We revisit a classic study [D. S. Hall, Phys. Rev. Lett. 81, 1539 (1998)10.1103/PhysRevLett.81.1539] of interpenetrating Bose-Einstein condensates in the hyperfine states |F=1,m{f}=-1 identical with |1 and |F=2,m{f}=+1 identical with |2 of 87Rb and observe striking new nonequilibrium component separation dynamics in the form of oscillating ringlike structures. The process of component separation is not significantly damped, a finding that also contrasts sharply with earlier experimental work, allowing a clean first look at a collective excitation of a binary superfluid. We further demonstrate extraordinary quantitative agreement between theoretical and experimental results using a multicomponent mean-field model with key additional features: the inclusion of atomic losses and the careful characterization of trap potentials (at the level of a fraction of a percent).

For a broad range of electron densities n and temperatures T , the in-plane magnetoconductivity of the two-dimensional system of electrons in silicon MOSFETs can be scaled onto a universal curve with a single parameter H s ͑n, T ͒, where H s obeys the empirical relation H s A͑n͒ ͓D͑n͒ 2 1 T 2 ͔ 1͞2 . The characteristic energy k B D associated with the magnetic field dependence of the conductivity decreases with decreasing density, and extrapolates to 0 at a critical density n 0 , signaling the approach to a zerotemperature quantum phase transition. We show that H s AT for densities near n 0 . [4][5][6]) density n c , raising the possibility of an unexpected metallic phase in two dimensions. An equally intriguing characteristic of these systems is their enormous response to magnetic fields applied in the plane of the electrons: the resistance increases dramatically with in-plane magnetic field and saturates to a new value above a characteristic magnetic field H sat on the order of several tesla [7][8][9][10]. For high electron densities, measurements of Shubnikov -de Haas oscillations [11][12][13] have established that the magnetic field H sat is the field at which full polarization of the electrons is reached. A parallel magnetic field has been shown to suppress the metallic temperature dependence [8,14]. Data obtained by Pudalov et al. [15] and by Shashkin et al. [16] indicate there is a substantial increase in the g factor as the electron density is decreased toward n c . These experimental findings all suggest that the behavior of the spins is key to understanding the enigmatic behavior of dilute, strongly interacting systems in two dimensions.In this paper we report measurements of the temperature dependence and density dependence of the in-plane magnetoconductivity of silicon metal-oxide-semiconductor field effect transistors (MOSFETs). For a broad range of electron densities and temperatures, we show that all data for the magnetoconductance can be collapsed onto a single universal curve using a single parameter H s which obeys an empirical relation given by H s ͑n, T͒ A͑n͒ ͓D͑n͒ 2 1 T 2 ͔ 1͞2 . The characteristic energy k B D associated with the response to magnetic field is found to decrease with decreasing electron density, and to exhibit critical behavior, extrapolating to 0 at a density n 0 near the critical density n c for the zero-field metal-insulator transition. H s AT for densities near n 0 , so that the magnetoconductivity scales with H͞T. Our results provide strong experimental evidence for a zero-temperature quantum phase transition at density n 0 . We suggest that this is a transition to a ferromagnetically ordered state in two dimensions.Measurements were taken on three silicon MOSFETs: the mobility m ഠ 30 000 V͞cm 2 s at 0.3 K for sample No. 1 and ഠ20 000 V͞cm 2 s for samples No. 2 and No. 3. Data were obtained on samples with split-gate geometry at City College to 12 T and at the National Magnetic Field Laboratory in fields up to 20 T using standard fourterminal ac techniques described ...

Measurements in magnetic fields applied at small angles relative to the electron plane in silicon MOSFETs indicate a factor of 2 increase of the frequency of Shubnikov -de Haas oscillations at H . H sat . This signals the onset of full spin polarization above H sat , the parallel field above which the resistivity saturates to a constant value. For H , H sat , the phase of the second harmonic of the oscillations relative to the first is consistent with scattering events that depend on the overlap instead of the sum of the spin-up and spin-down densities of states. This unusual behavior may reflect the importance of many-body interactions. PACS numbers: 71.30. + h, 72.20.My, 73.40.Hm, 73.40.Qv A great deal of interest has recently been focused on the anomalous behavior of two-dimensional (2D) systems of electrons [1,2] and holes [3][4][5] whose resistivities unexpectedly decrease with decreasing temperature, behavior that is generally associated with metals rather than insulators [6]. One of the most intriguing characteristics of these systems is their enormous response to magnetic fields applied in the plane of the electrons [7][8][9] or holes [5,10]: the resistivity increases sharply by more than an order of magnitude, saturating to a constant plateau value above a magnetic field H sat .In this paper we report studies of the resistivity of the 2D electron system in silicon metal-oxide-semiconductor field-effect transistors (MOSFETs) in magnetic fields applied at small angles f with respect to the plane. This allows a study of the Shubnikov-de Haas (SdH) oscillations in perpendicular fields sufficiently small that the orbital motion has a negligible effect on the response to the in-plane component of the magnetic field. At small tilt angles f, the SdH oscillations plotted versus filling factor have twice the period below H sat compared with the period above H sat . This implies that the electron system is fully spin polarized in high fields, H . H sat , where the resistivity has reached saturation. Detailed examination of the oscillations in fields below H sat indicates unusual behavior consistent with electron scattering that depends on the product rather than the sum of the spin-up and spin-down densities of states.Two silicon MOSFETs with mobilities m ഠ 20 000 V͞cm 2 s at T 4.2 K were used in these studies. Contact resistances were minimized by using samples with a split-gate geometry, which permit high densities in the vicinity of the contacts while allowing independent control of the density of the 2D system under investigation. Standard AC four-probe techniques were used at 3 Hz to measure the resistance in the linear regime using currents typically below 5 nA. Data were taken on samples mounted on a rotating platform in a 3 He Oxford Heliox system at temperatures down to 0.235 K in magnetic fields up to 12 T.

In magnetic fields applied parallel to the anisotropy axis, the relaxation of the magnetization of a Mn12-acetate single crystal measured for different sweep rates is shown to collapse onto a single scaled curve. The form of the scaling implies that the dominant symmetry-breaking process that gives rise to tunneling is a locally varying second-order anisotropy, forbidden by tetragonal symmetry in the perfect crystal, which gives rise to a broad distribution of tunnel splittings in a real crystal of Mn12-acetate. Different forms applied to even and odd-numbered steps provide a clear distinction between even step resonances (associated with crystal anisotropy) and odd resonances (which require a transverse component of magnetic field). , generally referred to as Mn 12 -acetate, is a particularly interesting and much-studied example of this class. The Mn 12 clusters are composed of twelve Mn atoms tightly coupled to give a sizable S = 10 spin magnetic moment that is stable at temperatures of the order of 10 K and below [1]. These identical weaklyinteracting magnetic molecules are regularly arranged on a tetragonal crystal. As illustrated by the double well potential shown in the inset to Fig. 1, strong uniaxial anisotropy (of the order of 65 K) yields a set of energy levels corresponding to different projections m = ±10, ±9, ....., 0 of the total spin along the easy c-axis of the crystal. Measurements [2,3] below the blocking temperature of 3 K have revealed a series of steep steps in the curves of M versus H at roughly equal intervals of magnetic field due to enhanced relaxation of the magnetization whenever levels on opposite sides of the anisotropy barrier coincide in energy. Below ≈ 0.56K the magnetization curves are independent of temperature, and the tunneling proceeds from the ground state of the metastable well (see inset to Fig. 1).The spin Hamiltonian for Mn 12 is given by:where D = 0.65 K is the longitudinal anisotropy, the second term is the Zeeman energy with g z ≈ 1.94, and the third on the right-hand side represents the next higherorder term in longitudinal anisotropy. In order for tunneling to occur, the Hamiltonian must also include terms that do not commute with S z . In a perfect crystal, the lowest transverse anisotropy term allowed by the tetragonal symmetry of Mn 12 is proportional to (S 4 + + S 4 − ). For ground state tunneling, such a term only permits every fourth step. In contrast, all steps are observed with no clear differences in amplitude between them. This suggests that transverse internal magnetic fields, which would allow all steps to occur on an equal footing, provide the dominant symmetry-breaking term that drives the tunneling in Mn 12 . However, dipolar fields [4][5][6][7] and 1

The response to a parallel magnetic field of the very dilute insulating two-dimensional system of electrons in silicon metal-oxide-semiconductor field-effect transistors is dramatic and similar to that found on the conducting side of the metal-insulator transition: there is a large initial increase in resistivity with increasing field, followed by saturation to a value that is approximately constant above a characteristic magnetic field of about 1 T. This is unexpected behavior in an insulator that exhibits Efros-Shklovskii variable-range hopping in zero field, and appears to be a general feature of very dilute electron systems. ͓S0163-1829͑99͒50932-6͔Until quite recently, it was believed that all twodimensional systems of electrons ͑or holes͒ are necessarily localized in the absence of a magnetic field in the limit of zero temperature. This conclusion was based on the scaling theory for noninteracting electrons of Abrahams et al., 1 was further confirmed theoretically for weakly interacting electrons, 2,3 and received experimental confirmation in a number of materials, including thin films 4 and ͑high-density͒ silicon metal-oxide-semiconductor field-effect transistors ͑MOSFET's͒. 5,6 In the last several years, however, measurements in very dilute two-dimensional systems have provided evidence of a transition from insulating to conducting behavior with increasing electron ͑hole͒ density above some low critical value on the order of 10 9 -10 11 cm Ϫ2 . 7-13 At these very low densities the energy of electron-electron interactions exceeds the Fermi energy by an order of magnitude or more, and correlations thus provide the dominant energy in the problem. Dilute, strongly interacting two-dimensional systems are currently the focus of intense theoretical interest, and have elicited a spate of theoretical attempts to account for the presence and nature of the unexpected conducting phase.One of the most interesting characteristics of the conducting phase is its dramatic response to a magnetic field applied parallel to the plane of the two-dimensional system. For example, the resistivity of very high-mobility silicon MOS-FET's increases by almost three orders of magnitude with increasing field, saturating to a new value in fields above ϳ2 -3 T. 14,15 A similar effect was observed in p-GaAs/Al x Ga 1Ϫx As heterostructures 11 confirming that this giant positive magnetoresistance is a general property of dilute conducting two-dimensional ͑2D͒ systems. 16 In Ref. 17, it was reported that the metal-insulator transition in Si MOSFET's shifts toward higher electron densities in a parallel magnetic field of the order of a few T, while at higher magnetic fields, the effect saturates. We note that a parallel magnetic field couples only to the spins of the electrons and not to their orbital motion. Spins are thus known to play a crucial role, and it has been suggested that full alignment of the electrons results in the complete suppression of the anomalous conducting phase.In this paper we report that the response of the very dilut...