Low-temperature Susceptibility Research Articles

Two-Dimensional Cobalt(II) Benzoquinone Frameworks for Putative Kitaev Quantum Spin Liquid Candidates.

The realization and discovery of quantum spin liquid (QSL) candidate materials are crucial for exploring exotic quantum phenomena and applications associated with QSLs. Most existing metal-organic two-dimensional (2D) quantum spin liquid candidates have structures with spins arranged on the triangular or kagome lattices, whereas honeycomb-structured metal-organic compounds with QSL characteristics are rare. Here, we report the use of 2,5-dihydroxy-1,4-benzoquinone (X2dhbq, X = Cl, Br, H) as the linkers to construct cobalt(II) honeycomb lattices (NEt4)2[Co2(X2dhbq)3] as promising Kitaev-type QSL candidate materials. The high-spin d7 Co2+ has pseudospin-1/2 ground-state doublets, and benzoquinone-based linkers not only provide two separate superexchange pathways that create bond-dependent frustrated interactions but also allow for chemical tunability to mediate magnetic coupling. Our magnetization data show antiferromagnetic interactions between neighboring metal centers with Weiss constants from -5.1 to -8.5 K depending on the X functional group in X2dhbq linkers (X = Cl, Br, H). No magnetic transition or spin freezing could be observed down to 2 K. Low-temperature susceptibility (down to 0.3 K) and specific heat (down to 0.055 K) of (NEt4)2[Co2(H2dhbq)3] were further analyzed. Heat capacity measurements confirmed no long-range order down to 0.055 K, evidenced by the broad peak instead of the λ-like anomaly. Our results indicate that these 2D cobalt benzoquinone frameworks are promising Kitaev QSL candidates with chemical tunability through ligands that can vary the magnetic coupling and frustration.

Rheological evaluation of paving asphalt binder containing bio-oil from rice straw pyrolysis

The conversion of rice straw to bio-oil for substituting asphalt paving materials not only contributes to sustainable development in construction industry, but is also beneficial for resource recovery in agriculture. In this study, rice straw was pyrolyzed to produce bio-oil by using fluidized bed, and the influences of key pyrolysis conditions on product distribution were investigated. Bio-asphalt was prepared by high-speed mixing of pyrolysis bio-oil and petroleum asphalt, and comprehensively evaluated through rheological tests and continuous grading of performance grade (PG). Moreover, microscopic characterization was conducted to further explore the mechanism of bio-oil modification of asphalt. The test results indicate that the yield of bio-oil first rises and then drops with the increase of pyrolysis temperature. As the gas flow rate increases and the biomass particle size decreases, the bio-oil yield shows an increasing trend. The bio-asphalt containing bio-oil from lower pyrolysis temperatures has stronger rutting resistance and lower temperature susceptibility. As the pyrolysis temperature rises, the resistances of bio-asphalt to fatigue and thermal cracking are enhanced. According to continuous PG grading, the widest safe working temperature range is obtained at 450 ℃. Compared to base asphalt, bio-asphalt has superior fatigue and low-temperature performances at high pyrolysis temperatures. Additionally, it can be known from Fourier transform infrared spectroscopy that the modification of petroleum asphalt by bio-oil is a physical fusion process.

Study of low-dimensional magnetism in zeolitic imidazolate frameworks

Applying the procedure of a rapid synthesis in the aqueous system, nanocrystalline form of ZIF-8 and Cu-ZIF was obtained. The composition of the latter was inferred from the comparison of vibration spectra and lattice specific heats of both compounds which become nearly identical. The nanocrystalline character of both compounds prevented direct comparison of powder XRD patterns and manifested by the appearance of a boson peak in the diamagnetic ZIF-8 specific heat. The low-temperature magnetic contribution in Cu-ZIF specific heat and a Curie-Weiss tail in low-temperature susceptibility may originate from the effect of surface spins while the round maximum observed in the susceptibility at 135 K indicates the presence of strong low-dimensional correlations with the exchange coupling ∼200 K. Corresponding magnetic contribution cannot be observed in the specific heat due to the huge overlap by the high-temperature lattice contribution. Negligible magnetization values at low temperatures correspond to the aforementioned strong antiferromagnetic coupling. Future experimental scenarios are discussed which should provide better understanding of the bulk and surface magnetism in this unique quantum system.

Kondo screening of single magnetic impurity doped type-II Ising superconductors

We theoretically study the Kondo effect in type-II Ising superconductors with a single magnetic impurity. Type-II Ising superconductivity was found in two-dimensional centrosymmetric materials with multiple degenerate orbitals, such as in few-layer stanene [Falson et al., Science 367, 1454 (2020)] and ultrathin ${\mathrm{PdTe}}_{2}$ films [Liu et al., Nano Lett. 20, 5728 (2020)]. The type-II Ising spin-orbit coupling (SOC) in these materials generates out-of-plane effective Zeeman fields orienting opposite directions for opposing orbitals, which strongly protects the interorbital superconducting pairing states against in-plane magnetic fields. We show that the SOC-induced band splitting and the chemical potential significantly influence the formation of a localized magnetic moment, with particle-hole asymmetry in the phase boundary between magnetic and nonmagnetic states. The behaviors of spin-induced Yu-Shiba-Rusinov bound states and low-temperature magnetic susceptibility demonstrate that the SOC suppresses the Kondo screening of the magnetic moment, while the interorbital mixing weakens the SOC at finite momentum, then enhances the Kondo effect. The quantum phase transition between magnetic doublet and Kondo singlet ground states can be tuned through chemical potential in experiments.

Comprehensive physico-chemical and rheo-mechanical characterization of multiple asphalt binder microphases to meet Egyptian conditions

Egypt, nowadays, has obvious complementary advantages in the infrastructure construction sector especially in the fields of highways and airports, resulting in drawing attention to utilizing polymer-modified asphalt (PMA). The main aim of this study is investigating physical, chemical, mechanical, and rheological characteristics of five asphalt binder microphases at different aging conditions to nominate which one best suit the Egyptian climatic conditions through a comprehensive experimental testing matrix. The five examined binder microphases are: base asphalt (BA), recovered asphalt (RA), crumb rubber-modified asphalt (CRMA), CRMA with RA (CRRA), and styrene–butadiene styrene-modified asphalt (SBSMA) which are locally available. First, qualitative, and quantitative analytical tests are used to study the physical and microstructural properties of each microphase component of the tested asphalt binders. Additionally, the mechanical and rheological properties of the investigated asphalt binder microphases at original, short-term aged, and long-term aged conditions are examined at different temperature levels. Overall, the testing results show physico-chemical interactions between the BA and the used polymers during mixing and aging processes. The CR and SBS play a significant role in delaying the decomposition process, improving thermal stability, softening point, and Superpave performance grade as well as enhancing rutting, fatigue, low thermal resistance, aging sensitivity, and temperature susceptibility. Carbonyl, Sulfoxide, and Phase angle aging indices are significantly correlated and are rationally able to characterize the aging behavior of the investigated binder microphases. Finally, CRMA, CRRA, and SBSMA proved their performance suitability among the investigated microphases to match the Egyptian climatic conditions.

The Effect of Magnetic Field on the Thermodynamic Properties of Three-Dimensional GaAs Quantum Dot

The problem of parabolically single three-dimensional semiconductor GaAs quantum dot in the presence of an external magnetic field and including the spin of the electron is studied using canonical formalism. The energy spectrum is obtained as a function of temperature and magnetic field. It is observed that the system tends to absorb the largest amount of heat at critical values of the magnetic field which depends on the temperature. A schottky-like anomaly in heat capacity is observed at low temperature, while at high temperature it converges rapidly and saturates. It was also found that the entropy is inversely proportional to the magnetic field strength, also entropy showed exciting behavior at low temperature, a shoulder is observed which becomes curvier when the magnetic field decreases. However, at high temperature, entropy increases monotonically with temperature and becomes essentially independent of the magnetic field. The substantial effect of magnetic field on the magnetic properties of quantum dot is observed at low temperature. It is shown that, magnetization increases significantly at low temperature and shows strong dependence on magnetic field, while its magnitude increases as the temperature increases and reduces to zero regardless the value of magnetic field strength. In addition, at low temperature susceptibility peaks and is found to be paramagnetic and at high temperature the diamagnetic state is found to be a favored state of the system and susceptibility becomes completely independent of magnetic field. It is also shown that for a fixed value of temperature, susceptibility increases rapidly with magnetic field and beyond a critical value of magnetic field, the increase becomes much slower, susceptibility exhibits a crossing behavior, and magnetization shows a significant drop as the magnetic field increases. So far, no study has been made in literature on the effect of magnetic field on the thermal and magnetic properties of three-dimensional quantum dot.

Magnetic properties of the triangular-lattice antiferromagnets Ba3RB9O18 (R=Yb, Er)

Frustration, spin correlations and interplay between competing degrees of freedom are some of the key ingredients that underlie exotic states with fractional excitations in quantum materials. Rare-earth based two dimensional magnetic lattice wherein crystal electric field, spin-orbit coupling, anisotropy and electron correlation between rare-earth moments offer a new paradigm in this context. Herein, we present crystal structure, magnetic susceptibility and specific heat accompanied by crystal electric field calculations on the polycrystalline sample of Ba3RB9O18 (R = Yb, Er) in which R3+ ions form a perfect triangular lattice without anti-site disorder. The localized R3+ spins show neither long-range order nor spin-glass state down to 1.9 K in Ba3RB9O18. Magnetization data reveal a pseudospin Jeff = 1/2 ( Yb3+) in the Kramers doublet state and a weak antiferromagnetic interaction between Jeff = 1/2 moments in the Yb variant. On the other hand, the effective moment {\mu}eff = 8.8 {\mu}B was obtained from the Curie-Weiss fit of the low-temperature susceptibility data of Er variant suggests the admixture of higher crystal electric field states with the ground state. The Curie-Weiss fit of low-temperature susceptibility data for Er system unveils the presence of a relatively strong antiferromagnetic interaction between Er3+ moments compared to its Yb3+ analog. Ba3ErB9O18 does not show long-range magnetic ordering down to 500 mK. Furthermore, our crystal electric field calculations based on magnetization data of Ba3ErB9O18 suggest the presence of a small gap between the ground and first excited Kramers doublets. The broad maximum around 4 K in magnetic specific heat in zero-field is attributed to the thermal population of the first CEF excited state in Ba3ErB9O18, which is consistent with our CEF calculations.

Intermetallic compounds RE 2Ga2Mg (RE = Tb–Tm, Lu) with Mo2B2Fe-type structure

Abstract The rare earth intermetallic compounds RE 2Ga2Mg with RE = Tb–Tm and Lu were synthesized from the elements in sealed tantalum ampoules in a high-frequency furnace. These rare earth-rich phases crystallize with the tetragonal Mo2B2Fe-type structure, space group P4/mbm and Z = 2. The polycrystalline samples were characterized through their Guinier powder patterns. The structures of Er2Ga2.092(1)Mg0.908(1), Tm2Ga2.037(1)Mg0.963(1) and Lu2Ga2.176(1)Mg0.824(1) have been refined from single crystal X-ray diffractometer data. The refinements revealed small homogeneity ranges (small degrees of Mg/Ga mixing on the 2a sites). The magnesium atoms show square planar coordination by Ga2 dumbbells (282 pm Mg–Ga and 257 pm Ga–Ga in the lutetium compound). Geometrically one can describe the RE 2Ga2Mg phases as 1:1 intergrowth structures of CsCl and AlB2-related slabs of compositions REMg and REGa2. From DFT based calculations, charge transfer from the rare earth and magnesium atoms towards gallium can be illustrated in electron localization function ELF slice planes showing strong localization around gallium in the basal plane as well as along the tetragonal c axis signaling Ga–Ga pair interactions. The site-projected density of states DOS and COOP data further quantify this observation. Temperature dependent magnetic susceptibility measurements show Pauli paramagnetism for Sc2Ga2Mg and Lu2Ga2Mg with low room temperature susceptibility values of 2.1(1) × 10−4 and 1.1(1) × 10−4 emu mol−1, respectively. Ho2Ga2Mg, Er2Ga2Mg and Tm2Ga2Mg are Curie-Weiss paramagnets with stable trivalent rare earth ground states. Antiferromagnetic ordering was detected below the Néel temperatures of T N = 18.6(1) (RE = Ho), 11.9(1) (RE = Er) and 6.4(1) K (RE = Tm). The three compounds show metamagnetic transitions in their 3 K magnetization isotherms. Tm2Ga2Mg exhibits a square loop behavior with small hysteresis.

Evaluating fatigue and crack resistance of asphalt mixture containing zinc tailing aggregates

Roads as one of the most important components of the transportation system involve a large quantity of construction aggregate. Limitation in natural-aggregates sources makes it necessary to use alternative materials as a substitute to natural-aggregates. To achieve this goal, the by-products tailings of zinc soil separation and concentration process named zinc tailings were used as an aggregate in asphalt mixture. In this research study, the fatigue, low-temperature, and moisture susceptibility performance of fabricated asphalt mixtures using limestone, siliceous and tailing aggregates were investigated. For this purpose, the four-point bending beam (4PB),semi-circular bending (SCB), and indirect tensile strength (ITS)tests were employed. Findings from 4PB tests indicate that asphalt mixture containing zinc tailings as aggregates have longer fatigue life than the mixture fabricated with limestone aggregates at the strain level of 600 microstrain. However, caution needs to be exercised at higher strain levels. Based on SCB test results, the fracture energy values for mixture with tailing aggregates were almost constant at temperatures of − 6, − 10, and − 12 °C while the results show fracture energy reduction for other mixtures at a lower temperature. Moreover, the cracking resistance index (CRI) indicates that the tailing aggregates fabricated mixture has acceptable low-temperature performance. Finally, the TSR values show that mixture containing zinc tailing aggregates are more resistant to moisture damage compared with siliceous fabricated mixture.

Low temperature magnetic properties of Gd doped CaMnO3

The Gadolinium (Gd) doped CaMnO 3 or Ca 0.7 Gd 0.3 MnO 3 (CGMO), structural and magnetic behavior were investigated through the X-ray diffraction and DC magnetization measurements. The high quality CGMO polycrystalline were prepared through the multiple heat treatment of solid-state reaction method. The X-ray diffraction measurement confirms the formation of single-phase with orthorhombic structure and Pnma space group. Scanning electron microscopy study reveals the surface morphology and average grain size about 2 μm. Rietveld refinement techniques were used to obtain the room temperature (RT) atomic parameters. The obtained atomic parameters of CGMO are a = 5.3465(4) Å, b = 7.5001 (5) Å and c = 5.3184 (4) Å are well matching with CaMnO 3 . Temperature-dependent (4–300 K) magnetic susceptibility (M)T measurements were carried out on CGMO at 500 Oe. Low-temperature magnetic susceptibility (ZFC and FC curves) confirms the magnetic transition i.e, paramagnetic to antiferromagnetic phase (T N ) at 67 K, and surprisingly below 10 K magnetic moments are increasing, it may be due to the formation of weak ferromagnetic ordering. Curie Weiss fitting was carried out on low-temperature inverse susceptibility of field cooled curve which shows hump around 67 K and below 10 K. From the Curie-Weiss fitting paramagnetic curie constant θp ∼ -72 K extracted, which is a clear indication of the formation of antiferromagnetic ordering and below 10 K weak ferromagnetic interaction.

Signature of CEF-phonon coupling in Kondo lattice system CeCuGa3

We present the results of inelastic neutron scattering (INS) measurements on Kondo lattice heavy fermion CeCuGa3. The low-temperature magnetic susceptibility exhibits an anomaly near 2.6 K associated with an antiferromagnetic transition which is further confirmed by the heat capacity measurement. The analysis of magnetic heat capacity C mag (T) based on the crystal electric field (CEF) model reveals an overall CEF splitting of ∼ 21 meV. The INS data reveal two strong magnetic excitations near 4.5 and 6.9 meV, which, however failed to reproduce the observed C mag (T). We therefore analyze the INS data by a model based on magneto-elastic (i.e. CEF-phonon) coupling which suggests that the excitations observed near 4.5 and 6.9 meV originate from the CEF-phonon coupling as observed in CeCuAl3 and CeAuAl3.

Using Plastic Waste in a Circular Economy Approach to Improve the Properties of Bituminous Binders

This work aims to use wax to modify a binder employed in the paving industry. This wax can be obtained either directly or as a by-product from plastic waste′s thermal cracking (pyrolysis). The study characterizes this sustainable material and the binders resulting from blending it with conventional or modified bitumen with other additives applied in the manufacture of bituminous mixtures. Different tests were used: thermogravimetric and spectroscopic analysis; consistency tests; testing of dynamic viscosity at various temperatures; and assessment of the rheologic properties of binders. As a result, several crucial findings were reached: this sustainable wax promotes changes in the viscosity of the binders, their handling temperatures can be reduced, and it contributes to some goals of the U.N. 2030 Agenda. In summary, this work allowed us to conclude that the positive effects of a suitable modification of the bituminous binders, which incorporated this wax and other additives, led to improved consistency and rheological behaviour, having provided, for example, lower temperature susceptibility and higher permanent deformation resistance.

Performance evaluation of recycled asphalt mixtures with various percentages of RAP from the rotary decomposition process

This paper conducted an experimental study to evaluate the performance of recycled asphalt mixtures containing various percentages of reclaimed asphalt pavement (RAP). The variabilities and properties of RAP materials from the rotary decomposition process were determined first, through which the RAP materials were mainly decomposed in three stages including reclaimed stone aggregates barely containing asphalt, and asphalt-rich mortar sand. The results demonstrated that the mineral grading and asphalt percentage of decomposition products were stable. Then, the design aggregate gradation of AC − 20F was selected and its optimum asphalt content (OAC) was obtained using the Marshall mix design method. In addition, the laboratory performance, including the high-temperature performance, low-temperature crack resistance, moisture susceptibility and dynamic modulus tests, of recycled asphalt mixtures with varying RAP contents was conducted. The test results indicated that when the RAP content increased, the rutting resistance improved, but the crack resistance at low temperature and moisture damage susceptibility worsened. The RAP content had an effect on the dynamic modulus, especially at a lower loading frequency (high temperature). And the dynamic modulus of recycled asphalt mixtures increased with the loading frequency increasing and temperature decreasing. The dynamic modulus of the recycled asphalt mixture under standard conditions (20 °C and 10 Hz) was determined to be 11500–13000 MPa. The recycled asphalt mixture with higher percentages of RAP (more than 40%) was applicable to be used as a high modulus asphalt mixture (HMAM) in the future based on the results of the dynamic modulus test. Finally, an empirical predictive model of the dynamic modulus for recycled asphalt mixtures was established.

Crystal electric field and possible coupling with phonons in Kondo lattice CeCuGa3

We investigate the magnetic and crystal electric field (CEF) states of the Kondo lattice system CeCuGa3 by muon spin relaxation (muSR), neutron diffraction, and inelastic neutron scattering (INS) measurements. A noncentrosymmetric BaNiSn3-type tetragonal crystal structure (space group I4mm) is inferred from x-ray as well as from neutron powder diffraction. The low-temperature magnetic susceptibility and heat capacity data show an anomaly near 2.3 - 2.5~K associated with long range magnetic ordering, which is further confirmed by muSR and neutron diffraction data. The neutron powder diffraction collected at 1.7 K shows the presence of magnetic Bragg peaks indexed by an incommensurate magnetic propagation vector k = (0.148, 0.148, 0) and the magnetic structure is best described by a longitudinal spin density wave with ordered moments lying in ab-plane. An analysis of the INS data based on a CEF model reveals the presence of two magnetic excitations near 4.5 meV and 6.9 meV. The magnetic heat capacity data suggest an overall CEF splitting of 20.7 meV, however the excitation between 20 and 30 meV is very broad and weak in our INS data, but could provide an evidence of CEF level in this energy range in agreement with the magnetic entropy. Our analysis of INS data based on the CEF-phonon model indicates that the two excitations at 4.5 meV and 6.9 meV have their origin in CEF-phonon coupling (i.e. splitting of one CEF peak into two peaks, called vibron), with an overall splitting of 28.16 meV, similar to the case of CeCuAl3 and CeAuAl3.

Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid.

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

High, intermediate and low temperature performance appraisal of elastomeric and plastomeric asphalt binders and mixes

This paper is oriented to appraise high, intermediate, and low temperature related performance of elastomeric and plastomeric binders and mixtures in order to evaluate their characteristics at various levels of environmental and loading conditions. Artificial oxidative hardening of asphalt binders and mixes was performed in the laboratory using short- and long-term aging protocols.At the binder level, the elastomers (styrene-butadiene-styrene (SBS) and rubber) and plastomer (ethylene-vinyl acetate (EVA)) materials improved high and intermediate temperature performance indices (G*/sin(δ) and G*.sin(δ), respectively). Interestingly, the aged SBS/bitumen blend had improved low-temperature cracking resistance compared to unaged counterpart. With the progress of oxidative hardening, the plastomer based binder did not show obvious change in the low-temperature cracking susceptibility compared to elastomer-modified binder. Seemingly, in the case of plastomer/bitumen blend, the propensity to low-temperature cracking is to a great extent controlled by the corresponding base bitumen. The plastomer based mixture had improved permanent deformation performance, whereas the elastomers afforded a tangible amelioration for the vulnerability to load and non-load associated cracking. The SBS based mixture showed highest low-temperature fracture energy compared to the EVA based mixture. Despite the determinantal effect of age-hardening to low and intermediate temperature-related cracking of mixes, the results confirmed that the elastomeric materials can retard the impact of aging level on the low temperature and fatigue cracking. Comparision of results was justified by the statistical analysis in order to determine the significance of bituminous material parameters on the measured properties.

Research on Aging Performance of AH-90 and PG70-28SBS Modified Asphalt

This paper studied the aging effect of the rolling thin film oven test (RTFOT) , pressurized aging vessel (PAV) and natural ultraviolet radiation aging method on AH-90 and PG70-28 asphalts. penetration degree , penetration degree index,softening point and ductility tests were used to evaluate the high temperature stability, low temperature split and temperature susceptibility of the two aged asphalts , it is pointed that the aging damaged the low temperature performance of the asphalts, improved the high temperature stability and the temperature susceptibility of the asphalts. Compared with the AH-90 asphalt, PG70-28 modified asphalt has better aging performance. The antiaging property and temperature susceptibility of two asphalts after ultraviolet photooxidation and thermal oxidation , were investigated by testing their viscosity index , antiaging index. which indicated that the viscosity index is correlative nearly with the penetration degree index and the influence of 10.5 kJ·cm-2 ultraviolet photooxidation on asphalt performance is more serious than PAV thermal oxidation. The results indicate that ultraviolet photooxidation research on asphalt is necessary in the intensive ultraviolet radiation region of Neimeng.

High and low temperature rheological characteristics of linear alkyl benzene sulfonic acid modified bitumen

The rheological properties of bitumen can be improved through modification with various additives. Alkyl benzene-derived amphiphiles have been considered as an effective surfactant that can help stabilizing the asphaltene structures within the bitumen. In this study, linear alkyl benzene sulfonic acid (LABSA) was investigated as a binder modifier by evaluating the rheological characteristics at different temperatures. The rheological properties of bitumen involving different rates of LABSA (1%, 2% and 3% of bitumen weight) together with neat (unmodified) bitumen as a control sample, were studied at critical temperatures using dynamic shear rheometer (DSR) and bending beam rheometer (BBR). The results pointed out that, LABSA modification exhibited increased resistance to rutting and fatigue cracking along with improved low temperature susceptibility characteristics. Furthermore, it also helped to serve heavier traffic levels compared to unmodified bitumen. Based on the study outcomes, LABSA can be considered as a potential modifier for asphalt binder, especially when the rate of utilization is chosen as 2% by bitumen weight.

Anomalous anisotropy of the lower critical field and Meissner effect in UTe2

We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$.

Curie–Weiss behavior of the low-temperature paramagnetic susceptibility of semiconductors doped and compensated with hydrogen-like impurities

For the first time, a quantitative model of the Curie–Weiss behavior of a low-temperature paramagnetic susceptibility of electrically neutral donors in n-type diamagnetic covalent semiconductors is proposed. The exchange interaction between nearest two neutral donors was calculated with the use of the Heitler–London model. In this model, we take into account the change in the thermal ionization energy of donors due to the shift of the bottom of the conduction band to the bandgap with doping and compensation. The energy of the exchange spin–spin interaction between electrons localized on donors is calculated as a function of the donor concentration and the degree of their compensation by acceptors. The broadening of the donor band due to the Coulomb interaction of the nearest impurity ions was taken into account. We considered crystals of n-type germanium doped with arsenic up to the concentration close to the insulator–metal phase transition (Mott transition) and compensated with gallium. The compensation ratio K is the ratio of the concentration of compensating acceptors KN to the concentration of doping donors N. The model predicts a change in the sign of the Curie–Weiss temperature from minus to plus (a transition from the antiferromagnetic to ferromagnetic local ordering of electron spins on donors) for K ≈ 0.15–0.3, reaching its maximum positive values of ≈1.3 K for K ≈ 0.5 with the following decrease (a transition to paramagnetism) for K > 0.85. The calculated behavior of the paramagnetic susceptibility of donors is consistent with the experimental data for compensated n-Ge:As,Ga samples close to the Mott transition.