Two-Dimensional Ferromagnetism of a ${}^3\mathrm{He}$ Film: Influence of Weak Frustration

${}^3\mathrm{He}$ films adsorbed on the atomically flat surface of graphite provide a model system for the study of two-dimensional magnetism on a triangular lattice. We have made a study of the regime in which the $T=0$ ground state of the second ${}^3\mathrm{He}$ layer is a fully polarized ferromagnet. NMR, using broadband SQUID detection, at a range of low fields above the spin-flop transition, and over a wide temperature range 0.3–200 mK, has enabled us to disentangle the influence of sample finite size effects and magnetic field on the spin-wave spectrum. We demonstrate that the spin-wave spectrum is governed by a different effective exchange constant than that determining the high temperature magnetism. This is understood in terms of frustrated atomic ring exchange.

Figure 1

NMR line shape for a thin film of ${}^3\mathrm{He}$ physisorbed on the surface of graphite for temperatures in the range 0.32–2 mK. Data shown are in a static magnetic field of 1.54 mT, at coverage $24.66{\mathrm{nm}}^{-2}$. Inset: fit to mosaic spread of platelet orientations for data taken at 0.32 mK (see text).

Figure 2

Magnetization of ${}^3\mathrm{He}$ film relative to its saturation value, as determined from the NMR line shift $\Delta f$, as a function of temperature. Measurements in 1.54 mT (closed blue circles) and 3.09 mT (open green squares) show a very weak dependence on magnetic field. Insert: Relative magnetization over full measured temperature range.

Figure 3

Frequency shift at a range of coverages above the ferromagnetic anomaly. Lines show theoretical fit, from spin-wave theory, extrapolated to $T=0$.

Figure 4

Comparison of second layer density (red circles) inferred in present experiment from $T=0$ dipolar frequency shift (green triangles), with neutron scattering data (blue squares) [28] and theoretical model (solid line) [27].

Figure 5

Comparison of $J_{\chi }$ (red circles) and $J_s$ (blue triangles) experimentally determined in this work. The difference arises from atomic ring exchanges that frustrate the dominant ferromagnetic Heisenberg exchange interaction.