Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte

Spin-Wellen-Berechnungen für Heisenberg-Magnete mit reduzierter Symmetrie

The phenomenon of magnetism is a pure quantum effect and has been studied since the beginning of civilization. The practical use of magnetic materials for technical purposes was well established in the 19th century; still nowadays there is no lack of new high-tech applications based on magnetism for example in information technology to store and process data. This thesis does not focus on the development of new applications of magnetism in technology, nor enhancement of known fields of application. Instead, the intention is to use a quantum theory of magnetism for obtaining new insights on physical effects that accompany the phenomenon of magnetism. Therefore three different model systems, each of which are believed to describe a class of real compounds, are considered. Starting from the idea that magnetism can be understood by use of the so-called Heisenberg model that microscopically characterizes the interaction between localized magnetic moments, we restrict ourselves to the case where a long-range magnetic order is present. In order to deduce consequences resulting from this microscopic picture we use the spin-wave theory that is introduced in the first chapter. Central objects of this theory are the magnons which are elementary quantum excitations in ordered magnets. An application of these mathematical techniques to a model that describes an antiferromagnet in an external magnetic field is presented in the second chapter. Quantities like the spin-wave velocity and the damping of magnons are calculated using a Hermitian operator approach in the framework of spin-wave theory. A strong renormalization of the magnetic excitations arises because the symmetry of the system is reduced due to the external magnetic field. In the second model system, that describes thin films of a ferromagnet, concepts of classical physics meet quantum physics: The magnetic dipole-dipole interaction that is also known in everyday life from the magnetic forces between magnets and was initially formulated in the theory of electromagnetism, is included in the microscopic model. Having a special compound in mind where the magnetic excitations are directly accessible in experiments, the energy dispersions of magnon modes in thin-film ferromagnets are deduced. Our approach is essentially a basis for further investigations beyond this thesis to describe strong correlations and condensation of magnons. A recent realization of data processing devices with spin waves puts the understanding of physical processes in these ferromagnetic films in the focus of upcoming research. The third model system brings in the so-called frustration where the interactions between the spins are such that the total energy cannot be minimized by an appropriate alignment of the magnetic moments in the classical picture. In the simplest case this appears because the antiferromagnetically coupled spins are located on a triangular lattice. This situation will lead to strong quantum fluctuations which make this model system interesting. Finally the overall symmetry is reduced by inclusion of spin anisotropies and an external magnetic field. Instead of focusing on the properties of the magnetic excitations, the effect of the magnetic field on the properties of the lattice vibrations is subject to the investigation. This is interesting because the characteristics of lattice vibrations can be measured experimentally using the supersonic technique.Magnetismus ist ein Naturphänomen, das schon vor Jahrtausenden beschrieben und diskutiert wurde. Eine physikalische Erklärung ist jedoch erst auf der Basis der Anfang des 20. Jahrhunderts entwickelten Quantentheorie möglich. Schon vorher spielten magnetische Werkstoffe in technischen Anwendungen eine wichtige Rolle. Auch in jüngster Zeit finden sich immer neue Anwendungsmöglichkeiten für magnetische Materialien, zum Beispiel in der Informationstechnologie. Die vorliegende Arbeit beschäftigt sich weder mit neuen Anwendungsgebieten von magnetischen Effekten, noch mit der gezielten Optimierung bekannter Einsatzgebiete. Vielmehr wollen wir mit Hilfe der Quantentheorie neue Erkenntnisse über physikalische Effekte gewinnen, die mit dem Phänomen des Magnetismus zusammenhängen. Dazu starten wir nacheinander mit drei verschiedenen mikroskopischen Modellen, die jeweils eine Klasse magnetischer Materialien beschreiben. Das sogenannte Heisenberg-Modell, das die Wechselwirkungen zwischen lokalisierten Spins beschreibt, ist der Ausgangspunkt für die drei Untersuchungen. Wir beschränken uns weiterhin auf geordnete Magnete, in denen eine langreichweitige magnetische Ordnung vorliegt, um die Methode der Spinwellentheorie anzuwenden. Im ersten Kapitel werden die Grundzüge der Spinwellentheorie sowie einige für die späteren Ausführungen wichtige Besonderheiten beschrieben. Die sogenannten Magnonen oder Spinwellen stellen in dieser Herangehensweise die elementaren Anregungen in geordneten Magneten dar. Im zweiten Kapitel wenden wir die Spinwellentheorie auf ein Modellsystem an, das einen Antiferromagneten in einem externen Magnetfeld beschreibt. Unter Verwendung einer sogenannten hermiteschen Parametrisierung werden physikalische Größen wie die Spinwellengeschwindigkeit sowie die Dämpfung der Spinwellen berechnet. Wir sind dabei insbesondere am Einfluss des Magnetfeldes interessiert, welches die Symmetrie des Systems reduziert und die magnetischen Anregungen wesentlich renormiert. Im zweiten Modellsystem, welches zur Beschreibung dünner Filme von Ferromagneten geeignet ist, werden Konzepte der klassischen Magnetostatik mit denen der Quantenphysik vereinigt: Wir betrachten zusätzlich die Dipol-Dipol Wechselwirkungen zwischen den mikroskopischen magnetischen Momenten. Diese Wechselwirkung ist als magnetische Kraft zwischen zwei Magneten auch aus unserem Alltag bekannt. Unter Verwendung der Spinwellentheorie berechnen wir die Energie-Impuls-Beziehung, die sogenannte Dispersion, der magnetischen Anregungen in dünnen Filmen eines experimentell untersuchten Ferromagneten. Dieser theoretische Ansatz ist schließlich der Ausgangspunkt für weitere Untersuchungen im Hinblick auf starke Korrelationen und Kondensationsphänomene von Magnonen. Das physikalische Verständnis der Vorgänge in dünnen ferromagnetischen Filmen ist auch von technologischem Interesse, da kürzlich Bauteile zur Datenverarbeitung auf der Basis von Spinwellen realisiert wurden. Das dritte Modellsystem enthält schließlich zusätzlich die sogenannte magnetische Frustration. In diesem Fall sind die Wechselwirkungen zwischen benachbarten Spins derart, dass nicht alle Wechselwirkungsenergien gleichzeitig durch Ausrichtung der Spins minimiert werden können und starke Quantenfluktuationen auftreten. Ein Beispiel dafür ist der Antiferromagnet auf dem Dreiecksgitter, den wir in der vorliegenden Arbeit behandeln. Wir reduzieren die Symmetrie weiter durch Hinzunahme von Anisotropien, um mit unseren Ergebnissen auch an experimentelle Untersuchungen anknüpfen zu können. Der Schwerpunkt liegt jedoch nicht auf Einsichten in die magnetischen Anregungen, sondern auf dem Verständnis der Änderung der Gitterschwingungen in Anwesenheit der magnetischen Wechselwirkungen. Wir berechnen schließlich die Verschiebung der Schallgeschwindigkeit und die Dämpfung des Schalls als Funktion des angelegten Magnetfeldes und vergleichen die Ergebnisse mit experimentellen Daten aus Ultraschallmessungen

Theoretical study of impurity-induced magnetism in FeSe

Experimental evidence suggests that FeSe is close to a magnetic instability, and recent scanning tunneling microscopy (STM) measurements on FeSe multilayer films have revealed stripe order locally pinned near defect sites. Motivated by these findings, we perform a theoretical study of locally induced magnetic order near nonmagnetic impurities in a model relevant for FeSe. We find that relatively weak repulsive impurities indeed are capable of generating short-range magnetism, and explain the driving mechanism for the local order by resonant eg-orbital states. In addition, we investigate the importance of orbital-selective self-energy effects relevant for Hund's metals, and show how the structure of the induced magnetization cloud gets modified by orbital selectivity. Finally, we make concrete connection to STM measurements of iron-based superconductors by symmetry arguments of the induced magnetic order, and the basic properties of the Fe Wannier functions relevant for tunneling spectroscopy.Comment: 10 pages, 4 figure

Robustness of Quasiparticle Interference Test for Sign-changing Gaps in Multiband Superconductors

Recently, a test for a sign-changing gap function in a candidate multiband unconventional superconductor involving quasiparticle interference data was proposed. The test was based on the antisymmetric, Fourier transformed conductance maps integrated over a range of momenta $\bf q$ corresponding to interband processes, which was argued to display a particular resonant form, provided the gaps changed sign between the Fermi surface sheets connected by $\bf q$. The calculation was performed for a single impurity, however, raising the question of how robust this measure is as a test of sign-changing pairing in a realistic system with many impurities. Here we reproduce the results of the previous work within a model with two distinct Fermi surface sheets, and show explicitly that the previous result, while exact for a single nonmagnetic scatterer and also in the limit of a dense set of random impurities, can be difficult to implement for a few dilute impurities. In this case, however, appropriate isolation of a single impurity is sufficient to recover the expected result, allowing a robust statement about the gap signs to be made.Comment: 9 pages, 12 figure

Universality of scanning tunneling microscopy in cuprate superconductors

We consider the problem of local tunneling into cuprate superconductors, combining model based calculations for the superconducting order parameter with wavefunction information obtained from first principles electronic structure. For some time it has been proposed that scanning tunneling microscopy (STM) spectra do not reflect the properties of the superconducting layer in the CuO$_2$ plane directly beneath the STM tip, but rather a weighted sum of spatially proximate states determined by the details of the tunneling process. These "filter" ideas have been countered with the argument that similar conductance patterns have been seen around impurities and charge ordered states in systems with atomically quite different barrier layers. Here we use a recently developed Wannier function based method to calculate topographies, spectra, conductance maps and normalized conductance maps close to impurities. We find that it is the local planar Cu $d_{x^2-y^2}$ Wannier function, qualitatively similar for many systems, that controls the form of the tunneling spectrum and the spatial patterns near perturbations. We explain how, despite the fact that STM observables depend on the materials-specific details of the tunneling process and setup parameters, there is an overall universality in the qualitative features of conductance spectra. In particular, we discuss why STM results on Bi$_2$Sr$_2$CaCu$_2$O$_8$ and Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ are essentially identical