High-field behavior of the spin gap compound ${\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$

We report magnetization and heat capacity measurements of single crystal samples of the spin gap compound ${\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$. Low-field data show that the material has a singlet ground state comprising dimers with intradimer coupling $J=100\mathrm{K}$. High field data reveal the role of weak interdimer coupling. For fields that are large compared to the spin gap, triplet excitations are observed for significantly smaller fields than predicted for isolated dimers, indicating that weak interdimer coupling leads to triplet delocalization. High field magnetization behavior at low temperatures suggests additional cooperative effects.

Figure 1

${\mathrm{Cu}}_2{\mathrm{B}}_4{\mathrm{O}}_{12}$ layers from $\beta \text{−}{\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$. The open circles represent O, the gray circles Cu, and the black circles B. Dimer units comprise Cu(1) and Cu(2) atoms linked via $\mathrm{B}\left(3\right){\mathrm{O}}_3$ groups. Sr ions separating the layers are not shown.

Figure 2

(a) Magnetic lattice representing the structure of ${\mathrm{Cu}}_2{\mathrm{B}}_4{\mathrm{O}}_{12}$ planes in ${\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$. Atomic positions of Cu(1) and Cu(2) are taken from the real crystal structure. Exchange pathways are labelled in the legend. (b) In the limit $J⪢J^{\prime }$ and $J^{″}$, interdimer terms can be treated perturbatively, and the lattice mapped on to a distorted square lattice of dimers. Each dimer unit is represented by a solid circle positioned in the geometric center of the Cu(1) and Cu(2) atoms.

Figure 3

Temperature dependence of the magnetic susceptibility of a single crystal of ${\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$ for a field of $5000\mathrm{Oe}$ aligned along the principal crystal axes. Solid lines show fit to isolated dimer model, described in the main text.

Figure 4

Difference in heat capacity $\Delta C_p=C_p\left(18\mathrm{T}\right)\text{−}{C}_p\left(0\mathrm{T}\right)$ for a single crystal of ${\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$. Solid line shows calculated value for dimer model with $J=100\mathrm{K}$ and $g=2.14$. Inset shows total heat capacity in zero field between $2\mathrm{K}$ and $300\mathrm{K}$. Mol refers to the formula unit.

Figure 5

(Color online) Magnetization of ${\mathrm{Sr}}_2\mathrm{Cu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_2$ as a function of applied field at different temperatures. Calculated values for isolated dimer model with $J=100\mathrm{K}$ and $g=2.14$ shown by solid lines.

Figure 6

Magnetization as a function of temperature for different magnetic fields. Symbols (connected by dotted lines to guide the eye) indicate measured magnetization data extracted from Fig. 5, solid lines indicate isolated dimer model with $J=100\mathrm{K}$, and $g=2.14$.