The rare earth elements

The rare-earth elements have a unique place among the elements of the periodic table. The most significant fact about them is that they belong to group IIIA elements of the periodic table having filled 4f shell of electrons. Though, they are chemically alike, each having distinct and striking magnetic properties from the other. These 4f electrons play a small role in chemical bonding as they are closely bound inside the outer closed shells. In case of rare earth materials with f electrons having high angular momentum are responsible for the magnetic properties.

Most of the rare earth compounds occur in trivalent form and this is common for the metals as well.

The rare-earth based superconductivity has been discovered in 1970 for compounds RMo6Se8 and RRh4B4(R is the rare earth element). For above two families, superconductivity and local order magnetic moment coexist which is seen for several members of the rare earth series. The ions of this series are closely similar chemical properties having fascinating magnetic properties.

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Many of these rare earth compounds are related to each other only with the variation of the local moment. This gives an opportunity of investigating how superconductivity and local moments negotiate the nature of low-temperature ground states in these compounds. The discovery of superconductivity in multiphase quaternary borocarbide system is the major breakthrough in Condensed Matter Physics after the discovery of high Tc superconductor by Bednorz Muller. Studies on several members of the series of ternary borides, RENi4 B, (R stands for rare earth elements) show a weak but reproducible signal of superconductivity at Tc =12k [1].

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It has a quite exciting discovery due to two reasons:

Transition temperature is known to be high for these intermetallic compounds (Tc =10k). The superconducting is found in a compound containing Ni metal which is ferromagnetic at room temperature as the presence of small traces of this metal was assumed to destroy superconductivity.

The discovery is really a landmark in superconductivity and opened up a new era and continues to hold the interest of researchers internationally. The most surprising result of the investigations was the observation of superconductivity in the sample of YNi4B2, which was investigated as nonmagnetic having properties similar to the members of RNi4B series. It was seen earlier that presence of 2% Ni, suppresses Tc of Lu2 Fe3 Si5 (~ 6 K to ~2 K) [11]. Though in certain structural and atomic environment, a material containing Ni , lose its magnetic moment and superconductivity, which appear with Tc nearly equal to 4.2k.

Along the series, superconductivity has been observed [1-7] not only for non-magnetic compounds, like R = Lu (TC = 16.6 K) and Y (TC =15.6 K) but also for some of the heavy rare earth with non-vanishing magnetic moment, for example: Tm (TC = 10.8 K), Er(TC = 10.5 K), Ho (TC = 8.5 K), and Dy (TC=6.2 K). At low temperatures, these compounds display both superconductivity and long-range magnetic order, while for the lighter rare earth compounds no superconductivity is observed above 2K. These compounds are more readily accessible to experimental studies than compounds like RRh4B4, RM06S8 and RM06Se8 [7-13] families of magnetic superconductors due to their relatively high superconducting and magnetic transition.

They are a class of intermetallic superconductors within which some members of the family (e.g. YNi2B2C) appear to show conventional superconducting behaviour [14], others with R= Ln, Tm, Er, Ho undergo an antiferromagnetic transition at TN below superconducting transition, TC. Thus, in addition to the important question of the nature of superconductivity, issues corresponding to the interplay of long-range magnetism and superconductivity needs attention for these materials [15-17]. The valence state of rare earth ions in rare earth intermetallic compound is 3+ state. For Ce, Eu and Yb ions, 4+, 2+, 2+ valence states may also be favoured, as they correspond to empty 4f-shell, half-filled 4f-shell, and full filled 4f-shell, respectively. The f-electron wave function for these three rare earth compounds can be spatially extended and are relatively non-local, resulting in a hybridization of 4f-electrons with conduction electrons. Such f-electron hybridization manifests in a variety of anomalous properties which are of interesting in nature. From electronic band structure calculation Matthias et. al., [18] suggested that superconductivity in these systems arises due to conventional electron-phonon mechanism.

The chapters are divided as Chapter-1 outlines the structure and Fermi surface nesting found in these compounds. In chapter- II we reviewed the theoretical models to study some of the properties like specific heat, critical field, susceptibility and gap parameter in the co-existing state of superconductivity and antiferromagnetism. The conclusion of this review favours a conventional phonon mediated mechanism. Chapter- III explains about our calculation of gap parameter taking the model Hamiltonian as proposed by Fulda et. al .[19] and Sahu et.al.[66]. This model [21] emphasizes the electron-phonon coupling to describe the co-existence in these boro-carbide compounds. In chapter-IV, we give a brief review of the experimental work which studies the co-existing properties of nickel borocarbide compounds.

SECTION-1

Structural aspects of the quaternary systems R-T-B-C:

Single phase nickel based materials RNi_2 B_2C have been investigated most extensively among a variety of quaternary boro carbide systems RT_2 B_2C (R=rareearth compounds except Eu, Sc, Th, U); T= Co, Ni, Ru, Rh, Pd, Ir, Pt. They crystallize in the LuNi_2 B_2C structure. Siegrist et al. [19a] reported the crystal structure of the superconducting phase in LuNi_2 B_2C from the highly stable and well-known body-centered tetragonal ThCr_2 Si_2 structure (space group I4/mmm). For the last twenty years and more, this has played an important role in condensed matter physics. Several materials belonging to this structure are known to exhibit a variety of exotic phenomena. Unit cell of the LuNi_2 B_2C structure (a=3.46A^0, c=10.65A^0 ) as shown in fig.1 [19a, b, c] consists of square of Ni_2 B_2 and RC sheets, alternately stacked along the c-axis. C atoms occupy the centre of the square (special position, unoccupied in the ThCr_2 Si_2 structure) formed by four R atoms.

In the series, RT_2 B_2C (R = rare earth, Sc, Y, U, Th; T= transition d-element), the structure appears to be robust for T= Ni. Single phase materials are obtained for entire series of rare earth elements including, Th and U, even though the (trivalent) ionic radius monotonically decreases (known as lanthanide contraction) across the series from La (lightest rare earth) to Lu (heaviest rare earth). The stability is affected for Sc, which has the smallest ionic radius and ScNi_2 B_2 C forms the only metastable material on quenching. The sampleScNi_2 B_2 C shows superconductivity [20] (Tc ~15 K) whereas superconducting phase 1221 is lost on annealing [20, 21]. The lattice parameter, 'a' in RNi_2 B_2C series exhibits the classic lanthanide contraction. In Fig.2, the c parameter varies in the opposite direction (increases) [19a]. Thus it can be shown that the R-R bond dominates the structure on squeezing and distorting NiB_4 tetrahedron in the structure, as the size of R decreases. The deviation of the cell parameters of CeNi_2 B_2C from the regular structure is notable and indicates the non trivalent state of Ce in this material.

There is a striking similarity between the crystal structures of RNi_2 B_2C with that of the high-T_Ccuprates. In both cases, the structure is highly anisotropic (c/a~3 in RNi_2 B_2C); several high- T_Ccuprates crystallize in the same space group as that of the borocarbides, viz., I4/mmm. As an essential and integral ingredient, both structures contain stacks of square planar networks of potentially magnetic transition elements Ni and Cu. Owing to the partially unoccupied d-shells, both Ni and Cu form Mott insulators (example, NiO and CuO). Interestingly, large on-site repulsion parameter U~5 eV has been measured at the Ni site in YNi_2 B_2C [22a, b].

SECTION-2

BAND STRUCTURE:

Band structure calculations [24, 25-27] show that the electron density of states has a peak at Ef on both the compounds, LuNi2B2C and YNi2B2C. Nearly half the contribution of the peak comes from 3d band of Ni and the remaining contributions come from s and p electron states of B and C and d electron states of Lu/Y. Band properties of the quaternary superconductor LuNi2B2C (T ~17 K) and related intermetallic phases (including YNi2B2C) have been calculated in the local-density approximation via linear augmented-plane-wave method (LAPW). In this calculation, the atomic Lu(5d16s2 ), Ni(3d94s1 ), B(2s2 2p1), and C(2s22p2) states are treated as valence electrons, while a more frozen core approximation has been applied to the tightly bound core-type levels, including the Lu(4f) electrons.

Here both exchange and correlation effects have been included within the local density approximation (LDA) by using Wigner interpolation formulas. This rigid-core Lu (4f) where electrons are taken as valence states helps to simplify an already complicated valence-band. The lowest band originates from C(2s) level while the upper valence band begins at ~ -10 eV develops gradually from B(2s) to B(2s)-C(2p), and finally to Ni(3d) character near EF . Ni-B bonds are produced by tetrahedrally coordinated Ni which are relatively weak and leads to Ni-B hybridization effects that are moderate in strength. As a result of this the bands of LuNi2B2C near the Fermi level exhibit predominant Ni(3d) orbital character. All five Ni (3d) sub bands contribute in roughly equal proportions to the N(E) peak near EF. In actually, the dxy and dyz,zx ,N(EF) components exhibit a slight enhancement (by ~16% and 6%, respectively) relative to the corresponding d_(x^2-y^2 )and d_(?3z?^2-r^2 )terms. The Fig.4 shows the roughly equal contribution of all five Ni(3d) to the N(E) peak near E_F.

The report [28] for the intermediate compounds HoNi2B2C and DyNi2B2C is highly intriguing and unexpected. The magnetic and superconducting onset temperatures are found to be reversed in these compounds i.e. for Ho TC>TN while Dy TCTN) seems to be weakened close to TN and recovers again as the magnetic order is established. A second extraordinary property is basically the x-independent TC for 0.3

Updated: May 19, 2021

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The rare earth elements. (2019, Dec 14). Retrieved from https://studymoose.com/the-rare-earth-elements-essay

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