Magnetic field dependence of the neutron spin resonance inCeB6

Abstract

In zero magnetic field, the famous neutron spin resonance in the f-electron superconductor CeCoIn 5 is similar to the recently discovered exciton peak in the nonsuperconducting CeB 6 . A magnetic field splits the resonance in CeCoIn 5 into two components, indicating that it is a doublet. Here we employ inelastic neutron scattering (INS) to scrutinize the field dependence of spin fluctuations in CeB 6 . The exciton shows a markedly different behavior without any field splitting. Instead, we observe a second field-induced magnon whose energy increases with field. At the ferromagnetic zone center, however, we find only a single mode with a nonmonotonic field dependence. At low fields, it is initially suppressed to zero together with the antiferromagnetic order parameter, but then reappears at higher fields inside the hidden-order phase, following the energy of an electron spin resonance (ESR). This is a unique example of a ferromagnetic resonance in a heavy-fermion metal seen by both ESR and INS consistently over a broad range of magnetic fields. PACS numbers: 71.27.+a, 76.50.+g, 78.70.Nx, 76.30.Kg INTRODUCTIONThe observation of neutron spin resonance within a broad range of materials, in particular high-T c cuprates [1], iron pnictides [2,3], and heavy-fermion superconductors [4][5][6], is recognized as an indicator of unconventional superconductivity. It was shown that sign-changing gap symmetry can lead to the existence of resonance behavior [7][8][9][10]. Of particular interest are inelastic neutron scattering (INS) results obtained on CeCoIn 5 , where a sharp resonance peak was observed within the superconducting phase [5,[11][12][13]. At first glance similar peaks were found in the antiferromagnetic (AFM) superconductor UPd 2 Al 3 [14,15], as well as in the normal state of the heavy-fermion metal YbRh 2 Si 2 [16], where superconductivity was recently discovered below ∼ 2 mK [17]. Another striking example of a resonant mode is given by the well known nonsuperconducting heavyfermion antiferromagnet CeB 6 [18,19]. The microscopic origins of such resonant magnetic excitations persisting in f-electron systems either with or without superconductivity may well differ among materials and are still hotly debated.The application of an external magnetic field may help to unmask the differences between these various excitations. For instance, among f-electron compounds, a weak quasielastic signal gives rise to a field-induced ferromagnetic (FM) excitation in CeRu 2 Si 2 [20]. In YbRh 2 Si 2 , two incommensurate excitation branches merge into a commensurate FM resonance whose energy scales linearly with magnetic field [16], whereas in UPd 2 Al 3 the energy gap initially remains almost constant inside the superconducting phase, but starts following a monotonic linear dependence at higher magnetic fields [14]. The sharp resonance in CeCoIn 5 splits into a Zeeman doublet [11] rather than a theoretically predicted triplet [21], whereas in Ce 1−x La x B 6 the magnetic field reportedly leads to a crossover from an itinerant to ...

Magnetic resonance anisotropy in CeB6: an entangled state of the art

“…It is worth noting that the FM component in CeB 6 was later confirmed in neutron scattering experiments910. Moreover, recent comparative study revealed an excellent agreement between the dispersion laws ω(B ) for the main gapless resonant mode in the AFQ phase subtracted from the ESR measurements and from the neutron scattering in magnetic field data11. This mode corresponding to the g -factor g  ~ 1.6–1.7 may be traced up to ω/2π ~ 350 GHz for magnetic field aligned along [110] crystallographic direction1112.…”

“…Moreover, recent comparative study revealed an excellent agreement between the dispersion laws ω(B ) for the main gapless resonant mode in the AFQ phase subtracted from the ESR measurements and from the neutron scattering in magnetic field data11. This mode corresponding to the g -factor g  ~ 1.6–1.7 may be traced up to ω/2π ~ 350 GHz for magnetic field aligned along [110] crystallographic direction1112. However, the situation with the high-frequency ESR experiments in CeB 6 is more complicated as long as for ω/2π > 200 GHz the second mode with the g -factor g  ~ 1.2–1.3 is observed simultaneously with the main ESR mode1112.…”

“…This mode corresponding to the g -factor g  ~ 1.6–1.7 may be traced up to ω/2π ~ 350 GHz for magnetic field aligned along [110] crystallographic direction1112. However, the situation with the high-frequency ESR experiments in CeB 6 is more complicated as long as for ω/2π > 200 GHz the second mode with the g -factor g  ~ 1.2–1.3 is observed simultaneously with the main ESR mode1112.…”

Theory of Electron Spin Resonance in Ferromagnetically Correlated Heavy Fermion Compounds

“…(4) In unconventional superconductors, a strong magnetic field splits the resonant magnetic exciton mode into two components. This is not the case for CeB 6 , where a second field-induced magnon mode emerges whose energy increases with magnetic field [58]. At the FM zone center (Γ-point) only a single mode is found with a non-monotonic field dependence in phase III.…”

“…The two resonance energies are shown in Figure 6 as a function of magnetic field (figure adapted from Ref. [58]). The splitting is approximately linear in field indicating that it is a Zeeman splitting.…”