Nuclear magnetic susceptibility of solid3He with4He impurities

The nuclear magnetic susceptibility of bcc solid³He with a small concentration of⁴He is calculated in the high-temperature approximation. The exchange Hamiltonian used for the system is that obtained from a Hubbard-like cell model developed in earlier work. A brief discussion is also given of our general approach to the study of the magnetic properties of impure solid³He as compared to other approaches to the problem.     

Crystal structures and properties of BiMn1−xAlxO3 with x = 0.03 and 0.1

Crystal structures of BiMn_0.97Al_0.03O₃ (I) at 300 and 470 K and BiMn_0.9Al_0.1O₃ (II) at 90 and 300 K were studied with synchrotron X-ray powder diffraction. The strong Jahn-Teller distortion, observed at 300 K in I and associated with orbital order, disappeared at 470 K completely for one site and partially for the second site. The Mn/Al-O distances were very close to each other in I at 470 K and in II at 90 and 300 K indicating that orbital order did not appear in II even at 90 K. Magnetic properties of I and II were investigated with specific heat, high-temperature dc magnetic susceptibility, and ac magnetic susceptibility using different driving ac and applied dc magnetic fields and different ac magnetic field frequencies. The anomaly on the specific heat associated with a magnetic transition was strongly suppressed in II compared with that of I and BiMnO₃.     

Bulk nuclear polarization of solid3He

Measurements are given on the bulk nuclear spin polarization in a liquid-solid³He mixture cooled by compressional cooling to below 5 mK in a magnetic field of 54.5 kG. Owing to the low Pauli spin susceptibility of liquid³He, the observed polarization is primarily due to solid³He. A maximum average nuclear polarization of 47% was observed, although the corresponding solid³He polarization is believed to be higher. Our novel detection system, using a dual directional coupler for cw NMR, is a simple and versatile means of working in the awkward frequency range around 180 MHz. We also report transient heating measurements in the³He system which indicate that the internal thermal equilibrium time in bulk solid³He on the³He melting curve appears to be quite short (less than 5 min) at these temperatures. One type of transient measurement is complicated by the dramatic effect of the contribution of the³He nuclear magnetization to the total local magnetic field. This contribution is considered via a simple model.This work has been supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A. 143.     

Molar-Volume Dependence of the Pressure in hcp Solid 3He in Magnetic Fields

Pressure measurements have been made in a hcp solid ³ He at molar volumes from 18.90 to 19.45 cm ³ /mol, at temperatures down to 1 mK and in magnetic fields up to 0.16 Tesla. The results are analyzed by a high-temperature series expansion with multiple-exchange processes. The molar volume dependence of the multiple-exchange interactions has been determined by pressure measurements in magnetic fields. The results indicate that the exchange frequencies determined by the pressure measurements in a hcp solid ³ He are consistent with those obtained by magnetization measurements.     

Ferromagnetic anomalies in two dimensional3He adsorbed on graphite

The second layer of solid³He adsorbed on graphite exhibits a pronounced exchange anomaly which is peaked sharply at a surface density of 0.075Å^–2. The much weaker exchange anomaly in the submonolayer solid film, first detected in heat capacity studies, has been investigated by measurements of the nuclear magnetic susceptibility to temperatures below 1mK and found to be ferromagnetic. We report the dependence of the effective exchange constant on surface density and propose a model in which both anomalies arise from similar two dimensional commensurate structures.     

Intermediate valence behavior of ternary cerium and uranium transition metal borides

Low-temperature specific heat, electrical resistivity, ac magnetic susceptibility, and dc magnetization measurements were made on ternary cerium and uranium transition metal borides with the general formula CeT₃B₂ (T=Co, Ru, Rh, and Ir) and UT₃B₂ (T=Co, Ru, and Ir). The compound CeRu₃B₂ was found to exhibit superconductivity below 0.68 K. The values of the electronic specific heat coefficient range from 9.7 mJ/mole-K² for CeCo₃B₂ to 64 mJ/mole-K² for UIr₃B₂. The electrical resistivity versus temperature curves of all of the compounds exhibit negative curvature and are reminiscent of valence fluctuation behavior. In the case of CeIr₃B₂, the electrical resistivity attains a maximum value at 180 K, while the dc magnetic susceptibility has a temperature dependence that is typical of intermediate valence Ce compounds, approaching a finite value at zero temperature. The electrical resistivity of the ferromagnetic compound CeRh₃B₂ reveals a rapid decrease in spin disorder resistivity below 120 K. The dc magnetic susceptibility of this material can be described as the sum of a constant term and a Curie-Weiss contribution with an effective magnetic moment of 1.01 µ_B per formula unit and a Curie-Weiss temperature of 119 K. Magnetization measurements on CeRh₃B₂ yield a saturation magnetic moment of 0.37 µ_B per formula unit and a Curie temperature of 113 K.     

Triple exchange in solid3He

In a recent paper we have used triple exchange, the cyclic permutation of three atoms, to explain the anomalous behavior of the magnetic pressure of solid³He in the presence of high magnetic fields. The results of susceptibility, pressure, melting curve, and nuclear relaxation experiments are reexamined using a spin Hamiltonian which includes triple exchange. This systematic examination points out which experiments are best suited for testing the importance of triple exchange in solid³He.Work supported by National Science Foundation Grant No. GP-22553.     

Solid helium. I. Ground-state energy and compressibility

The ground-state energy and the compressibility of solid helium is calculated by means of a modified Brueckner theory. The Bethe-Goldstone equation is solved to give the reaction matrix or the effective interaction in coordinate space, and the ground-state energy for the two helium isotopes³He and⁴He is calculated. Also, the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. Both bcc and hcp structures are considered. The calculations are done for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. Theoretical results for the ground-state energy per particle are 0.2 to 2.6 K for solid³He at a molar volume of 24 cm³/mole, and –2.4 to –5.9 K for solid⁴He at a molar volume of 20 cm³/mole. The corresponding experimental results are –1.0 and –5.6 K, respectively. Theoretical results for the compressibility are 0.0031–0.0042 atm^–1 for solid³He at a molar volume of 22 cm³/mole, and 0.0014–0.0022 atm^–1 for solid⁴He at a molar volume of 18 cm³/mole. The corresponding experimental results are 0.0032 and 0.0014 atm^–1, respectively. The agreement with experimental results is reasonably good since higher order cluster terms are not included in this first approximation.     

Neutron experiments on solid3He in high field at very low temperature

The magnetic transition from the paramagnetic phase to the magnetically ordered high-field phase of solid³He is observed by polarized neutron transmission experiments. The transition shows the feasibility of neutron diffraction experiments on the high-field ground state of solid³He. The behavior of the boundary resistance between solid³He and silver powder in a magnetic field is discussed.     

Mean field calculation of magnetization,entropy, and the melting pressures of solid3He in high magnetic fields

Entropy and magnetization curves for solid³He as obtained from multiple exchange mean field calculations are presented as a function of temperature and magnetic field, and compared with experiments. Melting curves in high magnetic fields and end temperatures after adiabatic decompression of magnetic solid³He are also derived.     

NMR study of the solidification and melting of3He in porous glasses

TheP-T phase diagrams of the liquid-solid phase transition of³He in three porous glasses with different pore sizes have been determined from spin-lattice relaxation measurements in the temperature range 0.5–4.2 K. The onset of solidification of³He in the pores occurs at excess pressure over the bulk phase transition. The excess pressure depends on the pore size. A model of the phase transition in small pores which takes into account the contribution of the surface energy to the free energy is described and compared with experimental results. TheT ₁ relaxation mechanism of³He in the pores is found to be due to the surface relaxation when³He is in the liquid phase and due to the relaxation of bulk solid³He when it is in the solid phase.     

Apparent new phase of monolayer3He and4He films adsorbed on Grafoil as determined from heat capacity measurements

Heat capacity measurements in monolayer³He and⁴He films adsorbed on Grafoil at densities higher than the one corresponding to the substrate lattice registered phase show a series of sharp, narrow peaks at 1 K for densities between 0.072 and 0.077Å ^–2. The exact nature of the transition cannot be determined from this measurement alone, but several possibilities are discussed. It has been determined that the melting line of two-dimensional solid films starts atn=0.078Å ^–2 for both isotopes. Extensive heat capacity measurements at and above this density are presented for³He, and some new measurements for⁴He are shown to complement measurements reported elsewhere. The solid³He measurements are compared to predictions of recent models for melting in two dimensions.Work supported by National Science Foundation Grant # DMR72-03003A04.     

Nuclear magnetic susceptibility of3He adsorbed on graphite below 4.2 K

The nuclear magnetic susceptibility of³He films adsorbed on graphite substrates was measured by means of pulsed NMR techniques at 10 and 20 MHz. Submonolayer, monolayer, and multilayer coverages were examined, as well as one monolayer of³He mixed with various amounts of⁴He. The temperature range of measurements extended from 0.35 to 4.2 K. For pure³He and for³He mixed with⁴He the nuclear magnetic susceptibility displays departures from Curie's law. The observed behavior in pure³He layers can be fitted to an ideal-Fermi-gas curve with an effective degeneracy temperature of 0.15 K. The nuclear magnetic susceptibility of³He–⁴He films is also found to fall below the values predicted by Curie's law as the temperature is lowered, but the results suggest that in this case the film is not uniform, possibly as a result of a phase separation in the film at low temperatures.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

Ultra-Low Temperature Susceptibility of a Highly Frustrated Two-Dimensional Solid 3He Magnet

We report the first measurement of the ultra-low temperature (200 ,K) susceptibility of a two-dimensional antiferromagnetic solid ³ He system, the 4/7 commensurate phase of ³ He/ ⁴ He/graphite. In the high temperature range the data has been analyzed using the series expansions of the Multiple-Spin-Exchange model. At ultra-low temperatures the susceptibility displays a very unusual temperature dependence, characteristic of a highly frustrated two-dimensional system.     

Order of the PP-HFP transition in solid3He

New measurements of the melting pressure of solid³He P_m(T,B) have been made through the paramagnetic phase-to-high field phase transition. Temperatures were determined with Pt NMR and the³He melting pressure in zero field measured in a second cell. In a field of 0.405 T, we find a change in entropy through the HFP-PP transition of S/Rln2=0.13 over a temperature interval of only about 4 µK. Thus, we conclude that the transition is first-order at low fields. The entropy discontinuity decreases with field and the transition region broadens, with the transition possibly becoming second-order above a tricritical point near 0.6 T.     

A four-sublattice model for solid3He

Nuclear magnetic resonance measurements on the antiferromagnetic ordered phase of solid³He have indicated that the magnetic structure consists of ferromagnetically ordered parallel planes of atoms. The magnetization vectors lie in the planes and are aligned in a sequence with two or more in a row pointing in the same direction followed by the same number pointing in the opposite direction. In the simplest case, with only two in a row pointing in the same direction, the system can be described in terms of sublattices if four are used. In this work the appropriate four-sublattice model is solved for the uniform free normal modes and for the excitation of the modes by density oscillations.     

A model for the solid3He magnet?

The magnetic phase transition in solid³He is described as a first-order transition induced by a spin-lattice coupling. The magnetic ground state has both a spin density wave and a lattice distortion.Supported in part by the National Science Foundation.     

NMR Study of Solid 3He Droplets In Phase-Separated 3He-4He Mixtures

We report measurements on solid ³ He droplets embedded in a solid ⁴ He matrix. A feature of our experiments is that the mixture crystals, of 1% ³ He concentration, are grown under constant pressure conditions to minimise the formation of defects. Upon cooling the mixture isotopic phase separation is clearly observed in both pressure and NMR data. At a pressure of 36 bar the ³ He separates as solid droplets. NMR measurements on these droplets indicate values of T ₁ and T ₂ similar to those in bulk solid ³ He at the same pressure in the temperature-independent régime. Measurements of the bounded diffusion in the droplets indicate a spin diffusion coefficient similar to that in bulk solid ³ He at the same pressure. These measurements also show the size of the droplets to be a few microns.     

Susceptibility and magnetization studies of Gd3+ substituted Mg-Cd ferrites

Studies on lattice parameters, magnetization and ac susceptibility measurements for the ferrite system Cd _x Mg_1−x Gd _y Fe_2−y O₄ (withx = 0·2, 0·3, 0·4 andy = 0·1, 0·2, 0·3, 0·4) are presented. The ac susceptibility was measured from room temperature to 800K at a constant magnetic field of 7 oersted.X _ac vsT variations show that all the samples contain predominantly multidomain (MD) particles. Magnetization measurements of the system indicate that as the Cd²⁺ content increases magnetization increases while the addition of Gd³⁺ reduces the magnetization. The observations further indicate the existence of Y-K type of magnetic ordering in the system.     

Model formalism of paramagnetic solid helium-3

The statistical-thermodynamic formalism of a collection of localized spin-1/2 atoms whose spin Hamiltonian refers to the isotropic antiferromagnetic Heisenberg exchange-interaction scheme is applied here to account for a set of important equilibrium-thermodynamic measurements on paramagnetic solid³He performed some time ago by University of Florida investigators. The measured properties were the temperature-dependent modulations of the pressure, which were proved earlier to arise overwhelmingly from the nuclear spin system. The present formalism of the pressure modulations or of the spin pressures, along specified isochores of the solid, includes the density- or molar-volume-dependent microscopic exchange energy parameter and its derivative. In this paper we have derived directly hitherto unavailable exact values of these parameters from spin pressure data on magnetized solid³He, as well as indirectly through the intermediary of spin pressures in the absence of a magnetic field. The directly derived exact parameters result from a single characteristic equilibrium-thermodynamic state of the solid in the presence of a constant and uniform magnetic field of adequate strength. The indirectly derived but exact parameters, of possibly somewhat lower accuracy, require the knowledge of a single directly derived exchange-energy parameter together with a set of spin pressures of asymptotic high-temperature equilibrium states in the absence of a magnetic field. The indirectly derived microscopic parameters along two of the three experimentally explored magnetized solid isochores yielded calculated spin pressures in fair and acceptable agreement, respectively, with their measured values. The directly derived exact parameters used in calculating the spin pressures along the third experimentally investigated isochore, in the absence of a magnetic field and at three different field strengths, led to complete agreement with the data. These results lend support to the tentative proposition advanced in early work that over a range of temperatures and molar volumes of paramagnetic solid³He, the statistical-thermodynamic formalism based on the antiferromagnetic exchange-interaction scheme may give an acceptable account of the spin pressures as well as of other thermal properties of this quantum solid.