Magnetism: alternating chain

M"3+ diamagnetic, M2+ and M 2+ paramagnetic in this case, the magnetic ions form simple alternating chains [MM F] directed along the c-axis ... 

Figure 7 Some low-dimensional magnetic lattices (a) uniform chain, (b) alternating chain, (c) two-leg ladder, and (d) three-leg ladder...

The low-temperature magnetization (insert of previous figure) of BPCB is essentially zero until 5 tesla when the gap is closed by the Zeeman interaction. There is a rapid increase until 17 tesla when the field overcomes both the rung and rail exchanges. The ladder and alternating chain models make different predictions for M(H) leading to the conclusion that BPCB is a spin ladder with IJrwJk = -13.3 K and Trail/ = -3.8 K. 

An alternative way to describe the phenomenon is to consider that the ground state of a chain is already divided into domains at any temperatures. In order for the system to follow a small variation of the magnetic field some domains have to reverse their spin orientation. This occurs through a random walk of the DWs, that is, equal probability for the DW to move backward or forward, which implies that the DW needs a time proportional to d2 to reach the other end of a domain of length d. Given that d scales as the two spins correlation length, ., which, for the Ising model, is proportional to exp(2///rB7 ), for unitary spins, the same exponential relaxation is found... 

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