It's just a convention - you take the "mean field" such that the system magnetizes in the z direction, and take the magnetization in the other directions to zero.
More generally, in an arbitrary coordinate system, you assume that the system has a uniform magnetization given by
$$
\mathbf{M} = \langle \mathbf{S}_i \rangle = M \hat{e}
$$
where ##\hat{e}## is a unit vector in some direction. Now just choose your coordinate system such that the z direction points along ##\hat{e}##, and then you have ##\langle S^+ \rangle = \langle S^- \rangle = 0## in that coordinate system.
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling We Value Civility
• Positive and compassionate attitudes
• Patience while debating We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving