Magnon specific heat of single-crystal borocarbidesRNi2B2C(R=Tm,Er, Ho, Dy, Tb, Gd)

Abstract

Zero-field specific heats of the single crystals $R{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ $(R=\mathrm{Er},$ Ho, Dy, Tb, Gd) were measured within the temperature range $0.1\mathrm{K}<T<25\mathrm{K}.$ Linearized spin-wave analysis was successfully applied to account for and to rationalize the thermal evolution of the low-temperature magnetic specific heats of all the studied compounds (as well as the one reported for ${\mathrm{TmNi}}_{2}{\mathrm{B}}_{2}\mathrm{C})$ in terms of only two parameters, namely, an energy gap $\ensuremath{\Delta}$ and a characteristic temperature \ensuremath{\theta}. The evolution of \ensuremath{\theta} and \ensuremath{\Delta} across the studied compounds correlates very well with the known magnetic properties. \ensuremath{\theta}, as a measure of the effective Ruderman-Kittel-Kasuya-Yosida exchange couplings, scales reasonably well with the de Gennes factor. \ensuremath{\Delta}, on the other hand, reflects predominately the anisotropic properties: \ensuremath{\sim}2 K for ${\mathrm{GdNi}}_{2}{\mathrm{B}}_{2}\mathrm{C},$ \ensuremath{\sim}6 K for ${\mathrm{ErNi}}_{2}{\mathrm{B}}_{2}\mathrm{C},$ \ensuremath{\sim}7 K for ${\mathrm{TbNi}}_{2}{\mathrm{B}}_{2}\mathrm{C},$ and \ensuremath{\sim}8 K for each of ${\mathrm{HoNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ and ${\mathrm{DyNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ The equality in \ensuremath{\Delta} of ${\mathrm{HoNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ and ${\mathrm{DyNi}}_{2}{\mathrm{B}}_{2}\mathrm{C},$ coupled with the similarity in their magnetic configurations, indicates that a variation of x in the solid solution ${\mathrm{Ho}}_{x}{\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ $(x<0.8$ and ${T}_{c}<{T}_{N})$ would not lead to any softening of $\ensuremath{\Delta}.$ This supports the hypothesis of Cho et al. (Ref. 35) concerning the influence of the collective magnetic excitations on the superconducting state. This work underlines the importance of spin-wave excitations for a valid description of low-temperature thermodynamics of borocarbides.