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Theory of magnetic-induction bifurcation in the Condon domain phase of a three-dimensional ͑3D͒ electron gas under high-magnetic field is presented. The results-the diamagnetic phase transition temperature and the induction bifurcation values-are in good agreement with nuclear magnetic resonance data in silver. The temperature dependence of the order parameter of the diamagnetic phase transition-the magnetization in each Condon domain-is obtained by a comparison of the theory with the experiment. The mean-field approach has been shown to lead to the universal behavior of an electron gas of 2D and 3D dimensionality.

A theory of the magnetic induction bifurcation at a diamagnetic phase transition in normal metals is developed. Our results are in good agreement with the recent observation of the muon spin rotation resonance splitting in beryllium due to Condon domains, Solt et al. [Phys. Rev. Lett. 76, 2575; Hyperfine Interact. 104, 257 (1997)], being the first measurement of the onset of a diamagnetic phase transition. Temperature dependence of the order parameter, the magnetization in each Condon domain, is explained and reproduced quantitatively. A new kind of phase diagram for diamagnetic phase transitions is constructed. [S0031-9007(98)07181-6] PACS numbers: 75.20.En, 71.18. + y, There is a rich variety of magnetic metals that exhibit spontaneous long-range ordering of magnetic moments below a phase transition [1]. Their magnetism is of spin nature. There exists, however, an extremely interesting example of a long-range magnetic orbital order in normal metals, the diamagnetic phase transitions [2], known as Condon domains [3]. It is due to the nonscreened current-current interaction, which results in the non-Fermiliquid behavior of a normal metal at low temperatures under strong magnetic fields [4]. Moreover, in quasi-twodimensional metals the Condon domains are in a quantum Hall effect state [5].The orbital magnetic ordering appears at quantizing magnetic fields and low temperatures, in each cycle of de Haas-van Alphen oscillations (dHvA), when their amplitude starts to be comparable to the dHvA period [6]. To our knowledge, there have been discovered only two metals in which magnetic order is of orbital origin: silver and beryllium [7,8]. Condon domains were directly measured in silver by using the nuclear magnetic resonance [7] and in beryllium by the muon spin rotation resonance [8]. The properties of these domains have been extensively studied theoretically [5,6,9,10].While attention of experimentalists has been directed primarily at Condon domains [3,7,8] the presence of temperature critical phenomena which should accompany diamagnetic phase transitions remain uncertain, except for [11]. Recently the instability of an electron gas has been emphasized to occur as a phase transition accompanied by the strong (critical) temperature dependence of the spontaneous magnetization, specific heat, and susceptibility temperature jumps [12].The principal goal of this Letter is to provide a theoretical understanding of the recent intriguing experimental results by Solt et al. [11]. We show that the temperature dependence of the muon spin splitting measured by them in beryllium exhibits the critical temperature dependence of the order parameter of the diamagnetic phase transition, i.e., the magnetization in one Condon domain.In Fig. 1 the temperature dependence of the magnetic induction bifurcation, obtained in [11,13] by observing the muon spin resonance splitting in beryllium at the magnetic field 2.641 T, is shown. According to Fig. 4(a) of [11], the measurements were made in the center of the dHvA period or near it because th...

Manipulation of light-beams with subwavelenth metallic devices has motivated intensive studies, following the discovery of extraordinary transmission of electromagnetic waves through sub-wavelength apertures in thin noble-metal films. The propagation of light in these holes can be investigated at greately improved spatial resolution by means of focused electron-beams. Here we demonstrate direct e-beam excitation of radiative cavity modes well below the surface plasmon (SP) frequency, of isolated rectangular holes in gold films, illuminating the hotly debated phenomenon of the extraordinary optical transmission through subwavelength holes. The exceptionally long range e-beam interaction with the metal through the vacuum, involving electromagnetic excitations within the light cone, is allowed by momentum conservation breakdown along the e-beam axis. Two types of lowlying excited modes are revealed: radiative cavity modes which are nearly unaffected by SPs, and SP polariton modes with waveguide character in the near field region of the slit walls, which in spite of the strong hybridization preserve the waveguide cutoff frequencies and symmetry characteristics.

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