Indeed, in an isotropic magnetic material the susceptibility tensor does not depend on the direction of the magnetic field, only on its standard. It is simply represented by a scalar Khi(T, B) instead of a tensor

In fact, it 's a material where magnetization can take any direction in an equiprobable way.

In this case, the magnetization M and the magnetic field H can be effectively parallel.

In such a material, there is no constraint that forces the magnetization to take a privileged direction, unlike anisotropic materials where the magnetization prefers one or two specific directions (called easy magnetization axis) than another.

In general, magnetically, these materials are described by a Heisenberg Hamiltonian, while anisotropic materials are described by an Ising Hamiltonian , XY Hamiltonian, or an anistropic Heisenberg Hamitonian.

When a free atom (or ion) is engaged in a solid, its orbital moment or its spin, are infulenced by their new environment and therefore can no longer "rotate" freely due to the ligands surrounding them. They could be partially or totally blocked in a special direction.

As it was mentioned earlier, magnetization of isotropic magnetic material should always be parallel to the external field. In language of magnetic susceptibility, such behavior is described by diagonal susceptibility tensor with all components equal to each other. This is the case of paramagnet above the Curie temperature. But we are often told that many soft and amorphous magnetic materials are also magnetically isotropic. Is it correct? Well, if the sample is spherical then yes, it acts as an isotropic body. This is no longer true when exactly the same material is formed as a thin tape. Even when its magnetization is uniform (in uniform external field) then it not necessarily follows the direction of the field.

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Thank you for your answers.

In your answers Mohamed El Hafidi and Marek Wojciech Gutowski

you wrote " It is simply represented by a scalar Khi(T, B) instead of a tensor " .

and

" As it was mentioned earlier, magnetization of isotropic magnetic material should always be parallel to the external field. "

My question is : isotropic magnetic material => scalar khi : is this a definition or a conclusion from the fact that it doesn't depend on the magnetic field direction ?

My understanding is that if we start from a tensor susceptibility and then assume that this tensor does not depend on the direction of the field, and we apply 3 fields (1,0,0), (0,1,0) and (0,0,1) (knowing that the magnetization should be the same for these fields) and if the Khi is symmetric (Can you please explain why/why not it is/not symmetric) then we end up with a 3x3 ones tensor and not a diagonal tensor where the 3 diagonal terms are equal.

Another question for Marek Wojciech Gutowski regarding the "shape effect" what makes the magnetization parallel in the case of the sphere and not the thin film ?

Thank you in advance.