the superconducting state. This work underlines the importance of  spin-wave excitations for a valid description of low-temperature thermodynamics of borocarbides.'
author:
- 'M. El Massalami, R. E. Rapp, F. A. B. Chaves'
- 'H. Takeya,'
- 'C. M. Chaves,'
title: 'Magnon Specific Heat of Single Crystal Borocarbides $R$Ni$_{2}$B$_{2}$C ($R$=Tm, Er, Ho, Dy, Tb, Gd).'
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Introduction
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Wide varieties  of magnetic ground structures are manifested in $R$Ni$_{2}$B$_{2}$C series (see e.g. Refs.[@Lynn-RNi2B2C-mag-xrd; @Detlefs-GdNi2B2C-XRES] and Tab.I): members with $R=$Ho, Dy, Nd, Pr adopt commensurate antiferromagnetic (AF) arrangements while those with $R=$Tm, Er, Tb, Gd, assume squared-up spin-density wave (SDW) states. These ground structures are stabilized by a fine balance of exchange, crystalline electric field (CEF), and magnetoelastic forces. Under magnetic field or temperature variation, most of these structures undergo a cascade of phase transformations, yielding rich varieties of field-temperature ($H-T$) phase diagrams ( see e.g. Refs.[@Canfield-Ho-HT-Diagram; @Budko-Er-HT-diagram-2; @Detlefs-Ho-HT-Diagram; @Canfield-Dy-HT-diagram]).  Interestingly, most of the zero-field magnetic states of $R$=Tm, Er, Ho, Dy coexist with superconductivity, presenting model compounds wherein the interplay between superconductivity and magnetism can be investigated. Such investigations revealed that the superconductivity, though much influenced by, has a very weak influence on the prevailing magnetic order:[@Amici-thesis] the energy gain due to 