Spin Dynamics of 3He in Aerogel

We report continuous-wave NMR measurements on superfluid ³ He contained inside high porosity aerogel at 3.24 MPa, in a 28.4 mT magnetic field, and down to 0.9 mK. Three different purities of ³ He were used: pure ³ He, ³ He with enough ⁴ He to replace the first localized layer, and ³ He with enough ⁴ He to replace both localized layers. Below 2.26mK, the NMR spectrum does not consist of a single Lorentzian, but a distribution of NMR resonant frequencies both above and below the Larmor frequency, _L . Upon cooling, the component of the spectrum at frequencies below the Larmor frequency moves to higher frequencies over a narrow temperature range and does not return to < _L upon warming. The higher frequency component of the spectrum displays two resolvable peaks which become a complex structure upon removal of the localized ³ He spins. The spectrum changes as the magnetic field is rotated about the axis of the aerogel sample, indicating that the ³ He is able to detect a preferred direction in the aerogel. The shape of the spectrum shows no rotation or magnetic field hysteresis. We find that the average frequency shifts of our NMR spectra do not depend on the presence of the localized ³ He spins. These frequency shifts and the presence of a temperature-independent magnetization for the liquid ³ He suggest that the aerogel stabilizes a single equal-spin-pairing state in our experiments.     

Observation of NMR Signals from a Thin 3He Slab

NMR free precession signals from a slab of normal ³ He of thickness comparable to the superfluid coherence length have been observed using a SQUID NMR spectrometer at a frequency of 880 kHz. This spectrometer is based on a SQUID with Additional Positive Feedback, directly coupled to a low noise room temperature amplifier, and operated in flux locked loop mode using the direct offset integration technique, with a bandwidth of several MHz. The sensitivity is such that the signal from a 100 nm slab on a 1 cm ² surface, corresponding to 2×10 ¹⁷ spins, is clearly resolved.     

Application of a SQUID magnetometer to NMR at low temperatures

Using a SQUID magnetometer, changes in the nuclear magnetization of copper are observed when the nuclear spins absorb rf power at resonance. Since the detected flux change is directly proportional to the change in static magnetizationM, this method offers higher sensitivity at low frequencies than conventional NMR which responds todM/dt. The experimental arrangement for observingM at temperatures below1 K is described. The variation of signal amplitude with temperature and rf power is found to agree well with predictions from the Bloch equations. A comparison of the sensitivity of the SQUID magnetometer and conventional NMR methods shows the advantage of the new technique at low frequencies and for nuclear systems with broad lines and long spin-lattice relaxation times.     

Effect of impact modification on slow crack growth in poly(vinyl chloride)

The effect of impact modification on slow crack growth in a poly(vinyl chloride) (PVC) compound was examined in order to test a methodology for predicting long-term creep fracture from short-term tension-tension fatigue tests. In all cases the crack propagated in a stepwise manner through a crack tip craze zone. Step length was analyzed in terms of the Dugdale model for a crack tip plastic zone. The overall crack growth rate in fatigue and creep followed the conventional Paris power law with the same power 2.7, da/dt = A _f K _I ^2.7 and da/dt = BK _I ^2.7,respectively. The effects of frequency, temperature, and R-ratio (the ratio of the minimum to maximum stress intensity factor in the fatigue loading cycle) on the Paris prefactor were determined. Crack growth rate was modeled as the product of a creep contribution that depended only on the maximum stress intensity factor and a fatigue contribution that depended on strain rate da/dt = B _f K _I,max ^2.7 (1 + C , where C is a coefficient defining the strain rate sensitivity. A linear correlation allowed for extrapolation of the creep prefactor B _f from fatigue data. Impact modification decreased B _f but had no effect on C.     

On the thermal mechanism of microwave breakdown of high-temperature superconducting films

Theoretical arguments supporting the thermal nature of the microwave breakdown of high-temperature superconducting films are compared with experimental data. A comparison of the theoretical and experimental values of the threshold field for breakdown of a uniform film, B _f, and the threshold field for breakdown at nonsuperconducting defects, B _d, confirms the dependence corresponding to a thermal mechanism: B _f, B _d∝ (T _c-T ₀)^1/2. It is shown that the space-time picture of the observed breakdown is apparently due to overheating of the film near defects with a size of 10⁻⁵–10⁻⁶ m. The amplitude of the breakdown field may ultimately be limited by the abrupt decrease in the energy of critical disturbances for the initiation of breakdown. Pis’ma Zh. Tekh. Fiz. 24, 12–17 (June 12, 1998)     

Magnetic properties of RRh3B2(R=La,Ce, Nd,Gd) compounds

The¹¹Bnmr results on RRh₃B₂(R=La, Ce, Nd and Gd) are reported. For CeRh₃B₂, specific heat and electrical resistivity are reported. From a comparative study of the¹¹Bnmr Knight shifts and the spin lattice relaxation times of these compounds it is shown that in CeRh₃B₂, there is strong hybridization of 4f states with the conduction electrons. A local moment on Ce with admixture of 4f and 5d–6s orbitals is suggested.     

dc SQUID: Noise and optimization

A computer model is described for the dc SQUID in which the two Josephson junctions are nonhysteretic, resistively shunted tunnel junctions. In the absence of noise, current-voltage(I–V) characteristics are obtained as functions of the applied flux, _a , SQUID inductanceL, junction critical currentI ₀ , and shunt resistanceR. The effects of asymmetry inL, I ₀ , andR are discussed.I–V characteristics, flux-voltage transfer functions, and low-frequency spectral densities of the voltage noise are obtained at experimentally interesting values of the parameters in the presence of Johnson noise in the resistive shunts. The transfer functions and voltage spectral densities are used to calculate the flux and energy resolution of the SQUID operated as an open-loop, small-signal amplifier. The resolution of the SQUID with ac flux modulation is discussed. The flux resolution calculated for the SQUID of Clarke, Goubau, and Ketchen is1.6 × 10 ^–5 ₀ Hz^–1/2 , approximately one-half the experimental value. Optimization of the SQUID resolution is discussed: It is shown that the optimum operating condition is =2LI ₀ / ₀ 1. Finally, some speculations are made on the ultimate performance of the tunnel junction dc SQUID. When the dominant noise source is Johnson noise in the resistive shunts, the energy resolution per Hz is4k _B T(LC) ^1/2 , whereC is the junction capacitance, and the constraintR=( ₀ /2CI ₀ ) ^1/2 has been imposed. This result implies that the energy resolution is proportional to (junction area) ^1/2 . In the limiteI ₀ R k _B T, the dominant noise source is shot noise in the junctions; for =1, the energy resolution per Hz is then approximatelyh/2.Work supported by the U.S. ERDA.     

Orientational ordering in solid D2 from NMR studies. II. The cubic ordered phase

An NMR study in the cubic phase of D₂ which exhibits long-range orientational order is reported. The spin systems in both para D₂ (with angular momentum J=1 and spinI=1) and in ortho D₂ (with J=0 andI=2) were investigated. The integrated intensity ratio of theI=1 andI=2 components in the solid echo, the NMR line shapes obtained by Fourier transforming the solid echoes, and the longitudinal relaxation times for theI=1 andI=2 systems are presented. Samples with D₂ concentrationX between 0.69 and 0.62 were studied over the temperature range 0.12<T<4 K. Measurements were carried out before and after repeated thermal cycling through the ordering transition to study the effect of this cycling on the temperature dependence of the relaxation times. The complex behavior of these relaxation times was found to be similar to that in cubic H₂ at a comparable concentration, and the interpretation of this behavior is discussed. Over most of the temperature range, the relaxation time of theI=2 spins is larger than that of theI=1 spins and is believed to be determined by cross-relaxation with the latter, whose intrinsic spin-lattice relaxation is observed. However, at low enough temperatures, the relaxation time for theI=2 spins is found to be shorter than that for theI=1 spins, and this observation cannot be understood on the basis of predictions. Furthermore, theI=2 relaxation time in this temperature region is found to depend on the position within the NMR line. Another observation not yet understood is that the ratio of the integrated intensitiesS(I=1)/S(I=2) in the solid echo is smaller than the theoretically predicted one by about 20%. The NMR line shapes for theI=1 spins in the ordered phase obtained from pulse measurements are compared with those from continuous-wave methods and to those from H₂.     

dc SQUID: Current noise

The computer model used by Tesche and Clarke to calculate the voltage noise across the dc SQUID is extended to calculate the circulating current noise around the SQUID loop, and the correlation between the circulating current noise and the voltage noise across the SQUID. The parameters chosen are % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGycqGH9a% qpcaaIYaacbaGaa8htaiaa-LeadaWgaaWcbaacbiGaa4hmaaqabaGc% caGGVaacciGae0NPdy0aaSbaaSqaaiab9bcaGiab9bdaWaqabaGccq% GH9aqpcaaIXaGaaiilaiaabccacqqFtoWrcqqF9aqpcqqFYaGmcqaH% apaCcaWGRbWaaSbaaSqaaiaadkeaaeqaaOGaa8hvaiaa-9cacaWFjb% WaaSbaaSqaaiaa+bcacaGFWaaabeaakiab9z6agnaaBaaaleaacqqF% GaaicqqFWaamaeqaaOGaeyypa0JaaeiiaiaabcdacaqGUaGaaeimai% aabwdaaaa!51F9!\[\beta = 2LI_0 /\Phi _{ 0} = 1,{\rm{ }}\Gamma = 2\pi k_B T/I_{ 0} \Phi _{ 0} = {\rm{ 0}}{\rm{.05}}\], and an applied flux of ₀/4 (L is the SQUID inductance, I ₀ is the critical current per junction, T is the temperature, and ₀ is the flux quantum). At frequencies well below the Josephson frequency and at the optimum current bias, the voltage power spectral density is approximately 16 kBTR, the current power spectral density is approximately 11k_B T/R and the voltage-current correlation spectral density is approximately 12k _B T, where R is the resistance per junction.This work was supported by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy.Guggenheim Fellow.     

NMR on Systems of Low Spin Density Using DC Squids

We discuss the use of SQUID NMR for the study of systems of low spin density. The sample is located inside a coil which forms part of a series tuned resonant circuit attached to the input coil of a SQUID. Such a scheme was first discussed by Freeman et al. ¹ We have studied the pulsed NMR response at 1 MHz of a ³ He film adsorbed on the surface of closely packed Mylar sheets. In this case a monolayer corresponds to a spin density a factor of order 104 smaller than that of bulk liquid and a factor of order 10 ² smaller than with a Grafoil substrate. For our particular SQUID and input coil the calculated noise temperature is 60 mK, significantly better than that so far achieved with a cooled semiconductor preamplifier. We evaluate the present and potential performance of the spectrometer, some of the practicalities involved in its implementation, and discuss the minimum number of detectable spins.     

Surface structure and surface-spin induced magnetic properties and spin-glass transition in nanometer Co-granules of FCC crystal structure

Separated Co-granules, of an average diameter as small as D = 2.0 nm, of FCC crystal structure have been synthesized by co-reducing Co²⁺ cations dispersed in a liquid. They exhibit an enhancedsaturation magnetization _s by as much as 34% with a more than an order of enhanced magnitude for the effective anisotropy constant K _eff over the bulk values at 4.2 K. An irreversibility in the ZFC-FC (zero field cooled-field cooled) thermomagnetograms occurs at temperatures T T _B, where T _B is their blocking temperature. The ZFC thermomagnetogram peaks at T _B according to their K _eff and volume V. T _B = 152 K has been found for D = 10 nm granules in an applied magnetic field of H = 1 kA/m. The sample, which is superparamagnetic(coercivity H _c = 0) in nature at T T _B, develops H _c at T < T _B with a unique dependence on temperature, H _c(T) = H _c(0)[1 – T/T _B]^1/2, with H _c(0) = 40.0 kA/m. The results are discussed with a two-phase modelstructure of granules. In this model, the grain-surface atoms have amodified magnetic structure of the core atoms. An inter-couplingbetween the magnetic spins in the two regions occurs in aferromagnetic or antiferromagnetic manner according to theirinterface that mediates their exchange interactions through it. Thestudies of , K _eff, or H _c as a function of temperature (4.2 to 380 K) and/or size D (2 to 20 nm) demonstrate their strong correlation with the dynamics of the surface spins (DSS). An enhanced surfaceanisotropy with large total interface-energy in small granulesgoverns the DSS. An average value of the surface anisotropy constantK _s = 2.28 mJ/m² is determined by a linear plot of K _eff with D ^–1 at D 2.9 nm. Larger granules follow a modified K _eff – D ^–1 plot with an order of smaller K _s-value. The surface spins form a surface-spin-glass, which undergoes a magnetic transition to a spin-frozen state at a critical temperature T _F = 71 K. The T _F evolves following the well-known de Almeida-Thouless line, T _F H ^2/3, at H 42 kA/m.     

Collisionless spin waves in normal and superfluid3He

Standing spin-wave modes in liquid³He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF ₁ ^a =–0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time _D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A₁ and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.     

Study of surface relaxation mechanism of liquid3He in porous glass by using SQUID NMR

Nuclear spin relaxation of liquid³He in porous glass has been studied. In addition to measurements of the longitudinal spin relaxation timeT ₁ by a usual pulsed SQUID NMR, measurements of the transverse spin relaxation timeT ₂ have been performed by using a newly developed SQUID NMR method to observe a spin echo signal. Temperature and frequency dependences ofT ₁ andT ₂ have been measured. A simple model is proposed which explains the main features of the experimental results.     

Field-dependent spin-lattice relaxation of Cr3+ in Al2O3

The variation of spin-lattice relaxation time (T ₁) with magnetic field (B) for the Cr³⁺ ion in ruby has been measured under non-Kramers conditions for fields between 0.3 and 2.6 tesla, corresponding to microwave frequencies in the range 9 to 71 GHz. Below about 0.8 tesla there is a slow variation, approximately asT ₁, B ^–0.4; at higher fields the variation becomes more rapid, approachingT ₁, B ^–2.0 at 2.6 tesla. This behaviour is explained in terms of the non-linear divergence of the energy levels with field.     

Determination of the Parameters of High-T C RF SQUID from Its Small Signal Voltage-Frequency Characteristics

The present study is the extension of a recent theory of high-T_C RF SQUIDs, operating in the presence of large thermal fluctuations. First, the explicit analytical expressions for the amplitudes of higher harmonics of the current circulating in a SQUID loop which are necessary for the determination of the junction critical current I_C and the inductive coupling coefficient of the SQUID loop to its tank circuit, k² , are found. Second, in order to find the junction resistance R with acceptable accuracy, the solution of Fokker–Plank equation to first order in parameter q = L/R, where is a bias frequency, L is a loop inductance, is obtained. These results allow one to derive the simple expressions for the determination of the junction critical current I_C, its normal resistance R, and the inductive coupling coefficient of the SQUID loop to its tank circuit, k² , from the experimental measured small signal voltage-frequency characteristics.     

Ferromagnetism of 3He Films in Very Low Applied Fields

³ He films on graphite provide a model system for 2D magnetism. At low temperatures, the thermodynamic properties of these films are dominated by exchange interactions. However more subtle interactions such as dipolar coupling and other anisotropies may eventually play a substantial role, especially in small magnetic fields. Our recent experiments use a SQUID system for both pulsed and continuous wave NMR at very low applied fields (B<1mT). The spin polarization can be estimated from both the amplitude and frequency shift. We find that at coverages above 20 atoms/nm ² there is a field independent (zero field) magnetization at finite temperatures. The temperature where this magnetization develops is significantly below J/k where J is the effective exchange energy. Although the apparent ordering occurs over a broad temperature range, there is a trend towards a narrowing of the transition region down to the lowest applied fields. Contrary to recent estimates of exchange parameters which assume a single phase, we find that below 24 atoms/nm ² , only a fraction of the spins contribute to the ferromagnetic behavior. This is more consistent with a mixed phase system in that coverage region.     

Synthesis and characterization of Eu3+ activated hexagonal ABaGd(PO4)2 (A+=Li, Na, or K) phosphates

BaGd_0·5(PO₄)₂: Eu _0·5 ³⁺ and ABaGd_0·5(PO₄)₂: Eu _0·5 ³⁺ (where A⁺=Li, Na or K) double phosphates were synthesized by solid state diffusion method. These powders were characterized using X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. XRD results showed many distinct lines in the XRD spectra. SEM measurement showed grains of different sizes in double phosphates. The Eu³⁺-ion emission lines for⁵ D ₀→⁷ F _j (j=1, 2, 3, and 4) transitions showed a splitting into 3, 2, 1, and 2 components, respectively. Strength of these lines was enhanced by the addition of alkali ion to BaGd_0·5(PO₄)₂: Eu _0·5 ³⁺ double phosphate. However, as the alkali ion varied from Li⁺ to K⁺, the intensity of⁵ D ₀→⁷ F ₂ line (617 nm) in the red region increased at the cost of⁵ D ₀→⁷ F ₁ line (599 nm) in the orange region. Suitable explanation has been proposed for this phenomena.     

Bounds for traces in complete intersections and degrees in the Nullstellensatz

In this paper we obtain an effective Nullstellensatz using quantitative considerations of the classical duality theory in complete intersections. Letk be an infinite perfect field and let f₁,...,f n–rk[X₁,...,X_n] be a regular sequence with d:=max_j deg f_j. Denote byA the polynomial ringk [X₁,..., X_r] and byB the factor ring k[X₁,...,X_n]/(f₁,...,f_n r); assume that the canonical morphism AB is injective and integral and that the Jacobian determinant with respect to the variables X_r+1,...,X_n is not a zero divisor inB. Let finally B^*:=Hom_A(B, A) be the generator of B^* associated to the regular sequence.We show that for each polynomialf the inequality deg (¯f) dⁿ r(+1) holds (¯fdenotes the class off inB and is an upper bound for (n–r)d and degf). For the usual trace associated to the (free) extensionA B we obtain a somewhat more precise bound: deg Tr(¯f) dⁿ r degf. From these bounds and Bertini's theorem we deduce an elementary proof of the following effective Nullstellensatz: let f₁,..., f_s be polynomials in k[X₁,...,X_n] with degrees bounded by a constant d2; then 1 (f₁,..., f_s) if and only if there exist polynomials p₁,..., p_sk[X₁,..., X_n] with degrees bounded by 4n(d+ 1)ⁿ such that 1=_ip_if_i. in the particular cases when the characteristic of the base fieldk is zero ord=2 the sharper bound 4ndⁿ is obtained.Partially supported by UBACYT and CONICET (Argentina)     

Magnetic and Superconducting Properties of Doped and Undoped Double Perovskite Sr<Subscript>2</Subscript>YRuO<Subscript>6</Subscript>

We report here SQUID (magnetization) measurements, along with supporting specific heat, Raman, SEM (scanning electron microscope), EDX (energy dispersive X-ray) and XRD (X-ray diffraction) measurements, on Cu-doped and undoped double perovskite Sr₂²⁺Y³⁺Ru⁵⁺O₆^2-\mathrm{Sr}_{2}^{2+}\mathrm{Y}^{3+}\mathrm{Ru}^{5+}\mathrm{O}_{6}^{2-} (abbreviated as SrY2116) system grown as single crystal using high-temperature solution growth technique. These measurements show the undoped system to be a nonmetallic (insulating) spin glass (SG) and the ∼5–30% Cu-doped (i.e. Cu-concentration/(Cu + Ru-concentration) ∼5–30%) system to be a spin glass superconductor (SGSC) with T _c (critical temperature) ∼28–31 K and superconducting volume fraction, f _sc∼2.2–9%. To mention, similar measurements done on undoped and Cu-doped BaY2116 and BaPr2116 systems show for them the same (SG, SGSC) behaviors. However they show a decrease in T _c and f _sc when diamagnetic Y³⁺ ions are replaced by Pr³⁺ spins, presumably due to enhanced internal pair breaking, and also decreased Cu–O–Cu overlap, owing to Pr³⁺ presence; these phenomena are known to exist in the Pr123 compound, PrBa₂Cu₃O_7−δ (δ∼0), due to ∼10% of Pr³⁺ ions having tendency to occupy Ba²⁺ sites. Measurements done on undoped and Cu-doped SrHo2116 show similar SG and SGSC properties. Further, the undoped and Cu-doped SrY2116 crystals grown by hydrothermal growth technique (i.e., grown using lower temperature and high pressure) show same behaviors. From these investigations it can be said that the undoped Ru-double perovskites (A₂BB′O₆, B′=Ru) are SG systems and that Cu-doped Ru-double perovskites (A₂BB′O _δ , δ∼6, B′=Ru_1−x Cu _x , 0<x≲0.3) are SG superconductors (SGSCs). Results are discussed.