Rare-earth Nickel Borocarbides Research Articles

Study of effective de-Gennes factor and effect of doping on superconductivity in rare-earth nickel borocarbide superconductors

We theoretically study the effective de Gennes factor and effect of doping on the critical temperature in RNi2B2C (R = Ho). We formulate a mean-field Hamiltonian model where a BCS type of Cooper pair mechanism is considered. We self-consistently solve SC order parameter, AFM order parameter and dopant concentration. The de Gennes scaling on critical temperature and Neel temperature for different Nickel borocarbide compounds gives an idea about the competition between superconductivity and antiferromagnetism in rare earth quaternary borocarbide superconductors RNi2B2C. We study here the effect of doping on the parent borocarbide superconductor HoNi2B2C. We plot the effective de-Gennes factor vs. SC critical temperature for the pseudo quaternary borocarbide compound HoxLa1-xNi2B2C for different dopant concentrations which agrees well with experimental findings.

Effect of external magnetic field on the co-existence of superconductivity and antiferromagnetism in rare earth nickel borocarbides (RNi2B2C)

In this paper, we have studied the effect of external magnetic field in the co-existing phase of superconducting and antiferromagnetism (AFM) of rare earth nickel borocarbides. The AFM in these systems might have originated due to both localized “f” electrons as well as itinerant electrons which are responsible for conduction. On the other hand, superconductivity (SC) is due to spin density wave, arising out of Fermi surface instability. The AFM order is mostly influenced by hybridization of the “f” electron with the conduction electron. Here, we have obtained the dependence of superconducting energy gap as well as staggered magnetic field on temperature T and energy [Formula: see text] in a framework based on mean field Hamiltonian using double time electron Green’s function. We have shown in our calculation the effect of external magnetic field on superconducting and antiferromagnetic order parameters for [Formula: see text] in the presence of hybridization. The ratio of the calculated effective gap and [Formula: see text] is close to BCS value which agrees quite well with experimental results.

Effect of hybridization and dispersion of quasiparticles on the coexistent state of superconductivity and antiferromagnetism in RNi2B2C

The effect of hybridization of conduction electrons and f-level on superconductivity (SC) and antiferromagnetism (AFM) in the coexistent phase of rare-earth nickel borocarbide superconductors (RNi2B2C) is reported. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single-particle Green functions. It is assumed that superconductivity arises due to BCS pairing mechanism in the presence of antiferromagnetism in nickel lattices of Ni2B2 plane. The expressions for superconducting and antiferromagnetic order parameters are derived using double time electron Green functions. The quasiparticle energy bands are plotted and the nature of band dispersion of the quasiparticles is studied.

Competition of local-moment ferromagnetism and superconductivity in Co-substituted EuFe2As2

In contrast to SrFe2As2, where only the iron possesses a magnetic moment, in EuFe2As2 an additional large, local magnetic moment is carried by Eu2+. Like SrFe2As2, EuFe2As2 exhibits a spin-density wave transition at high temperatures, but in addition, the magnetic moments of the Eu2+ order at around 20 K. The interplay of pressure-induced superconductivity and the Eu2+ order leads to a behavior which is reminiscent of re-entrant superconductivity as it was observed, for example, in the ternary Chevrel phases or in the rare-earth nickel borocarbides. Here, we study the delicate interplay of the ordering of the Eu2+ moments and superconductivity in EuFe1.9Co0.1As2, where application of external pressure makes it possible to sensitively tune the ratio of the magnetic (TC) and the superconducting (Tc,onset) critical temperatures. We find that superconductivity disappears once TC > Tc,onset.

EFFECT OF EXTERNAL MAGNETIC FIELD AND STUDY OF DENSITY OF STATES OF SUPERCONDUCTIVITY IN RNi2B2C

A microscopic theoretical study of external magnetic field effect on superconductivity and density of states (DOS) in rare earth nickel borocarbide superconductors ( RNi 2 B 2 C ) is reported here. A Hamiltonian model is used to describe the system to which a BCS-type Cooper pairing mechanism is added. The expression for SC order parameter (z) is calculated by the Green's function technique of D. N. Zubarev. The variation of superconducting gap with temperature is investigated at different external magnetic fields. The phase diagram between temperature (θ) and critical magnetic field (bc) agrees with experimental observations. The gap edges in the DOS appear at ±2z in the absence of external magnetic field. On the application of external magnetic field in the DOS, the gap edges appear at ±(z - b) which resembles the tunneling conductance of STM experiment.

Observation of an anisotropic effect of antiferromagnetic ordering on the superconducting gap in ErNi2B2C

The point-contact spectra of the Andreev reflection dV∕dI curves of the superconducting rare-earth nickel borocarbide ErNi2B2C (Tc≈11K) have been analyzed in the “one-gap” and “two-gap” approximations using the generalized Blonder-Tinkham-Klapwijk model and the Beloborod’ko model allowing for the pair-breaking effect of magnetic impurities. Experimental and calculated curves have been compared not only in shape, but in magnitude as well, which provides more reliable data for determining the temperature dependence of the energy gap (or superconducting order parameter) Δ(T). The anisotropic effect of antiferromagnetic ordering at TN≈6K on the superconducting gap/order parameter has been determined: as the temperature is lowered, Δ decreases by ∼25% in the c-direction and only by ∼4% in the ab-plane. It is found that the pair-breaking parameter increases in the vicinity of the magnetic transitions, the increase being more pronounced in the c-direction. The efficiency of the models was tested for providing Δ(T) data for ErNi2B2C from Andreev reflection spectra.

Point-contact study of the LuNi2B2C borocarbide superconducting film

We present point-contact (PC) Andreev-reflection measurements of a superconducting epitaxialc-axis oriented nickelborocarbide film LuNi2B2C (Tc = 15.9 K). The averaged value of the superconducting gap is found to be meV in the one-gap approach, whereas the two-gap approach results in meV and meV. The better fit of the Andreev-reflection spectra for theLuNi2B2C–Cu PC obtained by the two-gap approach provides evidence for multiband superconductivity inLuNi2B2C. For the first time, PC electron–phonon interaction (EPI) spectra have beenmeasured for this compound. They demonstrate a pronounced phonon maximum at8.5 ± 0.4 meV and a secondshallow one at 15.8 ± 0.6 meV. The electron–phonon coupling constantλ estimated from the PC EPI spectra turned out to be small (withλPC ∼ 0.1), like in other superconducting rare-earth nickel borocarbides. Possible reasons for this arediscussed.

Evidence for a reentrant superconducting state inEuFe2As2under pressure

We studied the temperature-pressure phase diagram of ${\text{EuFe}}_{2}{\text{As}}_{2}$ by electrical resistivity measurements. The spin-density-wave transition at ${T}_{0}$ associated with the FeAs-layers is continuously suppressed with increasing pressure, while the antiferromagnetic ordering temperature of the ${\text{Eu}}^{2+}$ moments seems to be nearly pressure independent up to 2.6 GPa. Above 2 GPa a sharp drop of the resistivity, $\ensuremath{\rho}(T)$, indicates the onset of superconductivity at ${T}_{c}\ensuremath{\approx}29.5\text{ }\text{K}$. Surprisingly, on further reducing the temperature, $\ensuremath{\rho}(T)$ is increasing again and exhibiting a maximum caused by the ordering of the ${\text{Eu}}^{2+}$ moments, a behavior which is reminiscent of reentrant superconductivity as it is observed in the ternary Chevrel phases or in the rare-earth nickel borocarbides.

Fermi surfaces of rare-earth nickel borocarbides

A full three-dimensional study of the Fermi surface ofLuNi2B2C is presented, using positron annihilation. The previously identified nesting feature, part of acomplex multiply connected Fermi surface sheet, is clearly revealed and observed to extendacross approximately 20% of the Brillouin zone. A cuboidal Fermi surface sheet is alsofound, in agreement with de Haas–van Alphen observations. The Fermi surfacetopology of the rare-earth nickel borocarbides is shown to vary little for rare-earthelements such as Er, Tm and Yb, suggesting that this topology is broadly common.

Metamagnetic states in single crystal HoNi2B2C at T ≈ 1.9 K: Torque magnetometry study

Metamagnetic transitions in single-crystal rare-earth nickel borocarbide HoNi2B2C have been studied at T ≈ 1.9 K with a Quantum Design torque magnetometer. With increasing field, transitions to antiferromagnetic, ferrimagnetic, non-collinear, and saturated paramagnetic states take place. The critical fields of the transitions depend crucially on the angle θ between applied field and the easy axis [110]. Measurements of torque along the c axis have been made while changing the angular direction of the magnetic field (parallel to basal tetragonal ab planes) and with changing field at fixed angle over a wide angular range. Two new phase boundaries in the region of the non-collinear phase have been observed, and the direction of the magnetization in this phase has been precisely determined. At low field the antiferromagnetic phase is observed to be multidomain. In the angular range around the hard axis (−6° ≤ ϕ ≤ 6°, where ϕ is the angle between the field and hard axis [100]) the magnetic behavior is found to be “frustrated” with a mixture of phases with different directions of the magnetization.

Torque magnetometry study of metamagnetic transitions in single-crystalHoNi2B2CatT≈1.9K

Metamagnetic transitions in single-crystal rare-earth nickel borocarbide HoNi$_2$B$_2$C have been studied at T\approx 1.9 K with a Quantum Design torque magnetometer. This compound is highly anisotropic with a variety of metamagnetic states at low temperature which includes antiferromagnetic, ferrimagnetic, non-collinear and ferromagnetic-like (saturated paramagnet) states. The critical fields of the transitions depend crucially on the angle $\theta$ between applied field and the easy axis [110]. Measurements of torque along the c-axis have been made while changing the angular direction of the magnetic field (parallel to basal tetragonal $ab$-planes) and with changing field at fixed angle over a wide angular range. Two new phase boundaries in the region of the non-collinear phase have been observed, and the direction of the magnetization in this phase has been precisely determined. At low field the antiferromagnetic phase is observed to be multidomain. In the angular range very close to the hard axis [100] ($-6^{\circ} \lesssim\phi \lesssim 6^{\circ}$, where $\phi$ is the angle between field and the hard axis) the magnetic behavior is found to be ``frustrated'' with a mixture of phases with different directions of the magnetization.

Torque magnetometry: An effective tool for study of metamagnetic transitions in quaternary borocarbides RNi 2B 2C

The metamagnetic transitions in single-crystal rare-earth nickel borocarbide ErNi 2B 2C and TbNi 2B 2C have been studied at 1.9 K with a Quantum Design torque magnetometer. The critical fields of the transitions depend crucially on the angle between applied field and the easy axis [1 0 0]. Torque measurements have been made while changing angular direction of the magnetic field (parallel to basal tetragonal ab-planes) in a wide angular range (more than two quadrants). The results obtained permit discovery of new features of the metamagnetic states in these compounds, which were not revealed in previous studies. For both borocarbides the sequences of metamagnetic transitions with increasing field were different for the magnetic field along (or close enough to) the easy [1 0 0] axis from that near the hard [1 1 0] axis.

Radio-frequency magnetic response of vortex lattices undergoing structural transformations in superconducting borocarbide crystals

We report a clear anomaly in the rf response of tunnel-diode resonator measured in rare earth nickel borocarbide crystals with dc applied magnetic field along the crystallographic $c$ axis. We associate the anomaly in the dynamic magnetic susceptibility $\ensuremath{\chi}$ with a structural transition in the vortex lattice. $\ensuremath{\chi}$ is sensitive to the Campbell penetration depth ${\ensuremath{\lambda}}_{C}$ of the rf perturbation into the mixed state. ${\ensuremath{\lambda}}_{C}$ depends on the vortex lattice elastic moduli, which in turn depend on the vortex lattice structure. Using this technique, we map the high-field transition line for the square-to-rhombic transformation of the vortex lattice and provide a qualitative argument in favor of thermal vortex fluctuations as a major cause driving the transition.

Torque magnetometry studies of metamagnetic transitions in single-crystal HoNi2B2C and ErNi2B2C at T≈1.9K

The metamagnetic transitions in single-crystal rare-earth nickel borocarbide HoNi2B2C and ErNi2B2C have been studied at 1.9K with a Quantum Design torque magnetometer. The critical fields of the transitions depend crucially on the angle between applied field and the easy axis [110] for HoNi2B2C and [100] for ErNi2B2C. Torque measurements have been made while changing angular direction of the magnetic field (parallel to basal tetragonal ab planes) in a wide angular range (more than two quadrants). The results are used not only to check and refine the angular diagram for metamagnetic transitions in these compounds, but also to find new features of the metamagnetic states. Among new results for the Ho borocarbide are the influence of a multidomain antiferromagnetic state, and “frustrated” behavior of the magnetic system for field directions close to the hard axis [100]. Torque measurements of the Er borocarbide clearly show that the sequence of metamagnetic transitions with increasing field (and the corresponding number of metamagnetic states) depends on the angular direction of the magnetic field relative to the easy axis.

Magnetism and superconductivity in rare earth–nickel–borocarbides

The RNi 2B 2C ( R = Gd – Lu , Y ) series of compounds offers a spacious testing ground for the interaction between 4 f and conduction electrons and specifically for interactions between local magnetic moments and the superconducting ground state. In this review we will survey the effects that local moments have on the superconducting transition temperature ( T c ), the upper superconducting critical field ( H c 2 ( T ) ) and the vortex pinning and critical current density ( J c ). To cite this article: S.L. Bud'ko, P.C. Canfield, C. R. Physique 7 (2006).

Raman spectra of SDW superconductors

We report the calculation of the phonon response of the coexistent spin density wave (SDW) and superconducting (SC) state and predict the observation of SC gap in the Raman spectra of rare-earth nickel borocarbide superconductors. The SDW state normally does not couple to the lattice and hence, the phonons in the system are not expected to be affected by the SDW state. But there is a possibility of observing SC gap mode in the Raman spectra of a SDW superconductor due to the coupling of the SC gap excitation to the Raman active phonons in the system via the electron–phonon (e–p) interaction. A theoretical model is used for the coexistent phase and electron–phonon interaction. Phonon Green’s function is calculated by Zubarev’s technique and the phonon self-energy due to e–p interaction which is given by electron density response function in the coexistent state corresponding to the SDW wave vector q=Q is evaluated. The results so obtained exhibit agreement with the experimental observations.

Effect of SC-coupling and AFM-coupling on SC-gap in borocarbide superconductors

The competition between magnetism and superconductivity is being investigated for the recently discovered RNi 2B 2C superconductors with the magnetic rare-earth elements R. The effect of the superconducting coupling λ 1 and the anti-ferromagnetic coupling λ 2 on the superconducting gap and anti-ferromagnetic gap in rare-earth nickel borocarbides is presented in this paper. We have used the Zubarev’s double time Green’s function technique and equations of motion method to evaluate the superconducting gap and anti-ferromagnetic staggered field. It provides qualitative explanations to the experimental observations.

Symmetry analysis of the interplay between local moment anisotropies and propagation vectors in the borocarbides

Representational analysis is used to examine the interplay between Fermi surface nesting and local moment effects in the formation of the magnetically ordered states of the rare-earth nickel borocarbides, RNi2B2C. We derive compatibility tables for the propagation wavevector k, the local moment anisotropy and the ordered moment direction μ k for materials with this tetragonal crystal structure. The magnetic structures observed in the rare-earth nickel borocarbides are discussed in this context.

Thermal transport of the single-crystal rare-earth nickel borocarbidesRNi2B2C

The quaternary intermetallic rare-earth nickel borocarbides $R{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ are a family of compounds that show magnetic behavior, superconducting behavior, and/or both. Thermal transport measurements reveal both electron and phonon scattering mechanisms, and can provide information on the interplay of these two long-range phenomena. In general the thermal conductivity $\ensuremath{\kappa}$ is dominated by electrons, and the high temperature thermal conductivity is approximately linear in temperature and anomalous. For $R=\mathrm{Tm},$ Ho, and Dy the low-temperature thermal conductivity exhibits a marked loss of scattering at the antiferromagnetic ordering temperature ${T}_{N}.$ Magnon heat conduction is suggested for $R=\mathrm{Tm}.$ The $\ensuremath{\kappa}$ data for $R=\mathrm{Ho}$ lends evidence for gapless superconductivity in this material above ${T}_{N}.$ Unlike the case for the non-magnetic superconductors in the family, $R=\mathrm{Y}$ and Lu, a phonon peak in the thermal conductivity below ${T}_{c}$ is not observed down to $T=1.4\mathrm{K}$ for the magnetic superconductors. Single-crystal quality seems to have a strong effect on $\ensuremath{\kappa}.$ The electron-phonon interaction appears to weaken as one progresses from $R=\mathrm{Lu}$ to $R=\mathrm{Gd}.$ The resistivity data shows the loss of scattering at ${T}_{N}$ for $R=\mathrm{Dy},$ Tb, and Gd; and the thermoelectric power for all three of these materials exhibits an enhancement below ${T}_{N}.$

Magnetism and Superconductivity in the Rare Earth Nickel Borocarbides

Magnetism and Superconductivity in the Rare Earth Nickel Borocarbides