Our group in LLB (CEA-CNRS, Université Paris-Saclay) has expertise in using neutron scattering techniques. Such experiments will be carried out mostly at ILL (Grenoble), but likely also at other neutrons facilites in Europe. Thermal conductivity measurements will be performed in collaboration with B Fauqué (Collège de France).
Understanding the thermal conductivity in a crystal lattice has been a long-term challenge for physicists, as it is the key to design thermoelectric or thermal barrier devices. While lattice vibrations, phonons, mostly contribute to heat flow in insulators, magnets present another degree of complexity since magnetic excitations can also significantly contribute to heat transfer. Even more fascinating, while heat flows generally in the same direction as the temperature gradient, in the presence of a magnetic field, heat may also flow in the transverse direction. This is known as the thermal Hall effect. However, the question remains open whether the existence of such a transverse thermal conductivity is a purely magnetic effect or results from the interplay between magnetic and lattice degrees of freedom. The aim of the project is to bring answers to this question. It will rely on thorough investigations of the thermal properties, including specific heat, magneto-thermal, thermal Hall effect, in a series of oxides. The asset and originality of the project will be to combine those measurements with in depth inelastic neutron scattering experiments, versus temperature and magnetic field, to identify the dispersion of heat carriers, phonon and magnetic excitations.
In metals, the electron contribution to the thermal conductivity K is directly related to the electrical conductivity, so that the higher the latter, the higher the thermal conductivity . On the other side of the spectrum, in insulating materials, acoustic phonons are the main heat carriers. Peierls described heat transport in crystalline solids as the propagation and scattering of phonons between each other, using the Boltzmann transport equation .
Insulating magnets present another degree of complexity, since magnetic excitations can also significantly contribute to heat transfer . It was early established in the yttrium and iron garnet Y3Fe5O12, and latter observed in spin ladders (Sr,Ca,La)Cu24O41, Haldane spin chains AgVP2S6 or Y2BaNiO5 and antiferromagnetic spin ½ chains (like Sr2CuO3 and SrCuO2 cuprates for instance) .
In other cases, the coupling of phonons and spin excitations leading to hybrid magneto-elastic modes, triggers new properties: for instance, this so called “resonant coupling” between phonons and crystal field levels is likely to be at the origin of the extremely low K of Tb2Ti2O7  and Tb3Ga5O12 . More generally, such a resonant interaction has been observed in various paramagnetic crystals, including lanthanum cobalt nitrate  or rare-earth doped CaF2 . This particular coupling with crystal field levels opens further perspectives, making the thermal conductivity naturally sensitive to the magnetic field. Indeed, it is expected to modify the crystalline field scheme, shift the energy range where the resonant coupling appears and hence affect K(T).
But this picture is in fact too simple. While generally heat flows in the same direction as the temperature gradient, in the presence of a magnetic field, heat can flow in the transverse direction too. The existence of such a transverse thermal conductivity Kxy is known as the thermal Hall effect. This effect was actually discovered more than a decade ago, in the paramagnetic regime of the Tb3Ga5O12 garnet  and was quickly recognized in this very case as a result of a large magneto-elastic effect , , , , . According to a possible interpretation, this coupling would confer a Berry curvature to the phonon bands , . The scope of this result was extended to a number of exotic magnets, such as the pyrochlore Tb2Ti2O7 , Kagome ,  and Kitaev compounds , as well as high-Tc cuprates in their pseudo gap phase . These discoveries have aroused theoretical developments based on purely magnetic contribution and assuming a negligibly small phonon contribution. The recent discovery of Kxy in the non-magnetic insulator SrTiO3 has, however, reopened the debate .
The question thus remains open, whether the existence of such a transverse thermal conductivity Kxy is a purely magnetic effect or results from the interplay between magnetic and lattice degrees of freedom.
PhD experimental plan:
To bring answers to this question, this PhD work will rely on a thorough investigation of a series of terbium oxides carefully chosen for their giant magneto-elastic behaviours, Tb2Ti2O7 (TTO), Tb3Ga5O12 (TGG) and KTb3F10 (KTF).
Importantly, all of them exhibit large Verdet constants, with TGG and KTF being also widely used commercially as high power Faraday rotators (optical isolators). This naturally raises the question of the microscopic origin of those optical properties, and suggests that our investigations can lead to a better understanding of the role of Tb and indirectly to the discovery/optimisation of novel optical devices.
For efficient resonant phonon scattering, it is best to have crystal electric field excitations at fairly low energy, or a complex crystal-field structure of quasi-doublets, as found on low symmetry sites. Each of the compounds listed above is thus characterized by a different magnetic ground state, along with a different (low) symmetry of the Tb3+ crystal field, to lead to a comprehensive picture.
Two major experimental techniques will support this investigation:
- Thermal conductivity and specific heat measurements: while both traveling and localized excitations contribute to specific heat, only traveling quasiparticles, i.e. those with a finite mean-free-path, will contribute to thermal conductivity. Therefore, a combination of both techniques is indispensable to determine the mean free path of the quasiparticles. Their respective contribution and their coupling will be determined through systematic temperature and magnetic field studies.
- Neutron scattering experiments: phonons and magnetic excitations (spin waves and/or crystal field) will be accurately studied for each compound, as well as their behaviour vs. temperature (T) and magnetic field (H). Coupling with phonons will be investigated, at large momentum transfer to increase the dynamical phonon structure factor. Beam-time on neutron spectrometers will be requested in large-scale facilities such as ILL (Grenoble, France), PSI (Villigen, Switzerland), NIST (Gaithersburg, USA), FRMII (Munich, Germany), etc.
The PhD work will be performed in-between the Physics Institute of Collège de France (IPCDF, Paris), which specializes thermal conductivity measurements, and the Léon Brillouin Laboratory (LLB, Saclay), which offers unmatched expertise in neutron scattering techniques, and also provides a Quantum Design Physical Properties Measurement System (2 K – 300 K). TTO, TGG and KTF are already available as single-crystals. Additional sample synthesis if necessary can be performed at the Orsay Molecular Chemistry and Materials Institute (ICMMO, Orsay).
(i) In-depth measurements of Cp(T, H) and (T, H) (xx, xy) on the chosen terbium oxide compounds.
(ii) Characterization of the excitation spectra by INS (phonons, magnons and crystal field excitation), vs. T and H.
(iii) Data analysis (in-house developed softwares Spinwave  and Cefwave) for the determination of the crystal field parameters and the characteristics of the coupling. Thermal conductivity modelling
Contact LLB: Sylvain Petit (firstname.lastname@example.org ), Françoise Damay (email@example.com )
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