Studies of the Earth's atmosphere have shown that more than 90% of the expected amount of Xe is depleted, a finding often referred to as the 'missing Xe paradox'. Although several models for a Xe reservoir have been proposed, whether the missing Xe could be contained in the Earth's inner core has not yet been answered. The key to addressing this issue lies in the reactivity of Xe with Fe/Ni, the main constituents of the Earth's core. Here, we predict, through first-principles calculations and unbiased structure searching techniques, a chemical reaction of Xe with Fe/Ni at the temperatures and pressures found in the Earth's core. We find that, under these conditions, Xe and Fe/Ni can form intermetallic compounds, of which XeFe3 and XeNi3 are energetically the most stable. This shows that the Earth's inner core is a natural reservoir for Xe storage and provides a solution to the missing Xe paradox.

Reactions of xenon with iron and nickel are predicted in the Earth's inner core

Magnetic susceptibilities and magnetization isotherms have been measured for single crystal FeTiO 3  The susceptibility parallcl to the c -axis has a large and sharp peak at T N =580±03 K, while the perpendicular susceptibility is almost independent of temperature below T N  Magnetization isotherm at 42 K with fields applied along the c -axis exhibits a typical metamagnetic transition at H c =803±01 kOe, being the first observation of metamagnetism in 3 d transition metal oxides The transition is of the first order up to about 35 K, above which it is of the second order The experimental data are well reproduced by molecular field calculations with the best fit parameters of the anisotropy field H A =150 kOe, the ferromagnetic intrasublattice exchange interaction of 2 z 1 J 1 =285 K, and the antiferromagnetic intersublattice interaction of 2 z 2 J 2 =-667 K

Metamagnetic Phase Transitions in FeTiO 3

Magnetic order is usually associated with well-defined magnon excitations. Exotic magnetic fluctuations with fractional, topological or multipolar character, have been proposed for radically different forms of magnetic matter such as spin-liquids. As a result, considerable efforts have searched for, and uncovered, low-spin materials with suppressed dipolar order at low temperatures. Here, we report neutron-scattering experiments and quantitative theoretical modeling of an exceptional spin-1 system -- the uniaxial triangular magnet FeI2 -- where a bright and dispersive band of mixed dipolar-quadrupolar fluctuations emerges just above a dipolar ordered ground-state. This excitation arises from anisotropic exchange interactions that hybridize overlapping modes carrying fundamentally different quantum numbers. Remarkably, a generalization of spin-wave theory to local SU(3) degrees of freedom accounts for all details of the low-energy dynamical response of FeI2 without going beyond quadratic order. Our work highlights that quantum excitations without classical counterparts can be realized even in presence of fully developed magnetic order.

Hybridized quadrupolar excitations in the spin-anisotropic frustrated magnet FeI2

Magnetic order is usually associated with well-defined magnon excitations. Exotic magnetic fluctuations with fractional, topological or multipolar character have been proposed for unconventional forms of magnetic matter such as spin liquids1. As a result, considerable effort has been expended to search for, and uncover, low-spin materials with suppressed dipolar order at low temperatures2,3. However, long-range order of magnetic dipoles is much more common. Here we report neutron-scattering experiments and quantitative theoretical modelling of a spin-1 system—the uniaxial triangular magnet FeI2 (ref. 4)—where a dispersive band of mixed dipolar–quadrupolar fluctuations with large spectral weight emerges just above a dipolar ordered ground state. This excitation arises from anisotropic exchange interactions that hybridize overlapping modes carrying fundamentally different quantum numbers. A generalization of spin–wave theory to local SU(3) degrees of freedom5 accounts for all details of the low-energy dynamical response of FeI2, without going beyond quadratic order. Our work highlights that quantum excitations without classical counterparts can be realized, even in the presence of fully developed magnetic order. Neutron-scattering measurements on the magnetically ordered triangular-lattice compound FeI2 reveal a dispersive band of mixed dipolar–quadrupolar fluctuations just above its ground state—a quantum excitation without a classical counterpart.

The authors investigate the temperature renormalisation of the magnetic excitations in FeCl2, where, owing to the low value of the spin, a careful treatment of its large anisotropic effects appears to be necessary. A self-consistent renormalised theory which is not affected by kinematic inconsistencies is presented for a model Hamiltonian suitable to describe FeCl2, i.e. including both anisotropic exchange and single-ion uniaxial anisotropy. The correctness of this theory is tested by means of an exact calculation of the self-energy in the T-matrix formalism, which is exact in the low-temperature limit. Explicit calculations have been performed for the temperature dependence of the energy gap (k=0) and the results compared with the experimental (AFMR, neutron scattering) data. The existence of a significant exchange anisotropy seems to be necessary for explaining the AFMR data. Indications are given about the magnitude of this anisotropy.

https://iopscience.iop.org/article/10.1088/0022-3719/14/21/021/pdf

The influence of the anisotropy on the temperature renormalisation of the magnetic excitations in FeCl2

A far infrared investigation of antiferromagnetic resonance by means of Fourier-transform spectroscopy has been carried out in FeCl2, FeBr2 and FeI2. In FeCl2 and FeBr2 our results are found to agree well with the two-sublattice model with an anisotropy parameter D = 9.6 K. In FeI2 three absorption peaks situated at 21.6 cm-1, 29.2 cm-1, and 32.2 cm-1 have been attributed to excitation of zone-center spin waves, which can be understood only by assuming that FeI 2 has more than two sublattices. The AFMR frequencies in a simple four sublattice model have been calculated, and the parameters relevant to FeI 2 have been deduced. However the observation of a 3 cm-1 splitting between the two higher modes suggests that such a model may be too simple.

https://hal.archives-ouvertes.fr/jpa-00208542/document

D. Petitgrand

Papers

Far infrared antiferromagnetic resonance in FeCl2, FeBr 2 and FeI2