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Register a new userStructure, phonons, and orbital degrees of freedom in Fe$_2$Mo$_3$O$_8$
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We report on the structural and spectroscopic characterization of the multiferroic Fe$_2$Mo$_3$O$_8$. Synchrotron x-ray and neutron diffraction, as well as thermal expansion measurements reveal a lattice anomaly at $T_{mathrm{N}}simeq 60,$K but do not show any symmetry lowering in the magnetically ordered state. The lattice parameter $c$ exhibits a non-monotonic behavior with a pronounced minimum around $200,$K, which is also reflected in an anomalous behavior of some of the observed infrared-active optical excitations and parallels the onset of short-range magnetic order. The infrared reflectivity spectra measured between 5 and 300$,$K in the frequency range of $100-8000,$cm$^{-1}$ reveal most of the expected phonon modes in comparison with the eigenfrequencies obtained by density-functional calculations. The $A_1$ phonons show an overall hardening upon cooling, whereas a non-monotonic behavior is observed for some of the $E_1$ modes. These modes also show a strongly increased phonon lifetime below $T_mathrm{N}$, which we associate with the quenched direction of the orbital moment in the magnetically ordered state. A similar increase is observed in the lifetime of the higher-lying $d$-$d$ excitations of the tetrahedral Fe$^{2+}$ site, which become clearly visible below $T_mathrm{N}$ only.
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We report on optical excitations in the magnetically ordered phases of multiferroic Fe$_{1.86}$Zn$_{0.14}$Mo$_3$O$_8$ in the frequency range from 10-130 cm$^{-1}$ (0.3-3.9 THz). In the collinear easy-axis antiferromagnetic phase below $T_N=50$~K eleven optically active modes have been observed in finite magnetic fields, assuming that the lowest-lying mode is doubly degenerate. The large number of modes reflects either a more complex magnetic structure than in pure Fe$_{2}$Mo$_3$O$_8$ or that spin stretching modes become active in addition to the usual spin precessional modes. Their magnetic field dependence, for fields applied along the easy axis, reflects the irreversible magnetic-field driven phase transition from the antiferromagnetic ground state to a ferrimagnetic state, while the number of modes remains unchanged in the covered frequency region. We determined selection rules for some of the AFM modes by investigating all polarization configurations and identified magnetic- and electric-dipole active modes as well. In addition to these sharp resonances, a broad electric-dipole active excitation band, which is not influenced by the external magnetic field, occurs below $T_N$ with an onset at 12 cm$^{-1}$. We are able to model this absorption band as a vibronic excitation related to the lowest-lying Fe$^{2+}$ electronic states in tetrahedral environment.
We present both static and time-resolved second harmonic generation (SHG) measurements on polar antiferromagnet Fe$_2$Mo$_3$O$_8$ to monitor the evolution of the electric polarization change and its coupling to magnetic order. We find that only one of the second order tensor elements, $chi_{ccc}^{(2)}$ ,shows a prominent change below the Neel temperature $T_N = 60$ K, indicating a magnetic order induced electric polarization change along the c-axis. Time-resolved SHG measurement reveals an ultrafast recovery of the second order tensor element upon the ultrashort laser excitation with fluence above 0.3 $mJ/cm^2$, yielding evidence for a photoinduced ultrafast phase transition from the AFM ordered state to the paramagnetic state. Our work will help understand the spin induced polarization and the ultrafast optical tuning effect in Fe$_{2}$Mo$_{3}$O$_{8}$.
LiZn$_2$Mo$_3$O$_8$ has been proposed to contain $S~=~1/2$ Mo$_3$O$_{13}$ magnetic clusters arranged on a triangular lattice with antiferromagnetic nearest-neighbor interactions. Here, microwave and terahertz electron spin resonance (ESR), $^7$Li nuclear magnetic resonance (NMR), and muon spin rotation ($mu textrm{SR}$) spectroscopies are used to characterize the local magnetic properties of LiZn$_2$Mo$_3$O$_8$. These results show the magnetism in LiZn$_2$Mo$_3$O$_8$ arises from a single isotropic $S~=~1/2$ electron per cluster and that there is no static long-range magnetic ordering down to $T~=~0.07,textrm{K}$. Further, there is evidence of gapless spin excitations with spin fluctuations slowing down as the temperature is lowered. These data indicate strong spin correlations which, together with previous data, suggest a low-temperature resonating valence-bond state in LiZn$_2$Mo$_3$O$_8$.
Theoretical studies have predicted the existence of topological magnons in honeycomb compounds with zig-zag antiferromagnetic (AFM) order. Here we report the discovery of zig-zag AFM order in the layered and non-centrosymmetric honeycomb nickelate Ni$_2$Mo$_3$O$_8$ through a combination of magnetization, specific heat, x-ray and neutron diffraction and electron paramagnetic resonance measurements. It is the first example of such order in an integer-spin non-centrosymmetric structure ($P$$_6$3$mc$). Further, each of the two distinct sites of the bipartite honeycomb lattice has a unique crystal field environment, octahedral and tetrahedral Ni$^{2+}$ respectively, enabling independent substitution on each sublattice. Replacement of Ni by Mg on the octahedral site suppresses the long range magnetic order and results in a weakly ferromagnetic state. Conversely, substitution of Fe for Ni enhances the AFM ordering temperature. Thus Ni$_2$Mo$_3$O$_8$ provides a platform on which to explore the rich physics of $S = 1$ on the honeycomb in the presence of competing magnetic interactions with a non-centrosymmetric, formally piezeo-polar, crystal structure.
La$_2$O$_3$Fe$_2$Se$_2$ can be explained in terms of Mott localization in sharp contrast with the metallic behavior of FeSe and other parent parent compounds of iron superconductors. We demonstrate that the key ingredient that makes La$_2$O$_3$Fe$_2$Se$_2$ a Mott insulator, rather than a correlated metal dominated by the Hunds coupling is the enhanced crystal-field splitting, accompanied by a smaller orbital-resolved kinetic energy. The strong deviation from orbital degeneracy introduced by the crystal-field splitting also pushes this materials close to an orbital-selective Mott transition. We predict that either doping or uniaxial external pressure can drive the material into an orbital-selective Mott state, where only one or few orbitals are metallized while the others remain insulating.
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