  In correlated quantum materials, divergent critical fluctuations near the
quantum critical point are often closely associated with exotic quantum phases
of matter, such as unconventional superconductivity and quantum spin liquids.
Here we present a simple yet highly sensitive composite magnetoelectric (ME)
method for detecting the critical spin fluctuations in quantum magnets. The ME
signal is proportional the magnetostriction coefficient, which directly probes
the product of magnetization and spin-spin correlation. As a demonstration, the
composite ME method is applied to a Kitaev quantum spin liquid candidate
Na$_3$Co$_2$SbO$_6$, which shows signs of magnetic field-induced quantum
criticality. Notably, the ME signal prominently diverges at the magnetic
field-induced tricritical points, particularly at a tricritical point that lies
in close proximity to a zero-temperature quantum critical point. A crucial
aspect of these tricritical points is their tunability through the modification
of the in-plane magnetic field's direction. The direction of magnetic field can
thus serve as a handful yet important tuning parameter, alongside pressure and
chemical doping, for searching quantum critical points in quantum magnets with
pronounced magnetic anisotropy.
