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We numerically study energy spectra and localization properties of the double exchange model at irrational filling factor. To obtain variational ground state, we use a mumerical technique in momentum space by ``embedded boundary condition which has no finite size effect a priori. Although the Hamiltonian has translation invariance, the ground state spontaneously exhibits a self-similarity. Scaling and multi-fractal analysis for the wave functions are performed and the scaling indices $alpha$s are obtained. The energy spectrum is found to be a singular continuous, so-called the Cantor set with zero Lebesque measure.
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The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.
Coherent two-level systems, or qubits, based on electron spins in GaAs quantum dots are strongly coupled to the nuclear spins of the host lattice via the hyperfine interaction. Realizing nuclear spin control would likely improve electron spin coherence and potentially enable the nuclear environment to be harnessed for the long-term storage of quantum information. Toward this goal, we report experimental control of the relaxation of nuclear spin polarization in a gate-defined two-electron GaAs double quantum dot. A cyclic gate-pulse sequence transfers the spin of an electron pair to the host nuclear system, establishing a local nuclear polarization that relaxes on a time scale of seconds. We find nuclear relaxation depends on magnetic field and gate-controlled two-electron exchange, consistent with a model of electron mediated nuclear spin diffusion.
We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O. and T. Senthil, Phys. Rev. Lett. 96, 060601 (2006)] which relates fraction- alization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61, 10267 (2000)] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p+ip superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.
Magnetism in recently discovered van der Waals materials has opened new avenues in the study of fundamental spin interactions in truly two-dimensions. A paramount question is what effect higher-order interactions beyond bilinear Heisenberg exchange have on the magnetic properties of few-atom thick compounds. Here we demonstrate that biquadratic exchange interactions, which is the simplest and most natural form of non-Heisenberg coupling, assume a key role in the magnetic properties of layered magnets. Using a combination of nonperturbative analytical techniques, non-collinear first-principles methods and classical Monte Carlo calculations that incorporate higher-order exchange, we show that several quantities including magnetic anisotropies, spin-wave gaps and topological spin-excitations are intrinsically renormalized leading to further thermal stability of the layers. We develop a spin Hamiltonian that also contains antisymmetric exchanges (e.g. Dzyaloshinskii-Moriya interactions) to successfully rationalize numerous observations currently under debate, such as the non-Ising character of several compounds despite a strong magnetic anisotropy, peculiarities of the magnon spectrum of 2D magnets, and the discrepancy between measured and calculated Curie temperatures. Our results lay the foundation of a universal higher-order exchange theory for novel 2D magnetic design strategies.
The spectral distribution of parametrically excited dipole-exchange magnons in an in-plane magnetized epitaxial film of yttrium-iron garnet was studied by means of frequency- and wavevector-resolved Brillouin light scattering spectroscopy. The experiment was performed in a parallel pumping geometry where an exciting microwave magnetic field was parallel to the magnetizing field. It was found that for both dipolar and exchange spectral areas parallel pumping excites the lowest volume magnon modes propagating in the film plane perpendicularly to the magnetization direction. In order to interpret the experimental observations, we used a microscopic Heisenberg model that includes exchange as well as dipole-dipole interactions to calculate the magnon spectrum and construct the eigenstates. As proven in our calculations, the observed magnons are characterized by having the highest possible ellipticity of precession which suggests the lowest threshold of parametric generation. Applying different pumping powers we observe modifications in the magnon spectrum that are described theoretically by a softening of the spin stiffness.
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