The magnetization dynamics of the triangular lattice of Ising spin chains is investigated in the framework of a two-dimensional model. The rigid chains are assumed to interact with the nearest-neighboring chains, an external magnetic field, and a heat reservoir that causes the chains to change their states randomly with time. A probability of a single spin-flip process is assumed in a Glauber-type form. This technique allows describing properly the steps in the magnetization curves observed in Ca 3 Co 2 O 6 and their dependence on a magnetic-field sweep rate and temperature. A formation of domain walls due to the nonequilibrium magnetization process and a significant role of their motion are shown.Ising spin chains packed into a two-dimensional ͑2D͒ frustrated lattice demonstrate a complex magnetic behavior due to a combination of a low dimensionality and frustration. There are few groups of compounds in which the triangular lattice is formed by antiferromagnetic ͑AFM͒ Ising spin chains, e.g., CsCoCl 3 and CsCoBr 3 ͑Ref. 1͒ or ferromagnetic ͑FM͒ ones such as Ca 3 Co 2 O 6 . 2,3 A spin-chain system Sr 5 Rh 4 O 12 discovered recently has a complex magnetic structure of chains. 4 An interaction between the nearestneighboring chains in the lattice is of the AFM type and much weaker than the intrachain one. However, it causes the frustration and a large variety of magnetic structures. [1][2][3][4][5][6] A steplike magnetization curve in Ca 3 Co 2 O 6 has drawn recently considerable attention. 3,5-13 The number of the steps depends on a sweep rate of the external magnetic field and temperature. 3,8,10 Two steps become apparent in the temperature range from 12 to 24 K. 10 The first step takes place at the zero magnetic field. Then a plateau at about 1/3 of the full magnetization stretches up to the magnetic field of 3.6 T where the second step to the saturated FM state occurs. At least four equidistant steps are clearly visible below 12 K at a moderate magnetic-field sweep rate. 3,8 At an extremely low sweep rate the magnetization curve becomes close to the two-step shape. Similar to that is observed at high temperatures. 8 A response to alternating magnetic fields and its dependence on the temperature and magnetic field were investigated carefully in Ref. 7. The experimental results show that there exist two characteristic time scales of the magnetization dynamics. The first is of order of 1 s and the second reaches a few hours.A crystal structure of Ca 3 Co 2 O 6 consists of Co 2 O 6 chains running along the c axis. The Ca ions are situated between them and are not involved in magnetic interactions. The chains are made up of alternating face-sharing CoO 6 trigonal prisms and CoO 6 octahedra. The crystalline electric field splits the energy level of Co 3+ ions into the high-spin ͑S =2͒ and low-spin ͑S =0͒ states. The chains form triangular lattice in the ab plane that is perpendicular to the chains. An in-chain exchange interaction between high-spin cobalt ions through the octahedra with low-spin cobalt ions is ferroma...