Nuclear Heat Capacity Research Articles

Enhanced capability of model fitting to nuclear level density and heat capacity: testing on 93−98Mo nuclei

We propose an improved fitting approach that improves reliability in studying the nuclear level density (NLD) and thermodynamic quantities. The proposed method, which relies on the fact that experimental fluctuations or outliers, if they exist, should not be involved in the fitting process, is validated with a set of data artificially generated with anomalous data points being intentionally inserted. In order to showcase the advantages of the proposed technique, we have applied it to re-investigate the back-shifted Fermi gas (BSFG) level density parameters and thermodynamic quantities, particularly the heat capacities, of 93−98Mo isotopes. We have found that the range of values for the level density parameter of 93Mo (approximately from 8.5 to 9.0 MeV−1) is notably smaller than that obtained for the other isotopes of Mo (approximately from 10.5 to 11.5 MeV−1). This observation is different from previous predictions, in which the values of level density parameter of all Mo isotopes are in the same range. This is because among the Mo isotopes under examination, 93Mo (N = 51 neutrons) has the smallest number of valence neutrons, namely only a single neutron away from the closed N = 50 shell. In addition, thanks to the proposed method, we have discussed the effects of data fluctuations on the BSFG NLDs and thermodynamic quantities of 93−98Mo isotopes, from which our recommendation for future works is announced. On top of that, we should notice that the proposed approach can be further applied to any work involving the fitting of a phenomenological model to empirical data.

Homogeneous reduced moment in a gapful scalar chiral kagome antiferromagnet.

We present a quantitative experimental investigation of the scalar chiral magnetic order with in Nd3Sb3Mg2O14. Static magnetization reveals a net ferromagnetic ground state, and inelastic neutron scattering from the hyperfine coupled nuclear spin reveals a local ordered moment of 1.76(6) , just 61(2)% of the saturated moment size. The experiments exclude static disorder as the source of the reduced moment. A 38(1) gap in the magnetic excitation spectrum inferred from heat capacity rules out thermal fluctuations and suggests a multipolar explanation for the moment reduction. We compare Nd3Sb3Mg2O14 to Nd pyrochlores and show that Nd2Zr2O7 is in a spin fragmented state using nuclear Schottky heat capacity.

Effects of glassing matrix deuteration on the relaxation properties of hyperpolarized 13C spins and free radical electrons at cryogenic temperatures.

Glassing matrix deuteration could be a beneficial sample preparation method for 13C dynamic nuclear polarization (DNP) when large electron paramagnetic resonance (EPR) width free radicals are used. However, it could yield the opposite DNP effect when samples are doped with small EPR width free radicals. Herein, we have investigated the influence of solvent deuteration on the 13C nuclear and electron relaxation that go along with the effects on 13C DNP intensities at 3.35 T and 1.2 K. For 13C DNP samples doped with trityl OX063, the 13C DNP signals decreased significantly when the protons are replaced by deuterons in glycerol:water or DMSO:water solvents. Meanwhile, the corresponding solid-state 13C T1 relaxation times of trityl OX063-doped samples generally increased upon solvent deuteration. On the other hand, 13C DNP signals improved by a factor of ∼1.5 to 2 upon solvent deuteration of samples doped with 4-oxo-TEMPO. Despite this 13C DNP increase, there were no significant differences recorded in 13C T1 values of TEMPO-doped samples with nondeuterated or fully deuterated glassing matrices. While solvent deuteration appears to have a negligible effect on the electron T1 relaxation of both free radicals, the electron T2 relaxation times of these two free radicals generally increased upon solvent deuteration. These overall results suggest that while the solid-phase 13C DNP signals are dependent upon the changes in total nuclear Zeeman heat capacity, the 13C relaxation effects are related to 2H/1H nuclear spin diffusion-assisted 13C polarization leakage in addition to the dominant paramagnetic relaxation contribution of free radical centers.

Anisotropic magnetic properties and giant magnetocaloric effect of single-crystal PrSi

A single crystal of PrSi was grown by the Czochralski method in a tetra-arc furnace. Powder x-ray diffraction of the as-grown crystal revealed that PrSi crystallizes in an FeB-type structure with space group Pnma (No. 62). The anisotropic magnetic properties were investigated by means of magnetic susceptibility, isothermal magnetization, electrical transport, and heat capacity measurements. Magnetic susceptibility data clearly indicate the ferromagnetic transition in PrSi with a ${T}_{C}$ of 52 K. The relative easy axis of magnetization was found to be the [010] direction. Heat capacity data confirm the bulk nature of the transition at 52 K and exhibit a huge anomaly at the transition. A sharp rise in the low-temperature heat capacity has been observed (below 5 K) which is attributed to the ${}^{141}$Pr nuclear Schottky heat capacity arising from the hyperfine field of the Pr moment. The estimated Pr magnetic moment 2.88 ${\ensuremath{\mu}}_{\mathrm{B}}$/Pr from the hyperfine splitting is in agreement with the saturation magnetization value obtained from the magnetization data measured at 2 K. From the crystal electric field analysis of the magnetic susceptibility, magnetization, and heat capacity data it is found that the degenerate $J=4$ Hund's rule derived state of the Pr${}^{3+}$ ion splits into nine singlets with an overall splitting of 284 K, the first excited singlet state separated by just 9 K from the ground state. The magnetic ordering in PrGe appears to be due to the exchange-generated admixture of low-lying crystal field levels. The magnetocaloric effect (MCE) has been investigated from magnetization data along all three principal crystallographic directions. The large magnetic entropy change, $\ensuremath{-}\ensuremath{\Delta}{S}_{M}=$22.2 J/kg K, and the relative cooling power, RCP = 460 J/kg, characteristic of the giant magnetocaloric effect are achieved near the transition temperature (${T}_{C}$ = 52 K) for $H=$ 70 kOe along $[010]$. Furthermore, the PrSi single crystal exhibits a giant MCE anisotropy.

Note: Relaxation heat capacity measurements at low temperatures: Dealing with nuclear contribution

Nuclear heat capacity is a serious obstacle in low temperature heat capacity measurements by a relaxation technique. However, this method allows an experimenter to measure the electronic heat capacity directly, if the ratio of electronic heat capacity to the conductance of the calorimeter is sufficiently small in comparison with nuclear-spin relaxation times. This is because the initial rate of a temperature decay is always determined by the electronic degrees of freedom and does not depend on nuclear degrees of freedom. This previously unrecognized feature is clearly demonstrated through measurements of Cu in external magnetic fields.

Magnetic Phase Transition in a Nanonetwork of SolidHe3in Aerogel

When immersed in liquid 3He, the nanometer strands of aerogel are coated with a thin layer of solid 3He, forming a network of irregular nanotubes. Owing to its high purity and weak interactions, this system is ideal for studying fundamental processes. We report the first experiments on solid 3He in aerogel at ultralow temperatures, cooled by direct adiabatic demagnetization. Simultaneous nuclear magnetic susceptibility and heat capacity measurements indicate a magnetic phase transition.

31P Nuclear Spin Dynamics in Metallic Si:P at Very Low Temperature and High Magnetic Fields

Phosphorus-doped silicon (Si:P) is one of the most extensively studied condensed matter systems since a variety of physical phenomena accompanies with doping P in Si, such as impurity-band conduction, metal–insulator transition (M–I). Recently, it has attracted new interest for possible applications to quantum computer where P nuclear spins serve qubits and electron spins are completely polarized for isolated spins bound at the donor. This model of silconbased quantum computer requires NMR control of P nuclear spins under extreme conditions of several tesla magnetic field and millikelvin temperature. Spin dynamics of both nuclei and electrons are of great interest in this regard. However, despite a large amount of works devoted to the magnetic properties of Si:P, P-NMR has never been investigated under such experimental conditions. Here we present the P-NMR of metallic Si:P investigated at temperature between 40mK and 4K and a magnetic field of 7 T. We tried P-NMR in insulator Si:P but could not detect it. Our NMR data show several novel features in longitudinal relaxation time T1 and transverse relaxation time T2 associated with very low temperature and high magnetic field. We prepared a powdered sample from single crystalline silicon wafers with phosphorus dopant concentration of n 1⁄4 5:6 10 cm 3 which is above the critical concentration for M–I, nc ’ 3:7 10 cm . The dopant concentration of Si:P was determined by measuring room temperature resistivity with the Mousty scale. The sample was immersed in He–He mixture which was cooled by a dilution fridge. The NMR spectra at 120MHz were obtained by recording the spin-echo height with varying magnetic fields. The T2 was measured by decay of the echo height with varying time delay of the pulse sequence =2 . The T1 was obtained from the magnetization recovery after -pulse with varying waiting time t of the sequence t =2 . The NMR spectra were typical for metallic sample and did not depend on temperature. The linewidth of about 24mT and the Knight shift agree with those reported in the literature for similar dopant concentrations. The linewidth is believed to be determined by inhomogeneous broadening of hyperfine interactions. The longitudinal relaxation showed a substantial change only below 0.6K from the previous data. Nuclear magnetization was recovered in two steps, following double-exponential curves below 0.6K while the recovery followed single-exponential curves above 0.6K. Typical recovery curves are shown in the inset of Fig. 1. Below 0.6K, we obtained T1 separately for the fast and slow components of the relaxation, T1f and T1s. The T1f and T1s are plotted against temperatures in Fig. 1. T1f above 0.2K follows the Korringa’s relation as, T1T 1⁄4 ( is Korringa constant). It shows, however, a gradual deviation from the Korringa’s relation below 0.2K. The long T1s increases with decreasing temperature as T1s / T n with n ’ 1:3. A double-exponential form of recovery curve was observed only when the nuclear Zeeman bath decays through the electron bath to a third bath in series and the heat capacity of Zeeman bath, CN, becomes comparable to that of the electron bath, Ce. The second stage for the slow recovery process appeared in the magnetization recovery at T 1⁄4 0:6K when CN=Ce ’ 0:01 and [1 MðtÞ=M0] was measured in the range between 2 and 0.01. We understand that both the deviation of T1f from the Korringa’s relation and the appearance of long T1s arise from the large nuclear Zeeman heat capacity at high B=T . Because CN goes with ðB=TÞ while Ce with T , the temperature of electrons actually rises during nuclear spin relaxation when the electron system is decoupled to the third bath (He–He mixture bath) by T1s since T1f T1s. Due to heating up the electron temperature Te the nuclear spins relax at faster rate =Te than that expected from =T where Te > T . The T1s was first observed and was the time constant for the Zeeman and conduction electron baths to decay together to the He–He bath. The T1s is needed to cool down the nuclear spins at low temperatures and may be due to the Kapitza resistance between the sample and He–He mixture. Fig. 1. Longitudinal relaxation times T1f (circle) and T1s (square) with temperature. The inset shows the recovery curves. Dotted line represents the Korringa’s relation derived from the data above 1K. Solid line is a guide to the eye.

31P NMRstudy of Na2CuP2O7: an S = 1/2 two dimensional Heisenberg antiferromagnetic system

The magnetic properties of Na2CuP2O7 were investigated by means of 31P nuclear magnetic resonance (NMR), magnetic susceptibility, and heat capacity measurements. We reportthe 31P NMR shift, the spin–lattice , and spin–spin (1/T2) relaxation rate data as a function of temperatureT. The temperature dependence of the NMR shiftK(T) is welldescribed by the S = 1/2 square lattice Heisenberg antiferromagnetic model with an intraplanar exchange of K and a hyperfine coupling A = 3533 ± 185 Oe /μB. The 31P NMR spectrum was found to broaden abruptly belowT∼10 K,signifying some kind of transition. However, no anomaly was noticed in the bulk susceptibility data downto 1.8 K. The heat capacity appears to have a weak maximum around10 K. With decrease in temperature, the spin–lattice relaxation rate1/T1 decreases monotonically and appears to agree well with the high temperature series expansion expressionfor a S = 1/2 2D square lattice.

Observation of the Fermi Fluid in3He-4He Mixture Films Formed in One-Dimensional 28 Å Pores

A 3He film formed in quite narrow pores is one of the possible model systems for a one-dimensional Fermi fluid. Here we report our new heat capacity resugts of 3He and 4He film adsorbed in a straight pore 28 A in diameter down to 5 mK. The coverage and temperature dependence of the heat capacity indicates that a fluid phase appears between the second layer promotion and the complete filling of the pores. Since the heat capacity of 3He adsorbed on the bare substrate shows a large upturn due to the nuclear heat capacity of the localized 3He, it is difficugt to observe the true heat capacity of the fluid phase. By replacing the localized 3He, we can successfully suppress the upturn and observe the true heat capacity of the fluid phase.

Level densities andγ-strength functions in148,149Sm

The level densities and $\gamma$-strength functions of the weakly deformed $^{148}$Sm and $^{149}$Sm nuclei have been extracted. The temperature versus excitation energy curve, derived within the framework of the micro canonical ensemble, shows structures, which we associate with the break up of Cooper pairs. The nuclear heat capacity is deduced within the framework of both the micro canonical and the canonical ensemble. We observe negative heat capacity in the micro canonical ensemble whereas the canonical heat capacity exhibits an S-shape as function of temperature, both signals of a phase transition. The structures in the $\gamma$-strength functions are discussed in terms of the pygmy resonance and the scissors mode built on exited states. The samarium results are compared with data for the well deformed $^{161,162}$Dy, $^{166,167}$Er and $^{171,172}$Yb isotopes and with data from (n,$\gamma$)-experiments and giant dipole resonance studies.

Vapor Pressure and Heat Capacity Measurement of 3He Adsorbed on 18Å-Pores

We have measured the vapor pressure (0.84 K<T<9 K) and the heat capacity (80 mK<T<4 K) of 3He adsorbed on pores 18 A in diameter. The results of the vapor pressure measurement indicate that 3He film grows up to the second layer. In the first layer, the heat capacity of 3He shows the same temperature and coverage dependence as 4He, indicating a solid phase. Above a little higher coverage than second layer promotion, heat capacity isotherms for 3He at several hundred mK increase with coverage while those for 4He decrease. This large heat capacity of 3He is the nuclear spin heat capacity of the second layer fluid 3He.

Heavy fermions inLiV2O4: Kondo compensation versus geometric frustration

7Li nuclear magnetic resonance and heat capacity measurementswere performed on the metallic spinel LiV2O4 down to 30 mK.The temperature dependencies of the linewidth, the Knight shift andthe spin-lattice relaxation rate were investigated in thetemperature range 30 mK⩽T⩽280 K and at appliedmagnetic fields of 4.6, 10, 44 and 83 kOe. The longitudinal nuclearmagnetization was found to relax following a stretched-exponentialform with a stretching exponent in the range 0.5<β<1. Fortemperatures T<1 K and at the lowest applied magnetic field of4.6 kOe, we observe a spin-lattice relaxation rate which slows downexponentially, exhibiting a hindering barrier of the order of 1 K.This excitation energy separates different configurations of ahighly degenerate ground state of a completely frustrated magnet.

Critical temperature for quenching of pair correlations

The level density at low spin in the 161,162-Dy and 171,172-Yb nuclei has been extracted from primary gamma rays. The nuclear heat capacity is deduced within the framework of the canonical ensemble. The heat capacity exhibits an S-formed shape as a function of temperature, which is interpreted as a fingerprint of the phase transition from a strongly correlated to an uncorrelated phase. The critical temperature for the quenching of pair correlations is found at Tc=0.50(4) MeV.

The impact of nuclear magnetism on superconductivity in a metal with nuclear electric quadrupole splitting: Indium

We report the first investigation of the impact of nuclear magnetism on superconductivity in the tetragonal metal indium. We have measured the superconducting critical field B c (T) and in its vicinity the nuclear magnetic heat capacity at ultralow temperatures, 170 μK ≤ T < 200 mK. We compare the measured quantities with calculations which consider the nuclear magnetic Zeeman and the dominating nuclear electric quadrupole interaction in indium. The heat capacity data support the occurence of a positive sign of the electrical field gradient at nuclear sites and in consequence the existence of a nuclear low spin ground state. Surprisingly, at lowest investigated temperatures, 170 μK < T < 1 mK, the reduction of the critical field ΔB c (T) clearly exceeds the size of the calculated magnetization μ 0 M(B c , T) which is limited by the nuclear low spin ground state. In all other materials the interplay of nuclear magnetism and superconductivity has been studied so far (Al, AuAl 2 , AuIn 2 , Rh, and Sn), the bare nuclear magnetization appeared as an upper limit of the reduction of the critical field.

Heat capacity of a 2DEG

We review recent heat capacity experiments performed on GaAs/AlGaAs heterostructures containing two-dimensional electron layers. Near ν=1, the strong coupling to the nuclear spin system attributed to Skyrmion-induced low-energy spin excitations has a dramatic effect on the heat capacity which rises by orders of magnitude. We show that this giant heat capacity is consistent with the Schottky nuclear heat capacity of Ga and As atoms in the quantum wells, except at very low temperature where heat capacity exhibits a remarkably sharp peak suggestive of a phase transition in the electronic system. We also report quasi-adiabatic experiments providing quantitative evidence that the sharp peak in heat capacity is due to an enhanced nuclear-spin diffusion from the GaAs quantum wells into the AlGaAs barriers. Finally, we present the latest heat capacity results which probe the presence or the absence of Skyrmions at large Zeeman energy.

Heat capacity and nuclear-spin dynamics in GaAs/AlGaAs heterostructures around ν=1

We report low-temperature ( T) heat capacity ( C) data on a multiple-quantum-well GaAs/AlGaAs sample in the quantum Hall regime. Relative to its low field magnitude, C exhibits up to ≈10 5-fold enhancement near Landau level filling ν=1. We attribute this striking behavior to a Skyrmion-induced enhancement of the coupling between the nuclear spin system and the lattice. The data are consistent with the Schottky nuclear heat capacity of Ga and As atoms in the quantum wells, except at very low T where C versus T exhibits a remarkably sharp peak suggestive of a phase transition in the electronic system. Quasi-adiabatic experiments provide quantitative evidence that the sharp peak in C versus T is due to an enhanced nuclear-spin diffusion from the GaAs quantum wells into the AlGaAs barriers.

The Interplay of Electronic and Nuclear Magnetism in PtFex at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFexsamples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mT≤B≤248 mT. The susceptibility data have been measured at temperatures of 0.3 μK≤T≤100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 μK. The nuclear heat capacity data taken at 1.4 μK≤T≤10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 μK. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 μK≤T≤0.5 mK and 2.5 mT≤B≤22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 μK≤T≤0.5 mK and at 5.4 mT≤B≤200 mT. Spin-lattice and effective spin-spin relaxation times τ1and τ2* of 195Pt strongly depend on x and on the external magnetic field. No temperature dependence of τ1and τ2*could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 μK.

Influence of magnetic impurities on the heat capacity of nuclear spins

It is found that in a wide range of temperatures and magnetic fields even a small concentration of magnetic impurities in a sample leads to a $T^{-1}$ temperature dependence of the nuclear heat capacity. This effect is related to a nuclear-spin polarization by the magnetic impurities. The parameter that controls the theory turns out not to be the impurity concentration $C_{imp}$ but instead the quantity $c_{imp} \mu_e / \mu_n$, where $\mu_e$ and $\mu_n$ are the magnetic moments of an electron and a nucleus, respectively. The ratio of $\mu_e$ and $\mu_n$ is of order of $10^3$.

Nuclear specific heat of copper potassium tutton salt

The specific heat of copper potassium tutton salt has been measured down to 1 mK in order to investigate the hyperfine interaction of this copper compound. The magnetic ordering of the electronic system occurs at 29.5 mK in zero field. Below the transition temperature the electronic heat capacity decreases and the copper nuclear heat capacity of hyperfine splitting becomes dominant in the heat capacity of the compound. The nuclear heat capacity has a broad peak around 3.5 mK. The entropy of copper nuclear spin, which was calculated from the specific heat data, remains at 40% of ln(2I+1) at 1 mK.

Giant heat capacity and nuclear-spin diffusion in GaAs/AlGaAs heterostructures near ν=1

We report low temperature ( T ) heat capacity ( C ) data on a multiple-quantum-well GaAs/AlGaAs sample in the quantum-Hall regime. Relative to its low field magnitude, C exhibits up to ≈10 5 -fold enhancement near Landau level filling v =1 where skyrmions are the expected ground state of the confined two-dimensional electrons. We attribute this striking behavior to a skyrmion-induced enhancement of the coupling between the nuclear spin system and the lattice. The data are consistent with the Schottky nuclear heat capacity of Ga and As atoms in the quantum wells , except at very low T where C vs. T exhibits a remarkably sharp peak suggestive of a phase transition in the electronic system . Our quasi-adiabatic experiments provide quantitative evidence that the sharp peak in C vs. T is due to an enhanced nuclear-spin diffusion from the GaAs quantum wells into the AlGaAs barriers. We discuss the physical origin of this enhancement in terms of the possible Skyrme solid–liquid phase transition.