  Noncentrosymmetric triangular magnets offer a unique platform for realizing
strong quantum fluctuations. However, designing these quantum materials remains
an open challenge attributable to a knowledge gap in the tunability of
competing exchange interactions at the atomic level. Here, we create a new
noncentrosymmetric triangular S = 3/2 magnet CaMnTeO$_6$ based on careful
chemical and physical considerations. The model material displays competing
magnetic interactions and features nonlinear optical responses with the
capability of generating coherent photons. The incommensurate magnetic ground
state of CaMnTeO$_6$ with an unusually large spin rotation angle of 127 deg.(1)
indicates that the anisotropic interlayer exchange is strong and competing with
the isotropic interlayer Heisenberg interaction. The moment of 1.39(1) $\mu$B,
extracted from low-temperature heat capacity and neutron diffraction
measurements, is only 46% of the expected value of the static moment 3 $\mu$B.
This reduction indicates the presence of strong quantum fluctuations in the
half-integer spin S = 3/2 CaMnTeO$_6$ magnet, which is rare. By comparing the
spin-polarized band structure, chemical bonding, and physical properties of
AMnTeO$_6$ (A = Ca, Sr, Pb), we demonstrate how quantum-chemical interpretation
can illuminate insights into the fundamentals of magnetic exchange
interactions, providing a powerful tool for modulating spin dynamics with
atomically precise control.
