# Thermomagnetic convection

Hello!

I'm currently reading papers about ferrofluids and trying to understand the physics behind this topic.

I do understand, that if we consider a vertikal temperature gradient, we get a antiparallel magnetization gradient. The ferrofluid with a the higher magnetization will move to the area with higher magnetic field, if we have applied an external magnetic field gradient.

But if we consider a constant external magnetic field, the magnetization gradient induces a antiparallel magnetic field gradient. As far as I know, ferrofluids are superparamagnetic and therefore density of magnetic field lines will rise. So, in my mind, the magnetic field gradient has to be in the same direction as the magnetization gradient for a constant external magnetic field.
Here you can see an illustration of the above example: http://www.mpipks-dresden.mpg.de/~adlange/research.html#thermomagnetic"

Can somebody explain this phenomena?

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The mathematical solution is actually easy:

$div\vec{B}=0$

with

$\vec{B}= \mu_0(\vec{M}+\vec{H})$
$\vec{H}=\begin{pmatrix} 0 \\ 0 \\ H_z \end{pmatrix} ,\vec{M}=\begin{pmatrix} 0 \\ 0 \\ M_z \end{pmatrix}$

we get

$\frac{dH}{dz} = -\frac{dM}{dz}$

But the physical explanation?!