Experimentally, I think you need to follow this conversion:

1- Ms in emu/g into Ms in J/T.g : this is done by dividing with a factor of 1000

http://ieeemagnetics.org/index.php?option=com_content&view=article&id=118&Itemid=107

row 9

so you will have a unit of J/T.g

2- Ms in J/T.g to Ms in μB/g this is done by dividing with μB value 9.274×10−24 J/T . so you will have the Ms in unit of μB/g

https://en.wikipedia.org/wiki/Bohr_magneton

3- Ms in μB/g to Ms in μB/Fe3+: you must multiply by molecular weight of your composition then multiply by the number of Fe3+ atoms in the composition.

hopping this can help.

Thank you very much for your detailed explaination

Please distinguish between the effective moment

meff(uB)=g sqrt(S(S+1)) deduced from magnetic susceptibility measurments

and the moment m(uB) deduced from Ms

m(uB)=g S

You can take g=2 in your estimation

The answer to the question as it is formulated, is rather simple: you just divide the moment/f.u. by the number of Fe3+ ions in the f.u. assuming there are no other magnetic ions present ( the Bohr magneton is traditionally written as μB and not μB). In your computation you only must take care of the units for magnetic moment, as described in detail in the answer of Sadeq H. Lafta .

Dear Raman,

In your words ‘What is the difference between µB/f.u. and µB/Fe3+ ions’, in a General sense, the second is the magnetic moment of one iron cation (or atom). For an atom (ion) in the free state, the total moment is gJ*sqrt(J*(J+1), where J is the total quantum number, gJ is the Lande factor. The orbital momentum of 3d metals is almost completely inhibited ("quenched" orbital angular momentum L ~ 0) by the influence of the shells of neighboring atoms in the crystal, so only the spin component of the total magnetic moment plays a role, and the formula given by you works. However, again, this is not the whole truth. In the creation of the magnetic moment of the crystal of magnetically ordered substances, only the component of the magnetic moment of the atom (ion), parallel to the quantization axis (“acting moment”), the other components are averaged to 0 for different atoms. The average (resulting) magnetic moment of a ferromagnetic or sublattices of a ferrimagnetic in the roughest approximation for collinear structures (there are also features) is determined by the sum of gJ*S*µB, which in the case of Fe3+ gives 5µB (at gJ = gS = 2, S = 5/2). But that's not all. In many alloys, under the influence of the environment (neighboring atoms of another sorts) atoms may exhibit magnetic moment, different from their usual values. The result also depends on the fact that some ions may be in a high- or low-spin state.

Due to thermal oscillations, atomic magnetic moments also differ less from those obtained in the calculation of the vector model and Hund's rules.

Next, let's talk about the magnetic moment of the formula unit. Complex structures, compounds can be composed of a heterogeneous set of atoms or ions, some of which have a nonzero magnetic moment. For such substance, it is possible to write a General "chemical" (crystallochemical) formula, which displays the ratio between different elements in atomic fractions, taking into account their distribution in the structure of the magnet and the mutual orientation of the magnetic moments of the individual components of the formula. This minimally allocated structural unit is called a formula unit. Its magnetic moment is determined by the magnetic moments of the entering atoms\ions and their mutual arrangement (orientations) in the crystal lattice. The vector sum of the effective magnetic moments in the units of the Bohr magneton is the answer to the first part of your question.

Now let's say about your material which relates to the interesting class of high-temperature multiferroics-magnetoelectrics. Bismuth ferrite with perovskite structure refers to weak ferromagnets in which the magnetic moments of the atoms are ordered almost antiparallel (antiferromagnetic ordering). Thus, the components of the magnetic moments of the neighboring iron cations along the so-called axis of antiferromagnetism L (almost equal to the total magnetic moment µ(Fe3+), taking into account the comments made above about the effective value of the magnetic moment and thermal disorientation) compensate each other, and along the perpendicular axis (the axis of ferromagnetism) they form a weak ferromagnetic moment. It is extremely small, that explains the very modest result of your calculations. Your calculated value at a given temperature represents the contribution of each Fe3+ ion (= the corresponding formula units of BiFeO3 type) in the resultant moment. It is expected to be much lower than the total magnetic moment of the one Fe3+ cation. In order to convert this value in terms of µB/Fe3+ ions, it is necessary to know the angle of mutual orientation of the sublattices of iron in the structure of bismuth ferrite, for example, from the data of neutron diffraction experiments. In this case, µ(Fe3+) = 0.0049µB/sinA, where A is the angle between the magnetic sublattice and the antiferromagnetism axis.

In conclusion, I would like to mention an interesting feature of your material. It rotates the antiferromagnetism vector in one of the planes, and the spins of the Fe3+ ions are arranged in the form of a spatial cycloid. As a result, the size and direction of the lateral bevel (angularity) of the magnetic sublattices changes. Therefore, it should be noted that the observed value of the weak ferromagnetic moment can vary within different local regions of the sample. The spin cycloid can be destroyed\suppressed by a strong magnetic field or by mechanical stresses. In this case, a large linear magnetoelectric effect is manifested, which is of great research interest for practical applications of multiferroid materials.

Respected Researcher Alexander,

Thank you very much for your detailed and an impressive explanation about the correlation between Bohr magneton per formula unit with the Bohr magneton per Fe3+ ion. in this connection, is it possible to calculate the angle of mutual orientation of sublattices of iron other than neutron diffraction. For example, from Rietveld refinement analysis, we can calculate the tilt angle of FeO6 octahedra and the angle of tilt due to Fe1 - O - Fe2 bond angle may be around 140 . From these values is it possible to Bohr magneton/Fe3+ ion.

Thanks in advance

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