Magnetic phase transition and Mossbauer spectroscopy of ErNi2Mnx compounds
Investigation of ErNi2Mnx with 0.90 ≤ x ≤ 1.10 indicates that the MgCu2-type structure (with space group Fd-3m) is formed within x = 0.97−1.10. Curie temperature TC = 50 K of ErNi2Mn is significantly higher than those of the corresponding ErNi2 (TC = 7 K) and ErMn2 (TC = 15 K) compounds. Detailed analyses of DC magnetization data demonstrate that the magnetic phase transition at the Curie temperature is second order. The magnetic entropy change around TC has been found to be 4.8 J/kg K for a magnetic field change of 0 to 5 T with its relative cooling power ∼283 J/kg. 57Fe Mossbauer spectra below TC have been fitted with three sub-spectra representing three inequivalent local magnetic environments while the paramagnetic spectra are fitted using two sub-spectra for two inequivalent crystal sites (8a and 16d), which supports the conclusion based on Rietveld refinement that Mn atoms occupy at both 8a and 16d sites.
Structural properties and magnetic phase transition in HoNi2Mn (57Fe)
The structural and magnetic properties of HoNi2Mn(57Fe) have been investigated. The 57Fe-doped HoNi2Mn compound crystallizes in the MgCu2-type structure with Fd-3m space group similar to HoNi2 and HoMn2. HoNi2Mn(57Fe) exhibits ferrimagnetic ordering below a Curie temperature of TC ∼ 60 K—significantly higher than the corresponding values for HoNi2 (TC = 15 K) and HoMn2 (TC = 24 K)—with analyses of dc magnetization and ac susceptibility results confirming that the magnetic transition at TC is second order. The Mossbauer spectra above TC are described well by two sub-spectra representing the 8a and 16d sites while below TC the spectra have been fitted using a site model comprising three sub-spectra. The Debye temperature, θD = 190(20) K, has been determined.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.