Using polarized neutrons, we have determined phases as well as interference amplitudes for noncyclic spinor evolutions in static magnetic fields. Both these quantities depend on the angle subtended by the neutron spin with the field. This experiment elucidates the subtle, and widely misunderstood, concepts involved. [S0031-9007(98)

We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of p radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry. [S0031-9007(96)02278-8] PACS numbers: 03.65. Bz, 42.25.Hz, 42.25.Ja In general, a quantal system evolving under a timedependent Hamiltonian H͑t͒ acquires, apart from the dynamical phase 2Re R ͗H͑t͒͘dt͞", a nonintegrable and Hamiltonian-independent phase component called geometric phase, which depends only on the geometry of the curve traced in the ray space. Pancharatnam was the first to explicitly recognize geometric phase during his studies [1] of interference between optical beams of distinct polarizations. However, geometric phase attracted little further attention until Berry provided a general quantal framework [2] for geometric phase in the context of adiabatic evolutions, triggering an intense activity in this field. Geometric phase, already included in the standard formulation of quantum mechanics, can arise in any general evolution, be it nonadiabatic [3], noncyclic [4], or even nonunitary [4]. A completely general ray-space expression [5,6], in terms of just the pure state density operator, has been provided for geometric phase. Geometric phase has since been observed in a broad spectrum [7-15] of physical phenomena.In the first quantal prescription [2] of geometric phase an adiabatic evolution was considered. The early neutron experiments [10,11] therefore observed geometric phase for an eigenstate of a slowly rotating magnetic field. However, an adiabatic evolution generates a dynamical phase background which is much larger than the geometric phase signal. An ideal geometric phase experiment should therefore effect not an adiabatic evolution, but a parallel transportation [16], an intrinsically nonadiabatic evolution, that eliminates dynamical phase and yields a pure geometric phase. In an evolution which does not parallel transport the state, it is still possible to generate a pure geometric phase by arranging for a null dynamical phase [16][17][18] at the end of the evolution.The wave function of a spin 1 2 particle changes sign [19,20] when the spin precesses through 2p radians. This 4p spinor symmetry has been directly verified in neutron interference experiments [21][22][23]. The spinor phase also depends on the orientation [17] of the precession axis. While elucidating this dependence, Wagh and Rakhecha proposed the first experiment effecting a clear separation [18] of geometric and dynamical phases. Here a jz͘-polarized neutron beam incident on an interferometer (Fig. 1) permeated by a uniform guide field B 0ẑ splits into subbeams I and II. The subbeams pass through identical spin flippers F 1 and F 2 w...

In the Nd0.75Ho0.25Al2 alloy system, the magnetic moments of Nd and Ho occupying the same crystallographic site randomly are antiferromagnetically coupled via long-range indirect exchange interaction mediated by the conduction electrons. A single crystal grown at this stoichiometry displays a magnetic compensation behavior (Tcomp∼24 K) in all orientations. In the close vicinity of Tcomp, the magnetization hysteresis loops measured for H || [100] assume an asymmetric shape, and the notion of an exchange bias field (Hexch) surfaces. Hexch changes sign across Tcomp as the left shift of the loops transforms to the right shift. This phase reversal appears to correlate with the corresponding reversal in the directions of the local magnetic moments of Nd3+ and Ho3+ ions together with that of the conduction electron polarization (CEP). Near Tcomp, where the opposing contributions to the net magnetization from local magnetic moments are nearly equal, the contribution from CEP assumes an accentuated significance. Interestingly, the width of the M-H loop shows a divergence, followed by a collapse on approaching Tcomp from high- as well as low-temperature ends. The observed behavior confirms a long-standing prediction based on a phenomenological model for ferrimagnetic systems. The field-induced changes in the magnetization data leave an imprint of a quasi-phase transition in the heat capacity data. Magneto-resistance (ΔR/R vs. T) has an oscillatory response, in which onset of magnetic ordering and phase reversal in magnetic orientations can be recognized.

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