The growth of bars in isolated disc galaxies is governed by the exchange of angular momentum between different parts of the galaxy. To understand this better it is best to start with the pioneering paper of Lynden-Bell & Kalnajs (1972; LBK). Using linear analytic theory, these authors showed that it is mainly material at resonance that gains or loses angular momentum. Material at the inner Lindblad resonance (ILR) will lose angular momentum, while material at corotation (CR) and the outer Lindblad resonance (OLR) will absorb it. Since the spiral/bar within CR is a negative angular momentum perturbation, feeding it with angular momentum will damp it, while taking angular momentum from it will excite it. Following in their footsteps, Athanassoula (2003; A03) added a halo (or, more generally, a spheroidal component) and applied the results to the case of bars. Provided the halo distribution function is a function of the energy only, halo material at all resonances will gain angular momentum. This result should be generalisable to other distribution functions, provided energy is the main functional dependence and an appropriate perturbation expansion can be used. Both for the disc and for the halo, there is more angular momentum lost/gained at a given resonance if the density is higher there and if the resonant material is colder and thus more responsive (A03).
So, if a disc galaxy has no halo, or if the latter cannot participate in the angular momentum exchange, the inner disc will emit angular momentum, which will be absorbed by the outer disc. On the other hand, if a halo is present and responsive, then it also will absorb angular momentum. So more angular momentum can be extracted from the inner parts in the presence of a responsive dark matter halo and the bar will grow stronger than in its absence (A03). This explains the `paradox' that bars in halo dominated disc galaxies may grow stronger than in disc dominated cases (Athanassoula & Misiriotis 2002; AM02).
Tremaine & Weinberg (1984) and Weinberg (1985) used nonlinear theory to follow the effect of angular momentum exchange on the slowdown of the bar. They find that, as the bar loses angular momentum, it will slow down, as expected. These works, put together with the analytical studies discussed above, lead to the firm prediction that bars should become stronger and rotate slower in the presence of massive and responsive haloes.