Elastic Properties of Mn<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

The elastic properties of Mn${\mathrm{F}}_{2}$ have been investigated in the temperature range $4.2&lt;T&lt;330$ K using a cw transmission technique. The measured values at $T=300$ K of the six adiabatic elastic constants in units of ${10}^{11}$ dyn/${\mathrm{cm}}^{2}$ are ${c}_{11}=10.24$, ${c}_{33}=16.55$, ${c}_{44}=3.185$, ${c}_{66}=7.208$, ${c}_{12}=7.95$, and ${c}_{13}=7.07$. The elastic Debye temperature calculated from the low-temperature elastic-constant data is ${\ensuremath{\Theta}}_{D}(E)=261.6$ K. Using the force-constant model of Matossi for the rutile structure and the published frequencies of the Raman-active vibrational modes, theoretical values of the elastic constants are calculated and found to be in fair agreement with experiment. Each elastic constant [except ${c}^{\ensuremath{'}}=\frac{1}{2}({c}_{11}\ensuremath{-}{c}_{12})$] shows the expected linear decrease with increasing temperature in the region $T\ensuremath{\gtrsim}{\ensuremath{\Theta}}_{D}(E)$. On the other hand, ${c}^{\ensuremath{'}}$ has not yet reached this limiting high-temperature behavior at $T=330$ K. The effects on the elastic properties of volume magnetostrictive coupling to the spin fluctuations near the N\'eel temperature ($T\ensuremath{\approx}{T}_{N}$) and of linear magneto-elastic coupling to the magnetic modes in the antiferromagnetic state ($T&lt;{T}_{N}$) are discussed. The elastic constant ${c}_{44}$ is found to have a component at low temperatures ($T\ensuremath{\ll}{T}_{N}$) decreasing approximately as ${T}^{\ensuremath{-}1}$. This striking phenomenon is discussed on the basis of two possible processes, neither of which provides a completely satisfactory explanation.

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