Torque magnetization measurements on a Hg${\mathrm{Ba}}_2$${\mathrm{Ca}}_3$${\mathrm{Cu}}_4$${\mathrm{O}}_{10}$ microcrystal of mass $m\simeq 380$ ng were performed using a miniaturized torque sensor (120×90×4 μm) with a very high sensitivity of $\Delta \tau \simeq {10}^{-14\mathrm{}}$ N m. In an applied field of 1 T this allows the measurement of magnetic moments as small as $m={10}^{-14\mathrm{}}$ A ${\mathrm{m}}^2$, which is far beyond the sensitivity of the best commercial superconducting quantum interference device magnetometers. From the angle-dependent torque measurements an effective mass anisotropy of $\gamma =\sqrt{\frac{m_c^{*}}{m_{\mathrm{ab}}^{*}}}=52\mathrm{}\left(1\right)\mathrm{}$ and an estimate of the in-plane coherence length of ${\xi }_{\mathrm{ab}}=1.8\mathrm{}\left(5\right)\mathrm{}$ nm are extracted for Hg${\mathrm{Ba}}_2$${\mathrm{Ca}}_3$${\mathrm{Cu}}_4$${\mathrm{O}}_{10}$. The large value of $\gamma$ reflects the quasi-two-dimensional nature of the mercury based cuprates and demonstrates the importance of vortex fluctuations in these materials.

• Received 13 September 1995

DOI:https://doi.org/10.1103/PhysRevB.53.R6026