Domain-like magnetic structure in superconductors of ErRh4 B4 and HoMo6S8 type (original) (raw)
Coexistence of Superconductivity and Ferromagnetism in a Magnetic Superconductor
2013
A model is presented utilizing a Hamiltonian with equal spin singlet and triplet pairings based on quantum field theory and green function formalism, to show the correlation between the superconducting and ferromagnetic order parameters. The model exhibits a distinct possibility of the coexistence of superconductivity and ferromagnetism, which are two usually incompatible cooperative phenomena. The work is motivated by the recent experimental evidences of a long-range magnetic order below the superconducting phase temperature in a number of ternary or pseudo-ternary compounds of the lanthanides. The theoretical results are then applied to show the coexistence of superconductivity and ferromagnetism in the lanthanide compound HoMo6S8.
Superconductivity and ferromagnetism are antagonistic types of ordering, and their mutual effects give rise to several interesting phenomena which have recently been studied in rare earth compounds. A theoretical analysis shows that while a ferromagnetic superconductor is a type II superconductor near the superconducting transition point T cl , it becomes a type I superconductor near the ferromagnetic transition point T M . A new theory derived for the case T M •<7' cl predicts the formation of a transverse domain-like magnetic structure near T M . In clean superconductors the electron spectrum is gapless. A change in the behavior from type II to type I upon cooling to T M has been observed experimentally in ErRh 4 B 4 . Experimental data on ErRh 4 B 4 , HoMo 6 S g , and HoMo 6 Se g prove the existence of superconductivity and a magnetic ordering below T M . TABLE OF CONTENTS FIG. 1. Meissner superconducting ferromagnetic phase. The arrows show the directions of the screening currents j s flowing along the surface of the sample and of the magnetization M in the sample.
Theory of magnetic structure in reentrant magnetic superconductors Ho Mo 6 S 8 and Er Rh 4 B 4
Magnetic superconductors, in which the first-and the second-order phase transition to the ferromagnetic (FN) state would occur in the absence of superconductivity, are considered. The exchange and the electromagnetic dipolar interactions of localized moments and electrons as well as magnetic anisotropy are taken into account. It is shown that one realizes the transverse domainlike magnetic structure in a superconducting state (the DS phase). Transitions S-DS-FN are considered. The proposed theory (with the secondorder transition) explains well the experimental data for HOMO& The experimental data on ErRh4B4 may be explained in the framework of the similar microscopic theory with the assumption that it is a first-order magnetic transition and that the critical-temperature (0) variations over the sample investigated by Moncton et al. [ Phys. Rev. Lett. 45, 2060 (198111 and by Sinha et al. [Phys. Rev. Lett. 48, 950 (1982)l are due to inhomogeneous stresses.
REVIEWS OF TOPICAL PROBLEMS: Magnetic superconductors
Uspekhi Fizicheskih Nauk
Superconductivity and ferromagnetism are antagonistic types of ordering, and their mutual effects give rise to several interesting phenomena which have recently been studied in rare earth compounds. A theoretical analysis shows that while a ferromagnetic superconductor is a type II superconductor near the superconducting transition point T cl , it becomes a type I superconductor near the ferromagnetic transition point T M . A new theory derived for the case T M •<7' cl predicts the formation of a transverse domain-like magnetic structure near T M . In clean superconductors the electron spectrum is gapless. A change in the behavior from type II to type I upon cooling to T M has been observed experimentally in ErRh 4 B 4 . Experimental data on ErRh 4 B 4 , HoMo 6 S g , and HoMo 6 Se g prove the existence of superconductivity and a magnetic ordering below T M .
Magnetism in Fe-based superconductors
Journal of Physics: Condensed Matter, 2010
In this review, we present a summary of experimental studies of magnetism in Fe-based superconductors. The doping dependent phase diagram shows strong similarities to the generic phase diagram of the cuprates. Parent compounds exhibit magnetic order together with a structural phase transition both of which are progressively suppressed with doping allowing superconductivity to emerge. The stripe-like spin arrangement of Fe moments in the magnetically ordered state shows the identical in-plane structure for the RFeAsO (R=rare earth) and AFe 2 As 2 (A=Sr, Ca, Ba, Eu and K) parent compounds, notably different than the spin configuration of the cuprates. Interestingly, Fe 1+y Te orders with a different spin order despite very similar Fermi surface topology. Studies of the spin dynamics in the parent compounds shows that the interactions are best characterized as anisotropic three-dimensional (3D) interactions. Despite the room temperature tetragonal structure, analysis of the low temperature spin waves under the assumption of a Heisenberg Hamiltonian indicates strong in-plane anisotropy with a significant next-near neighbor interaction. In the superconducting state, a resonance, localized in both wavevector and energy is observed in the spin excitation spectrum as in the cuprates. This resonance is observed at a wavevector compatible with a Fermi surface nesting instability independent of the magnetic ordering of the relevant parent compound. The resonance energy (E r) scales with superconducting transition temperature (T C) as E r ∼4.9 k B T C consistent with the canonical value of ∼5 k B T C observed in the cuprates. Moreover, the relationship between the resonance energy and the superconducting gap, ∆, is similar to that observed in many unconventional superconductors (E r /2∆ ∼ 0.64). Material Max. T C (K) LaFeAsO 1−x F x [1] 26 NdFeAsO 1−x F x [2] 52 PrFeAsO 1−x F x [3] 52 SmFeAsO 1−x F x [4] 55 CeFeAsO 1−x F x [5] 41 GdFeAsO 1−x F x [7] 50 TbFeAsO 1−x F x [9] 46 DyFeAsO 1−x F x [9] 45 Gd 1−x Th x FeAsO [10] 56 LaFeAsO 1−y [11, 12] 28 NdFeAsO 1−y [11, 12, 13] 53 PrFeAsO 1−y [11, 12] 48 SmFeAsO 1−y [11] 55 GdFeAsO 1−y [14, 12] 53 TbFeAsO 1−y [12] 52 DyFeAsO 1−y [12] 52 LaFe 1−x Co x AsO [17] 14 SmFe 1−x Ni x AsO [26] 10 SmFe 1−x Co x AsO [27] 15 LaFe 1−x Ir x AsO [28] 12 Material Max. T C (K) Ba 1−x K x Fe 2 As 2 [16] 38 Ba 1−x Rb x Fe 2 As 2 [29] 23 K 1−x Sr x Fe 2 As 2 [30] 36 Cs 1−x Sr x Fe 2 As 2 [30] 37 Ca 1−x Na x Fe 2 As 2 [31] 20 Eu 1−x K x Fe 2 As 2 [32] 32 Eu 1−x Na x Fe 2 As 2 [33] 35 Ba(Fe 1−x Co x) 2 As 2 [18, 34] 22-24 Ba(Fe 1−x Ni x) 2 As 2 [19] 20 Sr(Fe 1−x Ni x) 2 As 2 [35] 10 Ca(Fe 1−x Co x) 2 As 2 [36] 17 Ba(Fe 1−x Rh x) 2 As 2 [20] 24 Ba(Fe 1−x Pd x) 2 As 2 [20] 19 Sr(Fe 1−x Rh x) 2 As 2 [21] 22 Sr(Fe 1−x Ir x) 2 As 2 [21] 22 Sr(Fe 1−x Pd x) 2 As 2 [21] 9 Ba(Fe 1−x Ru x) 2 As 2 [22] 21 Sr(Fe 1−x Ru x) 2 As 2 [23] 13.5 LiFeAs [37, 38, 39] 18 Na 1−x FeAs [40] 25 Fe 1+y Se x Te 1−x [41] 15
Magnetic order and crystal structure in the superconducting RNi2B2C materials
Physical Review B, 1997
Neutron-diffraction measurements have been carried out to investigate the crystal structure, magnetic structures, and magnetic phase transitions in RNi 2 B 2 C (Rϭ Y, Ce, Pr, Nd, Tb, Dy, Ho, Er, Tm, and Yb͒. The materials that order magnetically exhibit a wide variety of both commensurate and incommensurate magnetic structures, which argues strongly that the dominant exchange interactions are of the indirect Ruderman-Kittel-Kasuya-Yosida type. The Nd system exhibits a commensurate antiferromagnetic ordering at 4.8 K, with wave vector ␦ϭ(1/2,0,1/2) and moment direction along a ͑or equivalently with ␦ϭ(0,1/2,1/2) and moment direction along b in this tetragonal system͒. For Dy (T N ϭ10.6 K), Pr (T N ϭ4.0 K), and the low-temperature phase of Ho, the magnetic structure is also a commensurate antiferromagnet that consists of ferromagnetic sheets of rare-earth moments in the a-b plane, with the sheets coupled antiferromagnetically along the c axis ͓␦ϭ(0,0,1)͔. Pr is not superconducting, while for Dy (T c ϭ6 K) and Ho (T c ϭ8 K) this magnetic order coexists with superconductivity. For Ho, though, the magnetic state that initially forms at T N Ϸ8.5 K is an incommensurate spiral antiferromagnetic state along the c axis in which the direction of these ferromagnetic sheets are rotated in the a-b plane by ϳ17°from their low-temperature antiparallel configuration ͓␦ϭ(0,0,0.91)͔. The intensity for this spiral state reaches a maximum near the reentrant superconducting transition (ϳ5 K); the spiral state then collapses at lower temperature in favor of the commensurate antiferromagnetic state. An incommensurate a-axis modulation, with ␦ϭ(0.55,0,0), is also observed above the spiral-antiferromagnetic transition, but it exists over a narrower temperature range than the spiral state, and also collapses near the reentrant superconducting transition. The Er system forms an incommensurate, transversely polarized spin-density wave ͑SDW͒ state at T N ϭ6.8 K, with ␦ϭ(0.553,0,0) and moment direction along b ͑or with ␦ along b and the moment direction along a). The SDW squares up at low T, and coexists with the superconducting state (T c ϭ11 K) over the full temperature range where magnetic order is present. Tb, which does not superconduct, orders with a very similar wave vector, but the SDW is longitudinally polarized in this case and again squares up at low T. Tm orders at T N ϭ1.5 K in a transversely polarized SDW state, but with the moments along the c axis and ␦ϭ(0.093,0.093,0). This state is coexistent with superconductivity (T c ϭ11 K). No significant magnetic moment is found to develop on the Ni site in any of the materials, and there is no magnetic ordering of any kind in the Y, Yb, or Ce materials. Profile refinements have also been carried out on these same samples to investigate the systematics of the crystallography, and the crystal structure is I4/mmm over the full range of compositions and temperatures investigated. The area of the a-b plane and the volume of the unit cell both decrease smoothly with either decreasing lanthanide radius or decreasing temperature, but the strong boron-carbon and nickel-carbon bonding then forces the c axis to expand.
TOPICAL REVIEW: Magnetism in Fe-based superconductors
J Phys Condens Matter, 2010
In this review, we present a summary of experimental studies of magnetism in Fe-based superconductors. The doping dependent phase diagram shows strong similarities to the generic phase diagram of the cuprates. Parent compounds exhibit magnetic order together with a structural phase transition both of which are progressively suppressed with doping allowing superconductivity to emerge. The stripe-like spin arrangement of Fe moments in the magnetically ordered state shows the identical in-plane structure for the RFeAsO (R=rare earth) and AFe 2 As 2 (A=Sr, Ca, Ba, Eu and K) parent compounds, notably different than the spin configuration of the cuprates. Interestingly, Fe 1+y Te orders with a different spin order despite very similar Fermi surface topology. Studies of the spin dynamics in the parent compounds shows that the interactions are best characterized as anisotropic three-dimensional (3D) interactions. Despite the room temperature tetragonal structure, analysis of the low temperature spin waves under the assumption of a Heisenberg Hamiltonian indicates strong in-plane anisotropy with a significant next-near neighbor interaction. In the superconducting state, a resonance, localized in both wavevector and energy is observed in the spin excitation spectrum as in the cuprates. This resonance is observed at a wavevector compatible with a Fermi surface nesting instability independent of the magnetic ordering of the relevant parent compound. The resonance energy (E r) scales with superconducting transition temperature (T C) as E r ∼4.9 k B T C consistent with the canonical value of ∼5 k B T C observed in the cuprates. Moreover, the relationship between the resonance energy and the superconducting gap, ∆, is similar to that observed in many unconventional superconductors (E r /2∆ ∼ 0.64). Material Max. T C (K) LaFeAsO 1−x F x [1] 26 NdFeAsO 1−x F x [2] 52 PrFeAsO 1−x F x [3] 52 SmFeAsO 1−x F x [4] 55 CeFeAsO 1−x F x [5] 41 GdFeAsO 1−x F x [7] 50 TbFeAsO 1−x F x [9] 46 DyFeAsO 1−x F x [9] 45 Gd 1−x Th x FeAsO [10] 56 LaFeAsO 1−y [11, 12] 28 NdFeAsO 1−y [11, 12, 13] 53 PrFeAsO 1−y [11, 12] 48 SmFeAsO 1−y [11] 55 GdFeAsO 1−y [14, 12] 53 TbFeAsO 1−y [12] 52 DyFeAsO 1−y [12] 52 LaFe 1−x Co x AsO [17] 14 SmFe 1−x Ni x AsO [26] 10 SmFe 1−x Co x AsO [27] 15 LaFe 1−x Ir x AsO [28] 12 Material Max. T C (K) Ba 1−x K x Fe 2 As 2 [16] 38 Ba 1−x Rb x Fe 2 As 2 [29] 23 K 1−x Sr x Fe 2 As 2 [30] 36 Cs 1−x Sr x Fe 2 As 2 [30] 37 Ca 1−x Na x Fe 2 As 2 [31] 20 Eu 1−x K x Fe 2 As 2 [32] 32 Eu 1−x Na x Fe 2 As 2 [33] 35 Ba(Fe 1−x Co x) 2 As 2 [18, 34] 22-24 Ba(Fe 1−x Ni x) 2 As 2 [19] 20 Sr(Fe 1−x Ni x) 2 As 2 [35] 10 Ca(Fe 1−x Co x) 2 As 2 [36] 17 Ba(Fe 1−x Rh x) 2 As 2 [20] 24 Ba(Fe 1−x Pd x) 2 As 2 [20] 19 Sr(Fe 1−x Rh x) 2 As 2 [21] 22 Sr(Fe 1−x Ir x) 2 As 2 [21] 22 Sr(Fe 1−x Pd x) 2 As 2 [21] 9 Ba(Fe 1−x Ru x) 2 As 2 [22] 21 Sr(Fe 1−x Ru x) 2 As 2 [23] 13.5 LiFeAs [37, 38, 39] 18 Na 1−x FeAs [40] 25 Fe 1+y Se x Te 1−x [41] 15