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# Using magnetostriction to measure the spin-spin correlation function and magnetoelastic coupling in the quantum magnet NiCl$_2$-4SC(NH$_2$)$_2$

06/2007;
Source: arXiv

ABSTRACT We report a method for determining the spatial dependence of the magnetic exchange coupling, $dJ/dr$, from magnetostriction measurements of a quantum magnet. The organic Ni $S = 1$ system NiCl$_2$-4SC(NH$_2$)$_2$ exhibits lattice distortions in response to field-induced canted antiferromagnetism between $H_{c1} = 2.1$ T and $H_{c2} = 12.6$ T. We are able to model the magnetostriction in terms of uniaxial stress on the sample created by magnetic interactions between neighboring Ni atoms along the c-axis. The uniaxial strain is equal to $(1/E)dJ_c/dx_c < S_{\bf r} \cdot S_{{\bf r}+ {\bf e}_c} >$, where $E$, $J_c$, $x_c$ and ${\bf e}_c$ are the Young's modulus, the nearest neighbor (NN) exchange coupling, the variable lattice parameter, and the relative vector between NN sites along the c-axis. We present magnetostriction data taken at 25 mK together with Quantum Monte Carlo calculations of the NN spin-spin correlation function that are in excellent agreement with each other. We have also measured Young's modulus using resonant ultrasound, and we can thus extract $dJ_c/dx_c = 2.5$ K/$\AA$, yielding a total change in $J_c$ between $H_{c1}$ and $H_{c2}$ of 5.5 mK or 0.25% in response to an 0.022% change in length of the sample.

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• ##### Article: Resonant ultrasound spectroscopy
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ABSTRACT: Resonant ultrasound spectroscopy (RUS) involves the study of the mechanical resonances of solids. The resonant response of a particular object depends on its shape, elastic constants, crystallographic orientation, density, and dissipation. It is possible to obtain the complete elastic constant matrix of relatively low-symmetry materials from a RUS spectrum on a single small sample . The measurement and the computation of the RUS spectra of solids are reviewed. Several examples of the use of the technique are discussed.
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