Superconductivity in FerromagneticRuSr2GdCu2O8

Abstract

Relying on the inhomogeneous (layered) crystal, electronic, and magnetic structure, we show how superconductivity can coexist with the ferromagnetic phase of RuSr2GdCu2O8 as observed by Tallon and coworkers. Since the Cu d x 2 −y 2 orbitals couple only to apical O px, py orbitals (and only weakly), which also couple only weakly to the magnetic Ru t2g orbitals, there is sufficiently weak exchange splitting, especially of the symmetric CuO2 bilayer Fermi surface, to allow singlet pairing. The exchange splitting is calculated to be large enough that the superconducting order parameter may be of the Fulde-Ferrell-Larkin-Ovchinnikov type. We also note that π-phase formation is preferred by the magnetic characteristics of RuSr2GdCu2O8.The antagonism between ferromagnetism (FM) and singlet superconductivity (SC) was discussed early on by Ginsburg [1]. His simple conclusion, based upon an inverse Meissner effect that would set up surface currents to shield the external region from the frozen-in magnetic field B int = 4πM , was that coexistence was not viable except in samples not much larger that the field penetration depth. Krey showed how to circumvent this restriction [2] by the formation of spiral magnetic order or, in type II superconductors, by the formation of a spontaneous vortex phase (SVP). In the SVP the internal magnetic induction is screened locally, vortexby-vortex, so the problem considered by Ginsburg does not apply. Further work on SVPs has included the suggested realization in ErRh 4 B 4 , [3] in Eu x Sn 1−x Mo 6 S 8 , [4] in ErNi 2 B 2 C, [5] and possibly in p-wave systems. [6] A serious impediment to SC arising well within the FM phase is the Zeeman splitting of the carrier bands, which makes the majority and minority Fermi surfaces inequivalent, so the states | k ↑> and | − k ↓> do not both lie on the Fermi surface, and total momentum q ≡ k + k ′ =0 pairs are not available for pairing. Getting around this difficulty with q =0 pairs in the case of applied fields or dilute magnetic impurities has led to Fulde-Farrell-LarkinOvchinnikov (FFLO) type theories, [7] where either the SC or FM order parameter (or both) develops spatial variation to accommodate the other.Tallon et al. [8,9] have injected new excitement into this question of coexistence of SC and FM by reporting the superconducting ferromagnet RuSr 2 GdCu 2 O 8−δ (Ru1212). This system was first reported by Bauernfiend et al.[10] as superconducting but not magnetic, and other reports [11,12] indicate that properties are dependent on the method of preparation. Unlike almost all previously reported cases of coexisting SC and FM, this material is first magnetic (T M = 132 K, due to ordering of Ru ions with an ordered moment of 1 µ B /Ru) and then becomes SC only well within the FM phase. Superconductivity appears at T S ≈ 35-40 K, and only at 2.6 K do the Gd ions order (antiferromagnetically). The data are reproducible, specific heat data indicate a bulk SC transition, and muon spin rotation experiments indicate the magnetism is homogeneous and is ...

Oxygen nuclear magnetic resonance study of RuSr2EuCu2O8

“…Some reports have concluded that the magnetic order in RuSr 2 RCu 2 O 8 is ferromagnetic in the RuO 2 layers [3][4][5][6]9,10,13] in which case there should be a competition between the superconducting and magnetic order parameters possibly resulting in a spontaneous vortex phase or a spatial modulation of the respective order parameters [7]. However, powder neutron diffraction studies on RuSr 2 GdCu 2 O 8 and RuSr 2 YCu 2 O 8 showed that the low-field magnetic order is predominately antiferromagnetic (~1 µ B /Ru) and there is a spin-flop transition that gradually occurs for magnetic fields greater than 0.4 T [11,12].…”

“…There have been a number of reports of the coexistence of magnetic order and superconductivity in the ruthenate-cuprates, RuSr 2 R 2-x Ce x Cu 2 O 10+δ and RuSr 2 RCu 2 O 8 where R is Gd, Eu or Y [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These compounds were first synthesized by Bauernfeind, Widder and Braun [13,14].…”

“…Recent reports have focused on RuSr 2 RCu 2 O 8 [3][4][5][6][7][8][9][10][11][12][13]16] where a bulk Meissner phase is found to exist for temperatures below ~35 K for R=Gd and below ~10 K for R=Eu while the magnetic ordering transition occurs at a much higher temperature of ~132 K. The unit cell of RuSr 2 RCu 2 O 8 is similar to the high temperature superconducting cuprate (HTSC), YBa 2 Cu 3 O 7-δ , in that it contains two CuO 2 layers but the CuO chains are replaced by a RuO 2 layer. However, there is an additional complication in that the crystallite domain size is small and there are coherent rotations of the RuO 6 octahedra about the c-axis leading to a superstructure and subdomains of 5 nm to 20 nm in diameter [5,8].…”

Double exchange model for RuSr2(Eu,Gd)Cu2O8

“…This is supported by symmetry considerations and band-structure calculations. 6 We propose that the electronic structure of the RuO 2 planes can be described by an effective double exchange model, with one localized spin at each site representing the Ru +5 ions, and additional n itinerant electrons per Ru coupled ferromagnetically with the localized spins.The model is the two-dimensional (2D) version of one widely used in manganites:Here S i is the localized spin operator representing the Ru +5 ion at site i, c † iσ is the operator creating an itinerant electron of spin σ at this site, and s i = αβ c † iα σ αβ c iβ gives the spin of this electron. For simplicity we take the Hund coupling, J H → +∞.…”

“…This is supported by symmetry considerations and band-structure calculations. 6 We propose that the electronic structure of the RuO 2 planes can be described by an effective double exchange model, with one localized spin at each site representing the Ru +5 ions, and additional n itinerant electrons per Ru coupled ferromagnetically with the localized spins.…”