I wish to learn the basics of commensurate and Incommensurate phases in the magnetic systems.
We discussed this topic before in Research Gate. Please go through the previous discussion.
You asked the following questions in RG on May 30, 2013 (about a year ago):
Could you please explain what are the commensurate and incommensure phases in magnetic materials?
We have observed in the literature review that some magnetic transitions are because of the commensurate and incommensurate phases of the Mn-ions (in multiferroics RMn2O5).
My answer was:
The simple antiferromagnetic structures have those where magnetic moments are arranged in up and down fashion (black and white). This results in usualy cell doubling (or tripling etc.). For example in type-II fcc magnetic structures the chemical cell is doubled in all three a b c directions. We say that the magnetic structure has a propagation vector k =(1/2,1/1,1/2). Now suppose that the magnetic moments are not exactly antiparallel but vary slowly by small angular steps as you move in 111 direction. The propagation vector is then k = (delta, delta , delta) where delta say is delta=0.123. The magnetic structure is then incommensurate because the magnetic cell is not commensurate with the chemical cell.
There is a huge amount of literature on incommensurate (modulated) magnetic structure. Read the chapter "Marnetic Structure" of the book "Magnetic Neutron Scattering" ed. Tapan Chatterji, Elsevier (2006).
If the dimension of the magnetic unit cell is equal to integer multiple of nuclear unit cell, the magnetic structure is commensurate. For example, up-down arrangement of spins along all three directions, here the magnetic unit cell is doubled along all the three directions ( a_mag*b_mag*c_mag = 2a_nuc*2b_nuc*2c_nuc). When the magnetic unit is non-integer multiple of nuclear unit cell, the magnetic structure is incommensurate ( for example, a_mag*b_mag*c_mag = delta*a_nuc*delta*b_nuc*delta*c_nuc) where delta is non-integer say delata = 1.12.
In case the book by Tapan Chatterji is not available ,there are good articles like "Competing interactions, magnetic frustration, the“Devil’s Staircase”, and other exotic phenomena:How they become real in multiferroic compounds" ByBernd Lorenz and Commensurate-Incommensurate Magnetic Phase Transition in Magnetoelectric Single Crystal LiNiPO by Vanknin et al may provide answers to your questions.
Dear Philippe Lerch,
I understand the "A commensurate state with a very simple picture. ". Could you explain more about the system TbMnO3 where the spins of Mn3+ ions form an incommensurate cycloidal spin spiral below Tlock = 28 k? What field in the system TbMnO3 plays the role of gravitational potential in the simple picture? and the strength of the triangular bonds ?
Thank you everyone for your valuable comments. However, in a few of them, the commensuration/incommensuration has been described as the "integer/non-integer" multiple of the nuclear unit cell. It would be better to say the multiplier is a "rational/irrational" number rather than an "integer or non-integer". Thanks a lot.
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