Umbrella-coplanar transition in the triangular XXZ model with arbitrary spin

The quantum triangular XXZ model has recently enjoyed a wealth of new theoretical results, especially in relation to the modeling of the Ba3CoSb2O9 compound. In particular, it has been understood that in a longitudinal magnetic field the umbrella (cone) phase, classically stable in all the easy-plane region of the ground-state phase diagram, is considerably reduced by the effect of quantum fluctuations. We provide more quantitative information for this phenomenon at arbitrary value of the site spin S, by employing the dilute Bose gas expansion, valid in the high-field regime; our results improve the available estimates of the 1/S expansion. We quantify the extent to which a higher spin suppresses the effect of quantum fluctuations. Besides, we show how in three-dimensional layered systems a relatively small antiferromagnetic interlayer coupling has a similar consequence of bringing back the umbrella phase in some part of the phase diagram.