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

We elaborate here why the antiferromagnetically ordered ${\mathrm{GdCrO}}_3$ responds in a diamagnetic way under certain conditions by monitoring the evolution of the microscopic global and local magnetic phases. Using high-energy ($\sim 0.3\mathrm{eV}$) 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 Néel temperature (171 K); ($F_x^{Cr}$, $C_y^{Cr}$, $G_z^{Cr})·(F_x^{Gd}$, $C_y^{Gd}$) below 7 K; and an intermediate phase for 7 K $\le T\le$ 20 K in the vicinity of the spin-reorientation phase transition. Although bulk magnetometry reveals a huge negative magnetization (NM) in terms of both magnitude and temperature range [$M_{-max}\left(18\mathrm{K}\right)\sim 35M_{+max}\left(161\mathrm{K}\right)$, $\mathrm{\Delta }T\sim 110\mathrm{K}$ in the presence of ${\mu }_{0}H=0.01\mathrm{T}$], 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 neighboring interactions with values $J_1=2.3\mathrm{K}$, $J_2=-1.66\mathrm{K}$ and $J_3=2.19\mathrm{K}$ in the presence of internal field, governs the observance of NM in ${\mathrm{GdCrO}}_3$.

Figure 1

(a) Thermal evolution of NPD patterns. (b) $M\left(\mathrm{T}\right)$ curves in ZFC, FCC, and FCW modes with measuring field ${\mu }_{0}H=0.01\mathrm{T}$. Insets (i) and (ii) show the variation of magnetization curves across $T_{\mathrm{ZFC}}$ and $T_{\mathrm{comp}}$ in an enlarged version. Inset (iii) shows nonmonotonic variation of coercivity with respect to temperature, indicating the temperature-dependent evolution of magnetic phases.

Figure 2

(a)–(d) Neutron diffraction patterns along with Rietveld-generated calculated patterns at temperature values $T=160\mathrm{K}$, $T=20\mathrm{K}$, $T=7\mathrm{K}$, and $T=3\mathrm{K}$, respectively. Open circles and solid circles represent experimental and observed data points, respectively. Vertical bars denote Bragg's plane positions. Solid lines are a guide to the eyes. (e) Rietveld-generated patterns based on all possible magnetic configurations along with experimental pattern at $T=15\mathrm{K}$.

Figure 3

(a) and (b) Illustrations of ${\mathrm{\Gamma }}_4\equiv G_x,A_y,F_z$ and ${\mathrm{\Gamma }}_2\equiv F_x,C_y,G_z$ magnetic spin configurations. (c) Variation of magnetic moment components along the $x$, $y$, and $z$ directions. (d) Temperature-driven phase diagram of ${\mathrm{GdCrO}}_3$ along with the variation of total Cr and Gd ionic moments with respect to temperature.

Figure 4

(a) mPDF calculations with reference to two different base temperatures, $T=190$ and 20 K. (b) List of various bond lengths, where $r_{Cr}$, $r_{Gd}$, and $r^{\prime }$ represent the Cr-Cr, Gd-Gd, and Cr-Gd bond lengths, respectively. (c) Illustration of various atomic distances in a single unit cell of ${\mathrm{GdCrO}}_3$. Blue (large) and green (small) spheres represent Gd and Cr atoms, respectively. For the sake of clarity interatomic distances corresponding to $\mathrm{VI}\left[r_{N-N-N}\left(\mathrm{Cr}\text{−}\mathrm{Cr}\right)\right]$, $\mathrm{IX}\left[r_{N-N-N-N-N}\left(\mathrm{Cr}\text{−}\mathrm{Cr}\right)\right]$, and $\mathrm{X}\left(r_{N-N-N-N-N}^{\prime }\right)$ are omitted.

Figure 5

Unit cell of ${\mathrm{GdCrO}}_3$ (left) and pathways of magnetic exchange between Gd ions (right). $J_i$ are the magnetic exchange strengths.

Figure 6

Experimental magnetization data of ${\mathrm{GdCrO}}_3$ and theoretical fit for $J_1=2.3\mathrm{K}$, $J_2=-1.66\mathrm{K}$, $J_3=2.19\mathrm{K}$, and $J_4=-0.23\mathrm{K}$; $H_e^z=-0.18\mathrm{T}$; and $D=0.18\mathrm{K}$.

Figure 7

(a) Calculated eigenspectrum of the model in Eq. (4) for $J_1=2.3\mathrm{K}$, $J_2=-1.66\mathrm{K}$, $J_3=2.19\mathrm{K}$, and $J_4=-0.23\mathrm{K}$. Zoom of the eigenspectrum in the energy range 0 to 1 K for (b) $H_e^z=0$, (c) $H_e^z=-0.18\mathrm{T}$, and (d) $H_e^z=-0.18\mathrm{T}$, $D=0.18\mathrm{K}$. In the $H_e^z=0$ case, the spin states are $2S+1$ degenerate and hence are indexed only by their total spin $S^{\mathrm{tot}}$. For the $H_e^z=-0.18\mathrm{T}$ cases, the degeneracy is lifted, and the states are indexed with ($S^{\mathrm{tot}},M_S^{\mathrm{tot}}$).

Figure 8

Schematic of the kinetic process that involves internal conversion (IC) and intersystem crossings (ISC). The potential energy surface corresponding to various spin manifolds of the system is shown. Each spin manifold is connected to the other by an activation barrier $E_{\mathrm{act}}$.