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

• ##### A. Migliori
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: Spin-spin correlations of the spin-ladder compound (C5H12N)2CuBr4 measured by magnetostriction and comparison to quantum Monte Carlo results
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ABSTRACT: Magnetostriction and thermal expansion of the spin-ladder compound piperidinium copper bromide (C5H12N)2CuBr4 are analyzed in detail. We find perfect agreement between experiments and the theory of a two-leg spin-ladder Hamiltonian for more than a decade in temperature and in a wide range of magnetic fields. Relating the magnetostriction along different crystallographic directions to two static spin-spin correlation functions, which we compute with quantum Monte Carlo, allows us to reconstruct the magnetoelastic couplings of (C5H12N)2CuBr4 . We especially focus on the quantum critical behavior near the two critical magnetic fields Hc1 and Hc2 , which is characterized by strong singularities rooted in the low dimensionality of the critical spin system. Extending our discussion in Lorenz [ Phys. Rev. Lett. 100, 067208 (2008)], we show explicitly that the thermal expansion near the upper critical field Hc2 is quantitatively described by a parameter-free theory of one-dimensional, nonrelativistic fermions. We also point out that there exists a singular quantum critical correction to the elastic moduli. This correction is proportional to the magnetic susceptibility chi , which diverges as chi˜1/T at the critical fields and thus leads to a strong softening of the crystal.
Physical review. B, Condensed matter 01/2008; 77(23). · 3.77 Impact Factor