Triple point-type morphotropic phase boundary in ferromagnetic (1 − x)TbFe₂–xNdFe₂ system and corresponding magnetoelastic response

The morphotropic phase boundary (MPB) phenomenon plays a pivotal role in ferromagnetic systems for achieving field-induced enhancement of magnetoelastic responses. However, conventionally titled MPBs often show inferior temperature stability, resulting in significant degradation of magnetoelastic performance over broad temperature ranges. In this work, we designed a vertical phase boundary between the tetragonal and rhombohedral phases in the ferromagnetic (1 − x)TbFe₂–xNdFe₂ system, originating from a structural triple point (x _TP). At the MPB composition (x _MPB), large low-field magnetostriction, narrow magnetic hysteresis, and minimal magnetocrystalline anisotropy were simultaneously achieved at room temperature. In situ high-resolution transmission electron microscopy (HRTEM) revealed the coexistence of nanoscale rhombohedral and tetragonal magnetic domains (<10 nm) that persist over a wide temperature range. The formation of such nanodomains is attributed to reduced domain wall energy resulting from near-vanishing magnetocrystalline anisotropy between the two phases. Based on high-resolution synchrotron x-ray diffraction, in situ HRTEM, and magnetometry results, a comprehensive composition–temperature phase diagram was established for this system. The Landau free-energy analysis further demonstrates that the proximity of x _MPB to x _TP leads to an isotropic free-energy landscape, facilitating easy magnetization rotation under external fields and leading to enhanced magnetoelastic response with low hysteresis. This study demonstrates that engineering vertical MPBs provides an effective strategy for designing high-performance, temperature-stable functional magnetic materials.