Spin polarization contrast observed in GaAs by force-detected nuclear magnetic resonance

We applied the recently developed technique of force-detected nuclear magnetic resonance (NMR) to observe 71Ga, 69Ga, and 75As in GaAs. The nuclear spin-lattice relaxation time is 21$\pm$5 min for 69Ga at $\sim 5$ K and 4.6 Tesla. We have exploited this long relaxation time to first create and then observe spatially varying nuclear spin polarization within the sample, demonstrating a new form of contrast for magnetic resonance force microscopy (MRFM). Such nuclear spin contrast could be used to indirectly image electron spin polarization in GaAs-based spintronic devices.Comment: 3 pages, 2 figure

Temperature measurement at the end of a cantilever using oxygen paramagnetism in solid air

We demonstrate temperature measurement of a sample attached to the end of a cantilever using cantilever magnetometry of solid air ``contamination'' of the sample surface. In experiments like our Magnetic Resonance Force Microscopy (MRFM), the sample is mounted at the end of a thin cantilever with small thermal conductance. Thus, the sample can be at a significantly different temperature than the bulk of the instrument. Using cantilever magnetometry of the oxygen paramagnetism in solid air provides the temperature of the sample, without any modifications to our MRFM (Magnetic Resonance Force Microscopy) apparatus.Comment: Submitted to J of Applied Physic

Faraday effect revisited: sum rules and convergence issues

This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play an important role in solid state physics, and they give rise to certain convergence problems widely ignored by physicists. We give a complete answer in the case of smooth potentials and formulate an open problem related to less regular perturbations.Comment: Dedicated to the memory of our late friend Pierre Duclos. Accepted for publication in Journal of Physics A: Mathematical and Theoretical

Distributional Borel Summability of Odd Anharmonic Oscillators

It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances naturally associated with the system

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Convergence Radii for Eigenvalues of Tri--diagonal Matrices

Consider a family of infinite tri--diagonal matrices of the form $L+ zB,$ where the matrix $L$ is diagonal with entries $L_{kk}= k^2,$ and the matrix $B$ is off--diagonal, with nonzero entries $B_{k,{k+1}}=B_{{k+1},k}= k^\alpha, 0 \leq \alpha < 2.$ The spectrum of $L+ zB$ is discrete. For small $|z|$ the $n$-th eigenvalue $E_n (z), E_n (0) = n^2,$ is a well--defined analytic function. Let $R_n$ be the convergence radius of its Taylor's series about $z= 0.$ It is proved that $$ R_n \leq C(\alpha) n^{2-\alpha} \quad \text{if} 0 \leq \alpha <11/6.$

170 Nanometer Nuclear Magnetic Resonance Imaging using Magnetic Resonance Force Microscopy

We demonstrate one-dimensional nuclear magnetic resonance imaging of the semiconductor GaAs with 170 nanometer slice separation and resolve two regions of reduced nuclear spin polarization density separated by only 500 nanometers. This is achieved by force detection of the magnetic resonance, Magnetic Resonance Force Microscopy (MRFM), in combination with optical pumping to increase the nuclear spin polarization. Optical pumping of the GaAs creates spin polarization up to 12 times larger than the thermal nuclear spin polarization at 5 K and 4 T. The experiment is sensitive to sample volumes containing $\sim 4 \times 10^{11}$ $^{71}$Ga$/\sqrt{Hz}$. These results demonstrate the ability of force-detected magnetic resonance to apply magnetic resonance imaging to semiconductor devices and other nanostructures.Comment: Submitted to J of Magnetic Resonanc