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In this work, we propose a novel magnetic-coupled binary PFC model which, to the best of our knowledge, is the first to integrate ferromagnetic ordering and binary atomic density evolution within a unified formulation. The resulting system consists of three strongly coupled and highly nonlinear partial differential equations: two mass-conserved Allen\u2013Cahn type equations for the binary density fields, and a third Allen-Cahn type equation governing the magnetization field dynamics, derived via a Ginzburg\u2013Landau approach. To solve this challenging system efficiently, we further develop a fully discrete scheme that combines the Invariant Energy Quadratization (IEQ) and Zero-Energy-Contribution (ZEC) approaches for time discretization with a Fourier spectral method for spatial discretization. The proposed scheme is linear, fully decoupled, unconditionally energy stable, and second-order accurate in time, enabling robust and efficient simulation of magneto-structural dynamics. Extensive two- and three-dimensional numerical experiments demonstrate the method\u2019s capability to capture magnetically driven phenomena such as crystal growth and phase transitions. This work not only establishes a new theoretical framework for modeling magnetic field-coupled binary systems but also provides an effective computational tool for simulating complex ferromagnetic material behavior.<\/jats:p>","DOI":"10.1007\/s10444-026-10313-8","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T13:28:29Z","timestamp":1777555709000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A new magnetic-coupled binary phase-field crystal model and its efficient fully discrete decoupled energy-stable scheme"],"prefix":"10.1007","volume":"52","author":[{"given":"Hengrui","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kejia","family":"Pan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaofeng","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"10313_CR1","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.camwa.2022.01.029","volume":"113","author":"J An","year":"2022","unstructured":"An, J., Zhang, J., Yang, X.: A novel second-order time accurate fully discrete finite element scheme with decoupling structure for the hydrodynamically-coupled phase field crystal model. 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