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The zero-temperature angles of magnetic moments in a helix or sinusoidal fanconfined to the xy plane, with respect to an in-plane magnetic field Hx appliedperpendicular to the z axis of a helix or fan, are calculated for commensuratehelices and fans with field-independent turn angles kd between moments inadjacent layers of the helix or fan using the classical J0-J1-J2 Heisenbergmodel. For 0 < kd < $4\pi/9$, first-order transitions from helix to a fanstructure occur at fields Ht as previously inferred, where the fan is found tobe approximately sinusoidal. However, for $4 \pi/9$ < kd < $\pi$, differentbehaviors are found depending on the value of kd and these properties varynonmonotonically with kd. In this kd range, the change from helix to fanlikestructure is usually a crossover with no phase transition between them,although first-order and second order transitions are found. We also calculatedthe average x-axis moment per spin $\mu_{x ave}$ versus Hx for helices and fanswith crossovers and phase transitions between them. When smooth helix tofanlike crossovers occur in the range $4\pi/9$ < kd < $\pi$, $\mu_{x ave}$exhibits an S-shape behavior with increasing Hx. This predicted behavior isconsistent with $\mu_{x ave}$(Hx) data previously reported by Sangeetha, et al.[Phys. Rev. B 94, 014422 (2016)] for single-crystal EuCo2P2 possessing a helixground state with kd = $0.85\pi$. The low-field magnetic susceptibility and theratio Ht/Hc are calculated analytically or numerically versus kd for helices.

Magnetic Structure and Magnetization of Helical Antiferromagnets in High Magnetic Fields Perpendicular to the Helix Axis at Zero Temperature