Resolving the local distortions of Ising-like moments in magnetoelectric Ho-doped langasite

Abstract

The magnetic properties of Ho-doped langasites (La:Ho)${}_3$Ga${}_5$SiO${}_{14}$ are dominated by the Ising-like magnetic moments of the Ho${}^{3+}$ ions. In their saturated regime, the induced magnetic state breaks both time and space inversion symmetries, leading to a novel linear magnetoelectric effect. However, due to distortions induced by a shared Ga/Si occupancy of the 2d sites, resolving the microscopic nature of the magnetic configuration remains a difficult task. Here we combine polarized neutron diffraction and angular dependent magnetization experiments to determine the local distortions of the Ho${}^{3+}$ magnetic moments in doped langasites (La${}_{1-x}$Ho${}_x$)${}_3$Ga${}_5$SiO${}_{14}$ with $x\approx 0.015$ and $x\approx 0.045$. We propose a model for a field-induced magnetic configuration with arbitrary orientations of the local Ising axis of Ho${}^{3+}$ in distorted positions. The operations of broken local $C_2$ symmetry and rotations around the trigonal $C_3$ axis connect different sites, restoring the global P321 symmetry of the crystal and simplifying the description of the magnetic properties. The superposition of two distorted Ho${}^{3+}$ positions connected by $C_2$ symmetry determines the local magnetic susceptibility tensor, which no longer appears Ising-like at low fields.

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