Microscopic manifestation of the spin phase transition at filling factor 2/3

Journal of the Korean Physical Society, 2012

We developed a sensitive spectroscopic tool to probe resistively as low as a few percent of an ensemble of nuclear spin polarizations in a GaAs quantum well. We take advantage of the spinphase-transition (SPT) peak of the filling fraction ν = 2/3 quantum Hall effect at which the electronic systems are energetically degenerate. The non-zero nuclear spin polarization incorporated in the system would be perceived as an effective magnetic field BN that modifies the Zeeman energy exclusively. It would result in a change in the overall shape of the peak including the peak's position, width, and amplitude. The alteration of the shape of the overall peak provide essential information on the microscopic characteristics of nuclear spin polarization and its relation to the domain formations which was not well investigated in the previous reports.

Physical Review Letters, 2004

We introduce a frustrated spin 1/2 Hamiltonian which is an extension of the two dimensional J1 −J2 Heisenberg model. The ground states of this model are exactly obtained at a first order quantum phase transition between two regions with different valence bond solid order parameters. At this point, the low energy excitations are deconfined spinons and spin-charge separation occurs under doping in the limit of low concentration of holes. In addition, this point is characterized by the proliferation of topological defects that signal the emergence of Z2 gauge symmetry. PACS numbers: 71.27.+a, 71.28.+d, Frustrated magnets are the focus of considerable attention because exotic quantum effects are expected to emerge from the competition between two or more opposite tendencies. While several models in this category are solvable in one dimension, the list is much smaller for higher dimensions. One of the most studied frustrated magnets is the spin 1/2 Heisenberg model with first and second nearest neighbor interactions J 1 and J 2 . In one dimension, this model exhibits a quantum transition as a function of J 2 /J 1 from a critical state with quasi-long range antiferromagnetic (AF) order to a dimerized phase. Moreover, the exact dimerized ground state has been obtained for the point J 2 /J 1 = 0.5 by Majumdar and Ghosh [1]. In contrast, two dimensional (2D) frustrated magnets like the J 1 − J 2 Heisenberg model on a square lattice still hold many secrets. Different approaches predict a transition between a Néel ordered state and a gapped (non-magnetic) quantum phase for the region 0.4 J 2 /J 1 0.6. However, the nature of this phase is still debated. More precisely, the question is whether it is a uniform spin liquid [2, 3] or a spatially ordered valence bond crystal .

Journal of Physics: Condensed Matter

physica status solidi (b), 1974

The effect of intense magnetic fields i n semiconductors has been widely discussed for some time whereas to the knowledge of the present author there is no paper up to date devoted to this subject in the case of magnetic semiconductors.

Phys. Rev. B, 2016

A transport study of two-dimensional (2D) holes confined to wide GaAs quantum wells provides a glimpse of a subtle competition between different many-body phases at Landau level filling ν = 3/2 in tilted magnetic fields. At large tilt angles (θ), an anisotropic, stripe (or nematic) phase replaces the isotropic compressible Fermi sea at ν = 3/2 if the quantum well has a symmetric charge distribution. When the charge distribution is made asymmetric, instead of the stripe phase, an even-denominator fractional quantum state appears at ν = 3/2 in a range of large θ, and reverts back to a compressible state at even higher θ. We attribute this remarkable evolution to the significant mixing of the excited and ground-state Landau levels of 2D hole systems in tilted fields. A strong magnetic field perpendicular to a 2D electron system (2DES) quantizes the electron kinetic energy into a set of highly-degenerate Landau levels (LLs). The dominating Coulomb interaction then gives rise to numerous , exotic quantum many-body phases [1, 2]. When the Fermi energy (E F) lies in an N = 0 LL, there is a compressible Fermi sea of composite fermions at LL filling factors ν = 1/2 and 3/2 while numerous fractional quantum Hall states (FQHSs) are observed at nearby odd-denominator ν [1-5]. In N ≥ 2 LLs, FQHSs are typically absent and anisotropic phases dominate at half-filled LLs, e.g., at ν = 9/2 and 11/2 as the system breaks the rotational symmetry and forms unidirectional charge density waves-the so-called stripe (or nematic) phases [6-8]. The intermediate N = 1 LL is special. The electrons exhibit FQHSs not only at odd-denominator ν but also at the even-denominator fillings ν = 5/2 and 7/2 [1, 2, 9]. The latter are believed to be the Moore-Read Pfaffian state [10], obey non-Abelian statistics, and be of potential use in topological quantum computing [11]. The application of parallel magnetic field (B ||) or pressure can break the rotational symmetry and introduce LL mixing, leading to the destruction of the ν = 5/2 FQHS and stabilization of the stripe phase in the N = 1 LL [12-16]. In GaAs two-dimensional hole systems (2DHSs), the spin-orbit coupling mixes harmonic oscillators with different Landau and spin indices and leads to a complex set of LLs [17]. Nevertheless, in narrow quantum wells (QWs), the 2DHS is compressible at ν = 1/2 and 3/2 and numerous odd-denominator FQHSs are still prevalent as the filling deviates from ν = 1/2 and 3/2, qualitatively similar to those in 2DESs. However, the even-denominator FQHSs at ν = 5/2 and 7/2 are very weak [18, 19], and instead stripe phases are typically observed at these fillings, particularly at low densities [19-21]. Here, we report transport measurements in 2DHSs confined in wide GaAs QWs and subjected to strong B ||. We observe a remarkable metamorphosis of the ground state at ν = 3/2. The compressible Fermi sea seen at ν = 3/2 turns into a stripe phase when we apply a sufficiently large B || to a symmetric QW. The stripe phase can be destabilized in asymmetric QWs and, strikingly, an even-denominator FQHS forms at ν = 3/2 at intermediate B ||. At larger B || , the ν = 3/2 FQHS disappears and the 2DHS reverts back to becoming compressible. Our results highlight the rich and subtle many-body phenomena manifested by high-quality 2DHSs. Our samples were grown by molecular beam epitaxy, and each consists of a GaAs QW (well widths W = 35 or 30 nm) which is bounded on either side by undoped Al 0.3 Ga 0.7 As spacer layers and C δ-doped layers. They have as grown densities p 1 to 1.5 × 10 11 cm −2 and high mobility µ 100 m 2 /Vs. Each sample has a van der Pauw geometry, with alloyed InZn contacts at the four corners of a 4 × 4 mm 2 piece. We carefully control the density and the charge distribution symmetry in the QW by applying voltage biases to the back-and front-gates [22, 23]. For the low-temperature measurements, we use a dilution refrigerator with a sample platform which can be rotated in-situ in the magnetic field to induce a parallel field component B || along the x-direction (see Fig. 1(c)). We use θ to express the angle between the field and the normal to the sample plane, and denote the longitudinal resistances measured along and perpendicular to the direction of B || as R xx and R yy , respectively (Fig. 1(c)). Although the main focus of our study is the state of the 2DHS near ν = 3/2 in tilted magnetic fields, the data at θ = 0 are also very intriguing. Figure 2 shows R xx measured from a symmetric 35-nm-QW 2DHS at θ = 0 • and different densities. Strong odd-denominator FQHSs are seen as vertical, low-resistance (blue) stripes at ν = 5/3, 8/5, 7/5, and 4/3. With increasing density, R xx steeply increases above a boundary marked by the white solid line. This sharp transition is a signature of a LL crossing near ν = 3/2. We indeed expect such a crossing from the typical LL diagram (see Fig. 1(a)) for our wide-QW 2DHSs [24]. As depicted in Fig. 1(a), the light-hole-like β-level (blue) crosses the heavy-hole

Journal of Modern Physics

The spin polarization of a fractional quantum Hall state shows very interesting properties. The curve of polarization versus magnetic field has wide plateaus. The fractional quantum Hall effect is caused by the Coulomb interaction because the 2D electron system without the Coulomb interaction yields no energy gap at the fractional filling factor. Therefore, the wide plateau in the polarization curve is also caused by the Coulomb interaction. When the magnetic field is weak, some electrons have up-spins and the others down-spins. Therein the spin-exchange transition occurs between two electrons with up and down spins via the Coulomb interaction. Then the charge distribution before the transition is the same as one after the transition. So these two states have the same classical Coulomb energy. Accordingly, the partial Hamiltonian composed of the spin exchange interaction should be treated exactly. We have succeeded in diagonalizing the spin exchange interaction for the first and second nearest electron pairs. The theoretical results reproduce the wide plateaus very well. If the interval modulations between Landau orbitals are taken into the Hamiltonian, the total energy has the Peierls instability. We can diagonalize the Hamiltonian with the interval modulation. The results reproduce wide plateaus and small shoulders which are in good agreement with the experimental data.

Proceedings of the National Academy of Sciences, 2008

We measure a sequence of quantum Hall-like plateaux at 1/q: 9 ≥ q ≥ 2 and p/q = 2/9 fractions in the magnetisation with increasing magnetic field in the geometrically frustrated spin system SrCu2(BO3)2. We find that the entire observed sequence of plateaux is reproduced by solving the Hofstadter problem on the system lattice when short-range repulsive interactions are included, thus providing a sterling demonstration of bosons confined by a magnetic and lattice potential mimicking fermions in the extreme quantum limit.

physica status solidi (c), 2010

We perform resistively-detected nuclear-spin relaxation measurements by using the spin phase transition (SPT) peak in the fractional quantum Hall system at the filling factor ν = 2/3. We investigate nuclear spin relaxation for several electronic systems under a spatially inhomogeneous nuclear spin polarization. When Skyrmions are introduced in the ground state, the position of the SPT peak shifts to higher magnetic field. This result indicates that Skyrmions relax nuclear spins polarized anti-parallel to the external magnetic field more effectively than those parallel to the magnetic field.

Physical review, 1987

Journal of Applied Physics, 2019