Specific heat of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

We present measurements of the specific heat of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals from 2 to 10 K and from 0 to 10 T, including both twinned and untwinned crystals with various oxygen doping (7-δ=6.95, 6.97, and 6.99). The zero-field specific heat includes a linear-T term which is small compared to other ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ samples, but large compared to the ${\mathrm{T}}^2$ electronic specific heat predicted for a superconductor with clean lines of nodes in the gap function. This zero-field linear-T term is found to decrease with decreasing concentration of twin boundaries and oxygen vacancies δ. The specific heat increases in a magnetic field and has a strong dependence on field orientation. Several possible field-dependent contributions are compared to the data, including a Schottky anomaly, vortex-vortex interactions, a traditional mixed-state HT term associated with vortex cores, and a $\sqrt{H}$T term predicted by G. Volovik for the mixed state in superconductors with lines of nodes in the gap function. The field dependence of the specific heat, according to a comparison of fits based on these possibilities, supports the existence of lines of nodes and suggests the presence of quasiparticle excitations outside the vortex core.