Fractional Magnetization Plateaus and Magnetic Order in the Shastry-Sutherland MagnetTmB4 (original) (raw)
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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 .
Spin polarization in fractional quantum Hall effect
Surface Science, 2003
Experimental data show a number of plateaus of varying widths in the magnetic-field dependence of the electron-spin-polarization for fractional quantum Hall states. We have calculated the magnetic-field dependence of the spin-polarization using a new theory. We start by adopting the Landau gauge and ignoring Coulomb interactions between electrons; then we construct single electron states in equally spaced orbitals. For a number of filling factors we have examined the many-electron states with electron configurations having minimum classical Coulomb energy. The residual Coulomb interactions in each many-electron state produce spin-exchange-forces. We have solved the eigenvalue problem of the interaction Hamiltonian composed of nearest neighbor spin-exchange-interactions. From the eigenvalues we have calculated the magnetic-field dependence of the spin-polarization. Our results are in good accord with the magnetic-field dependence in experimental results, including the number and shape of the plateaus.
Magnetic ordering and fractional magnetization plateaus in the Shastry Sutherland magnet TmB4
2007
TmB4 is a realisation of a frustrated Shastry-Sutherland magnet. The phase diagram shows Neel order at low field. The high field ferrimagnetic phase and an intermediate field phase characterised by magnetisation plateaus at M/Msat = 1/7, 1/8, 1/9 show complex stripe structures. We discuss the experimental findings in terms of an effective spin 1/2 model close to the Ising limit on the Shastry Sutherland lattice. We speculate that the fractional plateaus in the intermediate phase can be interpreted as plateaus in the equivalent 2D fermion gas in a strong fictitious magnetic field.
Integral and fractional quantum Hall Ising ferromagnets
Physical Review B, 2007
We compare quantum Hall systems at filling factors ν = 2 to ν = 2 3 and 2 5 , corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P = 1) and paramagnetic (P = 0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At ν = 2, we find spin domains at half-polarization (P = 1 2 ), while antiferromagnetic order seems most favorable in the CF systems. The transition between P = 0 and 1, as seen when e.g. the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompresible half-polarized state is found in some models.
Spin Polarization Curve of Fractional Quantum Hall States with Filling Factor Smaller than 2
ISRN Condensed Matter Physics
Kukushkin et al. have measured the electron spin polarization versus magnetic field in the fractional quantum Hall states. The polarization curves show wide plateaus and small shoulders. The 2D electron system is described by the total Hamiltonian (). Therein, is the sum of the Landau energies and classical Coulomb energies. is the residual interaction yielding Coulomb transitions. It is proven for any filling factor that the most uniform electron configuration in the Landau states is only one. The configuration has the minimum energy of . When the magnetic field is weak, some electrons have up-spins and the others down-spins. Then, there are many spin arrangements. These spin arrangements give the degenerate ground states of . We consider the partial Hamiltonian only between the ground states. The partial Hamiltonian yields the Peierls instability and is diagonalized exactly. The sum of the classical Coulomb and spin exchange energies has minimum for an interval modulation between ...
Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2
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.
Fractional Quantum Hall States at Zero Magnetic Field
Physical Review Letters, 2011
We present a simple prescription to flatten isolated Bloch bands with non-zero Chern number. We first show that approximate flattening of bands with non-zero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.
SciPost Physics, 2022
Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu_22(BO_33)_22, which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extended hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization plateaux for moderate values of the interdimer coupling. A possible existence of a striking quantum phase of bound triplons is also revealed at low enough magnetic fields.
Fractional quantum Hall effect
Physics Subject Headings (PhySH), 2018
We have studied the effects of hydrostatic pressure on a high-quality two-dimensional electron system under high magnetic field. The ϭ2/5 and 3/7 fractional quantum Hall effect ͑FQHE͒ states dramatically vanish and then subsequently reappear with increasing pressure. In the high-pressure ϭ2/5 state, tilting of the magnetic field away from the normal is found to suppress the FQHE state. These results suggest that the high-pressure ϭ2/5 FQHE state is spin unpolarized with the spin transition being driven by reduction of Landé g factor experienced by electrons due to application of pressure. ͓S0163-1829͑97͒50444-9͔ RAPID COMMUNICATIONS