Long-range spin-pairing order

Singlets and long-range spin-pairing-order... 

Recently, in Ref. 30, it has been shown that monoconfigurational covalent VB structures for ladder materials show a long-range spin-pairing order (LR-SPO). This LR-SPO can be easily generalized to our present strips. 

Table 1 Long-range spin-pairing order p as defined by Eq. (23) of the RVB ansatz and the energy per site in units of J for the linear spin-1/2 Heisenberg chain with nearest- and next-nearest-neighbor spin interactions yield by the M = 5 bonds RVB ansatz with SP parterns of Eqs. (54)-(56) and the M = 5 sites NSBA ansatz with the spin-flip paterns of Eqs. (16)-(18). The lower and upper bounds and the extrapolated results from finite systems of van den Broek et al. [26], the exact results at a = 0 of Hulthen [19] and at a = 0.5 of Majumdar [25] have been included for comparison. At a = 0.5 the RVB ansatz yield the exact result p(J = 1/2) = 3/16.

The property of the spin-triplet components fi,2,z un) = — /i,2,3(—w ) means that their presence is not easy to observe. For example, the order parameter A is related to the sum X n=-oo /(wn) in which all contributions of the odd functions f 1,2,3 cancel. However, there are phenomena where the presence of the spin-triplet pairing plays a crucial role. One of them is the effect of the Tc dependence on the mutual orientation of magnetizations in the F/S/F structure. Another one is the predicted long-range proximity effect based on the spin-triplet component, which should lead to a Josephson current in F/S/F/S structures with anomalously thick F-layers.[10] The latter is relevant for experimental results of Ref. [5]. 

In order to reduce the dimension of the model space, several attempts have been made to find associated topological quantum numbers which would allow to separate the covalent VB space into non-mixing different subspaces (see Ref. 30 and references therein). For the linear chain, preliminary attempts were made early in 1979 [31], when a parameter measuring the spin-pairing long-range order was suggested,... 

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