B03  Timedependent spin dynamics and electron transport
This project aims at the construction of solvable analytical models for the building up and decay of magnetic excitations. By focusing on an analytical approach it complements the other theory projects, which have a strong numerical component. This project is divided into two parts, which focus on magnetic excitations in conducting and insulating systems, respectively.
The goal of the first part is to develop a theory of spindependent quantum transport in hybrid magnetic/metallic systems that systematically goes beyond the wellestablished timeindependent theory, by including stimuli in the time domain, nonadiabatic contributions to the electronic response to magnetization changes, and finite passage times in metallic components. It is our ultimate aim to formulate the theory as a flexible “circuit theory”, in which the experimental system is modelled by a collection of discrete elements connected by links. We also intend to include Coulomb charging effects in confined geometries, as they appear, e.g., in the vicinity of a metal tip in a scanning probe experiment.
The second part involves timedependent aspects of magnons in magnetic insulators. Its first goal is the development of a theory for the coupling between magnons and electrons at the interface between a magnetic insulator and a normal metal. Its second goal is the investigation of simplified model systems for the magnonphonon interaction, focusing on the existence of approximate conservation laws and their relation to typical time scales for magnonphonon interaction. An important application of our theory is in the area of the “ultrafast Spin Seebeck effect”, in which a temperature gradient applied over a magnetic insulator induces the flow of a spin current.
Publications (1^{st} Funding Period 2018  2021)

Theory of the lowtemperature longitudinal spin Seebeck effect
R. Schmidt and P. W. Brouwer
Phys. Rev. B 103, 014412 (2021)  DOI: 10.1103/PhysRevB.103.014412 
Boltzmann approach to the longitudinal spin Seebeck effect
R. Schmidt, F. Wilken, T. S. Nunner, and P. W. Brouwer
Phys. Rev. B 98, 134421 (2018)  DOI: 10.1103/PhysRevB.98.134421  Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy
T. S. Seifert, S. Jaiswal, J. Barker, S. T. Weber, I. Razdolski, J. Cramer, O. Gueckstock, S. F. Maehrlein, L. Nadvornik, S. Watanabe, C. Ciccarelli, A. Melnikov, G. Jakob, M. Münzenberg, S. T. B. Goennenwein, G. Woltersdorf, B. Rethfeld, P. W. Brouwer, M. Wolf, M. Kläui, and T. Kampfrath
Nat. Commun. 9:2899 (2018)  DOI: 10.1038/s41467018051352