Magnetic structure and magnetization of z -axis helical Heisenberg antiferromagnets with XY anisotropy in high magnetic fields transverse to the helix axis at zero temperature

A helix has a wave vector along the z axis with the magnetic moments ferromagnetically aligned within xy planes with a turn angle kd between the moments in adjacent planes in transverse field H=Hxî=0. The magnetic structure and x-axis average magnetization per spin of this system in a classical XY anisotropy field HA is studied versus kd, HA, and large Hx at zero temperature. For values of HA below a kd-dependent maximum value, the xy helix phase transitions with increasing Hx into a spin-flop (SF) phase where the ordered moments have x, y, and z components. The moments in the SF phase are taken to be distributed on either one or two xyz spherical ellipses. The minor axes of the ellipses are oriented along the z axis and the major axes along the y axis where the ellipses are flattened along the z axis due to the presence of the XY anisotropy. From energy minimization of the SF spherical ellipse parameters for given values of kd, HA, and Hx, four kd-dependent SF phases are found: either one or two xyz spherical ellipses and either one or two xy fans, in addition to the xy helix/fan phase and the paramagnetic (PM) phase with all moments aligned along H. The PM phase occurs via second-order transitions from the xy fan and SF phases with increasing Hx. Phase diagrams in the Hx−HA plane are constructed by energy minimization with respect to the SF phases, the xy helix/fan phase, and the xy SF fan phase for five kd values. One of these five phase diagrams is compared with the magnetic properties found experimentally for the model helical Heisenberg antiferromagnet EuCo2P2 and semiquantitative agreement is found.