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We model and analyse the secular evolution of stellar bars in spinning darkmatter (DM) haloes with the cosmological spin lambda ~ 0 -- 0.09. Usinghigh-resolution stellar and DM numerical simulations, we focus on angularmomentum exchange between stellar discs and DM haloes of various axisymmetricshapes --- spherical, oblate and prolate. We find that stellar bars experiencea diverse evolution which is guided by the ability of parent haloes to absorbangular momentum lost by the disc through the action of gravitational torques,resonant and non-resonant. We confirm the previous claim that dynamical barinstability is accelerated via resonant angular momentum transfer to the halo.Our main findings relate to the long-term, secular evolution of disc-halosystems: with an increasing lambda, bars experience less growth and dissolveafter they pass through the vertical buckling instability. Specifically, withan increasing halo spin, (1) The vertical buckling instability in stellar barscolludes with inability of the inner halo to absorb angular momentum --- thisemerges as the main factor weakening or destroying bars in spinning haloes; (2)Bars lose progressively less angular momentum, and their pattern speeds leveloff; (3) Bars are smaller, and for lambda >= 0.06 cease their growth completelyfollowing buckling; (4) Bars in lambda > 0.03 haloes have ratio ofcorotation-to-bar radii, R_CR / R_b > 2, and represent so-called slow barswhich do not show offset dust lanes. We provide a quantitative analysis ofangular momentum transfer in disc-halo systems, and explain the reasons forabsence of growth in fast spinning haloes and its observational corollaries. Weconclude that stellar bar evolution is substantially more complex thananticipated, and bars are not as resilient as has been considered so far.

What Makes the Family of Barred Disc Galaxies So Rich: Damping Stellar Bars in Spinning Haloes