Longitudinal Spin Fluctuations and Superconductivity in FerromagneticZrZn2fromAb InitioCalculations

Abstract

The recent discovery of superconductivity coexisting with weak itinerant ferromagnetism in the d-electron intermetallic compound ZrZn2 strongly suggests spin-fluctuation mediated superconductivity. Ab initio electronic structure calculations of the Fermi surface and generalized susceptibilities are performed to investigate the viability of longitudinal spinfluctuation-induced spin-triplet superconductivity in the ferromagnetic state. The critical temperature is estimated to be of the order of 1 K. Additionally, it is shown that in spite of a strong electron-phonon coupling (λ ph = 0.7), conventional swave superconductivity is inhibited by the presence of strong spin-fluctuations.The generalization of the Bardeen-Cooper-Schrieffer (BCS) theory to electron-electron interactions by Kohn and Luttinger [1], paved the way for speculation about the possibility of non-s-wave, or "unconventional" superconductivity. Following the suggestion that a magnetically mediated interaction plays an important role in the superfluidity of liquid 3 He [2], the search began for superconductivity in nearly magnetic metals where strong spin fluctuations might provide the pairing mechanism [3,4]. Recent experiments on Sr 2 RuO 4 [5] have made it a strong candidate for exhibiting spin-triplet, possibly pwave superconductivity. For a spin-singlet Cooper pair, where the electrons have anti-parallel spins, the presence of ferromagnetic spin-fluctuations will be antagonistic towards the development of such a superconducting state. However, the recent reports of the coexistence of ferromagnetism with superconductivity in UGe 2 [6] and ZrZn 2[7] suggest a spin-triplet Cooper pairing, probably driven by such spin-fluctuations. Moreover, in ZrZn 2 , the disappearance of superconductivity at the same point as magnetism, and the sensitivity of its occurrence to sample purity [7,8] are perhaps the strongest indications yet that the superconductivity is intimately connected with the magnetism in this material.Unlike other "magnetic" superconductors (e.g. borocarbides [9] , RuSr 2 GdCu 2 O 8 [10]) where the magnetism and superconductivity occur in different parts of the unit cell, in both UGe 2 and ZrZn 2 it is the same itinerant electrons that are thought to form the Cooper pairs as well as produce ferromagnetism. Moreover, whereas some questions regarding the itineracy of 5f electrons and the roles of the strong magnetocrystalline anisotropy and quasitwo-dimensional electronic structure can be raised with respect to UGe 2 , ZrZn 2 is a three-dimensional intermetallic compound free of such effects. Discovered by Matthias and Bozorth [11] in the 1950s, it was initially of interest because of the presence of weak ferromagnetism, in spite of the fact that neither constituent was ferromagnetic. It has the C15 cubic Laves crystal structure, with a lattice constant of 7.393Å (13.97 a.u.) [7]. The possibility of there being triplet pairing in high-purity C15 compounds like TiBe 2 and ZrZn 2 was first suggested by Fay and Appel [4]. In this Letter we investi...

Probing the Fermi surface by positron annihilation and Compton scattering

“…24 and 25) caused great excitement, following so soon after the discovery of triplet superconductivity in UGe 2 . 26 The shape of the Fermi surface was the focus of much attention, 27,28 and measurements of de Haas-van Alphen oscillations in the ferromagnetic phase 29 and the paramagnetic Fermi surface by positron annihilation 24 revealed four separate sheets of Fermi surface (see Fig. 2) which were in excellent agreement with the predictions of band structure calculations.…”

Quantum Phase Transitions in the Itinerant FerromagnetZrZn2

“…An extension to this model [23,24] suggests that the application of a magnetic field can lead to a metamagnetic QPT, if the criterium for ferromagnetism is not quite satisfied. The applicability of the 'Stoner' model to ZrZn 2 is supported by band structure calculations [25,26] and the experimental determination of the Fermi surface [14], which suggest that the paramagnetic Fermi energy lies about 30 meV below a double-peak in the one-electron density of states. In a second description of ferromagnetic quantum criticality [8,10], the transition is found to be generically first order due to a coupling of long-wavelength magnetisation modes to soft particlehole excitations.…”

Quantum critical behavior and possible triplet superconductivity in electron-dopedCoO2sheets

“…Although the exact pairing mechanism has not been established in these materials, it is presumed that spin fluctuations are involved, most probably the quantum critical fluctuations in the materials with co-existing ferromagnetism and superconductivity. [8][9][10][11][12][13][14] In Sr 2 RuO 4 , strong nesting related antiferromagnetic spin fluctuations are found in local density approximation (LDA) calculations and experiment. 15,16 In addition ferromagnetic fluctuations may also be present, and if so these would favor a triplet superconducting state.…”