Quadrupole and dipole orders in URu2Si2

Exotic magnetism below T-N similar or equal to 17.5 K is studied within the level scheme where the lowest multiplet is a doubler within the 5f(2) configuration. Effective g-factors of pseudo-spins with S = 1/2 which describe the degree of freedom of the doubler, are highly anisotropic: g(x) = g(y) = 0 for the xy-components and g(z) not equal 0 for the z-component. It is proposed that a recently discovered transition of first order at a critical pressure p(c) similar or equal to 1.5 GPa is that between an ordered state of quadrupoles, with order parameter Ox2-y2 Or O-xy, below p(c) and an ordered state of dipoles, with order parameter O-z, above p(c); pseudo-spins are ordered within the xy-plane below p(c), and they are along the z-axis above p(c). The proposal of this scenario is followed by many predictions. No static magnetic moments exist below p(c). The anisotropy of Van Vleck's susceptibility within the xy-plane is of twofold symmetry corresponding to Ox2-y2 or O-xy What one observes by means of neutron diffraction and mu SR (muon spin resonance) below p(c) are dynamically but slowly fluctuating magnetic moments. The softening of magnons occurs with pressures approaching p(c) below p(c). Although static magnetic moments exist above p(c), no magnon excitations can be observed there.