Magnetism in layered ruthenates [Elektronische Ressource] = Magnetismus in geschichteten Ruthenaten / vorgelegt von Paul C. Steffens

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• Physik

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• Publié par: universitat_zu_koln
• Publié le: 01 janvier 2007
• Nombre de lectures: 13
• Langue: English
• Poids de l'ouvrage: 31 Mo

Extrait

Magnetism in layered Ruthenates
Magnetismus in geschichteten Ruthenaten
Inaugural-Dissertation
zur Erlangung des Doktorgrades
der Mathematisch-Naturwissenschaftlichen Fakult¨at
der Universitat zu Koln¨ ¨
vorgelegt von
Paul C. Steffens
aus Koln¨
Koln, 2008¨Berichterstatter: Prof. Dr. M. Braden
Prof. Dr. A. Rosch
Vorsitzender
der Prufungsk¨ ommission: Prof. Dr. L. Bohaty´
Tag der letzten mundlichen¨ Prufung:¨ 23.10.2007Contents
1 Introduction 7
2 Experimental and theoretical tools 9
2.1 Inelastic neutron scattering experiments . . . . . . . . . . . . . . . . . . 9
2.1.1 Magnetic neutron scattering . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Using polarized neutrons . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Neutrons and the susceptibility . . . . . . . . . . . . . . . . . . . 12
2.2 Spin fluctuations in metals . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 The susceptibility in the metallic state . . . . . . . . . . . . . . . 15
The generalized susceptibility . . . . . . . . . . . . . . . . . . . . 17
The exchange interaction . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Calculating the . . . . . . . . . . . . . . . . . . . . 20
Relation to the neutron scattering cross section . . . . . . . . . . 23
002.2.3 Approximations ofχ (Q,ω) near magnetic instabilities . . . . . . 23
Nearly ferromagnetic metal. . . . . . . . . . . . . . . . . . . . . . 23
Nearly antif metal. . . . . . . . . . . . . . . . . . . . 24
2.2.4 Contribution of spin fluctuations to the specific heat. . . . . . . . 27
2.3 Spin densities and polarized neutron diffraction . . . . . . . . . . . . . . 29
2.3.1 The measurement of flipping ratios . . . . . . . . . . . . . . . . . 29
2.3.2 Constructing the spin density from flipping ratio data . . . . . . . 31
Maximum Entropy Method . . . . . . . . . . . . . . . . . . . . . . 32
Computation of the maximum entropy map . . . . . . . . . . . . 33
3 Ca Sr RuO and the metamagnetic transition 372-x x 4
3.1 Magnetism in Ca Sr RuO . . . . . . . . . . . . . . . . . . . . . . . . 372 x x 4
3.1.1 Magnetic properties in the metallic state . . . . . . . . . . . . . . 37
3.1.2 The metamagnetic transition . . . . . . . . . . . . . . . . . . . . 43
Metamagnetic transitions, crossovers, and quantum criticality . . 43 transition in the bilayer Ruthenate . . . . . . . . . 45 tr in the single layer Ruthenate – is it
quantum critical? . . . . . . . . . . . . . . . . . . . . . 46
3.1.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Experimental aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Magnetic neutron scattering on Ca Sr RuO . . . . . . . . . . . . . . . 532 x x 4
3Contents
3.3.1 Magnetic origin of the signal and magnetic form factor . . . . . . 53
3.3.2 Spin density in Ca Sr RuO . . . . . . . . . . . . . . . . . . . 551.8 0.2 4
3.4 Magnetic correlations in Ca Sr RuO . . . . . . . . . . . . . . . . . . 581.8 0.2 4
3.4.1 Below the metamagnetic transition . . . . . . . . . . . . . . . . . 58
Detailed structure of the signal. . . . . . . . . . . . . . . . . . . . 60
Energy dependence. . . . . . . . . . . . . . . . . . . . . . . . . . 60
Antiferromagnetic nature of the signal and possible ferromag
netic contribution. . . . . . . . . . . . . . . . . . . . . . 62
Relation to the band structure . . . . . . . . . . . . . . . . . . . . 64
Nesting of theα andβ bands . . . . . . . . . . . . . . . . . . . . 68
Relation to macroscopic measurement methods . . . . . . . . . 68
3.4.2 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . 69
Quasi ferromagnetic signal as function of Temperature . . . . . . 70
Overall evolution of the signal at higher temperatures . . . . . . 72
3.4.3 The dependence on the magnetic field . . . . . . . . . . . . . . . 74
Response at different fields . . . . . . . . . . . . . . . 74
Enhancement of fluctuations at the transition . . . . . . . . . . . 77
3.4.4 Above the metamagnetic transition . . . . . . . . . . . . . . . . . 80
Excitations in the high field state . . . . . . . . . . . . . . . . . . 80
Modelling the spin wave . . . . . . . . . . . . . . . . . . . . . . . 82
Is it a magnon? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.5 Magnetic correlations in Ca Sr RuO . . . . . . . . . . . . . . . . . 881.38 0.62 4
3.5.1 Magnetic response close to the ferromagnetic instability . . . . . 89
3.5.2 A universal description of the magnetic response . . . . . . . . . 91
3.5.3 Temperature dependence . . . . . . . . . . . . . . . . . . . . . . 96
Qualitative description . . . . . . . . . . . . . . . . . . . . . . . . 97
A quantitative model . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.6 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Strontium Ruthenate 107
4.1 Sr RuO and spin triplet superconductivity . . . . . . . . . . . . . . . . . 1072 4
4.2 Basic properties of Sr RuO and magnetic fluctuations . . . . . . . . . . 1092 4
4.3 Measurement of magnetic excitations in Sr RuO by inelastic neutron2 4
scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.3.1 Neutron scattering experiments on Sr RuO . . . . . . . . . . . . 1122 4
4.3.2 Polarization analysis . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.3 Quantitative of the susceptibility . . . . . . . . . . . . . 118
4.3.4 Comparison with NMR data . . . . . . . . . . . . . . . . . . . . . 121
4.3.5 Further possible implications of the results . . . . . . . . . . . . 123
4.3.6 Magnetic fluctuations in the superconducting state . . . . . . . . 126
4.4 Sr RuO and Ti doping . . . . . . . . . . . . . . . . . . . . . . . . . . . 1282 4
4.4.1 In the ordered state: 9% Ti . . . . . . . . . . . . . . . . . . . . . 129
4Contents
4.4.2 Near the critical concentration: 2.5% Ti . . . . . . . . . . . . . . 132
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5 Bilayer Ruthenates 137
5.1 Spin density in Ca Ru O . . . . . . . . . . . . . . . . . . . . . . . . . . 1373 2 7
5.1.1 The bilayer Ruthenate Ca Ru O and its metamagnetic transition1373 2 7
5.1.2 Measurement of the spin density in Ca Ru O . . . . . . . . . . 1403 2 7
Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2 Magnetism in Ti doped Sr Ru O . . . . . . . . . . . . . . . . . . . . . . 1473 2 7
5.2.1 Ti doping and magnetic order in Sr Ru O . . . . . . . . . . . . 1473 2 7
5.2.2 Magnetic order probed by elastic neutron scattering . . . . . . . 149
5.2.3 excitations in Sr (Ru Ti ) O . . . . . . . . . . . . . 1543 0.9 0.1 2 7
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6 Summary, conclusions and outlook 161
A Appendix 165
A.1 The calibration of magnetic scattering intensity . . . . . . . . . . . . . . 165
A.2 Some remarks about the maximum entropy algorithm . . . . . . . . . . 167
Kurzfassung (Deutsch) 169
Abstract (English) 171
Danksagung 173
List of Publications 175
Bibliography 177
Index 188
Offizielle Erklarung 193¨
5Contents
61 Introduction
BydiscussingthemagnetismofthelayeredRuthenates, thisthesis addressesa vari
ety of intriguing phenomena in solid state physics. The restriction on this single class
of materials does by no means limit the number of interesting topics to be discussed:
they include metamagnetic transitions, quantum critical behavior, magnetic order in
general, magnetic fluctuations in highly correlated materials, and unconventional su
perconductivity.
In the recent years, two members of the family of layered Ruthenates have made
these materials widely recognized and attracted significant attention: firstly, this is
Sr RuO – an unconventional superconductor in which the Cooper pairs are most2 4
likely in a triplet state. Secondly, in Sr Ru O the concept of metamagnetic quantum3 2 7
criticality is currently under active debate.
While there are also layered Ruthenates with a higher number of layers, these two
cases – the layered perovskite with one or two layers – are the only ones
considered here. Starting from these two materials, a variety of other substances
are obtained which have very different properties and are of interest on their own
right. Substituting Strontium by Calcium, one can continuously vary the chemical
composition and arrives finally at Calcium Ruthenate (Ca RuO or Ca Ru O ) which2 4 3 2 7
has, driven by structural distortions, entirely different properties. These substances
are therefore very well suited to study the interplay between the structural, electronic,
orbitalandmagneticdegreesoffreedom. Anotherinterestingvariationisachievedby
substituting Ruthenium with Titanium, which leads to magnetically ordered states.
This thesis contains the results of experimental work. For the investigation of mag
netic properties, neutron scattering is an extremely powerful tool. A number of differ
ent neutron scattering techniques has been applied, thereby addressing very diverse
aspects of magnetism in the layered Ruthenates and yielding a detailed picture of
these materials.
This thesis contains four large chapters, which are organized as follows:
• Chapter 2 does not contain experime