Magnetic anisotropies of (Ga,Mn)As films and nanostructures [Elektronische Ressource] / vorgelegt von Frank Hoffmann

Sujets

• Physik

Informations

• Publié par: universitat_regensburg
• Publié le: 01 janvier 2010
• Nombre de lectures: 39
• Poids de l'ouvrage: 3 Mo

Extrait

Magnetic anisotropies of
(Ga,Mn)As lms and
nanostructures
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften (Dr. rer. nat.)
der Fakultat Physik
der Universitat Regensburg
vorgelegt von
Frank Ho mann
aus Passau
2010Promotionsgesuch eingereicht am 06.10.2010
Die Arbeit wurde angeleitet von: Prof. Dr. C. H. Back
Pruf ungsausschuss:
Vorsitzender: Prof. Dr. J. Fabian
1. Gutachter: Prof. Dr. C. H. Back
2.hter: Prof. Dr. D. Weiss
Weiterer Prufer: Prof. Dr. J. Lupton
Tag des Promotionskolloquiums: 02.02.2011Contents
1 Introduction 1
2 Theoretical basics 5
2.1 Ferromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Magnetic energies and elds . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Exchange Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Demagnetizing energy . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Anisotropy energy . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.4 Zeeman Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Magnetization Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 The Landau-Lifshitz-Gilbert Equation . . . . . . . . . . . . . . . 11
2.3.3 Basic concept of ferromagnetic resonance . . . . . . . . . . . . . . 11
2.3.4 Ferromagnetic resonance condition . . . . . . . . . . . . . . . . . 12
2.3.5 Calculation of the FMR lineshape . . . . . . . . . . . . . . . . . . 13
3 Structural and magnetic properties of (Ga,Mn)As 17
3.1 Structural properties of (Ga,Mn)As lms . . . . . . . . . . . . . . . . . . 17
3.1.1 Point defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.2 Lattice constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Ferromagnetism in (Ga,Mn)As . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Mean eld Zener model . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Magneto-crystalline anisotropies . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.1 Cubic anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.2 Perpendicular anisotropy . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.3 Uniaxial in-plane anisotropy . . . . . . . . . . . . . . . . . . . . . 24
4 Experimental techniques 27
4.1 Magneto-optic Kerr e ect . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Stroboscopic pump-probe technique . . . . . . . . . . . . . . . . . . . . . 29
4.3 Components of the low-temperature time-resolved MOKE setup . . . . . 30
4.3.1 Microscope cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.2 Magnetic DC eld . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.4 Ferromagnetic resonance scanning Kerr microscopy . . . . . . . . . . . . 31
4.4.1 Excitation of the precessional motion . . . . . . . . . . . . . . . . 31
4.4.2 Scanning Kerr microscopy . . . . . . . . . . . . . . . . . . . . . . 32
iii Contents
4.5 All-optical pump-probe technique . . . . . . . . . . . . . . . . . . . . . . 35
5 Magnetic anisotropy and damping of (Ga,Mn)As lms 39
5.1 Comparison of local and integral FMR techniques . . . . . . . . . . . . . 39
5.2 E ects of microwave excitation . . . . . . . . . . . . . . . . . . . . . . . 42
5.3 Magnetic anisotropies of (Ga,Mn)As lms . . . . . . . . . . . . . . . . . 43
5.3.1 In uence of annealing and Mn-concentration . . . . . . . . . . . . 47
5.3.2 Temperature dependence of the magnetic anisotropies . . . . . . . 49
5.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4 Electrical detection of the ferromagnetic resonance . . . . . . . . . . . . . 53
5.5 Magnetic relaxation mechanisms . . . . . . . . . . . . . . . . . . . . . . . 57
5.5.1 Intrinsic and extrinsic contributions of the FMR linewidth . . . . 58
5.5.2 Previous studies of the FMR linewidth in (Ga,Mn)As lms . . . . 60
5.5.3 Homogeneity of the magnetic properties on macroscopic length
scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5.4y of the magnetic anisotropies on a sub-micrometer
length scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.5.5 Intrinsic damping in (Ga,Mn)As lms . . . . . . . . . . . . . . . . 67
5.5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.6 Time-resolved experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.6.1 All-optical pump-probe measurements . . . . . . . . . . . . . . . 70
5.6.2 Acoustic strain waves . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.6.3 Transient changes of the magnetic anisotropies . . . . . . . . . . . 75
6 Magnetic anisotropy and coercive elds of (Ga,Mn)As nanostructures 81
6.1 Magnetic anisotropies of rectangular elements . . . . . . . . . 82
6.1.1 Structural properties . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.1.2 Quantitative determination of the anisotropies . . . . . . . . . . . 83
6.2 Magnetic anisotropies of circular (Ga,Mn)As elements . . . . . . . . . . . 86
6.3 Visualization of local variations of the magnetic anisotropy . . . . . . . . 87
6.4 Magnetization reversal in (Ga,Mn)As micro- and nanostructures . . . . . 89
6.5 Origin of the intrinsic uniaxial in-plane anisotropy . . . . . . . . . . . . . 93
7 Summary and Outlook 99
8 Appendix 101
8.1 Molecular beam epitaxy of (Ga,Mn)As lms . . . . . . . . . . . . . . . . 101
8.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.3 Coplanar Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Bibliography 107
Publications 117
Acknowledgements 1191 Introduction
The rapidly emerging eld of spintronics, which makes use of both the electron spin
and charge has already found its way into everyday’s life. The most prominent example
is the read head of a commercial magnetic hard disk drive which is based on the so
called giant magneto-resistance e ect (GMR) or the tunneling magneto-resistance ef-
fect (TMR). The GMR e ect which was discovered independently by P. Grun berg and
A. Fert in 1988 [1, 2], describes the dependence of the electrical resistance in a stack
of thin ferromagnetic and nonmagnetic layers on the relative orientation of the magne-
tization in adjacent layers. The successful implementation of GMR based read heads
has contributed signi cantly to the increase of the storage density in magnetic hard
disk drives. In spintronics, during the last two decades, diluted magnetic semiconduc-
tors have attracted much attention due to their potential of combining both the storage
and manipulation of data by means of a single material system. In 1996 for the rst
time the diluted magnetic semiconductor (Ga,Mn)As with ferromagnetic properties at
low temperatures was grown successfully [3]. For many years this material has been
considered as the most promising candidate for a magnetic semiconductor at room tem-
perature. In theory, a Curie temperature of 300 K was predicted for 10% concentration
of uncompensated Mn acceptors [4]. Although substantial e orts have been put intoGa
the optimization of the growth and the post-growth treatment of (Ga,Mn)As a further
increase in the Curie temperature from currently 180-190 K [5, 6] up to temperatures
well above room temperature is unlikely. Nevertheless, from a physical point of view
(Ga,Mn)As is a very interesting material exhibiting a multitude of novel physical ef-
fects. As an example, by applying a gate voltage purely electrical manipulations of
the magnetic properties such as magnetic anisotropies or Curie temperature have been
demonstrated for the very rst time [7,8].
For various kinds of experiments and also for applications the possibility to control
the magnetic anisotropies is desirable. The anisotropies directly in uence the magnetic
ground state, the width of domain walls, the coercive elds, etc. Yet, the magnetic
anisotropies in (Ga,Mn)As can hardly be adjusted or not even be reproduced because
they depend crucially on various parameters such as hole and Mn-concentration, post-
growth annealing, etc. which cannot be fully controlled during the fabrication process.
However, recent SQUID and magnetotransport experiments have shown that the mag-
netic anisotropies in lithographically prepared (Ga,Mn)As elements di er clearly from
the unpatterned (Ga,Mn)As lms [9{11]. Such nanostructured elements can be used to
adjust the magnetic anisotropy well-directed and reproducible.
In order to quantitatively determine various magnetic properties of such small mag-
netic elements, a combination of ferromagnetic resonance (FMR) and Kerr microscopy
is employed in this thesis. The technique o ers several advantages compared to the
12 1 Introduction
SQUID and magneto-transport measurements of the earlier publications [9{11]. On
the one hand, a quantitative determination of the magnetic anisotropy in these type
of experiments is very complex and is only possible under the assumption of a single
domain state. This, however, is not justi ed for elements in the size range of hun-
dreds of nanometers to micrometer. On the other hand, these techniques only measure
the average magnetic properties of one or an array of similar magnetic elements. The
novel low-temperature Kerr-FMR setup o ers the possibility to dete