Observation of a lattice instability at the field-induced phase transition of the spin-gapped compound ${\mathrm{Cu}}_2{\left({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2\right)}_2{\mathrm{Cl}}_4$

We report the observation of a jump in the $a$- and $c$-lattice constants at the critical field $H_{c1}$ and at temperatures of the order $40\mathrm{mK}$ in the $S=\frac{1}{2}$ spin-gapped compound ${\mathrm{Cu}}_2{\left({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2\right)}_2{\mathrm{Cl}}_4$ by means of synchrotron x-ray diffraction. This anomaly, characteristic of a first-order phase transition, results from the development and further stabilization of a symmetry breaking magnetic long-range order.

Figure 1

Magnetic field versus temperature phase diagram of $\mathrm{CuHpCl}$ determined from specific heat measurements (Ref. 8). The solid line is a guide for the eyes. Inset: A magnetization curve between 0 and $20\mathrm{T}$( Ref. 9). The critical fields at the temperature of the present experiment are $H_{c1}=7.3\mathrm{T}$ and $H_{c2}=13.2\mathrm{T}$.

Figure 2

Longitudinal scans taken at $H=6\mathrm{T}$ and $H=8\mathrm{T}$ in the increasing field run, i.e., below and above $H_{c1}$. A shift in lattice parameters is clearly visible between the scans. The line shape is asymmetric, and no fit has been carried out, just a statistical analysis of the position of the peak and of the center of mass.

Figure 3

Fractional shift displayed in units of the $a$-lattice parameter $\left(\Delta a=a\left(H\right)-a\left(0\right)\right)$ as a function of the magnetic field, for increasing $(●)$ and decreasing $(◻)$ field runs. At $H\approx H_{c1}=7.3\mathrm{T}$, the position of the peak experiences a jump of magnitude $\Delta a∕a=-2.5\times {10}^{-4}$. Beyond that field, we observed a linear dependence of the magnetostriction that can be well described by the relation $\Delta a∕a\left(H\right)=2.4\times {10}^{-4}-6.61\times {10}^{-5}·\mathrm{H}$. A hysteresis of about $2\mathrm{T}$ has been observed between both regimes.

Figure 4

Variation of the peak intensity, $I_m$, as a function of the applied magnetic field. Identical results were obtained for the integrated intensity. Lines are guides for the eyes.