Theory: Electronic Properties of Unconventional Superconductors

 

Electronic entities unearthed by X-ray diffraction in experiments conducted during the past few years were initially thought strange but, with the passage of time, they emerge as central characters in various material properties. The entities in question are magneto-electric multipoles, and best known are a magnetic charge (monopole) and an anapole (toroidal dipole)^{1, 2}.

 The family of atomic multipoles is constructed with the magnetic moment and electric moment of electrons, and is known generically as magneto-electric. By construction, magneto-electric multipoles change their sign when either time or spatial coordinates change direction - they are time-odd and parity-odd entities. The label magnetic charge is justified by the observation that a “magnetic charge” inserted in Maxwell’s equations, with symmetries of the electric and magnetic field unchanged, is both time-odd and parity-odd. While the magnetic charge in question and Dirac’s magnetic monopole share the same discrete symmetries, one is attached to a magnetic ion while Dirac’s magnetic monopole - yet to be observed - is a fundamental unit of charge, just like its brother ‘the electron’ is the fundamental unit of electric charge³. It now appears certain that magneto-electric multipoles are protagonists in a saga that has captivated many researchers for almost three decades.

 Mechanisms for superconductivity in hard, brittle ceramic materials formed from layers paved with squared CuO2 plaquettes remain unsettled, long after the surprising property was discovered in a barium-doped compound of lanthanum and copper oxide⁴. Below optimal doping of holes, at which the critical temperature is a maximum, a pseudo-gap phase exists with unconventional electronic properties. There is no clear jump in the specific heat on entering the phase, and there is no experimental evidence to show that translation symmetry of the lattice changes either.

Compelling evidence for long-range magnetic order in the pseudo-gap phase in the underdoped region of the phase diagram has come from elegant Bragg diffraction experiments on crystals of YBCOx (YBa2Cu3O6 + x) with different hole doping, using the technique of neutron polarisation analysis⁵. A key finding from the studies is that magnetic order in the pseudo-gap phase of YBCO is indexed on the chemical structure. No less compelling is observation of the rotation of polarisation of reflected light (Kerr effect) that is a direct manifestation of broken time-reversal symmetry generally associated with long-range order in which there is a net magnetic moment⁶. Both sets of observation, neutron Bragg diffraction and Kerr effect, are fully explained by a ferro-type order of magneto-electric quadrupoles that is depicted in Fig. 1. To achieve this new direction in understanding the physical properties of cuprate superconductors it was first necessary to prove that neutrons, like photons, are diffracted by magneto-electric multipoles⁸.

Inevitable gloss and glitter in welcoming literature for a new family of superconductors has been followed with girth and gravitas in numerous studies. Despite which, a mechanism of superconductivity in iron pnictides and iron chalcogenides is not settled¹. Interplay between magnetic and structural degrees of freedom is a central problem, for knowledge of the normal state from which superconductivity emerges is crucial to uncovering its true nature.

A seemingly subtle facet of the electron structure of Ba1 – x Nax Fe2 As2 with x ≈ 0.24 – 0.28 might prove exceptionally insightful. At a temperature ≈ 38 K, well above the temperature where superconductivity emerges (Tc ≈ 25 K), the orthorhombic magnetic material undergoes a structural transition that restores tetragonal symmetry of the parent (paramagnetic) structure. However, the re-entrant tetragonal phase actually hosts two orbital motifs depicted in Fig. 1 and neither one is labelled by a set of ion displacements, relative to the parent structure, that could be picked up by standard Bragg diffraction experiment².

Figure 1: Ferrous ions - Fe2+ (5D) in tetrahedral coordination with As ions - possess degenerate xz and yz orbitals as shown in the picture in the tetragonal parent structure with the I4/mmm1’ symmetry. In the low temperature re-entrant tetragonal phase with either P4/mnc1’ or I4221’ symmetry orbital degeneracy is removed, but the symmetry of the orbital ordering does not allow any coupling to atomic displacements or symmetry-breaking strain components.

A similar, purely electronic, transition has been discovered in neptunium dioxide (NpO2) by exploiting Templeton & Templeton X-ray scattering^{3, 4}. In the case of Ba1 – x Nax Fe2 As2 it has been shown that Templeton & Templeton scattering does indeed distinguish between the three tetragonal structures of interest; the parent (I4/mmm1’) and the two depicted orbital motifs (P4/mnc1’ and I4221’).

Observation of the orbital motifs offers more insight to electronic properties of Ba1 – x Nax Fe2 As2 than meets the naked eye, because they are distinct signatures of the mechanism by which the orthorhombic magnetic phase is created. The two motifs arise from orbital ordering of the iron 3d-electrons that renormalises exchange parameters in the material and triggers magnetic order. Other folk argue that orthorhombic magnetic order is instead created by magnetic fluctuations, but this mechanism does not lead to tetragonal orbital motifs in the re-entrant phase².