The results of an ultrasonic study of the magnetic-field-temperature (
H-T) phase diagram of hexagonal CsNiCl3 as a function of the angle bet
ween the magnetic field and the c axis are presented. Upon rotation of
the field, the structure of the phase diagram is modified from four p
hases joined at a multicritical point for H parallel-to c to three pha
ses without a multicritical point at other field directions. A previou
sly unseen transition has been detected at intermediate field angles.
The behavior of the spin-flop anomaly on the acoustic velocity is also
investigated as a function of field angle and temperature. The amplit
ude of this anomaly has been found to exhibit a strong dependence on t
hese two parameters. An analysis of these phase diagrams has been made
using a nonlocal Landau free-energy approach