Thermodynamic Study of 3D ``Harmonic'' Honeycomb Li$_{2}$IrO$_{3}$

Honeycomb iridates have been the focus of substantial interest due to the strong magnetic frustration that arises from their edge-shared bonding environment, which favors a strongly anisotropic Ising-like exchange between bonds. In materials with edge-shared IrO$_6$ octahedra, spin-anisotropy of the exchange between neighboring effective spin-1/2 states is enhanced by the interference of the two exchange paths across the planar Ir-O$_2$-Ir bond. In the honeycomb lattice, such an interaction couples different orthogonal spin components for the three nearest neighbors; no single exchange direction can be simultaneously satisfied, leading to strong frustration which can be described by the Kitaev-model. We have recently synthesized a new structure that retains the same bonding environment as the honeycomb lattice, and extends this physics to three-dimensions. Previous RMXD experiments on our orthorhombic $^{\mathcal{H}}\langle 1\rangle$-Li$_{2}$IrO$_{3}$ samples revealed an incommensurate, non-coplanar magnetic structure with counter-rotating moments, suggesting that Kitaev exchange is the dominant spin interaction in this system. In this work, we study the thermal properties of our single crystals as a function of temperature and applied magnetic field.