The origin of the metal to insulator transition in ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ remains a challenge due to the complexity of the system: it is a mixed valent, strongly correlated system where many interactions such as Jahn-Teller distortion, exchange, and phonons are very close in energetics. A recent interpretation of the Verwey transition as an ordering of a three-site magnetic polaron, the trimeron, has been put forward. Here we investigate the existence of the trimeron correlations in the high-temperature phase of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ using high-resolution iron $2p3d$ resonant inelastic scattering magnetic linear dichroism. Guided by theoretical simulations, we reveal that the polarization dependence of the low-energy spin-orbital excitations is incompatible with tetragonal Jahn-Teller trimeron-type distortion. We conclude that the lowest-energy state of the high-temperature phase of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ arises from an intricate interplay between trigonal crystal-field, exchange, and spin-orbit interactions.

D. Meyers, ∗ Ken Nakatsukasa, Sai Mu, Lin Hao, Junyi Yang, Yue Cao, G. Fabbris, Hu Miao, J. Pelliciari, D. McNally, M. Dantz, E. Paris, E. Karapetrova, Yongseong Choi, D. Haskel, P. Shafer, E. Arenholz, Thorsten Schmitt, Tom Berlijn, 8, † S. Johnston, 9, ‡ Jian Liu, § and M. P. M. Dean ¶ Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton, New York 11973, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA Department of Condensed Matter Physics and Materials Science, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA Research Department Synchrotron Radiation and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Computational Science and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Joint Institute of Advanced Materials at The University of Tennessee, Knoxville, Tennessee 37996, USA (Dated: October 19, 2018)

M. Kang,1 J. Pelliciari,1 Y. Krockenberger,2 J. Li,1 D. E. McNally,3 E. Paris,3 R. Liang,4,5 W. N. Hardy,4,5 D. A. Bonn,4,5 H. Yamamoto,2 T. Schmitt,3 and R. Comin1,* 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan 3Research Department Synchrotron Radiation and Nanotechnology, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 4Department of Physics and Astronomy, University of British Columbia V6T 1Z1, Canada 5Quantum Matter Institute, University of British Columbia V6T 1Z4, Canada

$Fe_3O_4$ is a mixed-valence strongly correlated transition metal oxide which displays the intriguing metal to insulator Verwey transition. Here we investigate the electronic and magnetic structure of $Fe_3O_4$ by a unique combination of high-resolution Fe 2p3d resonant inelastic scattering magnetic circular (RIXS-MCD) and magnetic linear (RIXS-MLD) dichroism. We show that by coupling the site selectivity of RIXS with the magnetic selectivity imposed by the incident polarization handedness, we can unambiguously identify spin-flip excitations and quantify the exchange interaction of the different sublattices. Furthermore, our RIXS-MLD measurements show spin-orbital excitations that exhibit strong polarization and magnetic field dependence. Guided by theoretical simulations, we reveal that the angular dependence arises from a strong interplay between trigonal crystal-field, magnetic exchange and spin-orbit interaction at the nominal $Fe^{2+}$ sites. Our results highlight the capabilities of RIXS magnetic dichroism studies to investigate the ground state of complex systems where in-equivalent sites and bonds are simultaneously present.

We report the observation of multiple phonon satellite features in ultrathin superlattices of the form nSrIrO_{3}/mSrTiO_{3} using resonant inelastic x-ray scattering (RIXS). As the values of n and m vary, the energy loss spectra show a systematic evolution in the relative intensity of the phonon satellites. Using a closed-form solution for the RIXS cross section, we extract the variation in the electron-phonon coupling strength as a function of n and m. Combined with the negligible carrier doping into the SrTiO_{3} layers, these results indicate that the tuning of the electron-phonon coupling can be effectively decoupled from doping. This work both showcases a feasible method to extract the electron-phonon coupling in superlattices and unveils a potential route for tuning this coupling, which is often associated with superconductivity in SrTiO_{3}-based systems.