Magnetization Dynamics in Diluted Magnetic Semiconductor Heterostructures

Magnetization Dynamics
inDiluted Magnetic SemiconductorHeterostructures

Dissertation
presented to the Institute of Physics of theUniversity of Technology, Dortmund, Germany
in partial fulfilment of the requirements for the degree of
Doktor rer. nat.

presented by
Martin K. Kneip
dipl.-phys. dipl.-kfm.
Dortmund, 26th August 2008

CONTENTS

Introduction1

1II-VI diluted magnetic semiconductors9

1.1Crystal structure of (Cd,Mn)Te and (Zn,Mn)Se .11

1.2Band structure of (Cd,Mn)Te and (Zn,Mn)Se .14

1.2.1Band structure of zincblende semiconductors .14

1.2.2Band structure of zincblende semiconductors containing manganese . .19

1.3Magnetic properties .24

1.3.1Basic principles of magnetism .24

1.3.1.1Larmor Diamagnetism .25

1.3.1.2Paramagnetism.26

1.3.1.3Heisenberg model .27

1.3.1.4Ferromagnetism .28

1.3.1.5Ferrimagnetism .28

1.3.1.6Antiferromagnetism .28

1.3.2Magnetic effects of free electrons .29

1.3.3Magnetic properties of (Cd,Mn)Te and (Zn,Mn)Se without Mn-Mn-interaction.31

1.3.4Exchange Interactions .33

1.3.4.1sp-d exchange interaction .34

1.3.4.2d-d exchange interaction .35

1.3.4.3Magnetic properties of (Cd,Mn)Te and (Zn,Mn)Se with Mn-Mn interactions .39

1.3.4.4Giant Zeeman-splitting .42

1.4Quantum well heterostructures .46

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CONTENTS

1.4.1Single-particle states in quantum wells .48
1.4.2Spin-orbit-splitting in quantum wells .50
1.4.3Heterostructures in magnetic field .50
1.4.4Density of states in quantum wells .52
1.4.5Selection rules and polarization degree in quantum wells .55
1.4.6Parabolic and half-parabolic quantum wells .56
1.5Excitons .60
1.5.1Free exciton .61
1.5.2Interaction of excitons with Mn2+-ions .63
1.5.3Quasi-two-dimensional excitons in quantum wells .63
1.5.4Quasi-two-dimensional excitons in magnetic field .64
1.5.5Trions .66

2Magnetization dynamics67
2.1Spin and energy transfer .68
2.1.1Coupled systems in diluted magnetic semiconductors .68
2.1.2Theoretical formulation of spin and energy transfer .71
2.1.3Manganese spin temperature in stationary condition .75
2.2Mechanisms for spin relaxation .76
2.2.1D′yakonov-Perel mechanism .77
2.2.2Elliott-Yafet mechanism .78
2.2.3Bir-Aronov-Pikus mechanism .78
2.2.4Hyperfine-interaction mechanism .79
2.2.5Spin relaxation in excitons .79
2.3Spin lattice relaxation .80
2.4Spin diffusion .82

3Experimental technique87
3.1Optical detection of Mn spin temperature .88
3.2Heating of the Mn spin system .92
3.2.1Heating by laser light .92
3.2.2Heating by electric current .94

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CONTENTS

3.2.3Heating by phonons .95
3.3Time-resolved measurements .95
3.4Experimental setup .98

4Interaction between carriers and Mn-spin system101
4.1Twofold dynamic impact for Mn heating 102
4.2Direct energy and spin transfer 104
4.3Competition between direct and indirect energy and spin transfer 106
4.4Influence of excitation density 110
4.5Distinction between direct and indirect heating of the Mn system 112
4.5.1Steady-state optical excitation 112
4.5.2Long pulses with low and moderate excitation densities 112
4.5.3Short pulses with high excitation densities 114

5Spin-lattice relaxation115
5.1Dependence of the spin-lattice relaxation on the Mn content115
5.2Effect of free carriers in doped structures 121

6Control of spin-lattice relaxation129
6.1Electric field control of 2DEG 130
6.2Engineering of spin-lattice relaxation by digital growth 134
6.3Spin-lattice relaxation in parabolic and half-parabolic quantum wells 139
6.4Acceleration of spin-lattice relaxation by spin diffusion 145

Summary155

A Samples159
A.1 Preparation of the samples 159
A.1.1Molecular beam epitaxy 159
A.1.2Quantum well heterostructures 160
A.1.3Structure with electric contacts 161
A.1.4Digital growth technique 161
A.2 Tables of samples 162
A.3 Lattice and electronic properties 164

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CONTENTS

B Measurement and treatment of the experimental data167
B.1 Giant Zeeman shift 167
B.2 Spin-lattice relaxation time 176

Bibliography181
Index237
Symbols and Abbreviations239
List of Acronyms249
List of Publications253
Acknowledgments255

LIST OF FIGURES

1.1Unit cell of zincblende structure .12

1.2First Brillouin zone of zincblende lattice .13

1.3Schematic representation of the band structure of zincblende semiconductors .16

1.4Calculated band structure of ZnSe and CdTe .18

1.5Relation between lattice constant and fundamental band gap in II-VI semiconductors .20

1.6Variation of the energy gap in Cd1-xMnxTe with Mn concentration 21

1.7Variation of the energy gap in Zn1-xMnxSe with Mn concentration 22

1.8Lowest energy states of the Mn 3d-shell .24

1.9Change of the density of states in magnetic field .30

1.10 Brillouin function .32

1.11 Energy level scheme of an interacting Mn2+-ion pair as function of magnetic field 38

1.12 Magnetic phase diagram of Cd1-xMnxTe 40

1.13 The dependencies of the phenomenological parameters Seff and T0 on the Mn-concentration .42

1.14 Competition between Landau level and giant Zeeman-splitting term for different Mn concentrations .44

1.15 Schematic picture of the giant Zeeman-splitting of conduction band (6) and valence band (8) for a

wide-band-gap AII Mn1-xxBV I alloy in magnetic field atthe center of the Brillouin-zone at the -point .45

1.16 Temperature and magnetic field dependence of the giant Zeeman-splitting . . .45

1.17 Band edge devolution of type-I and type-II quantum wells.47

1.18 Schematical illustration of a type-I quantum well .47

1.19 Potential change of a type-I quantum well in magnetic field .51

1.20 Density of states without or with magnetic field in a quantum well .53

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LIST OF FIGURES

1.21 Filling factors of Landau-levels .56
1.22 Potential of the conduction and valence band of a parabolic quantum well with or without magnetic field .57
1.23 Devolution of the conduction band edge, wavefunctions and energy levels for parabolic and half-parabolic quantum wells .59
1.24 Theoretical Zeeman-splitting of a parabolic quantum well for different - polarized optical transitions in magnetic field .60
1.25 Schematical picture of exciton creation .62

2.1Interacting systems of DMS and channels for energy transfer .69
2.2Energy diagram of electron exchange scattering on Mn2+-ion in external magnetic field .73
2.3Scheme of D′yakonov-Perel mechanism .77
2.4Schematical picture of the three possible spin-phonon transition mechanisms with phonon absorption .81
2.5Times for spin-spin interaction depending on Mn content .83
2.6Time evolution of the relative changes in magnetization in a type-II heterostructure 83
2.7Band scheme of a heteromagnetic nanostructure .84

3.1PL, PLE and reflectivity spectra of (Zn,Mn)Se and (Cd,Mn)Te QWs .89
3.2Comparison of circular polarization degree and giant Zeeman shift of excitonicPL line .90
3.3Giant Zeeman shift of excitons for different excitation densities .91
3.4Interacting systems of undoped DMS under heating by laser light .93
3.5Mn spin temperature dependency on excitation density for different Mn con-centrations .94
3.6Energy scheme for photoexcitation with different photons .95
3.7PL spectra in different time regime .96
3.8Temporal variation of the PL spectral line and circular polarization degree . . .97
3.9Experimental setup .99
3.10 Schematical assembly of the intensifier of an ICCD camera 100

 

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LIST OF FIGURES

4.1Temporal evolution of a Nd:YAG laser pulse and of the PL signal of a(Zn,Mn)Se-based QW 102
4.2Schematical picture of the two impacts for Mn heating 103
4.3Schematic presentation of the dynamical response of the Mn-system on the im-pact pulses under various experimental conditions 104
4.4Normalized energy shifts of PL lines induced laser pluses in magnetic field in(Zn,Mn)Se-based QWs 105
4.5Rise in energy in (Zn,Mn)Se-based QWs with different Mn concentrations incomparison with the laser pulse integral 105
4.6Energy scheme for photoexcitation with different photons 106
4.7Dynamics of the Mn temperature for two different laser excitation energies. . 107
4.8Spin-lattice and nonequilibrium phonon relaxation times measured for differentpowers of 355 nm laser excitation 108
4.9Dynamics of the Mn temperature for a (Zn,Mn)Se-based QW with low Mnconcentration under two different laser excitation energies 109
4.10 Temporal behavior of the PL line energy shift in (Cd,Mn)Te109
4.11 Mn-spin temperature versus time measured at different excitation densities . . . 111
4.12 Maximal Mn-spin temperatures achieved by direct carrier heating and bynonequilibrium phonons as function of excitation density 111

5.1Temporal evolution of PL spectral line shift for different Mn content 116
5.2Spin-lattice relaxation time as function of Mn content for nominally undoped(Zn,Mn)Se/(Zn,Be)Se structures 117
5.3Energy scheme for a manganese pair cluster 118
5.4Dependence of the spin-lattice relaxation time on the concentration of free elec-trons 122
5.5SLR time as function of the carrier density 123
5.6Illustration of the bypass channel for energy transfer from the Mn-system to thelattice through the 2DEG 123
5.7Model calculations of the SLR time as function of the magnetic field 125
5.8Fermi energy of the 2DEG in CdTe and ZnSe for different electron concentrations126

6.1PL spectra at different magnetic fields for two gate voltages 131
6.2Giant Zeeman shift of photoluminescence line for two different gate voltages . 132
6.3Temporal evolution of PL line shift corresponding to the cooling of the Mn spinsystem heated by pulsed laser excitation 133

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LIST OF FIGURES

6.4SLR time dependence on gate voltage for a n-type modulation-doped(Zn,Mn)Se-based QW 133
6.5Gate voltage dependence of the PL line maxima energy and current134
6.6Schematic diagram of the conduction and valence band profile and Mn-ion pro-file in (Cd,Mn)Te digital alloy structures 135
6.7PL spectra for digital alloy samples 136
6.8Giant Zeeman shift of the photoluminescence line for the three different DAsamples 137
6.9Dynamical shift of the PL lines in digital alloys showing the cooling of the Mnspin system heated by pulsed laser excitation137
6.10 SLR times versus Mn content x in disordered alloys and digital alloys 138
6.11 Diagram linking the static and the dynamic magnetic characteristics of disordered and digital alloys 138
6.12 Scheme of digital growth profile for parabolic and half-parabolic QW 140
6.13 Giant Zeeman shift of the PL line for one HPQW and two PQW samples 141
6.14 Dynamical shift of the PL lines in (H)PQWs, showing the cooling of the Mn spin system heated by pulsed laser excitation142
6.15 Temporal evolution of the PL line maximum position after laser pulse for theHPQW samples 143
6.16 Diagram linking the static and the dynamic magnetic characteristics of PQWsand HPQWs 144
6.17 Power dependence of the magnetization dynamics in the HPQW sample 11155A 145
6.18 Comparison of the relation between effective Mn contents x and x for DAsand (H)PQWs 146
6.19 Analytical representation of the dependence of the SLR time on the Mn con-centration 148
6.20 Calculated spin-lattice relaxation times for different spin-spin diffusion coefficients for a (Zn,Mn)Se type-II QW 148
6.21 Calculated kinetics of the Mn temperature for different diffusion coefficients in the center of a (Zn,Mn)Se type-II QW 149
6.22 Profiles of Mn spin temperature during spin-lattice relaxation 150
6.23 Temporal profile of the Mn temperature in a QW 150
6.24 Comparison of model calculations including spin diffusion with experimental results in (Cd,Mn)Te-based digital alloys 151

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LIST OF FIGURES

6.25 Comparison of model calculations including spin diffusion with experimental results for PQWs 152
A.1 Schematical picture of MBE chamber 160
B.1 Spectrally resolved PL line of a ZnMnSe-based QW for different magnetic fieldstrengths 168
B.2 Giant Zeeman-splitting of the PL line in magnetic field 171
B.3 Time scheme of GCCD measurement 176
B.4 Dynamics of PL line 178

Introduction

Already in ancient times the Greek had the knowledge about electrostatic charging of amber, the resin of conifers, which was denoted by the Greek word electron(νηλεκτρoν).The first realization of this effect is accredited to the great Greek philosopher ThalesofMilet1. Nevertheless, the effect was not used for centuries until beginning of modern times in 18thcentury. Since then our life was revolutionized by applications and devices based on the electric charge, so that our contemporary life is unimaginable without this technology. Especially the rapid development in the last hundred years has its reason in the comprehension of the underlying mechanisms. The cognition of the particle electron is of particular importance in this regard. The name electron for the unit of the electric charge was introduced by George Johnstone Stoney together with Hermann Ludwig Ferdinand von Helmholtzin 1894[Sto94,Sto95], closely followed by the experimental discovery of the electron by Joseph John Thomson [Tho97]and Emil Wiechert [Wie97] in 1897. Motivated by the discovery of the electron, Thomson developed the famous “Plumpuddingmodel”of the atom [Tho04], which was later proved incorrect by Ernest Rutherford and substituted by the “Rutherfordmodel”[Rut11]. However, this model could not explain origin and principle of the observed spectrallines of different gases like e.g. hydrogen, for which already several empirical correlations had been discovered [Bal85,Lym06,Pas08]. Therefore, Niels Bohr has advanced the “Rutherfordmodel”to the “Bohrmodel” in 1913 [Boh13]. In the“Bohrmodel” the electrons have discrete orbits around the nucleus. Although this model achieved success, it could not explain the abnormal Zeeman-effect and the fine structure of atomic spectra. These phenomena could be explained by an eigen angular momentum of electrons, the so-called spin. The half-integerelectron spin was postulated by George Eugene Uhlenbeck and Samuel Abraham Goudsmit in 1925 [ Uhl25,Uhl26]because of spectroscopic investigations. They have interpreted the spin as the fourthquantumnumber, which was proposed byWolfgang Pauli [Pau25]beside the energyE,the orbital angular momentum Landits projection Lz. This concept of an intrinsic angular momentum was very successful and could simultaneously explain earlier experiments by Albert Einstein and Wander Johannes de Haas [Ein15], as well as Otto Stern and Walter Gerlach [Ger22c,Ger22b,Ger22a,Ste88].