Free induction decay with radiation damping I. General treatment

The problem of the free induction decay of a two-level spin system in the presence of a strong coupling between a resonant circuit and the system is discussed under different experimental conditions. It is shown that under certain conditions the shapes of these signals are profoundly modifled by this coupling. In some cases one obtains, after a pulse excitation of the system, several emission peaks of energy from the spin system having a population difference below inversion, creating some sort of photon-bottleneck or of coherent echo.     

On the mobility of very pure semiconductors at very low temperatures

The mobility μ of a very pure semiconductor at very low temperatures is investigated in terms of a model where electrons are scattered by charged impurities distributed uniformly in space, and the electron-electron interaction is taken into account by the Debye-Hueckel screening in the interaction potential. The equation for the current relaxation rate Γ, derived previously by the proper connected diagram expansion, incorporates the quasi-particle effect in a self-consistent manner. The solution of this equation at high carrier concentrations n yields the so-called Brooks-Herring formula. At lower concentrations, the solution deviates significantly from the latter. The solution is in general smaller than the standard expression for the rate based on the Boltzmann equation; and this is consistent with the existing conductivity data available. At the very low concentrations e.g. n = n₃ = 10¹³cm^?3 or lower for Ge, the mobility calculated is inversely proportional to the square-root of the impurity concentration n_s, and has a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$-dependence (T: temperature).

$\text{μ = 0.3597\&z.xl;h}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{k(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^1{}^{\mathrm{<mtext>?3</mtext><mtext>4</mtext>}}$

, where k is the dielectric constant. The conductivity data directly comparable with this formula are not available at present. However, the quasi-particle effect which led to this peculiar concentration-dependence should also show itself in the cyclotron resonance width; there, experiment and theory both show the ${}_{\mathrm{n}}{}_{\mathrm{s}}$-dependence for very pure semiconductors.     

NMR on gallium single crystals: Not yet an absolute thermometer at very low temperatures

A twin crystal of Ga was investigated in the temperature and field ranges of 0.5 to 10 mK and 60 to 250 mT, respectively. In these fields the magnetic interaction is too large to be treated as a perturbation of the quadrupolar interaction. Therefore, the eigenvalues of the Schrödinger equation were calculated numerically, and then used to determine the crystalline axes by pulsed NMR on ⁶⁹Ga and ⁷¹Ga. The temperature dependence of the NMR line intensities was measured using ¹⁹⁵Pt-NMR for thermometry. The observed intensities do not follow the theoretical expectations for a spin system of low nuclear polarization. In addition, a temperature-dependent frequency shift was observed. These results suggest that the effect of interactions between the spins, as well as more complicated spin dynamics, need to be considered in order to use gallium as an absolute thermometer at temperatures below 1 mK.     

Superconductivity of compressed platinum powder at very low temperatures

Superconductivity of compressed, high-purity platinum powder (average grain size 2–3 μm) was found by measurements of resistivity, AC susceptibility and magnetization. The transition temperature into the superconducting state T_c and the critical magnetic field B_c strongly depend on the packing fraction f of the samples: we found 0.62T_c(0)1.38 mK and 6.6B_c(0)67 μT for 0.8f0.5, respectively. The temperature dependence of the critical magnetic fields can be described by B_c(T)=B_c(0)(1−(T/T_c)²). The discussion of these results includes possible explanations for the origin of superconductivity in this new superconducting material.     

Diffusion and localization of muons at very low temperatures

Conclusion The measurements of muon diffusion below 2 K have provided many new data and ideas in the metals Cu and Al, although the understanding is far from complete. Especially intriguing are theAlMn data with their very clear temperature and concentration dependence over a wide temperature range. My feeling is that we now approach well-defined situations where the basic properties of muon diffusion and localization can be seen. Still I would hesitate to draw any definite conclusions regarding the existence of e. g. coherent motion, and I strongly hope that the existing theories of low-temperature diffusion can be further developed, hopefully yielding less extreme results for muons in the very low temperature range.     

Thermal properties of smoky quartz at very low temperatures

The existence of a distribution of low-lying energy levels associated with holes trapped at substitutional aluminium impurities is confirmed by measurements of low temperature specific heat and dielectric loss. A large linearly temperature-dependent contribution to the specific heat is observed at temperatures below 1 K, down to 30 mK. A localization temperature describing the width of the distribution of the energy levels is estimated to vary between 3 and 6 K.

We determined the thermal conductivity down to 30 mK and attribute the decrease below the boundary-scattering value to irradiation damage generally, arguing that it is not attributable to resonant scattering.     

Deformation of Cd-based alloys single crystals at very low temperatures

The temperature dependence of the critical resolved shear stress — CRSS on Cd-Ag andCd-Zn single crystals was studied at very low temperatures 1·5–80 K. The deformation experi-ments were made by a creep technique. The CRSS for Cd-Ag alloys was determined from re-constructed shear stress — shear strain curves, while the method of one sample was applied tothe determination of ₀-T dependence for Cd-Zn alloys. The difference in the temperaturedependences of ₀ for both Cd-based alloys can be caused by different methods for determiningthe CRSS.     

Anomalous temperature dependence of paraelectric relaxation at very low temperatures

Hydroxyl doped KCl crystals were subjected to two dimensional stress in a (001)-plane so that the paraelectric hydroxyl dipoles can be described by a double-well system with a small tunneling splitting. In the temperature range from 0.025 to 0.3 K this system exhibits a dielectric relaxation rate that increases with decreasing temperature.     

Deuteron NMR spectra of ammonium ion isotopomers at low temperatures

Partially deuterated ammonium compounds contain ammonium ion isotopomers with relative abundances given by the binomial distribution of protons and deuterons. All isotopomers with deuterons contribute characteristic deuteron NMR spectra at 5K. Experimental NMR spectra were separated and respective contributions of isotopomers were determined. The derived contributions agree with expected values for a given deuteration in the case of ammonium hexafluorophosphate. In ammonium hexachlorotellurate both NH2D2+ and about 50% of NH3D+ ions are rigid, while the remaining NH3D+ perform limited jumps. NHD3+ and ND4+ ions undergo tunnelling rotation, NH3D+ ions perform either jumps about C2 axis or limited jumps, but some stay rigid in ammonium hexachlorostannate. NH2D2+, NHD 3+ and ND4+ undergo rotational tunnelling. In the case of ammonium perchlorate, the NH3D+ ions perform either jumps about C3 axis or limited jumps whilst some remain rigid. Very low values of activation energies were derived for all spectral components from the temperature dependence of their spectra, up to about 20K, which indicates an incoherent tunnelling nature of the observed dynamic processes. The diverse mobility of NH3D+ ions appears to be the most interesting and new feature.     

On the use of STM superconducting tips at very low temperatures

We report on high quality local tunnel spectroscopy measurements in superconductors using in-situ fabricated superconducting tips as counterelectrode. The experiments were made at very low temperatures using a dilution refrigerator and a ³He cryostat. Spectra obtained with superconducting tip and sample of Al show that the spectroscopic resolution of our set-up is of 15 eV. Following the observation of Josephson current in tunnelling regime (with tips of Pb and of Al), we discuss the feasibility of Scanning Josephson Spectroscopy with atomic size resolution. Experiments showing new applications of these superconducting tips under applied external magnetic fields are also reported.Received: 12 May 2004, Published online: 7 September 2004PACS: 73.63.Rt Nanoscale contacts - 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.25.Ha Magnetic properties - 74.50. + r Tunnelling phenomena; point contacts, weak links, Josephson effects - 74.78.Na Mesoscopic and nanoscale systems - 74.80.Fp Point contacts; SN and SNS junctions     

Magnetization of single-crystal terbium at very low temperatures by nuclear orientation

We report an investigation of the magnetization of high-purity single crystal terbium below 50 mK, using the nuclear orientation of¹⁶⁰Tb, which substitutionally replaces naturally-occurring, monoisotopic¹⁵⁹Tb. The nuclear alignment is determined as a function of applied magnetic field, and can be related to the macroscopic magnetization of the host crystal by a suitable model. In the easy direction (b-axis), a very rapid rise is seen in the first 7 mT of applied field; this is followed by a pleateau region up to 0.1 T, then a slow saturation, completed at ca. 0.4 T. Along an a-axis, a similar rapid increase to about 50% of saturation is observed below 10 mT, followed by a slow, nearly linear increase which agrees with that calculated for domain rotation using the measured crystalline anisotropy constants.     

Propagation of transverse sound waves in glasses at very low temperatures

For both longitudinal and transverse polarizations the variation of the velocity of sound has been measured in borosilicate glass BK7. The experiment has been carried out in the temperature range between 0.28 and 4.2 K and at frequencies between 30 and 150 MHz. The coupling between low energy two-level systems and phonons is found to be similar for both acoustic polarizations. Using our results we also calculate the magnitude of the thermal conductivity without additional assumptions and find complete agreement with existing experimental data.     

Nonstandard behavior of a negative ion reaction at very low temperatures

We have studied the negative ion reaction NH2-+H_{2}-->NH_{3}+H- in the temperature range from 300 to 8 K. We observe a strongly suppressed probability for proton transfer at room temperature. With decreasing temperature, this probability increases, in accordance with a longer lifetime of an intermediate anion-neutral complex. At low temperatures, a maximum in the reaction rate coefficient is observed that suggests the presence of a very small barrier at long range or a quantum mechanical resonance feature.     

NMR study of KCuF3 at low temperatures

The NMR of F¹⁹ nuclei in KCuF₃ has been measured in the a-type single crystal at 1.7 K. Two types of magnetic domains exist; one occupies most part of the crystal and has easy axis along <110>, and the other occupies the rest of the crystal and has easy axis along <100>. In both domains the moment directions are distributed around the easy axes over a considerable angular range. The spin-flop begins with nearly zero applied field in the <110>;-domain. When the magnetic field is rotated in the c-plane, an angular dependence has been observed for those F¹⁹ nuclei which lie on the c-axis. This dependence arises from the alternate stacking of the ground state wave functions of Cu²⁺ ions.     

Magnetization measurements of polycrystal ZnMn alloys at very low temperatures

The magnetization of ZnMn alloys with Mn concentration ranging from 68 to 1 ppm has been measured from 2 K down to 10 mK. The results show large departures from free spin behavior due to impurity-impurity interactions and some concentration independent effects.     

Mössbauer study of very dilute Pd(Fe) alloys at very low temperatures

The magnetic behaviour of very dilute (7 ppm and 0.6 ppm) Pd(Fe) alloys has been studied by Mössbauer spectroscopy in external fields up to 6 T in the temperature range between 0.018 and 300 K. No magnetic ordering was observed even at the lowest temperature. Above 0.067 K the magnetization exhibits free-spin behaviour. The saturation moment was found to be independent of temperature. Magnetic hyperfine patterns observed below 0.067 K were interpreted in terms of paramagnetic hyperfine interactions in the regime of slow electronic relaxation.     

On the dense phases of He3 at very low temperatures

A class of physical properties of the dense phases of He³ are dominated at low temperatures by their nuclear spin systems. The latter determine the lower limits of these properties, and yield thereby approximately their behavior and limiting values at very low temperatures and at the absolute zero. The theory of the spin system allows one to estimate the lowest temperatures at which the various thermal properties of this class have to be determined experimentally to approach with a preset deviation their limiting values in the ground state of these dense phases. These determinations, with a common relative value of this difference, of the nuclear paramagnetic susceptibility, heat capacity, expansion coefficient, and their temperature rates of variation require decreasingly lower temperatures, with the latter finite quantities imposing temperatures one order of magnitude lower than the susceptibility. These studies suggest that in order to obtain satisfactory, experimentally inaccessible, extrapolated very low temperature behaviors and finite limits of the above class of properties, careful prior analysis of their finite temperature values will have to be performed in terms of the partial properties of the spin systems as well as those of the degrees of freedom other than spin of the dense phases of He³.     

NMR investigation of the structure of NiZrF6·.6H2O at low temperatures

Previous studies have shown that NiZrF₆.6H₂O can be described by an axial spin Hamiltonian with parameters g = 2.33 and $\text{D}\text{k}\text{= ?3.14}\text{K}$, and exhibits ferromagnetic ordering at T_c = 164mK. Our room temperature X-ray measurements confirm that NiZrF₆·.6H₂O is isomorphous with NiSnCl₆·.6H₂O and give lattice parameters of $\text{a = 6.55}\text{A}\text{?}$ and α = 96°09′. Proton NMR measurements show that there exist important molecular motions at room temperature and that the space group remains $\text{R}\text{3}$ down to liquid helium temperatures. The positions of all twelve protons have been determined and are found to lie on a sphere of radius 2.9 Å centered on the nickel ion.