Picture of magnons/spin waves is misleading right? I am talking about this picture you can find in any textbook on solid state physics:

In the picture the upper level is a view from the side onto the spins whereas the lower level is a view from above.
If you have a system as a ferromagnet and the magnetisation is saturated, the energy required to flip one spin state (from up to down) is proportional to the thermal energy at the Curie temperature. Now many textbooks just say that a energetically more favourable excitation of your spin system is the one given in the picture, where you have a collective precession of the spins around the axis of magnetisation in your material.
It is often said that a magnon reduces the spin in the System by 1 (meaning effectively one spin is turned down from up to down). But in the given picture the spins are all still facing the up direction. Spin is theoretically handled by introducing $m_s$ as a quantum number reffering to the projection of the spin onto the z axis. This value can be $\pm1/2$ where the "+" stands for the orientation as can be seen in the picture (given the z axis points upwards). How is this represented in the picture?
The only explenation I came up with was:
Maybe it is just meant to be a lower energy excitation of the system (which this precession is) but does not imediately have to do anithing with flipping a spin. This however is contradicted by the wikipedia entry on Spin waves where it sais:
"The combined effect of the two operators (raising and lowering operator of spin) is therefore to propagate the rotated spin to a new position, which is a hint that the correct eigenstate is a spin wave, namely a superposition of states with one reduced spin. The exchange energy penalty associated with changing the orientation of one spin is reduced by spreading the disturbance over a long wavelength."
So I guess that in the picture above on spin should be flipped but quantum mechanics doesn't really tell you which one, so each one of them are flipped at the same time in a superposition of states (with normalisation) giving an overall lower energy to excite this as flipping one fixed spin. This of corse is an over simplification but please tell me where I go wrong.
 A: 
It is often said that a magnon reduces the spin in the System by 1 (meaning effectively one spin is turned down from up to down). But in the given picture the spins are all still facing the up direction.

There are exist different spin models: xy-model, Ising model, Heisenberg model, etc. Some of them come in classical and quantum varieties. Thus, how exactly spins move depends on the choice of the model. E.g., if we think of spins as classical magnetic moments coupled via their components perpendicular to the magnetic field, the excitations like the one shown in the OP are very likely. On the other hand, once we talk about spin-1, we imply quantum description, and showing perpendicular and longitudinal components simultaneously is meaningless (since they cannot be simultaneously measured.)

Picture of magnons/spin waves is misleading right?

On a more general level, most spin Hamiltonians do not have boson excitations as their solutions. These appear either as a result of approximations (see, e.g., Holstein-Primakoff transformation), usually implying that only few waves are present or, more formally, as poles in the Green's function (if applying QFT methods.)
