Magnetoelastic coupling and Grüneisen scaling in NdB4

We report high-resolution capacitance dilatometry studies on the uniaxial length changes in a ${\mathrm{NdB}}_{4}$ single crystal. The evolution of magnetically ordered phases below ${T}_{\mathrm{N}}=17.2$ K [commensurate antiferromagnetic phase (cAFM)], ${T}_{\mathrm{IT}}=6.8$ K [intermediate incommensurate phase (IT)], and ${T}_{\mathrm{LT}}=4.8$ K [low-temperature phase (LT)] is associated with pronounced anomalies in the thermal expansion coefficients. The data imply significant magnetoelastic coupling and evidence of a structural phase transition at ${T}_{\mathrm{LT}}$. While both cAFM and LT favor structural anisotropy $\ensuremath{\delta}$ between in-plane and out-of-plane length changes, it competes with the IT type of order, i.e., $\ensuremath{\delta}$ is suppressed in that phase. Notably, finite anisotropy well above ${T}_{\mathrm{N}}$ indicates short-range correlations which are, however, of neither cAFM, IT, nor LT type. Gr\"uneisen analysis of the ratio of thermal expansion coefficient and specific heat enables the derivation of uniaxial as well as hydrostatic pressure dependencies. While $\ensuremath{\alpha}/{c}_{\mathrm{p}}$ evidences a single dominant energy scale in LT, our data imply precursory fluctuations of a competing phase in IT and cAFM, respectively. Our results suggest the presence of orbital degrees of freedom competing with cAFM, and successive evolution of a magnetically and orbitally ordered ground state.