Fu L, Kane CL (2007) Topological insulators with inversion symmetry. Phys Rev B 76:045302
68.
Zhang Y, Tang T-T, Girit C, Hao Z, Martin MC, Zettl A, Crommie MF, Shen YR, Wang F (2009) Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459:820–823CrossRef
69.
Schindler F, Cook AM, Vergniory MG, Wang Z, Parkin SSP, Bernevig BA, Neupert T (2018) Higher-order topological insulators. Sci Adv 4
70.
Min H, Hill JE, Sinitsyn NA, Sahu BR, Kleinman L, MacDonald AH (2006) Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys Rev B 74:165310
71.
Huertas-Hernando D, Guinea F, Brataas A (2006) Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps. Phys Rev B 74:155426
72.
Gmitra M, Konschuh S, Ertler C, Ambrosch-Draxl C, Fabian J (2009) Band-structure topologies of graphene: Spin-orbit coupling effects from first principles. Phys Rev B 80:235431
73.
Konschuh S, Gmitra M, Fabian J (2010) Tight-binding theory of the spin-orbit coupling in graphene. Phys Rev B 82:245412
74.
Wojtaszek M, Vera-Marun IJ, van Wees BJ (2014) Transition between one-dimensional and zero-dimensional spin transport studied by Hanle precession. Phys Rev B 89:245427
75.
Ertler C, Konschuh S, Gmitra M, Fabian J (2009) Electron spin relaxation in graphene: the role of the substrate. Phys Rev B 80:041405
76.
Huertas-Hernando D, Guinea F, Brataas A (2009) Spin-orbit-mediated spin relaxation in graphene. Phys Rev Lett 103:146801
77.
Zhou Y, Wu MW (2010) Electron spin relaxation in graphene from a microscopic approach: Role of electron-electron interaction. Phys. Rev. B 82:085304CrossRef
78.
Fratini S, Gosálbez-Martínez D, Merodio Cámara P, Fernández-Rossier J Anisotropic intrinsic spin relaxation in graphene due to flexural distortions. Phys Rev B 88:115426 (2013)
79.
Vicent IM, Ochoa H, Guinea F (2017) Spin relaxation in corrugated graphene. Phys Rev B 95:195402
80.
Ochoa H, Castro Neto AH, Fal’ko VI, Guinea F (2012) Spin-orbit coupling assisted by flexural phonons in graphene. Phys Rev B 86:245411
81.
Tombros N, Jozsa C, Popinciuc M, Jonkman HT, van Wees BJ (2007) Electronic spin transport and spin precession in single graphene layers at room temperature. Nature 448:571–574CrossRef
82.
Tombros N, Tanabe S, Veligura A, Jozsa C, Popinciuc M, Jonkman HT, van Wees BJ (2008) Anisotropic spin relaxation in graphene. Phys Rev Lett 101:046601
83.
Avsar A, Yang T-Y, Bae S, Balakrishnan J, Volmer F, Jaiswal M, Yi Z, Ali SR, Güntherodt G, Hong BH, Beschoten B, Özyilmaz B (2011) Toward wafer scale fabrication of graphene based spin valve devices. Nano Lett 11:2363–2368CrossRef
84.
Zomer PJ, Guimarães MHD, Tombros N, van Wees BJ (2012) Long-distance spin transport in high-mobility graphene on hexagonal boron nitride. Phys Rev B 86:161416
85.
Guimarães MHD, Veligura A, Zomer PJ, Maassen T, Vera-Marun IJ, Tombros N, van Wees BJ (2012) Spin transport in high-quality suspended graphene devices. Nano Lett 12:3512–3517CrossRef
86.
Neumann I, Van de Vondel J, Bridoux G, Costache MV, Alzina F, Torres CMS, Valenzuela SO (2013) Electrical detection of spin precession in freely suspended graphene spin valves on cross-linked poly (methyl methacrylate). Small 9:156–160CrossRef
87.
Han W, Pi K, Bao W, McCreary KM, Li Y, Wang WH, Lau CN, Kawakami RK (2009) Electrical detection of spin precession in single layer graphene spin valves with transparent contacts. Appl Phys Lett 94:222109
88.
Han W, Pi K, McCreary KM, Li Y, Wong JJI, Swartz AG, Kawakami RK (2010) Tunneling spin injection into single layer graphene. Phys Rev Lett 105:167202
89.
Popinciuc M, Józsa C, Zomer PJ, Tombros N, Veligura A, Jonkman HT, van Wees BJ (2009) Electronic spin transport in graphene field-effect transistors. Phys Rev B 80:214427
90.
Volmer F, Drögeler M, Maynicke E, von den Driesch N, Boschen ML, Güntherodt G, Beschoten B (2013) Role of MgO barriers for spin and charge transport in Co/MgO/graphene nonlocal spin-valve devices. Phys Rev B 88:161405
91.
Volmer F, Drögeler M, Maynicke E, von den Driesch N, Boschen ML, Güntherodt G, Stampfer C, Beschoten B (2014) Suppression of contact-induced spin dephasing in graphene/MgO/Co spin-valve devices by successive oxygen treatments. Phys Rev B 90:165403
92.
Maassen T, Vera-Marun IJ, Guimarães MHD, van Wees BJ (2012) Contact-induced spin relaxation in Hanle spin precession measurements. Phys Rev B 86:235408
93.
Sosenko E, Wei H, Aji V (2014) Effect of contacts on spin lifetime measurements in graphene. Phys Rev B 89:245436
94.
Idzuchi H, Fukuma Y, Takahashi S, Maekawa S, Otani Y (2014) Effect of anisotropic spin absorption on the Hanle effect in lateral spin valves. Phys Rev B 89:081308
95.
Idzuchi H, Fert A, Otani Y (2015) Revisiting the measurement of the spin relaxation time in graphene-based devices. Phys Rev B 91:241407
96.
Amamou W, Lin Z, van Baren J, Turkyilmaz S, Shi J, Kawakami RK (2016) Contact induced spin relaxation in graphene spin valves with Al\(_2\)O\(_3\) and MgO tunnel barriers. APL Mater 4:032503
97.
Stecklein G, Crowell PA, Li J, Anugrah Y, Su Q, Koester SJ (2016) Contact-induced spin relaxation in graphene nonlocal spin valves. Phys Rev Appl 6:054015
98.
O’Brien L, Spivak D, Krueger N, Peterson TA, Erickson MJ, Bolon B, Geppert CC, Leighton C, Crowell PA (2016) Observation and modelling of ferromagnetic contact-induced spin relaxation in Hanle spin precession measurements. Phys Rev B 94:094431
99.
Lundeberg MB, Yang R, Renard J, Folk JA (2013) Defect-mediated spin relaxation and dephasing in graphene. Phys Rev Lett 110:156601
100.
Kochan D, Gmitra M, Fabian J (2014) Spin relaxation mechanism in graphene: resonant scattering by magnetic impurities. Phys Rev Lett 112:116602
101.
Soriano D, Van Tuan D, Dubois SM, Gmitra M, Cummings AW, Kochan D, Ortmann F, Charlier JC, Fabian J, Roche S (2015) Spin transport in hydrogenated graphene. 2D Mater 2:022002
102.
Guimarães MHD, Zomer PJ, Ingla-Aynés J, Brant JC, Tombros N, van Wees BJ (2014) Controlling spin relaxation in hexagonal BN-encapsulated graphene with a transverse electric field. Phys Rev Lett. 113:086602
103.
Drögeler M, Volmer F, Wolter M, Terrés B, Watanabe K, Taniguchi T, GuÃ?Ë?ntherodt G, Stampfer C, Beschoten B (2014) Nanosecond spin lifetimes in single-and few-layer graphene–hBN heterostructures at room temperature. Nano Lett 14:6050–6055
104.
Kamalakar MV, Groenveld C, Dankert A, Dash SP (2015) Long distance spin communication in chemical vapour deposited graphene. Nat Commun 6:6766CrossRef
105.
Singh S, Katoch J, Xu J, Tan C, Zhu T, Amamou W, Hone J, Kawakami R (2016) Nanosecond spin relaxation times in single layer graphene spin valves with hexagonal boron nitride tunnel barriers. Appl Phys Lett 109:122411
106.
Drögeler M, Franzen C, Volmer F, Pohlmann T, Banszerus L, Wolter M, Watanabe K, Taniguchi T, Stampfer C, Beschoten B (2016) Spin lifetimes exceeding 12 nanoseconds in graphene non-local spin valve devices. Nano Lett 16:3533CrossRef
107.
Drögeler M, Volmer F, Stampfer C, Beschoten B (2017) Simulations on the influence of spatially varying spin transport parameters on the measured spin lifetime in graphene non-local spin valves. Phys Status Solidi 254:1700293CrossRef
108.
Gurram M, Omar S, van Wees BJ (2017) Bias induced up to 100% spin-injection and detection polarizations in ferromagnet/bilayer-hBN/graphene/hBN heterostructures. Nature Commun 8:1CrossRef
109.
Roche S, Valenzuela SO (2014) Graphene spintronics: puzzling controversies and challenges for spin manipulation. J Phys D: Appl Phys 47:094011
110.
Roche S, Åkerman JJ, Beschoten B, Charlier JC, Chshiev M, Dash SP, Dlubak B, Fabian J, Fert A, Guimarães M, et al Graphene spintronics: the European flagship perspective 2D Mater 2:030202
111.
Tuan DV, Ortmann F, Soriano D, Valenzuela SO, Roche S (2014) Pseudospin-driven spin relaxation mechanism in graphene. Nat Phys 10:857–863CrossRef
112.
Van Tuan D, Ortmann F, Cummings AW, Soriano D, Roche S (2016) Spin dynamics and relaxation in graphene dictated by electron-hole puddles. Sci Rep 6
113.
Wang L, Meric I, Huang PY, Gao Q, Gao Y, Tran H, Taniguchi T, Watanabe K, Campos LM, Muller DA, Guo J, Kim P, Hone J, Shepard KL, Dean CR (2013) One-dimensional electrical contact to a two-dimensional material. Science 342:614–617CrossRef
114.
Banszerus L, Schmitz M, Engels S, Dauber J, Oellers M, Haupt F, Watanabe K, Taniguchi T, Beschoten B, Stampfer C (2015) Ultrahigh-mobility graphene devices from chemical vapor deposition on reusable copper. Sci Adv 1:e1500222
115.
Banszerus L, Schmitz M, Engels S, Goldsche M, Watanabe K, Taniguchi T, Beschoten B, Stampfer C (2015) Ballistic transport exceeding 28 \(\upmu \)m in CVD grown graphene. Nano Lett 16:1387–1391CrossRef
116.
Oltscher M, Ciorga M, Utz M, Schuh D, Bougeard D, Weiss D (2014) Electrical spin injection into high mobility 2D systems. Phys Rev Lett 113:236602
117.
Buchner M, Kuczmik T, Oltscher M, Ciorga M, Korn T, Loher J, Schuh D, Schüller C, Bougeard D, Weiss D, Back CH (2017) Optical investigation of electrical spin injection into an inverted two-dimensional electron gas structure. Phys Rev B 95:035304
118.
Liefeith L-K, Tholapi R, Ishikura T, Hänze M, Hartmann R, Slobodskyy T, Hansen W (2017) Spin injection beyond the diffusive limit in the presence of spin-orbit coupling. Phys Rev B 95:081303
119.
Kravchenko VY, Rashba EI (2003) Spin injection into a ballistic semiconductor microstructure. Phys Rev B 67:121310
120.
Chen K, Zhang S (2015) Enhancement of spin accumulation in ballistic transport regime. Phys Rev B 92:214402
121.
Mireles F, Kirczenow G (2001) Ballistic spin-polarized transport and Rashba spin precession in semiconductor nanowires. Phys Rev B 64:024426
122.
Lee H-W, Çalışkan S, Park H (2005) Mesoscopic effects in a single-mode Datta-Das spin field-effect transistor. Phys Rev B 72:153305
123.
Jeong J-S, Lee H-W (2006) Ballistic spin field-effect transistors: multichannel effects. Phys Rev B 74:195311
124.
Datta S, Das B (1990) Electronic analog of the electro-optic modulator. Appl Phys Lett 56:665–667CrossRef
125.
Tang HX, Monzon FG, Lifshitz R, Cross MC, Roukes ML (2000) Ballistic spin transport in a two-dimensional electron gas. Phys Rev B 61:4437–4440CrossRef
126.
Zainuddin ANM, Hong S, Siddiqui L, Srinivasan S, Datta S (2011) Voltage-controlled spin precession. Phys Rev B 84:165306
127.
Cummings AW, Roche S (2016) Effects of dephasing on spin lifetime in ballistic spin-orbit materials. Phys Rev Lett 116:086602
128.
Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK (2005) Two-dimensional atomic crystals. Proc Natil Acad Sci 102:10451–10453CrossRef
129.
Chhowalla M, Shin HS, Eda G, Li L-J, Loh KP, Zhang H (2013) The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets. Nat Chem 5:263–275CrossRef
130.
Manzeli S, Ovchinnikov D, Pasquier D, Yazyev OV, Kis A (2017) 2D transition metal dichalcogenides. Nat Rev Mater 2:17033CrossRef
131.
Xu S-Y, Ma Q, Shen H, Fatemi V, Wu S, Chang T-R, Chang G, Valdivia AMM, Chan C-K, Gibson QD, Zhou J, Liu Z, Watanabe K, Taniguchi T, Lin H, Cava RJ, Fu L, Gedik N, Jarillo-Herrero P (2018) Electrically switchable berry curvature dipole in the monolayer topological insulator WTe\(_2\). Nat Phys 14:900–906CrossRef
132.
Song P, Hsu C-H, Vignale G, Zhao M, Liu J, Deng Y, Fu W, Liu Y, Zhang Y, Lin H, Pereira VM, Loh KP (2020) Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature. Nat Mater 19:292–298CrossRef
133.
Xiao D, Liu G-B, Feng W, Xu X, Yao W (2012) Coupled spin and valley physics in monolayers of MoS\(_{2}\) and other group-VI dichalcogenides. Phys Rev Lett 108:196802
134.
Cao T, Wang G, Han W, Ye H, Zhu C, Shi J, Niu Q, Tan P, Wang E, Liu B, Feng J (2012) Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat Commun 3:885–887CrossRef
135.
Zeng H, Dai J, Yao W, Xiao D, Cui X (2012) Valley polarization in MoS\(_2\) monolayers by optical pumping. Nat Nanotechnol 7:490–493CrossRef
136.
Mak KF, He K, Shan J, Heinz TF (2012) Control of valley polarization in monolayer MoS\(_2\) by optical helicity. Nat Nanotechnol 7:494–498CrossRef
137.
Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M, Dai X, Bernevig BA (2015) Type-II Weyl semimetals. Nature 527:495–498CrossRef
138.
Sun Y, Wu S-C, Ali MN, Felser C, Yan B (2015) Prediction of Weyl semimetal in orthorhombic MoTe\(_2\). Phys Rev B 92:161107
139.
Xu S-Y, Belopolski I, Alidoust N, Neupane M, Bian G, Zhang C, Sankar R, Chang G, Yuan Z, Lee C-C, Huang S-M, Zheng H, Ma J, Sanchez DS, Wang B, Bansil A, Chou F, Shibayev PP, Lin H, Jia S, Hasan MZ (2015) Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349:613–617CrossRef
140.
Jiang J, Liu ZK, Sun Y, Yang HF, Rajamathi CR, Qi YP, Yang LX, Chen C, Peng H, Hwang C-C, Sun SZ, Mo S-K, Vobornik I, Fujii J, Parkin SSP, Felser C, Yan BH, Chen YL (2017) Signature of type-II Weyl semimetal phase in MoTe\(_2\). Nat Commun 8:13973CrossRef
141.
Li P, Wen Y, He X, Zhang Q, Xia C, Yu Z-M, Yang SA, Zhu Z, Alshareef HN, Zhang X-X (2017) Evidence for topological type-II Weyl semimetal WTe2. Nat Commun 8:2150CrossRef
142.
Qi Y, Naumov PG, Ali MN, Rajamathi CR, Schnelle W, Barkalov O, Hanfland M, Wu S-C, Shekhar C, Sun Y, Süß V, Schmidt M, Schwarz U, Pippel E, Werner P, Hillebrand R, Förster T, Kampert E, Parkin S, Cava RJ, Felser C, Yan B, Medvedev SA (2016) Superconductivity in Weyl semimetal candidate MoTe\(_2\). Nat Commun 7:11038CrossRef
143.
Fatemi V, Wu S, Cao Y, Bretheau L, Gibson QD, Watanabe K, Taniguchi T, Cava RJ, Jarillo-Herrero P (2018) Electrically tunable low-density superconductivity in a monolayer topological insulator. Science 362:926–929CrossRef
144.
Sajadi E, Palomaki T, Fei Z, Zhao W, Bement P, Olsen C, Luescher S, Xu X, Folk JA, Cobden DH (2018) Gate-induced superconductivity in a monolayer topological insulator. Science 362:922–925CrossRef
145.
Ma Q, Xu SY, Shen H, MacNeill D, Fatemi V, Chang TR, Mier Valdivia AM, Wu S, Du Z, Hsu CH, Fang S, Gibson QD, Watanabe K, Taniguchi T, Cava RJ, Kaxiras E, Lu HZ, Lin H, Fu L, Gedik N, Jarillo-Herrero P (2019) Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565:337–342
146.
Kang K, Li T, Sohn E, Shan J, Mak KF (2019) Nonlinear anomalous Hall effect in few-layer WTe\(_2\). Nat Mater 18:324–328CrossRef
147.
Zhang Y, van den Brink J, Felser C, Yan B (2018) Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe\(_2\) and MoTe\(_2\). 2D Mater 5:044001
148.
Singh S, Kim J, Rabe KM, Vanderbilt D (2020) Engineering Weyl phases and nonlinear Hall effects in T\(_\text{d}\)-MoTe\(_2\). Phys Rev Lett 125:046402
149.
Zhou J, Qiao J, Bournel A, Zhao W (2019) Intrinsic spin Hall conductivity of the semimetals. Phys Rev B 99:60408CrossRef
150.
MacNeill D, Stiehl GM, Guimaraes MHD, Buhrman RA, Park J, Ralph DC (2017) Control of spin-orbit torques through crystal symmetry in WTe\(_2\)/ferromagnet bilayers. Nat Phys 13:300–305CrossRef
151.
Qian X, Liu J, Fu L, Li J (2014) Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346:1344–1347CrossRef
152.
Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H-Z, Jia C, Moritz B, Claassen M, Ryu H, Kahn S, Jiang J, Yan H, Hashimoto M, Lu D, Moore RG, Hwang C-C, Hwang C, Hussain Z, Chen Y, Ugeda MM, Liu Z, Xie X, Devereaux TP, Crommie MF, Mo S-K, Shen Z-X (2017) Quantum spin Hall state in monolayer 1T\(^\prime \)-WTe\(_2\). Nat Phys 13:683–687CrossRef
153.
Fei Z, Palomaki T, Wu S, Zhao W, Cai X, Sun B, Nguyen P, Finney J, Xu X, Cobden DH (2017) Edge conduction in monolayer WTe\(_2\). Nat Phys 13:677–682CrossRef
154.
Jia Z-Y, Song Y-H, Li X-B, Ran K, Lu P, Zheng H-J, Zhu X-Y, Shi Z-Q, Sun J, Wen J, Xing D, Li S-C (2017) Direct visualization of a two-dimensional topological insulator in the single-layer 1T\(^\prime \)-WTe\(_2\). Phys Rev B 96:041108
155.
Peng L, Yuan Y, Li G, Yang X, Xian J-J, Yi C-J, Shi Y-G, Fu Y-S (2017) Observation of topological states residing at step edges of WTe\(_2\). Nat Commun 8(1):659CrossRef
156.
Chen P, Pai WW, Chan Y-H, Sun W-L, Xu C-Z, Lin D-S, Chou MY, Fedorov A-V, Chiang T-C (2018) Large quantum-spin-Hall gap in single-layer 1T\(^\prime \)WSe\(_2\). Nat Commun 9:1–7
157.
Wu S, Fatemi V, Gibson QD, Watanabe K, Taniguchi T, Cava RJ, Jarillo-Herrero P (2018) Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359:76–79CrossRef
158.
Shi Y, Kahn J, Niu B, Fei Z, Sun B, Cai X, Francisco BA, Wu D, Shen ZX, Xu X, Cobden DH, Cui YT, Imaging quantum spin Hall edges in monolayer WTe\(_2\). Sci Adv 5
159.
Zhao C, Hu M, Qin J, Xia B, Liu C, Wang S, Guan D, Li Y, Zheng H, Liu J, Jia J (2020) Strain tunable semimetal-topological-insulator transition in monolayer \(1{\rm T\rm ^{^{\prime }}\text{- }{\rm WTe}}_{2}\). Phys Rev Lett 125:046801
160.
Safeer CK, Ontoso N, Ingla-Aynés J, Herling F, Pham VT, Kurzmann A, Ensslin K, Chuvilin A, Robredo I, Vergniory MG, de Juan F, Hueso LE, Calvo MR, Casanova F (2019) Large multidirectional spin-to-charge conversion in low-symmetry semimetal MoTe\(_2\) at room temperature. Nano Lett 19:8758–8766CrossRef
161.
Zhao B, Khokhriakov D, Zhang Y, Fu H, Karpiak B, Hoque AM, Xu X, Jiang Y, Yan B, Dash SP (2020) Observation of charge to spin conversion in Weyl semimetal WTe\(_{2}\) at room temperature. Phys Rev Res 2:013286
162.
Zhao B, Karpiak B, Khokhriakov D, Johansson A, Hoque AM, Xu X, Jiang Y, Mertig I, Dash SP (2020) Unconventional charge-to-spin conversion in Weyl-semimetal WTe\(_2\). Adv Mater 32:2000818CrossRef
163.
Hoffmann A (2013) Spin Hall effects in metals. IEEE Trans Magn 49:5172–5193CrossRef
164.
Isasa M, Villamor E, Hueso LE, Gradhand M, Casanova F (2015) Temperature dependence of spin diffusion length and spin Hall angle in Au and Pt. Phys Rev B 91:024402
165.
Laczkowski P, Fu Y, Yang H, Rojas-Sánchez J-C, Noel P, Pham VT, Zahnd G, Deranlot C, Collin S, Bouard C, Warin P, Maurel V, Chshiev M, Marty A, Attané J-P, Fert A, Jaffrès H, Vila L, George J-M (2017) Large enhancement of the spin Hall effect in Au by side-jump scattering on Ta impurities. Phys Rev B 96:140405
166.
Sagasta E, Omori Y, Vélez S, Llopis R, Tollan C, Chuvilin A, Hueso LE, Gradhand M, Otani Y, Casanova F (2018) Unveiling the mechanisms of the spin Hall effect in Ta. Phys Rev B 98:060410
167.
König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp LW, Qi X-L, Zhang S-C (2007) Quantum spin Hall insulator state in HgTe quantum wells. Science 318:766–770CrossRef
168.
Bernevig BA, Hughes TL, Zhang S-C (2006) Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314:1757–1761CrossRef
169.
Ok S, Muechler L, Di Sante D, Sangiovanni G, Thomale R, Neupert T (2019) Custodial glide symmetry of quantum spin Hall edge modes in monolayer WTe\(_2\). Phys Rev B 99:121105
170.
Cysne TP, Ferreira A, Rappoport TG (2018) Crystal-field effects in graphene with interface-induced spin-orbit coupling. Phys Rev B 98:045407
Metadata
Title
Fundamentals of Spin Dynamics in Two-Dimensional Materials
Author
Dr. Marc Vila Tusell
Copyright Year
2022
Book
Spin Dynamics in Two-Dimensional Quantum Materials

Print ISBN: 978-3-030-86113-1

Electronic ISBN: 978-3-030-86114-8

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-3-030-86114-8_2

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