Author Correction: SciPy 1.0: fundamental algorithms for scientific computing in Python.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

SciPy 1.0: fundamental algorithms for scientific computing in Python.

SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto standard for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per year. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent technical developments.

Correction: Dynamic nuclear polarization in a magnetic resonance force microscope experiment.

Correction for 'Dynamic nuclear polarization in a magnetic resonance force microscope experiment' by Corinne E. Isaac et al., Phys. Chem. Chem. Phys., 2016, 18, 8806-8819.

Dynamic nuclear polarization in a magnetic resonance force microscope experiment.

We report achieving enhanced nuclear magnetization in a magnetic resonance force microscope experiment at 0.6 tesla and 4.2 kelvin using the dynamic nuclear polarization (DNP) effect. In our experiments a microwire coplanar waveguide delivered radiowaves to excite nuclear spins and microwaves to excite electron spins in a 250 nm thick nitroxide-doped polystyrene sample. Both electron and proton spin resonance were observed as a change in the mechanical resonance frequency of a nearby cantilever having a micron-scale nickel tip. NMR signal, not observable from Curie-law magnetization at 0.6 T, became observable when microwave irradiation was applied to saturate the electron spins. The resulting NMR signal's size, buildup time, dependence on microwave power, and dependence on irradiation frequency was consistent with a transfer of magnetization from electron spins to nuclear spins. Due to the presence of an inhomogeneous magnetic field introduced by the cantilever's magnetic tip, the electron spins in the sample were saturated in a microwave-resonant slice 10's of nm thick. The spatial distribution of the nuclear polarization enhancement factor ε was mapped by varying the frequency of the applied radiowaves. The observed enhancement factor was zero for spins in the center of the resonant slice, was ε = +10 to +20 for spins proximal to the magnet, and was ε = -10 to -20 for spins distal to the magnet. We show that this bipolar nuclear magnetization profile is consistent with cross-effect DNP in a ∼10(5) T m(-1) magnetic field gradient. Potential challenges associated with generating and using DNP-enhanced nuclear magnetization in a nanometer-resolution magnetic resonance imaging experiment are elucidated and discussed.

Long-lived frequency shifts observed in a magnetic resonance force microscope experiment following microwave irradiation of a nitroxide spin probe.

We introduce a spin-modulation protocol for force-gradient detection of magnetic resonance that enables the real-time readout of longitudinal magnetization in an electron spin resonance experiment involving fast-relaxing spins. We applied this method to observe a prompt change in longitudinal magnetization following the microwave irradiation of a nitroxide-doped perdeuterated polystyrene film having an electron spin-lattice relaxation time of [Formula: see text]. The protocol allowed us to discover a large, long-lived cantilever frequency shift. Based on its magnitude, lifetime, and field dependence, we tentatively attribute this persistent signal to deuteron spin magnetization created via transfer of polarization from nitroxide spins.

Magnetic Resonance Force Microscopy Detected Long-Lived Spin Magnetization.

Magnetic resonance force microscopy (MRFM), which combines magnetic resonance imaging with scanning probe microscopy together, is capable of performing ultra-sensitive detection of spin magnetization. In an attempt to observe dynamic nuclear polarization (DNP) in an MRFM experiment, which could possibly further improve its sensitivity towards a single proton spin, a film of perdeuterated polystyrene doped with a nitroxide electron-spin probe was prepared. A high-compliance cantilever with a 4 µm diameter magnetic tip was brought near the film at a temperature of 7.3 K and in a background magnetic field of ~0.6 T. The film was irradiated with 16.7 GHz microwaves while the resulting transient change in cantilever frequency was recorded in real time. In addition to observing the expected prompt change in cantilever frequency due to saturation of the nitroxide's electron-spin magnetization, we observed a persistent cantilever frequency change. Based on its magnitude, lifetime, and field dependence, we tentatively attribute the persistent signal to polarized deuteron magnetization created via transfer of magnetization from electron spins. Further measurements of the persistent signal's dependence on the cantilever amplitude and tip-sample separation are presented and explained by the cross-effect DNP mechanism in high magnetic field gradients.

Switching through intermediate states seen in a single nickel nanorod by cantilever magnetometry.

In-plane to out-of-plane magnetization switching in a single nickel nanorod affixed to an attonewton-sensitivity cantilever was studied at cryogenic temperatures. We observe multiple sharp, simultaneous transitions in cantilever frequency, dissipation, and frequency jitter associated with magnetic switching through distinct intermediate states. These findings suggest a new route for detecting magnetic fields at the nanoscale.

A Unified Picture of Cantilever Frequency-Shift Measurements of Magnetic Resonance.

We report a unified framework describing all existing protocols for spin manipulation and signal creation in frequency-modulation magnetic resonance force microscopy using classical perturbation theory. The framework is well suited for studying the dependence of the frequency shift on the cantilever amplitude via numerical simulation. We demonstrate the formalism by recovering an exact result for a single spin signal and by simulating, for the first time as a function of cantilever amplitude, the frequency shift due to a volume of noninteracting spins inverted by an adiabatic rapid passage. We show that an optimal cantilever amplitude exists that maximizes the signal. Our findings suggest that understanding the amplitude dependence of the spin signal will be important for designing future high-sensitivity experiments.

Rapid serial prototyping of magnet-tipped attonewton-sensitivity cantilevers by focused ion beam manipulation.

The authors report a method for rapidly prototyping attonewton-sensitivity cantilevers with custom-fabricated tips and illustrate the method by preparing tips consisting of a magnetic nanorod overhanging the leading edge of the cantilevers. Micron-long nickel nanorods with widths of 120-220 nm were fabricated on silicon chips by electron beam lithography, deposition, and lift-off. Each silicon chip, with its integral nanomagnet, was attached serially to a custom-fabricated attonewton-sensitivity cantilever using focused ion beam manipulation. The magnetic nanorod tips were prepared with and without an alumina capping layer, and the minimum detectable force and tip magnetic moment of the resulting cantilevers was characterized by cantilever magnetometry. The results indicate that this serial but high-yield approach is an effective way to rapidly prepare and characterize magnetic tips for the proposed single-electron-spin and single-proton magnetic resonance imaging experiments. The approach also represents a versatile route for affixing essentially any vacuum-compatible sample to the leading edge of an attonewton-sensitivity cantilever.

Batch-fabrication of cantilevered magnets on attonewton-sensitivity mechanical oscillators for scanned-probe nanoscale magnetic resonance imaging.

We have batch-fabricated cantilevers with ∼100 nm diameter nickel nanorod tips and force sensitivities of a few attonewtons at 4.2 K. The magnetic nanorods were engineered to overhang the leading edge of the cantilever, and consequently the cantilevers experience what we believe is the lowest surface noise ever achieved in a scanned probe experiment. Cantilever magnetometry indicated that the tips were well magnetized, with a ≤ 20 nm dead layer; the composition of the dead layer was studied by electron microscopy and electron energy loss spectroscopy. In what we believe is the first demonstration of scanned probe detection of electron-spin resonance from a batch-fabricated tip, the cantilevers were used to observe electron-spin resonance from nitroxide spin labels in a film via force-gradient-induced shifts in cantilever resonance frequency. The magnetic field dependence of the magnetic resonance signal suggests a nonuniform tip magnetization at an applied field near 0.6 T.

Evading surface and detector frequency noise in harmonic oscillator measurements of force gradients.

We introduce and demonstrate a method of measuring small force gradients acting on a harmonic oscillator in which the force-gradient signal of interest is used to parametrically up-convert a forced oscillation below resonance into an amplitude signal at the oscillator's resonance frequency. The approach, which we demonstrate in a mechanically detected electron spin resonance experiment, allows the force-gradient signal to evade detector frequency noise by converting a slowly modulated frequency signal into an amplitude signal.

Scanned-probe detection of electron spin resonance from a nitroxide spin probe.

We report an approach that extends the applicability of ultrasensitive force-gradient detection of magnetic resonance to samples with spin-lattice relaxation times (T (1)) as short as a single cantilever period. To demonstrate the generality of the approach, which relies on detecting either cantilever frequency or phase, we used it to detect electron spin resonance from a T (1) = 1 ms nitroxide spin probe in a thin film at 4.2 K and 0.6 T. By using a custom-fabricated cantilever with a 4 microm-diameter nickel tip, we achieve a magnetic resonance sensitivity of 400 Bohr magnetons in a 1 Hz bandwidth. A theory is presented that quantitatively predicts both the lineshape and the magnitude of the observed cantilever frequency shift as a function of field and cantilever-sample separation. Good agreement was found between nitroxide T (1) 's measured mechanically and inductively, indicating that the cantilever magnet is not an appreciable source of spin-lattice relaxation here. We suggest that the new approach has a number of advantages that make it well suited to push magnetic resonance detection and imaging of nitroxide spin labels in an individual macromolecule to single-spin sensitivity.