Magnetic structure and magnetization of helical antiferromagnets in high magnetic fields perpendicular to the helix axis at zero temperature

The zero-temperature angles of magnetic moments in a helix or sinusoidal fan confined to the $xy$ plane, with respect to an in-plane magnetic field Hₓ applied perpendicular to the z axis of a helix or fan, are calculated for commensurate helices and fans with field-independent turn angles $kd$ between moments in adjacent layers of the helix or fan using the classical J₀-J₁-J₂ Heisenberg model. For 0<kd<4π/9, first-order transitions from helix to a fan structure occur at fields Hₜ as previously inferred, where the fan is found to be approximately sinusoidal. However, for 4π/9≤kd≤π, different behaviors are found depending on the value of $kd$ and these properties vary nonmonotonically with $kd$. In this $kd$ range, the change from helix to fanlike structure is usually a crossover with no phase transition between them, although first-order transitions are found for kd=3π/5 and 8π/11 and a second-order transition for kd=3π/4. At a critical field Hc, the fan or fanlike structures exhibit a second-order transition to the paramagnetic state. The Hc for a helix undergoing a field-induced change to a fan or fanlike structure is found to be the same as for a sinusoidal fan with the same $kd$ and interlayer interactions. Analytical expressions for Hc versus $kd$ are presented. We also calculated the average x-axis moment per spin μₓₐᵥₑ versus Hₓ for helices and fans with crossovers and phase transitions between them. When smooth helix to fanlike crossovers occur in the range 4π/9≤kd≤π,0.16em0exμₓₐᵥₑ exhibits an S-shape behavior with increasing Hₓ. This predicted behavior is consistent with μₓₐᵥₑ(Hₓ) data previously reported by Sangeetha et al. [Phys. Rev. B 94, 014422 (2016)] for single-crystal EuCo₂P₂ possessing a helix ground state with kd≈0.85π. The low-field magnetic susceptibility and the ratio Hₜ/Hc are calculated analytically or numerically versus $kd$ for helices, and are shown to approach the respective known limits for kd→0.