Magnetization reversal driven by electron localization-delocalization crossover in the inverse spinel ${\mathrm{Co}}_2{\mathrm{VO}}_4$

Neutron diffraction, magnetization, and muon spin relaxation measurements, supplemented by density functional theory (DFT) calculations are employed to unravel temperature-driven magnetization reversal in inverse spinel ${\mathrm{Co}}_2{\mathrm{VO}}_4$. All measurements show a second-order magnetic phase transition at $T_{\mathrm{C}}=168\mathrm{K}$ to a collinear ferrimagnetic phase. Neutron diffraction measurements reveal two antiparallel ferromagnetic (FM) sublattices, belonging to magnetic ions on two distinct crystal lattice sites, where the relative balance between the two sublattices determine the net FM moment in the unit cell. As the evolution of the ordered moment with temperature differs between the two sublattices, the net magnetic moment reaches a maximum at $T_{\mathrm{NC}}=138\mathrm{K}$ and reverses its sign at $T_{\mathrm{MR}}=65\mathrm{K}$. The DFT results suggest that the underlying microscopic mechanism for the reversal is a delocalization of the unfilled $3d$-shell electrons on one sublattice just below $T_{\mathrm{C}}$, followed by a gradual localization as the temperature is lowered. This delocalized-localized crossover is supported by muon spectroscopy results, as strong $T_1$ relaxation observed below $T_{\mathrm{C}}$ indicates fluctuating internal fields.

Figure 1

Temperature dependence of zero-field-cooled (ZFC; black circle) and field-cooled (FC; red triangle) magnetization measurements performed for applied magnetic fields 0.03, 0.25, and 5 T. $T_{\mathrm{C}}$ and $T_{\mathrm{NC}}$ represent the transition temperatures to collinear and noncollinear magnetic structures, respectively, as explained in the text. Magnetization reversal temperature is represented by $T_{\mathrm{MR}}$ for $B=0.03\mathrm{T}$

Figure 2

Neutron diffraction patterns (NPD; black open circles), fits from the Rietveld refinement (red solid lines), and their differences (blue solid lines). The vertical bars are the expected Bragg peak positions as mentioned in the panels. The asterisks indicate impurity peaks. NPD observed (measured on POWGEN) (a) $T=140\mathrm{K}$ and (b) $T=25\mathrm{K}$, corresponding to the data collected with center wavelengths 1.333 Å. In the inset of (b), one can see the emergence of (200) between 140 and 25 K. (c) Magnetic structure of ${\mathrm{Co}}_2{\mathrm{VO}}_4$ at 140 K. (d) Magnetic structure at 25 K. The $A$ site is occupied by Co (red), whereas $B$ site occupancy is shared between Co and V (purple).

Figure 3

Temperature dependencies of integrated intensities of the Bragg peak (111), (220), and (200) reflections for $B=0\mathrm{T}$. The solid lines represent respective power law fits. $T_{\mathrm{C}}$ features can be identified from the ordering of (111) and (220) and $T_{\mathrm{NC}}$ from ordering of (200).

Figure 4

(a) The magnitude of $A$- and $B$-sublattice moments obtained from Rietveld refinement for $B=0\mathrm{T}$. (b) Total moment (per f.u.) calculated by adding ferromagnetic (FM) moments. Temperature dependence of total moment emulates the magnetization reversal as observed in magnetization measurement.

Figure 5

(a) Magnitude of $A$- and $B$-sublattice moments obtained from Rietveld refinement for $B=2\mathrm{T}$. (Inset) Total moment (per f.u.) calculated by adding moments along the $c$ direction. Temperature dependence of total moment emulates magnetization for fields >0.25 T.

Figure 6

(a) Initial polarization and (b) relaxation rate extracted from fits to the zero applied field muon spin relaxation (ZF-${\mu }^{+}\mathrm{SR}$) polarization spectra. For $T<T_{\mathrm{C}}$, fits are to Eq. (2), with $\beta$ as a free parameter below $T_{\mathrm{MR}}$ (red points). Above $T_{\mathrm{C}}$, fits are carried out to Eq. (1) (green points). Inset of (a) $\beta$ vs $T$, where $\beta$ reaches 0.5 at 12 K.

Figure 7

(a) Initial polarization and (b) relaxation rate extracted from fits to the longitudinal field muon spin relaxation (LF-${\mu }^{+}\mathrm{SR}$) polarization spectra with Eq. (2). At 125 K, complete decoupling was realized with a tiny field of 0.005 T. Due to instrument effects, $P_s\left(0\right)$ goes beyond 1 for higher fields.

Figure 8

Spin-resolved partial density of states (PDOS) of ${\text{Co}}_A, {\text{Co}}_B$, and ${\text{V}}_B$. The positive and negative values indicate PDOS of majority and minority spin electrons, respectively. The spins of ${\text{Co}}_A$ are aligned antiferromagnetically with respect to ${\text{Co}}_B$ and ${\text{V}}_B$. Both Co at $A$ and $B$ sites have $3d^7$ valence electrons, indicating the formation of a ${\mathrm{Co}}^{2+}$ ion. The distorted octahedral crystal field splits $t_{2g}$ into $a_{1g}$ and doubly degenerate $e_g$ states at site $B$. For ${\text{Co}}_B$, two electrons occupy the lower $e_g$ states forming a $S=\frac{3}{2}$ state, while for ${\text{V}}_B$, one electron occupies $a_{1g}$, yielding ${\mathrm{V}}^{4+}$ oxidation state with $S=\frac{1}{2}$.