Phonon Energy Gaps in the Charged Incommensurate Planes of the Spin-LadderSr14Cu24O41Compound by Raman and Infrared Spectroscopy

Abstract

The terahertz (THz) excitations in the quantum spin-ladder system Sr14Cu24O41 have been determined along the c-axis using THz time-domain, Raman and infrared spectroscopy. Low-frequency infrared and Raman active modes are observed above and below the charge-ordering temperature Tco 200 K over a narrow interval 1 − 2 meV ( 8 − 16 cm −1 ). A new infrared mode at 1 meV develops below 100 K. The temperature dependence of these modes shows that they are coupled to the charge-and spin-density-wave correlations in this system. These low-energy features are conjectured to originate in the gapped sliding-motion of the chain and ladder sub-systems, which are both incommensurate and charged.PACS numbers: 71.45. Lr, 78.70.Gq More than three decades ago, new normal modes were predicted to occur in ionic materials with incommensurate (IC) layers which can slide past each other [1][2][3][4]. These new degrees of freedom allow separate phonons in each subsystem at high frequencies with a crossover to slow oscillations due to relative sliding motions of the two almost rigid subsystems at ultralow frequencies, leading effectively to an extra acoustic mode. If the IC layers are charged these sliding modes become gapped due to the restoring Coulomb forces. These modes are the ionic complements of the electronic plasmons in metals and their dynamics also resemble the sliding motion in density wave (DW) systems [5]. Thus far,unambiguous experimental evidence for sliding gapped acoustic mode resonances has remained, to our knowledge, elusive. A promising avenue of investigation is the low-dimensional quantum spin-ladder system Sr 14 Cu 24 O 41 containing such substructures in the form of Cu 2 O 3 ladders and one-dimensional (1D) CuO 2 chains [6]. The chains and ladders run parallel along the caxis with the rungs of the ladders along the a-axis [6], shown in Fig. 1. The two subsystems are structurally IC, resulting in a buckling along the c-axis with a period c = 27.5Å 10 c ch 7 c ld , where c ch and c ld represent the lattice constants for the chain and ladder subcells, respectively.This intrinsically hole-doped material exhibits a variety of unusual charge, magnetic and vibrational phenomena [7] that have been probed by several techniques, among them magnetic resonance [8], neutron scattering [9] and resonant x-ray scattering [10][11][12]. The unusual DW order is attributed to cooperative phenomena driven and stabilized by charge and spin correlations, in conjunction with the IC lattice degrees of freedom. Lowenergy features spanning frequencies from the kHz to the THz range and associated with the DW dynamics have also been observed. However, while the microwave data have been consistently interpreted in terms of screened DW relaxational dynamics [13][14][15][16], the nature of the excitations in the THz regime, which are seen to be strongly coupled to the charge/spin ordering, remains controversial [10][11][12][13][14][15][16][17][18][19]. An important and open question is, what are the salient spectroscopic features in the 1 me...

Excess specific heat from the gapped sliding phonon modes in the incommensurate composite crystal Sr14Cu24O41

“…The THz electric field of the as-grown crystal can be broadly characterized by the presence of two types of oscil- lations having periods ∼1 and ∼4 ps. For E a (not shown), the THz signal showed no oscillations in line with the data reported earlier by Thorsmølle et al [18]. As shown in fig.…”

“…For this we estimated the change δω in ω for a small value of ∆α. The frequency ω of the sliding mode for a system with incommensuarte, oppositely charged layers is given by [30]: ω 2 = ω 2 0 (1 + µα), where µ is the ratio of the unit cell masses of the two sublattices; ω 0 is analogous to the plasma frequency in metals and is given by ω 2 0 = n c q 2 c / 0 m c , where n c is atomic mass number density and m c , the unit cell mass (subscript c is for the chain sublattice); is the permittivity which can be taken as 15 [18]. Using this expression, and by taking a reasonably small and experimentally accessible value of δα = 0.01, and the average frequency < ω > = 0.28 THz, we found ∆ω = ∼0.03 THz, which is in fairly good agreement with the shift of the absorption band in the THz transmittance upon annealing.…”

Effects of Ca substitution on quasiacoustic sliding modes in Sr14−xCaxCu24O41

“…In combination, the different techniques provide a picture of the low-energy lattice dynamics in relation to changes in temperature and Ca concentration. We observe a number of highly anisotropic optical excitations below 3 THz including strong absorption bands in the sub-THz energy range of SCCO consistent with previous works [17,26,33,34]. Our results show a transfer of spectral weight between sliding mode excitations associated with slow in-phase and fast out-of-phase chainladder sliding dynamics.…”

“…As such, the nature of superconductivity in SCCO remains poorly understood. Remarkably, recent spectroscopic experiments on the order of 1 meV have revealed the presence of additional acoustic vibrational modes supported by a long-wavelength sliding oscillation of the incommensurate chain and ladder sublattices [33,34]. Theoretically predicted over 30 years earlier [35,36], these quasiacoustic sliding modes invoke similarities to the low-frequency vibrational modes of other quasiperiodic superconductors [5,6,8,9] and therefore warrant further attention.…”

Magnetocaloric effect in Fe2P : Magnetic and phonon degrees of freedom

“…Interestingly there is no anisotropy between the temperature dependence of the energy gap for the two orthogonal directions. A gap in the acoustic phonon is rather unusual but has previously been observed in spin-ladder compounds containing one-dimensional (1D) chains and two dimensional (2D) ladder substructures [20,21]. Gaps in the acoustic-phonon modes could be derived from sliding motions of one sublattice relative to the other with the precise gap value indicative of the strength of the Coulomb forces between the two charged sublattices [22].…”