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The magnetism of magnetoelectric $S$ = 3/2 pyroxenes LiCrSi$_2$O$_6$ andLiCrGe$_2$O$_6$ is studied by density functional theory (DFT) calculations,quantum Monte Carlo (QMC) simulations, neutron diffraction, as well aslow-field and high-field magnetization measurements. In contrast with earlierreports, we find that the two compounds feature remarkably different, albeitnon-frustrated magnetic models. In LiCrSi$_2$O$_6$, two relevant exchangeintegrals, $J_1 \simeq$ 9 K along the structural chains and $J_{\text{ic1}}$$\simeq$ 2 K between the chains, form a 2D anisotropic honeycomb lattice. Incontrast, the spin model of LiCrGe$_2$O$_6$ is constituted of three differentexchange couplings. Surprisingly, the leading exchange $J_{\text{ic1}}$$\simeq$ 2.3 K operates between the chains, while $J_1$ $\simeq$ 1.2 K is abouttwo times smaller. The additional interlayer coupling $J_{\text{ic2}}$ $\simeq$$J_1$ renders this model 3D. QMC simulations reveal excellent agreement betweenour magnetic models and the available experimental data. Underlying mechanismsof the exchange couplings, magnetostructural correlations, as well asimplications for other pyroxene systems are discussed.

Magnetic pyroxenes LiCrGe2O6 and LiCrSi2O6: dimensionality crossover in a non-frustrated S=3/2 Heisenberg model