Nonlinear electromagnetic probes for the study of ultrafast processes in condensed matter

Abstract

This thesis is dedicated to improving the understanding of nonlinear electromagnetic probes of solid-state properties in the ultrafast temporal domain. Nonlinear methods are able to provide an unparalleled sensitivity in the search for new physics in solid-state science. They can yield insight into the material symmetry and potentially induced changes thereof, which enables e.g. to track the inversion of polarization in a ferroelectric material 1. The latter is of great interest in the search for novel and fast electronic gates and storage devices. More fundamentally, nonlinear probes can reveal coupling between various degrees of freedom and hence can give insight into the interplay and causal relations between electronic, magnetic and lattice excitations of a material. As switching processes are inherently time-dependent, it is crucial to fully comprehend the mechanism that generates such a nonlinear signal in the space and time-domain in order to make definite statements about the time-evolution of ordering based on these techniques. Here, we present two major studies focusing on improving the understanding of ultrafast nonlinear probes in the optical and the terahertz (THz) range of frequencies. The first part of this thesis examines previous observations made in the prototypical anti-ferromagnet nickel(II) oxide (NiO) with the time-resolved nonlinear method of magnetic-dipole sensitive second-harmonic generation (SHG). These findings suggested that the material provides a coherent gateway to a non-thermal state of magnetic ordering via an ultrafast change in magnetic anisotropy. Using a complementary direct probe of antiferromagnetic order, i.e. picosecond-time-resolved non-resonant magnetic x-ray diffraction, we study the sublattice magnetism after ultrafast optical excitation and our findings suggest that the previously observed dynamics in the second-harmonic response of NiO do not directly reflect dynamics of the antiferromagnetic order parameter. Our re-investigation of the experimental observations using SHG supplement the prior experiments and reveal inconsistencies with the current explanation for the ultrafast response of SHG in NiO which can instead be reconciled with an acoustic origin of the dynamics. The simulations of this process are likely to present the first treatment of second-order stimulated Brillouin scattering in non-ideally phase-matched crystals. Consistent with the experimental observations, the simulation gives rise to two signature frequencies ω +,− = Re(2k ω ± k 2ω )v s leading to oscillations at frequencies that are different by orders of magnitude. The higher of these frequencies resembles linear stimulated Brillouin scattering but is shifted by phase mismatch. In the second part of this work, we investigate the novel method of broadband 2D THz-spectroscopy. The technique combines the process of driving intrinsic infrared active material excitations, while at the same time probing the very same and associated, i.e. coupled, modes. Even in an excitation regime far away from driving permanent changes, the method can provide information about the curvature and symmetry of the energy landscape in which the modes reside. To improve the understanding of this means of spectroscopy, we perform reflective 2D THz measurements accompanied by time-domain simulations on low band gap III-V semiconductors. These materials represent well-understood polaron systems with an early onset of electric field- nonlinearity. Experimentally, we observe in indium antimonide and indium arsenide on timescales on the order of 7.5 ps inter and intraband changes of carrier population. Interestingly, for excitation fields below 80 kV/cm we find that the nonlinear response observed at very early times is composed of a multitude of combination tones of the material’s intrinsic excitations, i.e. the plasmon and phonon modes, in the 2D frequency spectrum. Observing the full phase information and having control over the polarity of the excitation fields allowed us to further differentiate between the parity of these spectral features. To understand this coherent response in more detail, we simulate field-driven ballistic carrier transport using realistic band structures in the time domain. For this, we solve Maxwell’s equations in the presence of a polaronic medium using Yee’s algorithm. The calculated ballistic transport leads the mean conduction band population into regions distant from the equilibrium position at the Γ-point by as far as 3% of the zone-boundary. The simulations are able to reproduce the approximate magnitude as well as all observed spectral features and their correct parity. The nonlinear 2D spectra, including features at phonon frequencies, can thus be assigned to be solely based on plasmonic anharmonicity and their explanation does not require additional coupling between the material’s intrinsic excitations. Our studies show that nonlinear probes can lead to rather complex results when used under conditions of low absorption and non-ideal phase matching. The latter can be transiently altered by pulsed laser excitation, which is here discussed for the case of acoustic perturbation of SHG, and hence for extended sample volumes the assignment of the detected intensity to the nonlinear susceptibility cannot readily be made on ultrafast timescales. In addition, we find that 2D THz-spectroscopy provides a sensitive tool to study electric field nonlinearities, in which e.g. purely plasmonic excitations can lead to a manifold of spectral features observed in the nonlinear response. Nonetheless, we can show that these spectra can be qualitatively and quantitatively understood using suitable simulation techniques. In the light of the findings presented in this thesis, we propose that evaluation of nonlinear probes should always be accompanied by considerations of the signal’s generation process with the implications of inhomogeneous ultrafast excitation. It appears essential to develop comprehensive time-dependent analysis tools in order to achieve a solid understanding of these signals.