Magnetic polaron bound to the positive muon in SmS: Exchange-driven formation of a mixed-valence state

Abstract

Muon spin-rotation experiments ͑supported by magnetization measurements͒ have been carried out in the canonical 4f mixed-valence narrow-gap semiconductor SmS from 10 to 900 K in magnetic fields up to 3.5 T. A bound state of an electron around a positive muon is found to form up to about 800 K. This state is a magnetic polaron: the electron wave function is confined within R Ϸ 0.5 nm ͑the first two coordination spheres͒ due to its exchange interaction with Sm magnetic moments. As such, it may serve as a model system for the hypothetical bound state suggested to account for a transition from divalent Sm 2+ to trivalent Sm 3+ , which is invoked to explain the transformation of SmS from a paramagnetic insulator into a magnetic metal at high pressure.The problem of spin and charge fluctuations close to a magnetic instability in mixed-valence ͑MV͒ systems has attracted considerable attention ͑see, e.g., Ref. 1 and references therein͒. In strongly correlated 4f electron systems, the class of MV materials known as narrow-gap semiconductors or Kondo insulators ͑SmB 6 , YbB 12 , TmSe, etc.͒ supports hybridization between localized 4f states and itinerant 5d-6s states causing instabilities in charge and magnetic configurations. These materials have been studied for almost four decades 2 but the mechanism of the valence fluctuation remains mysterious. Among them, the canonical MV system SmS makes an ideal material in which to study charge fluctuations in the vicinity of a quantum critical point because of the relative ease with which the Sm ion changes its ion charge state. Although a consensus has been reached that the remarkable properties of SmS may be understood in terms of a Sm 2+ ͑4f 6 ; J =0͒ → Sm 3+ ͑4f 5 ; J =5/ 2͒ + e͑d , s͒ transition, 3 the mechanism of the electron capture/release remains a subject of current interest.Unlike classical magnetic semiconductors ͑Eu chalcogenides, magnetic spinels, etc.͒ which experience metalinsulator transitions ͑MIT͒ close to the magnetic ordering temperature 4,5 at ambient pressure SmS remains a paramagnetic semiconductor within a NaCl crystal structure down to low temperature. 2 As the pressure is increased, SmS exhibits two successive phase transitions. First it undergoes an isostructural transition at the remarkably low pressure of p BG Ϸ 0.65 GPa ͑at room temperature͒, 6 involving a valence change from a Sm 2+ to a homogeneous mixed-valent ͑2.6-2.8͒ state. 2 This first-order phase transition is characterized by a huge volume collapse of up to 15% accompanied by a color change from black to golden. 7 In the black phase, the Fermi level E F falls into a gap between a 4f 6 level and an unoccupied 5d band, thus making Sm 2+ S 2− a nonmagnetic narrow-gap semiconductor. 8 In the golden phase, the 4f 6 level may be pushed into the conduction band, 8,9 resulting in a mix of divalent 4f 6 and trivalent 4f 5 configurations. In this phase the high-temperature resistivity is metallic but at low temperature the ground state is a strongly correlated semiconductor as long as the pressure i...

Electron localization into spin-polaron state in MnSi

“…The value of S extracted from the slope of the linear dependence of ν on 1/T (Ref. 34) in the 40-300 K range amounts to S = 24 ± 2, reasonably consistent with a fully polarized core of four Mn ions plus an unsaturated halo similar to that in MS. 29,34,35 As the exchange term J is the dominant interaction leading to SP formation (the Coulomb interaction is effectively screened), the role of the muon is reduced to that of an "innocent observer": we suggest that the host lattice is populated by free SP, one of which is captured by the muon, from which we detect Mu-like spectra characteristic of a bound electron state, as in Cd 2 Re 2 O 7 . 30 The exchange contribution amounts to the difference between the PM disorder of the host and the enhanced (FM) order within the SP.…”

“…However, in the PM phase, fast spin fluctuations reduce any local fields at such sites to an average Knight shift, which is typically 2 to 3 orders of magnitude less than the observed splittings. 29,30,34,35 The fact that the splittings do not change abruptly at T c rules out this conventional interpretation. Moreover, observation of a unique level-crossing resonance 41 confirms a single stopping site for the muon in MnSi.…”

“…1. of the two-line SP spectra scales with the bulk susceptibility, similar to corresponding shifts in 3d and 4f MS. 29,34,35 At all T below ∼75 K, hints of structure appear in both peaks of the Fourier spectra, suggesting possible effects of crystalline anisotropies. 30 However, rapid muon spin relaxation precludes resolution of any possible additional lines.…”

“…1 constitute the characteristic signature of a coupled μ + e − spin system in high field. 29,30,34,35,38,39 For such a system, these signals correspond to two muon spin-flip transitions between states with fixed electron spin orientation, the splitting between them being determined by the muon-electron hyperfine interaction A. 34 In a metal, the Coulomb interaction is screened, so electrostatically bound Mu can not form; thus, the conventional interpretation of multiple signals in magnetic metals is that bare muons stop in several magnetically inequivalent lattice sites.…”

Magnetic polarons in Eu-based films of magnetic semiconductors

“…In contrast, the unique sensitivity of polarized positive muons as a local magnetic probe ͑the muon is sensitive to its immediate environment only͒ makes muon spin relaxation ͑SR͒ ideally suited for mapping the magnetic state on the atomic ͑sub-nm͒ scale. 28 This approach has already contributed greatly to the understanding of magnetic materials, 28 DMS films, 14 and bulk DMS materials 29 as well as bulk MS. 30 Routine SR studies in condensed matter physics employ highly energetic 4.2 MeV muons with stopping range on the scale of mm in a solid. The recent development of SR with a 100% polarized low energy muon beam ͑LE-SR͒ ͑Ref.…”