Peter Heller

A Tunable NMR Spectrometer for the vhf‐uhf Range

A nuclear magnetic resonance detection system for the vhf‐uhf frequency range is described in detail. It consists of a radio frequency bridge built around a coaxial hybrid T. The sample is contained in a tunable L‐C resonator coupled with an adjustable impedance transformer to a 50 Ω airline. The system is thus fully tunable over wide ranges of frequency from a remote location. For example, using a two‐turn copper ribbon coil, the range 270–710 MHz is covered: The system may be set to any desired point in this range within a few minutes. The system was used with standard lock‐in detection to obtain the absorption derivative ∂χ″/∂H. An absolute noise measurement was made at a radio frequency of 300 MHz and an audio detection frequency of 200 Hz. This showed that the root mean square noise at the lock‐in output was between four and seven times the value corresponding to the rf Johnson noise at the bridge. The system was used to observe a proton resonance in a Bitter type solenoid at 125 kG.

Nitrogen temperature superconducting ring experiment

A student experiment is described for studying persistent currents in a commercially obtained ring of the ‘‘123’’ superconducting material at liquid‐nitrogen temperature. The currents are easily detected with a standard analog Hall probe. From observations extended over a 3‐week period, an upper limit on the possible resistance of one such ring was set at about 2×10−16 Ω. For the rings studied, the induced current saturated at about 2 A as the applied flux change was increased. An ac technique for checking the continuity of the superconducting path around the ring is also described. These experiments provide an interesting supplement for topics in first‐year electricity and magnetism. The effects are striking and easily discussed at an introductory level. For example, the current induced by turning the ring over in the Earth’s field is readily seen.

Analog demonstrations of Ampere’s law and magnetic flux

The Ampere circuital law, that the line integral of the magnetic field around a closed path depends only on the total enclosed current and not on the shape of either the current or the integration path, may be strikingly demonstrated. The setup for this is based on the electromagnetic induction taking place in a fine helical coil wound on a nearly closed iron loop. The construction and theory of this device is discussed. Its operation is similar to that of a standard ac ‘‘clamp‐on’’ ammeter. The method is simple and can be carried out very quickly. Some analog demonstrations of magnetic flux are also described. These experiments are related to the circuital law demonstration through the electromagnetic reciprocity theorem.

Inelastic Neutron Scattering Studies of Critical Fluctuations in MnF2 Above and Below TN

Detailed inelastic neutron scattering measurements have yielded the behavior of the scattering function S(q, ω) for both the transverse and the longitudinal fluctuations throughout the critical region of the uniaxial antiferromagnet MnF2. The results are discussed in the light of the theory of dynamic scaling. The results below TN are discussed with reference to quasihydrodynamic theories of the spin fluctuations in the ordered state.

Electromagnetic waves in space: Visualization of E and B, and pedagogical approaches using superposition

A beam of electromagnetic waves, produced by a “ham” transmitter at a frequency just below 450 MHz, is studied using a pair of antennas, one an electric and the other a magnetic “dipole,” each coupled to subminiature lamp bulb. These bulbs become very brightly lit in response to the local time average values of |E|2 and |B|2, respectively. Most strikingly, the interleaving of the electric and magnetic oscillation maxima in a standing wave is seen. This and other aspects of the phenomena are described using an accompanying pedagogical approach which emphasizes the primary idea of wave superposition.

Erratum: ‘‘Analog demonstrations of Ampere’s law and magnetic flux’’ [Am. J. Phys. 60, 17–25 (1992)]

We reproduce here Fig. 3 from that paper in its correct originally submitted form, which also appeared in the proof sent to the author. Subsequently, in their desire for a more uniform typographical style, the figure was altered by the American Institute of Physics staff at Woodbury, New York, without consultation with either the author or the editor. In so doing the letters indicating the figure sub‐units were pasted back in the wrong order. The Woodbury staff has apologized to the author for this regrettable error. That apology is hereby transmitted to the readers of this Journal.

Low temperature spin wave dynamics in classical Heisenberg chains

A detailed and quantitative study of the low‐temperature spin‐wave dynamics has been made for the classical Heisenberg‐coupled chain using computer simulation. Results for the spin‐wave frequencies are presented and compared with existing predictions.

Computer simulation of the approach to equilibrium in the classical Heisenberg chain

Computer studies of the approach to equilibrium in the classical 3‐component Heisenberg chain, starting from a configuration with a large staggered magnetization (i. e., far from equilibrium) are reported. The equal time transverse and reduced longitudinal correlations g⊥(l, t) and g∥(l, t), respectively, were monitored for times long enough to show the approach to equilibrium. Results for g⊥ confirm predictions by Nelson and Fisher of wave‐like behavior with a propagation speed equal to twice the zero‐temperature spin wave velocity. The equilibration of g∥ was found to be slower and diffusive in nature. The fitted diffusivity appears to be comparable to the value of the spin diffusivity for the corresponding equilibrium problem.

Inelastic Scattering from MnF2 in the Critical Region

The scattering law S(q, ω) in the anisotropic antiferromagnet MnF2 has been measured over an extended range of ω, q, and temperature in the neighborhood of the transition. The data have yielded values for the relaxation rate of transverse (Γ⊥) and longitudinal (Γ∥) fluctuations, the range of the spin‐spin correlations (ξ) and the static staggered susceptibilities.1 From our results we find the relaxation rate at TN linear in q3/2 for both longitudinal and transverse. Above TN for q = 0 the longitudinal Γ∥ ∝ [(T ‐ TN) / TN]0.95±0.05. The relaxation rates, when plotted on a reduced scale Γ∥ (q, ξ) ξ3/2 vs qξ, fall on a single curve indicating the existence of a homogeneous scaling function. This substantiates the prediction of general dynamical scaling.2 The scaling function has a different behavior above and below TN, joining continuously as ξ becomes large. A detailed comparison of the experimental S(q, ω) with theory awaits a more explicit calculation of the behavior of the critical fluctuations in the a...