Helical-to-Fan Transitions under Magnetic Fields in the Noncentrosymmetric Tetragonal Magnet EuRhGe$_3$

Abstract

The magnetic structure of EuRhGe$_3$, a noncentrosymmetric body-centered tetragonal magnet with the space group $I4mm$, has been investigated by resonant X-ray diffraction. Below $T_{\text{N}}=12$ K, EuRhGe$_3$ undergoes a helical magnetic ordering with an incommensurate propagation vector $q=(0, 0, 0.809)$, in which the magnetic moments lie in the $ab$ plane and rotate by a constant turn angle of $145.8^{\circ}$ between adjacent layers. When a magnetic field is applied along the $a$ axis at 2 K, a second-harmonic $2q$ peak develops, indicating that the circular helix is gradually distorted into a helimagnetic soliton-lattice state, which eventually undergoes a lock-in transition to the commensurate structure with $q=0.8$ at 3.8 T. Above the subsequent phase boundary at 5 T, the helicity is lost, and a spin-flop $xyz$-fan (elliptic conical) state is realized, in which the moments oscillate predominantly along the $b$ axis but are accompanied by a small $c$-axis component. At higher fields, the system enters a conventional planar $xy$-fan phase without a $c$-axis component. EuRhGe$_3$ provides a prototypical example of a helimagnet that exhibits a full sequence of field-induced structures, evolving from a circular helix to a spin-flop $xyz$-fan (elliptic conical), and finally to a planar $xy$-fan structure, which has been theoretically predicted.