Exchange bias (EB) phenomena have been observed in Nd 2/3 Ca 1/3 MnO 3 colossal magnetoresistance perovskite below the Curie temperature T C ~ 70 K and attributed to an antiferromagnetic (AFM) -ferromagnetic (FM) spontaneous phase segregated state of this compound. Field cooled magnetic hysteresis loops exhibit shifts toward negative direction of the magnetic field axis. The values of exchange field H EB and coercivity H C are found to be strongly dependent of temperature and strength of the cooling magnetic field H cool . These effects are attributed to evolution of the FM phase content and a size of FM clusters. A contribution to the total magnetization of the system due to the FM phase has been evaluated. The exchange bias effect decreases with increasing temperature up to T C and vanishes above this temperature with disappearance of FM phase.Relaxation of a non-equilibrium magnetic state of the compound manifests itself through a training effect also observed while studying EB in Nd 2/3 Ca 1/3 MnO 3 .

It is proved that the two-photon Rabi Hamiltonian is quasi exactly solvable on the basis of the two different quadratic Lie algebras.

A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd 2/3 Ca 1/3 MnO 3 perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at T g ~ 60 K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature T max of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole-Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at "macroscopic" time scale. Slow relaxation in the zerofield-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below T g , associated with its antiferromagnetic-ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature T g and above it are strongly different. Magnetic field up to about m 0 H ~ 0.4 T suppresses the glassy magnetic state of the compound.

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We suggest a systematic method of extension of quasi-exactly solvable (QES) systems. We construct finite-dimensional subspaces on the basis of special functions (hypergeometric, Airy, Bessel ones) invariant with respect to the action of differential operators of the second order with polynomial coefficients. As a example of physical applications, we show that the known two-photon Rabi Hamiltonian becomes quasi-exactly solvable at certain values of parameters when it can be expressed in terms of corresponding QES operators related to the hypergeometric function.Comment: 15 pages. Typos correcte