Since it is hard to measure the mass of your thin film, I wonder if you convert magnetisation to emu/g. According to my knowledge, typical VSM measurements provide emu/cm3 unit for an M-T measurement. How can we determine the mass of a thin film?
For very thin films, an estimate of thickness, leading to estimate the mass of the deposit, an altenative way is using X-ray grazing incidence experiment leading receiving reflectometry fringes. So one can evaluate the magnetization per gram of matter. But as said by Muhammad and Halkom, an estimate is not esasy to refine and should be conducted using different methods if possible.
Another way, especially appkicable to well known ferromagnetic materials is to determine the saturation magnetization and compare to data from bulk materials. In this way you have to account for a possible deviation of the magnetyic properties of the interface layers between substrate and deposit (chemically or mechanically related effects).
As well and in in particular cases, one has made profit of neutron absorption iif the checked elements of the defined structure have cross sections significantly high, provide the chemical composition is well known.But you have to know parallel if your material is well crystallised.
For thicker deposits (µm scale) some have used the technique of bias cutting with SEM or profilometry observations.
For all cases, it is difficult to get very precise information (esd. > 10%)
Usually, we measure magnetization in a magnetometer in units of emu. If you know the are of substrate and thickness of the film, then you can convert emu into emu/cm3. To measure magnetization in units of emu/g. You should know correct value of mass of the film. You should measure the substrate mass before deposition and then measure again after deposition. The difference between mass values before and after the deposition will be the mass of the films deposited on your substrate. You have to me careful about the mass of the glue used to attached the substrate with substrate holder. If you know a correct value of volume of the film then use density to calculate the mass.
For very thin films, an estimate of thickness, leading to estimate the mass of the deposit, an altenative way is using X-ray grazing incidence experiment leading receiving reflectometry fringes. So one can evaluate the magnetization per gram of matter. But as said by Muhammad and Halkom, an estimate is not esasy to refine and should be conducted using different methods if possible.
Another way, especially appkicable to well known ferromagnetic materials is to determine the saturation magnetization and compare to data from bulk materials. In this way you have to account for a possible deviation of the magnetyic properties of the interface layers between substrate and deposit (chemically or mechanically related effects).
As well and in in particular cases, one has made profit of neutron absorption iif the checked elements of the defined structure have cross sections significantly high, provide the chemical composition is well known.But you have to know parallel if your material is well crystallised.
For thicker deposits (µm scale) some have used the technique of bias cutting with SEM or profilometry observations.
For all cases, it is difficult to get very precise information (esd. > 10%)
Yet another method would consist in controlling/monitoring the deposition rate. Still, the instruments / methods used for this purpose must be properly calibrated to produce reliable results. out of the box, being better than 10% is not easy to achieve, as mentioned before.
If you can reliably produce a shadow mask on some part of the sample during deposition, profilometry might prove of good use.
Edit:
anyway, I don't like emu's. My preferred unit would be Bohr magnetons per atom... (but that's just me and may bear the risk of being misleading, e.g. in alloys or compounds). The proper definition of magnetization is magnetic moment per volume.
According to http://www.ieeemagnetics.org/index.php?option=com_content&view=article&id=118&Itemid=107, the IEEE magnetic units table, one can express magnetisation in terms of volume or in terms of mass.
If I receive a non compact magnetic material (non densified powder, foam etc etc...) it seems me very difficult to try defining the number of Bohr magnetons per atom,
If I don't know the effective density,(volume of pores), if I don't know the formula (leading to attribute a magnetic moment to each of the species) if I don't know the electronic state of each of the atoms) etc... This is why e.g. the magnet makers express magnetization in Am2/kg (=emu/g).
Also for thin films, the effective volume is not so easy to define.(as you said above), but knowing the mass before and after deposit on the substrate, it seems me that emu/g is a unit more directly readible, also to compare more easily from a sample to another one.
Now when using magnetic neutron diffraction or XMCD, it appears absolutely obvious to consider .Bohr magnetons per atom.. since your "visible units" from refinement are atoms.