The magnetic configuration of crystalline solids can have a profound impact on material properties, ranging from subtle structural effects to macroscopic phenomena. With the increased adoption of magnetic crystals for advanced applications, there is a significant need for tools that can characterize and predict the nature of magnetic ordering in solids. While there certainly exist techniques for acquiring such insight, those methods can be plagued by constraints (such as requiring certain elements), ultimately limiting their utility. Here, the strong-dependence of low-frequency (terahertz) vibrational dynamics on weak and long-range forces in crystals is leveraged to determine the spin state of iron phosphate — a promising material for cathodes in lithium ion batteries. We highlight how terahertz time-domain spectroscopy — coupled with quantum mechanical simulations — can discern between various spin configurations in FePO4. Furthermore, the results of this work unambiguously show that the well-accepted space group symmetry for FePO4 is actually incorrect, and that low-frequency spectroscopic measurements provide a clearer picture of the correct structure over the gold-standard of X-ray diffraction. This work opens the door for characterizing, predicting, and interpreting crystalline magnetic ordering using low-frequency vibrational spectroscopy
Error in the calculation of intensities in figure 4 has been corrected.