magnetic pyrochlore oxide with chemical composition A2B2O7(A is a rare-earth ion and B is usually a transition metal) in spin ice phases (for example Ho2Ti2O7 or Dy2Ti2O7 ) with two spinis in and two spins out of the tetrohedron are geometrical frustration systems with ferromagnetic magnetic order.beacuse when plot the cheakerboard of this systems show ferromagnetic order.also these system have positive Weiss temperature.

I think this article is a good referece for magnetic pyrochlore oxide

Thank you so much . If I am not wrong can I say even though theeta is positive there is a possibility of antiferromagnetic coupling if theeta/TC is greater than one?

@S gupta. Please give some references which explain these details.

Thank you so much..

In mean field theory, we expect Tc to be equal to theta. However in real systems Tc is normally less than theta, i.e. Tc/theta < 1. So your observation is not unusual. In order to get long range order (three dimensional) we need communication between spins throughout the solid . In many systems (particularly in molecular materials), there may be strong interactions between spins in, say, one or two dimensions but long range magnetic order only sets in at much lower temperatures once the interactions between 1-D chains or 2-D layers becomes significant. Thus strong ferromagnetic interactions may exist in the system but bulk order need not exist unless those interactions lead to 3-D cooperativity. Long range order is therefore really dependent upon the weakest of your interactions.

Frustration can only occur in the presence of antiferromagnetic (AF) interactions when the AF interactions cannot be simultaneously satisfied e.g.on a triangular plaquette. In these cases it proves impossible to write a spin configuration in which the AF interactions between all spins are simultaneously satisfied and the spin arrangement is termed 'frustrated'. If interactions between spins are all ferromagnetic then there is no possibility of frustration.

Hope that helps.

@ J Rawson Thank you so much for such a clear explanation. In my system there are two magnetic ions one from 4f and another from 3d with layered crystal structure. Above 200 K I have fitted C-W with a slope change at this temperature again a linear part is there which fits to unusual effective magnetic moment. I could not find second ordering temperature regarding 4f ion. Can I say it as a ferromagnetic transition?

Thanks

Ultimately you need to see clear evidence for your long range ordering in order to say you have a ferromagnetic transition, e.g. below Tc you should see your susceptibility become field dependent (i.e. chi depends upon the applied field H below Tc). If you are able to run ac susceptibility measurements then you should see an out-of-phase component in the ac data (chi") below Tc. You will most likely see hysteresis in M vs H plots too. The magnitude of the saturation magnetisation in your M vs H plot below Tc should saturate at approx gS(TM) + gJ(Ln) Bohr magnetons where g corresponds to the different g values for each ion present.

There are other reasons why you might see changes in gradient of your Curie-weiss plot which may include a spin transition for your d-block metal from high spin to low spin (depends on coordination environment at the metal), or the presence of residual orbital angular momentum, especially common for cobalt(II) ions.

If you have any information regarding (i) the metal ions present and coordination geometry for the d-block metal; (ii) any data relating to the field dependence of either chi or the magnetisation at/below Tc then this'd help trememdously in making any further comment.

@ J Rawson Thanks a lot. M(H) does not show saturation and its become linear in high fields (above 5 kOe) with magnetic moments around 0.4 Bohr magnetons as well as increasing at lower temperatures (recorded lowest at 10 K though Tc is around 80 K). There is negligible Hc (

Hi Brajesh, A magnetic moment of 0.4 BM seems very low for a system containing Co(II) and a rare earth element. Could you tell me which rare earth you have and, in the high T region, what is the value fo your Curie constant and Weiss constant? If you prefer you can send me the raw SQUID data you have.I'll see if I can make sense of it.

@ J Rawson Thank you so much. Pr is the rare earth and Curie constant Cmol = 4.38 emu. mol-1.Oe-1K Theeta is 136 (positive ferromagnetic). Sorry I cant send the data now.

Thanks.

Thank you so much.

You might also consider having a ferrimagnet, i.e. TM and RE moments exhibiting AFM coupling with respect to each other, but nevertheless a net moment. Also, the Pr response in particular, may be altered by crystal field splitting and therefore develop characteristics that look like some ordering phenomenon.

Magnetic moments are expected to order when cooled below a certain temperature. The value of this temperature is set by the strength of coupling between the individual moments (spins). In most magnetic solids these magnetic moments form a long-range ordered ferromagnetic (parallel moments) or antiferromagnetic (alternating moments) structure, depending on the nature and strength of the interactions of the spins. However, in some “frustrated” magnetic solids, the low temperature phase has no long-range order. Instead, they develop some exotic states with short-range spin correlations.

One of the causes for frustration in magnetic materials is geometric, arising purely from crystal symmetries which result in triangular or tetrahedral arrangements of anti-ferromagnetically (AFM) coupled spins. Typical examples of geometrically frustrated structures are pyrochlore or kagome lattices, where the lattice consists of linked corner-sharing triangles or tetrahedra. This kind of lattice geometry creates a high degeneracy of ground states between which the system can fluctuate with almost no energy expenditure, even down to a few milliKelvin temperatures. Geometric frustration in magnetic solids leads to a variety of cooperative spin states, some of which are spin liquids, some spin glasses, and spin ice systems.

Reference by web link:-

http://faculty1.ucmerced.edu/sghosh/2.cfm?pm=235&lvl=3&menuid=238

Thank you both of you. @ k. Fauth. In your comment " looks like some ordering.." due to crystal field effect that means it is not exactly some type of ordering. Can you please suggest some references which make to understand these phenomenon in some more detail. Please explain. Thank you.

I am willing to do so but may take a little time.

ok no problem for me.. Thank you so much.