Bose-Einstein Condensation of $S=1$ Nickel Spin Degrees of Freedom in ${\mathrm{NiCl}}_2\mathrm{\text{−}}4\mathrm{SC}({\mathrm{NH}}_2{)}_2$

It has recently been suggested that the organic compound ${\mathrm{NiCl}}_2\mathrm{\text{−}}4\mathrm{SC}({\mathrm{NH}}_2{)}_2$ (DTN) undergoes field-induced Bose-Einstein condensation (BEC) of the Ni spin degrees of freedom. The Ni $S=1$ spins exhibit three-dimensional $XY$ antiferromagnetism above a critical field $H_{c1}\sim 2\mathrm{T}$. The spin fluid can be described as a gas of hard-core bosons where the field-induced antiferromagnetic transition corresponds to Bose-Einstein condensation. We have determined the spin Hamiltonian of DTN using inelastic neutron diffraction measurements, and we have studied the high-field phase diagram by means of specific heat and magnetocaloric effect measurements. Our results show that the field-temperature phase boundary approaches a power-law $H-H_{c1}\propto T_c^{\alpha }$ near the quantum critical point, with an exponent that is consistent with the 3D BEC universal value of $\alpha =1.5$.

Figure 1

(a)–(c) Dispersion of the magnetic excitations at $T=80\mathrm{mK}$ along three crystallographic directions. The solid line is a fit to the data using Eq. (2). (d) Background subtracted scans for the $\mathbf{Q}=(h,h,0.5)$ direction in reciprocal space. The dashed line is a fit to a single-mode cross section as described in the text.

Figure 2

Specific heat $C$ versus temperature $T$ of ${\mathrm{NiCl}}_2\mathrm{\text{−}}4\mathrm{SC}({\mathrm{NH}}_2{)}_2$ for $H\Vert c$ in applied magnetic fields of 0, 2, 3.5, and 10 T.

Figure 3

Left: Magnetocaloric effect data determined by monitoring $T$ while sweeping $B$ up and down with a fixed bath temperature. Right: $dT/dH$ for several temperatures, where the transition is identified as the peak.

Figure 4

Temperature $T$—magnetic field $H$ phase diagram from specific heat and magnetocaloric effect data. Bose-Einstein condensation or canted AF order is thought to occur in the area under the symbols.

Figure 5

Results from fits of two separate data sets by the expression $H_c(T)-H_{c1}\propto T^{\alpha }$ up to a maximum fit temperature $T_{\max }$ (see text). (a) and (b) show $H_{c1}$ for various trials values of $\alpha$. In (c) and (d), $\alpha (T_{\max })$ is determined using the value of $H_{c1}$ found in (a) and (b). The upper and lower curves in (c) and (d) are determined using the upper and lower errors bars of $H_{c1}$.