Probing magnetoelectric effect in the spin-modulated magnet Fe2GeO4

The distinct spin amplitude wave was reported in a highly frustrated magnetic compound Fe _2 GeO _4 , which is very different from observations on other members of the M _2 GeO _4 (M = Fe, Co, and Ni) family, raising interest in this compound for some additional emergent phenomena. In particular, this non-uniform spin order allows the intrinsic connection between ferroelectric polarization and magnetically gradient structure to probe the potential linear magnetoelectric (ME) effect. In this work, we address this issue and investigate the magnetism of Fe _2 GeO _4 single crystal that hosts two successive anomalies at antiferromagnetic (AFM) Néel temperatures T _N1 ∼ 7.5 K and T _N2 ∼ 6.7 K, respectively. Our results reveal a remarkable metamagnetic transition in the magnetization as a function of the magnetic field, occurring at a critical magnetic field H _c ∼ 4.1 T when applied along the [110] and [1–10] directions, while such transition along the [001] direction is pointedly absent. Further exploration uncovers two predominant off-diagonal ME coefficients α _yz and α _zy in the incommensurate AFM phase between T _N1 and T _N2 . Additionally, all components of the linear ME tensor remain non-vanishing in the canting AFM phase below T _N2 . This indicates the ME mechanisms for the two phases that may be driven by different magnetic structures. All these presented results are sufficient for us to draw a non-trivial ME phase diagram, which is beneficial to understanding the ME behavior of Fe _2 GeO _4 . Therefore, our study implies that Fe _2 GeO _4 , an unusual frustrated magnet, provides a platform for manipulating the fascinating ME effect in the spinel structure.