Magnetocaloric (MC) materials present an avenue for chemical-free, solid state refrigeration through cooling via adiabatic demagnetization. We have used inelastic neutron scattering to measure the lattice dynamics in the MC material Ni45Co5Mn36.6In13.4. Upon heating across the Curie Temperature (TC), the material exhibits an anomalous increase in phonon entropy of 0.22 ± 0.04 /atom, which is ten times larger than expected from conventional thermal expansion. This transition is accompanied by an abrupt softening of the transverse optic phonon. We present first-principle calculations showing a strong coupling between lattice distortions and magnetic excitations.PACS numbers: 78.70. Nx, 75.30.Sg, 65.40.gd, 63.20.kk The coupling between magnetism and lattice excitations has been a recent topic of interest due to its importance in several solid-state systems, such as influencing decoherence in quantum magnets [1] and inducing a spin-Peierls transition in CuGeO 3 [2,3] and ZnCr 2 O 4 [4]. Studies of magnetoelastic materials have focused on metamagnetic shape memory alloys (MMSMA), which are able to reversibly deform with strains of up to ~6% [5,6] via a structural first-order phase transition (FOPT) [7][8][9]. The FOPT allows the alloy to function as magnetocaloric (MC) material, in which an adiabatic change in magnetization of the MMSMA causes an increase in its entropy, thus lowering its temperature [9][10][11][12]. While the change in entropy can be quite large, the FOPT is often accompanied by thermal and/or magnetic hysteresis, which limits the material's long term cycling efficiency. In addition, materials requiring a magnetic field of more than 2 T to induce the FOPT are not feasible for use in any magnetic refrigerator using permanent magnets [13,14].The paramagnetic-to-ferromagnetic secondorder phase transition (SOPT) offers a means to extract heat from a magnetic material using weaker applied magnetic fields and without hysteresis. This SOPT is present in any magnetic material at its Curie temperature ( ), but the change in entropy is typically significantly less than across the FOPT.In this letter, we quantify the phonon entropy and the magnon-phonon coupling in Ni45Co5Mn50-xInx (x=13.4) near the austenite using neutron scattering [15]. When annealed at temperatures below 900K, this compound forms a Huesler L21 structure that is stable down to the martensitic transition temperature , with Mn atoms occupying the 4a positions, Mn1-x/25Inx/25 the 4b, and Ni0.9Co0.1 the 8c positions (Wyckoff notation) [16]. The composition of the crystal puts it at a morphotropic phase boundary; decreasing x from 13.4 to 13.3 leads to an increase in by ~100K [17]. Ab initio calculations of similar compounds point to magnetic frustration as a possible explanation of the morphotropic phase boundary [18][19][20][21]. The magnetic exchange integral for nearest-neighbors Mn-Mn in the 4a and 4b positions -i.e. aligned along [100] -is predicted to be a large negative value (antiferromagnetic). Such an interaction competes ...