Magnetostriction, magnetoelastic coupling, and the magnetic Grüneisen constant in the antiferromagnet RbMn F 3

The magnetostriction in RbMn${\mathrm{F}}_{3}$ (a cubic low-anisotropy Heisenberg antiferromagnet) was measured at 4.2 K in magnetic fields $H$ up to 137 kOe. Capacitance dilatometers were used. The change $\ensuremath{\Delta}l$ in the length $l$ along the [001] direction was measured with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the [001], [100], or [110] directions. Two distinct phenomena were observed. At low fields, of order 1 kOe, $l$ underwent a fractional change of order 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$. The sign and magnitude of this change depended on the direction of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$. This low-field magnetostriction is related to the $H$-induced reorientation of the sublattice magnetizations (analogous to the spin-flop transition), and is interpreted quantitatively in terms of a model for the magnetoelastic coupling in RbMn${\mathrm{F}}_{3}$ which was originally proposed by Eastman et al. The low-field magnetostriction data for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}[001]$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}[100]$ lead to the values ${b}_{1}=(1.88\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}{10}^{6} \mathrm{and} (1.77\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ erg/${\mathrm{cm}}^{3}$, respectively, for the dominant magnetoelastic coupling constant. These values are in agreement with other determinations of ${b}_{1}$. In fields above several kilo-oersted, $l$ increased linearly with ${H}^{2}$, with a slope $\frac{d(\frac{\ensuremath{\Delta}l}{l})}{d({H}^{2})}=4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ ${\mathrm{Oe}}^{\ensuremath{-}2}$ which was the same (within the experimental error) for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}[001]$ and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}[100]$. This high-field magnetostriction is related to the $H$-induced canting of the sublattice magnetizations and the concomitant change in the exchange energy. The high-field magnetostriction arises from the dependence of the dominant exchange "constant" $J$ on the volume $V$. Analysis of the data yields a magnetic Gr\"uneisen constant ${\ensuremath{\gamma}}_{\mathrm{mag}}=\ensuremath{-}(\frac{\ensuremath{\partial}\mathrm{ln}J}{\ensuremath{\partial}\mathrm{ln}V})=4.5\ifmmode\pm\else\textpm\fi{}0.4$. This value corresponds to $\frac{\ensuremath{\partial}{T}_{N}}{\ensuremath{\partial}P}=0.53\ifmmode\pm\else\textpm\fi{}0.05$ K/kbar, where ${T}_{N}$ is the N\'eel temperature and $P$ is the hydrostatic pressure. At zero pressure, ${T}_{N}=83.03\ifmmode\pm\else\textpm\fi{}0.03$ K for our sample. Our value for ${\ensuremath{\gamma}}_{\mathrm{mag}}$ agrees well with most other data which are related to this parameter, but is inconsistent with the thermal-expansion data of Teaney et al. Our own thermal-expansion data agree with the value of ${\ensuremath{\gamma}}_{\mathrm{mag}}$ obtained from the magnetostriction data. Detailed calculations of the low- and high-field magnetostriction are presented. The similarity between the underlying mechanisms responsible for the magnetostriction of antiferromagnets and ferromagnets is discussed.