Crystal symmetry and high-magnetic-field specific heat of $\mathrm{Sr}{\mathrm{Cu}}_2{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$

We report measurements of the specific heat of the quantum spin liquid system $\mathrm{Sr}{\mathrm{Cu}}_2{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$ in continuous magnetic fields $H$ of up to $33\mathrm{T}$. The specific heat data, when combined with a finite temperature Lanczos diagonalization of the Shastry-Sutherland Hamiltonian, indicate the presence of a nearest neighbor Dzyaloshinsky-Moriya (DM) interaction that violates the crystal symmetry. Moreover, the same DM interaction is required to explain the observed electron spin resonance lines for $H\Vert c$.

Figure 1

(Color online) Magnetization vs field for $\mathrm{Sr}{\mathrm{Cu}}_2{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$ at different temperatures between 0.6 and $10\mathrm{K}$, as indicated, reveal a gradual evolution of the magnetization plateaux. The square point on the $10\mathrm{K}$ curve was used to compare with SQUID magnetometer data in order to obtain the magnetization units. Inset (a) Magnetic susceptibility measured at $H=4\mathrm{T}$ in a SQUID magnetometer (circles). The solid line is the susceptibility calculated with the FTL method. Inset (b) Two copper dimers in the $\mathrm{Cu}\mathrm{B}{\mathrm{O}}_3$ plane where the coupling constants $J$ (nn) and $J^{\prime }$ (nnn) are indicated.

Figure 2

(Color online) Measured specific heat divided by $T$ (symbols) vs $T$ compared with the calculated one for the Hamiltonian of Eq. (1) (solid lines) for the magnetic field along the $c$ axis: (a) $0⩽H⩽18\mathrm{T}$ and (b) $20⩽H⩽33\mathrm{T}$. The parameters are the same ones used to compute the magnetic susceptibility. The dashed line is the calculated $C∕T$ for $\mathbf{D}=0$ and $H=22\mathrm{T}$.

Figure 3

(Color online) Measured specific heat divided by $T$ (symbols) vs $T$ compared with the calculated one for the Hamiltonian of Eq. (1) (solid lines) for the magnetic field perpendicular to the $c$ axis: (a) $0⩽H⩽18\mathrm{T}$ and (b) $22⩽H⩽33\mathrm{T}$. The parameters are the same ones used to compute the magnetic susceptibility. The dashed line is the calculated $C∕T$ for $\mathbf{D}=0$ and $H=25.5\mathrm{T}$.

Figure 4

(Color online) Contour color plot for the ESR spectrum for $H\Vert c$ calculated with the Lanczos method in a 20 sites cluster for (a) $D_z=5.2\mathrm{K}$ and (b) $D_z=0$. The values of the other parameters are the same ones used to compute the magnetic susceptibility. The experimental data points in (a) are from Cepas et al. (See Ref. 6).