Applications of the NRSE method and current areas of research
The main application of NRSE spectroscopy is in measurements of the linewidths of low-energy dispersive excitations in non-magnetic and antiferromagnetic materials. Lattice dynamics is investigated to access wavevector-resolved phonon relaxation times important for a microscopic understanding of thermal transport in thermoelectric materials. Magnetic model systems provide a playground to study temporal decoherence phenomena in dynamically strongly correlated materials beyond exponential decay. Beside inelastic applications, the NRSE apparatus is ideal for Larmor diffraction, a high resolution elastic scattering technique based on neutron Larmor precession for single crystal and powder samples.
Current areas of research
Research on thermoelectric materials exploits the NRSE method to measure phonon lifetimes of transverse acoustic modes which largely govern thermal conductivity. The long-term goal is to benchmark theoretical results for mode Grüneisen parameters obtained by first-principles calculations against experimental data. Alongside the NRSE methodology is further developed by extending the resolution theory to describe more than one excitation mode within the resolution ellipsoid of the background spectrometer or unusual lineshapes.
In thermoelectric compounds, an inherently low thermal conductivity is beneficial for the efficiency of thermal to electrical energy conversion. The detailed understanding of the relation between the crystal structure and the phonon dynamics on the microscopic level is essential for novel strategies aiming at the optimization of thermoelectric material parameters and is thus ultimately relevant for device applications such as thermoelectric generators. However, so far investigations of lattice thermal conductivity have mostly been based on empirical models either with fitting or adjustable parameters. In contrast, our microscopic measurements directly access phonon lifetimes taking advantage of the high energy resolution of NRSE spectroscopy.
Current research efforts focus on measuring phonon lifetimes in the perovskite model system SrTiO3 which is known to offer good thermoelectric properties. SrTiO3 is an incipient ferroelectric material with a phase transition from cubic perovskite to an antiferrodistortive tetragonal phase at TC=105 K, and has been shown to have a high power factor S2σ which qualifies the compound as a potential TE system. SrTiO3 is thus an ideal model material to study the relationship between the TE properties and the proximity to a structural phase transition and incipient ferroelectricity.
In terms of method development, new experiments beyond the standard measurements of exponentially damped excitations are aspired. The NRSE experiments carried out at the triple axis spectrometer TRISP, FRM II, MLZ, Garching, were motivated by the recently discovered phenomenon on strong dynamic correlations leading to non-Lorentzian line broadening of magnetic excitations [1, 2]. They confirm results of earlier measurements obtained by neutron time-of-flight spectroscopy. Here, the direct access to decoherence in the time domain is the particular advantage of the NRSE method, and thus NRSE spectroscopy complements conventional neutron spectroscopy, which probes the scattering system in the energy domain. Interestingly, the simple linear relationship between the phase shift and the mean energy of the excitation breaks down if the lineshape is asymmetric. A correct description of the phase shift is obtained by a model which takes into account the full numerical evaluation of the neutron spin precession. The non-linear evolution of the phase shift as a function of the spin-echo time is a direct consequence of the non-Lorentzian lineshape.
The analytical treatment of the resolution for NRSE-TAS experiments is an important prerequisite to the interpretation of experimental data on phonon and magnon linewidths. We have developed an analytical framework for the resolution function for NRSE spectroscopy . The resolution theory of triple-axis spectrometers was extended by introducing a phase matrix, which corresponds to the mean Larmor phase accumulated by the neutrons with a particular trajectory precessing in the effective magnetic fields. Thus each point within the resolution ellipsoid of the TAS instrument in the wavevector-energy space is attributed a total Larmor precession angle which takes divergence effects into account (see Fig. 1). Summing up all Larmor phases weighted by the corresponding transmission probability yields the resolution function for NRSE-TAS. The formalism includes the effects of important sample properties such as mosaicity and curvature of the dispersion surface.
Fig. 1a: Larmor phase diagram calculated for the transverse acoustic phonon in SrTiO3 with total wavevector transfer Q=(1 1 1) + (-ζ −ζ +ζ), ζ=0.05 r.l.u. The Larmor phase topology in the energy-wavevector plane is shown. Δω denotes the energy difference with respect to the nominal phonon energy. Δq⊥ is the wavevector difference perpendicular to the phonon wavevector. The dispersion (black line) closely follows the curvature of the lines of constant Larmor phase (color-coded) within the resolution ellipse of the triple-axis spectrometer (red line).
Fig. 1b: Larmor phase diagram calculated for the transverse acoustic phonon in SrTiO3 with total wavevector transfer Q=(1 1 1) + (-ζ −ζ +ζ), ζ=0.05 r.l.u. The Larmor phase topology in the two-dimensional wavevector space is shown, with axes parallel and perpendicular to the phonon wavevector q along the vertical z-direction. In contrast to the negligible phase variations in the direction of q|| there is significant Larmor phase variation along qz leading to a depolarization of the spin-echo signal.
 F. Groitl, T. Keller, K. Rolfs, D.A. Tennant, K. Habicht, Anomalous thermal decoherence in a quantum magnet measured with neutron spin-echo spectroscopy, Phys. Rev. B 93 (2016) 134404.
 B. Fauseweh, F. Groitl, T. Keller, K. Rolfs, D.A. Tennant, K. Habicht, G.S. Uhrig; Time-dependent correlations in quantum magnets at finite temperature, Phys. Rev. B Rapid Commun. 94 (2016) 180404(R).
 K. Habicht, T. Keller, R. Golub, The resolution function in neutron spin-echo spectroscopy with three-axis spectrometers, J. Appl. Cryst. 36 (2003) 1307-1318.