Lattice vibrations boost demagnetization entropy in a shape-memory alloy

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 $\mathrm{N}{\mathrm{i}}_{45}\mathrm{C}{\mathrm{o}}_5\mathrm{M}{\mathrm{n}}_{36.6}\mathrm{I}{\mathrm{n}}_{13.4}$. Upon heating across the Curie temperature $\left(T_C\right)$, the material exhibits an anomalous increase in phonon entropy of $0.22\pm 0.04k_B/\mathrm{atom}$, 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-principles calculations showing a strong coupling between lattice distortions and magnetic excitations.

Figure 1

Phonons in $\mathrm{N}{\mathrm{i}}_{45}\mathrm{C}{\mathrm{o}}_5\mathrm{M}{\mathrm{n}}_{50-x}\mathrm{I}{\mathrm{n}}_x(x=13.4)$: (a) Measured DOS from the powder sample at 300 K (solid blue) and 450 K (open red). The arrows indicate the boundaries of the largest phonon softening. The point size represents the largest uncertainty. (b) Phonon dispersion measurements (points) and model calculations (lines) from the single crystal sample at 300 K (solid blue) and 450 K (open red). The shaded region along $X\to \mathrm{\Gamma }$ represents the region of largest phonon softening. The phonon polarizations are indicated by the point shapes: longitudinal (circle), transverse along even/odd Miller indices (triangle/upside-down triangle), and $\left[1\overline{1}0\right]$ polarized (diamond). Data along $K\to L$ is limited due to indium absorption self-shielding. Error bars represent the quadrature sum of the counting statistics' uncertainty and the standard deviation of rebinned data points. (c) The Brillouin zone, representing the scattering geometry on ARCS.

Figure 2

Triple-axis inelastic neutron scattering data from $\mathrm{N}{\mathrm{i}}_{45}\mathrm{C}{\mathrm{o}}_5\mathrm{M}{\mathrm{n}}_{50-x}\mathrm{I}{\mathrm{n}}_x(x=13.4)$: (a), (b) the color plots of the raw scattering data at temperatures above and below $T_C(T_C=395\mathrm{K})$; (c) the energies of the peak in the phonon; and (d) the energy of the phonon at the $X$ point vs temperature. Dashed lines are best fits, mentioned in text. The solid line represents a possible power law decay discussed in text. The Curie and martensitic transformation temperatures are indicated with vertical lines. Where omitted, error bars in (c) and (d) are less than or equal to the size of the data points.

Figure 3

First-principles magnon calculations: (a) magnon dispersion for lattice parameters $a_0=5.91\AA$ (red, dash-dotted), $5.95\AA$ (green, solid), $6.00\AA$ (blue, dashed), and $5.95\AA$ with a $1\%$ frozen phonon distortion (black, dotted); (b) image plot of the measured inelastic neutron scattering along the $\left[\xi 00\right]$ direction with the sample at 300 K. The overlaid black lines correspond to the calculated magnon for $a_0=5.95\AA$.; and (c) cartoon of the supercell, with arrows indicating displacement directions of the $1\%$ frozen phonon distortion used in (a). Atoms on the Ni/Co, Mn, and In sublattices are shown in black, white, and gray, respectively.