Role of local short-scale correlations in the mechanism of pseudo-diamagnetism

We elaborate here why the antiferromagnetically ordered GdCrO$_3$ responses in diamagnetic way under certain conditions, by monitoring the evolution of microscopic global and local magnetic phases. Using high energy E $\sim$ 0.3 eV neutrons, the long range ordering is inferred comprising of thermal variation of three distinct magnetic phases : G$_x^{Cr}$,A$_y^{Cr}$,F$_z^{Cr}$ just below N\'eel temperature = 171 K; (F$_x^{Cr}$, C$_y^{Cr}$, G$_z^{Cr}$)$\bullet$( F$_x$$^{Gd}$,C$_y$$^{Gd}$) below 7 K and an intermediate phase in the vicinity of spin-reorientation phase transition; T$_{SRPT}$ (H) = (20 K $\leq$ T $\leq$ 7.5 K). Although, the bulk magnetometry reveals huge negative magnetization (NM) in context of magnitude and broadness ( M$_{- max}\geq 30 \times M$$_{+ max}$, $\Delta$T $\sim$ 110 K in presence of $\mu$$_0$H = 100 Oe ); the long-range magnetic structure and derived ordered moments remain silent about NM. The real-space analysis of total (Bragg's + diffuse) scattering reveals the significant AFM correlations functioning up to $\sim$ 10 $\AA$. Accounting these short-range correlations with `anisotropic next-nearest neighborhood interactions' model and considering the degenerate ground state of Gd$^{3+}$ comprising three distinct Ising spin interactions J$_i$ (i = 1-3), we divulge that the unique combination of J$_i$s governs the observance of NM in GdCrO$_{3}$.