Neutron scattering study of the charge-density wave transitions in2H−TaSe2and2H−NbSe2

Abstract

We have used the triple-axis neutron-scattering technique to study $2H\ensuremath{-}\mathrm{Ta}{\mathrm{Se}}_{2}$ and $2H\ensuremath{-}\mathrm{Nb}{\mathrm{Se}}_{2}$ which undergo charge-density wave transitions at ${T}_{0}=122.3$ K and ${T}_{0}=33.5$ K, respectively. The transitions in both compounds appear to be second-order and involve atomic displacements of ${\ensuremath{\Sigma}}_{1}$ symmetry. At inception, the superlattices in both compounds have nearly identical incommensurate wave vectors with magnitude ${q}_{\ensuremath{\delta}}=\frac{1}{3(1\ensuremath{-}\ensuremath{\delta}){a}^{*}}$, with $\ensuremath{\delta}\ensuremath{\sim}0.02$. The Nb${\mathrm{Se}}_{2}$ superlattice remains incommensurate to 5 K but Ta${\mathrm{Se}}_{2}$ undergoes a first-order lock-in transition where $\ensuremath{\delta}\ensuremath{\rightarrow}0$ at 90 K. The temperature dependence of the superlattice wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ in the incommensurate phase and the lock-in transition are discussed using a free energy involving third-order "umklapp" terms and a secondary order parameter. The secondary lattice distortion which is predicted in this model is observed experimentally. Most phonon branches having energies less than 10 meV with propagation vectors in the [$\ensuremath{\zeta}00$] and [$00\ensuremath{\zeta}$] directions have been measured at 300 K. Strong anomalies are found in the ${\ensuremath{\Sigma}}_{1}[\ensuremath{\zeta}00]$ phonon branches in both materials near the wave vector ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}}_{c}=(\frac{1}{3},0,0)$ characteristic of the low-temperature superlattices. Substantial softening of this phonon is observed as the transition is approached. In addition, the spectral profile exhibits a central peak which is not measurably inelastic.