Observation of competing magnetic phases, mechanical stability, electronic structure, magnetism, and remarkable thermoelectric aspects of Ba ₂ GdRuO ₆

The Ba₂GdRuO₆ double perovskite oxide demonstrates intriguing behavior, arising from competing antiferromagnetic (AFM) and ferrimagnetic (FiM) phases. Under the GGA+<i>U</i>+SOC scheme, the system exhibits an AFM ground state with a very small energy difference of -11.39 meV compared to the FiM one. In contrast, spin modeling reveals significant magnetic frustrations along the <i>z</i>-axis and favors the FiM phase. Also, the magnetic phase transition discloses a Curie temperature (<i>T</i>_C) of 60 K. Additionally, magnetization measurements also affirm the FiM nature which loses saturation at higher temperatures, indicating a transition from FiM to paramagnetic, above <i>T</i>_C. The electronic structure displays the semiconductor nature owing to a direct energy gap of 1.04/0.89 eV in the AFM/FiM state. The determined spin moments on the Gd(1-2)/Ru(1-2) and Gd(3-4)/Ru(3-4) ions are +6.9/+2.0<i>μ</i>_B and -6.9/-2.0<i>μ</i>_B in the AFM spin-orbit, respectively, while they are +6.89/-2.0 on the Gd(1-4)/Ru(1-4) ion in the FiM one. It is found that the Gd³⁺ and Ru⁴⁺ ions lie in +3(4f⁷) and +4(4d⁴) valence states with electronic configurations [f_{<i>x</i>(<i>x</i>²-3<i>y</i>²)}]↑⁰↓¹ [f_{<i>y</i>(3<i>x</i>²-<i>y</i>²)}]↑⁰↓¹ [f_{<i>z</i>(<i>x</i>²-<i>y</i>²)}]↑⁰↓¹ [f_<i>xyz</i>]↑⁰↓¹ [f_<i>xz</i>²]↑⁰↓¹ [f_<i>yz</i>²]↑⁰↓¹ [f_<i>z</i>³]↑⁰↓¹ and t32g↑t12g↓e0g↑e0g↓ with spin quantum numbers of 7/2 and 1, correspondingly. Furthermore, the mechanical stability of the material is validated by satisfying the Born stability criteria and the ductility is determined using Pugh's ratio . Noticeably, the presence of a positive Cauchy pressure of 66.53 GPa further supports the ionic nature of the motif. Besides, the system illustrates a positive Seebeck coefficient, indicating holes as the dominant charge carriers with the highest value of 279 μV K^-1 at 400 K. Remarkably, the system achieves a high figure of merit of 0.86 at 550 K even with the inclusion of lattice thermal conductivity, as well as sustaining excellent thermoelectric performance, suggesting a strong potential for elevated temperature energy harvesting applications along with spintronics.