Role of local short-scale correlations in the mechanism of negative magnetization

We elaborate here why the antiferromagnetically ordered GdCrO$_3$ responds in a diamagnetic way under certain conditions, by monitoring the evolution of the microscopic global and local magnetic phases. Using high energy $\sim$ 0.3 eV neutrons, the magnetic ordering is shown to adopt three distinct magnetic phases at different temperatures: G$_x^{Cr}$,A$_y^{Cr}$,F$_z^{Cr}$ 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 for 7 K $ \le T \le$ 20 K in the vicinity of spin-reorientation phase transition. Although, bulk magnetometry reveals a huge negative magnetization (NM) in the terms of both magnitude and temperature range ( $M_{- max}$ ( 18 K)$\sim$ 35 $\times M_{+ max}$ (161 K), $\Delta T \sim 110$ K in presence of $\mu_0H$ = 0.01 T); the long-range magnetic structure and derived ordered moments are unable to explain the NM. Real-space analysis of the total (Bragg's + diffuse) scattering reveals significant magnetic correlations extending up to $\sim$ 9 $\AA$. Accounting for these short-range correlations with a spin model reveals spin frustration in the S= 3 ground state, comprising competing first, second and third next nearest exchange interactions with values J$_1$ = 2.3 K, J$_2$ = -1.66 K and J$_3$ = 2.19 K in presence of internal field, governs the observance of NM in GdCrO$_{3}$.