All researchers. How could we separately calculate magnetic and lattice entropy for a magneto-structural transition (i.e. magnetic and structure are coupled)?
Do you wish to calculate by ab-inito methods? That will not be easy. But if you have good specific heat data then you may be able to separate these two contributions.
I have specific heat and magnetization data in zero and in the presence of field. In specific heat we will get total entropy of the transition. Now how do we calculate lattice entropy and magnetic entropy? The difficulty is that lattice and magnetism are coupled.
First make sure that there is no hyperfine field contribution which only important at very low temperatures (most millikelvin range). Probably your data are at T >2 K. Then you do not have worry about it. You must model the lattice term by Debye and Einstein functions. If you know phon dispersion and density of states you can calculate the lattice contribution of specific heat (entropy). Your life will e simpler if your system orders at low temperature giving rise to a lambda type anomaly. If this is so then you just substract the lattice specific heat (entropy) from the measured specific heat (entropy). Then you get the magnetic contribution. Your success depends on how well you model the lattice specific heat. The specific heat depends on your system and its structure. If you have a single Bravais lattice then you just have accoust modes and the life is simpler. The Debye function will fit your data well. If you have non-Bravais lattice then your phonon dispersions have both acoustic and opic modes. If the optic modes form more or less flat branches then each such group flat branchs can be modelled approximately by Einstein functions. Read the excellent book of E.S.R Gopal, Specific heats at low temperaturesHeywod books London (1966). This book will give you ideas of modelling the lattice specfic heat. You order t suceed you must fiddle around a it here. If however you have good quality 5 g powdr sample hen you can measure phonon density of states by inelastic neutron scattering. In that case you can directly evaluate the lattice specific heat from these data. Sure for substances with strong spin phonon coupling the job will ore difficult but feasible. Read papers from our group. We have done this for a number of systems.
Suppose we have a structural transition and no magnetic transition. Then in specific heat a peak will come, which is due to structural transition only. Now If magnetic transition also takes place at the same temperature then total entropy of the transition will increased, as a results peak value in the specific heat is increased. But in Debye and Einstein model there has no parts regarding this.
If there is no clear manetic phase transition then the magnetic contribution will come from the short-range magnetic order. If the system is low dimensional then there are analytic expressions of the magnetic specific heat (Onsager, Boner-Fischer etc.). You can try to ft those if the dimensionality of your system is known. But I am afraid that a broad hump like structure on top of lattice contribution will be more difficult to tackel by least squar fit. But you can try.
We know for first order magnetic phase transition, the order parameter is either sub-lattice magnetization or magnetization. If we know how much is the change in magnetization, then we can calculate magnetic entropy from Clausius-Clapeyron equation. But the problem is change of magnetization at magnetostructural transition is depends on structure also. If we can calculate the magnetic moment of the individual atom in the unit cell for two structure then can it be possible to calculate magnetic entropy at the transition?
@Tapan Sir...you wrote in your earlier comment that "First make sure that there is no hyperfine field contribution which only important at very low temperatures (most millikelvin range)". If we have hyperfine field contribution, how to subtract that?
Please read the recent paper attached herewith. The essential point is if you have nuclear spin then the hyperfine field splits the nuclear levels and produces Schooky type of anomaly at low temperature in specific heat. If you know the hyperfine field then it is easy to calculate the contribution otherwise you have to determine the hyperfine field by fitting your specific heat data. This has been done in the attached paper.
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