The choice of the magnetic field results from the physical property you want to measure. A paramagnet shows a magnetization proportional to the magnetic field. If you want to measure the paramagnetic property of your sample this is fine. If your sample is ferromagnetic but consists of a very small amount of material on a paramagnetic sample holder that has orders of magnitude more weight, the large field results in a sizable magnetic moment of your sample holder but negligible moment from your sample. In this case you want to have a small field that conserves the moment from your sample but does not induce a large moment in the sample holder. A second reason could be if you want to measure the phase transition from ferromagnetism to paramagnetism, a large field will smear out this phase transition due to the huge paramagnetism in the vicinity of the Curie temperature.

Though the measurements of MH and MT seem quite similar, there is a vast difference in the purpose of measurements. In MH measurements, we actually measure the effect of the field along with the effect of temperature. But in MT measurement we are interested to observe the effect of temperature only. For an ordered magnetic system, exchange interactions play a major role in its magnetization, which creates an aligned moment system in the lattice. If all of them are perfectly parallel to each other, then the moment is maximum. But in reality, they are not so. This deviation can occur in two ways, one is due to the initial structure they can be parallel, antiparallel, canted, inequal, etc. Another one is deviation by fluctuation from its initial position due to thermal agitation.

With an increase in this thermal energy, this fluctuation increases, and that exchange interaction starts to get decreased from its previous value, and a change in magnetization is observed.

However, this change in value is very less compared to the initial value obtained at the lowest measured temperature.

Actually, the here main purpose is not what is the value, rather main interest is in the nature of variation.

So, here the intention is to observe the effect of temperature (not the effect of field) on the internal magnetic structure. Now with the applied external magnetic field, the intrinsic moments will get affected, and the actual magnetism will be changed and cannot be observed. Even with a very high field, the effect of exchange interaction gets completely dominated by that external field and no magnetic transition can be observed. So, we try not to disturb the actual magnetic structure during measurements. But without applying field, magnetization measurement is not possible in VSM or SQUID. So, we try to apply a magnetic field as minimum as possible. Also with very low applied field measurement data will get fluctuation noise. So for a normal ordered magnetic system, a 100 - 300 Oe field is applied in SQUID and 300 - 500 Oe in VSM.

Appendix: Though a measurement with a low field you can observe a bifurcation in FC - ZFC curve in the case of superparamagnetic, antiferromagnetic, etc. systems. But with the high field they will merge up, and even the nature of variation will look like a paramagnetic type hyperbola, without any transition peak at the specific transition temperature of that sample. (I personally investigated that with different ordered magnetic systems with two different fields 300 Oe and 30000 Oe)

Thank you Prof. H. J. Elmers and Sukhendu Sadhukhan for your kind response.