A Tale of Two Plateaus: Competing Orders in Spin-1 and Spin-$\frac{3}{2}$ Pyrochlore Magnets

We use large-scale density-matrix renormalization group simulations with bond dimensions up to $20000$ to determine the magnetization curves of spin-1 and spin-$\frac{3}{2}$ pyrochlore Heisenberg antiferromagnets. Both models exhibit a robust half-magnetization plateau, and we find that the same 16-site state (quadrupled unit cell) is selected in both cases on the largest 64-site cubic cluster we consider for the plateau state. This contrasts sharply with the effective quantum dimer model prediction which favors the ``R’’ state, and demonstrates the breakdown of the perturbative mechanism at the Heisenberg point. These results provide a nonperturbative characterization of field-induced phases in pyrochlore magnets and predictive guidance for spin-1 and spin-$\frac{3}{2}$ materials.