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

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 $(1/E)d{J}_c/d{x}_c<S_{\mathbf{r}}\cdot S_{\mathbf{r}+{\mathbf{e}}_c}>$, where $E$, $J_c$, $x_c$ and ${\mathbf{e}}_c$ 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 $d{J}_c/d{x}_c=2.5$ K/$\tilde{A}$, 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.