Magnetic field frustration of the metal-insulator transition in ${\mathrm{V}}_2{\mathrm{O}}_3$

Despite decades of efforts, the origin of metal-insulator transitions (MITs) in strongly correlated materials remains one of the main long-standing problems in condensed-matter physics. An archetypal example is ${\mathrm{V}}_2{\mathrm{O}}_3$, which undergoes simultaneous electronic, structural, and magnetic phase transitions. This remarkable feature highlights the many degrees of freedom at play in this material. In this work, acting solely on the magnetic degree of freedom, we reveal an anomalous feature in the electronic transport of ${\mathrm{V}}_2{\mathrm{O}}_3$: On cooling, the magnetoresistance changes from positive to negative values well above the MIT temperature, and shows divergent behavior at the transition. The effects are attributed to the magnetic field quenching antiferromagnetic fluctuations above the Néel temperature $T_N$, and preventing long-range antiferromagnetic ordering below $T_N$. In both cases, suppressing the antiferromagnetic ordering prevents the opening of the incipient electronic gap. This interpretation is supported by Hubbard model calculations which fully reproduce the experimental behavior. Our study sheds light on this classic problem providing a clear and physical interpretation of the nature of the metal-insulator transition.

Figure 1

The metal-insulator transition (MIT) and its associated magnetoresistance (MR). Resistivity ρ (a) and MR at 9 T (b) as a function of temperature for a virgin ${\mathrm{V}}_2{\mathrm{O}}_3$ microbridge. The MR curve shows that a crossover from positive to negative values above the MIT takes place, and seems to diverge as the transition takes place. The gray dotted lines are a guide to the eyes indicating the two MR behaviors before and after the transition. Insets: (a) Optical microscope image of the ${\mathrm{V}}_2{\mathrm{O}}_3$ microbridge inserted in a sketch showing the measurement configuration. Four-lead magnetoresistance measurements were performed in a magnetic field applied out of plane and perpendicular to the current. The voltage is measured between the longitudinal contacts. (b) The quadratic dependence of MR vs field $H$ at several temperatures from 280 K (red) to 160 K (light blue) for the same ${\mathrm{V}}_2{\mathrm{O}}_3$ sample.

Figure 2

The metal-insulator transition (MIT) and its associated magnetoresistance (MR). Resistivity ρ (a) and MR at 9 T (b) as a function of temperature for a series of ${\mathrm{V}}_2{\mathrm{O}}_3$ samples irradiated with increasing $\mathrm{H}{\mathrm{e}}^{+}$ doses (in units of $\mathrm{ions}\mathrm{c}{\mathrm{m}}^{-2}$). The ρ and MR curves are displaced to lower temperatures for increasing irradiation dose. (c), (d) show the collapse obtained for ρ and MR, respectively, when $T$ is scaled to $\left(T\text{–}{T}_a\right)/T_b$. Insets: (a) Detail of the ρ($T$) curve for the highest-irradiation sample, which shows the hysteretic behavior, a hallmark of the first-order MIT. (c) $T_a$ and $T_b$ scaling parameters as a function of the irradiation dose. The evolution is linear.

Figure 3

Neutron diffraction measurements. (a) Neutron diffraction along the $\left(0k0\right)$ direction for the sample irradiated with $8\times {10}^{14}\mathrm{ions}/\mathrm{c}{\mathrm{m}}^2$ . The blue data, measured at low temperature, show a peak at (010) corresponding to the antiferromagnetic ordering of ${\mathrm{V}}_2{\mathrm{O}}_3$. Nothing is observed at high temperature. The blue curve is a Gaussian fit to the data. (b) (010) diffraction peak intensity as a function of temperature for the same sample. The red line is a guide to the eye. Error bars are representative of the uncertainty for the intensity data. (c) Linear decrease of the Néel ($T_N$,), MIT ($T_{\mathrm{MIT}}$), and structural transition ($T_S$) temperatures with increasing irradiation dose. Errors in transition temperatures estimated from least-square fits.

Figure 4

The calculated effect of the magnetic field on the antiferromagnetic (AF) ordering. (a) Calculated magnetoresistance as a function of temperature using DMFT calculations of the Hubbard model. Inset: Calculated magnetoresistance (squares) for $T\left(W\right)=0.07$ (red), 0.05 (yellow), 0.0425 (light blue), and 0.04 (blue). Lines are parabolic fits, showing the dependence with field is quadratic as in the experiments. (b) Calculated evolution as a function of temperature of the AF staggered moment $m_{\mathrm{AF}}$ (black line) in zero field, and the two magnetic sublattices $m_A$ (red line) and $m_B$ (blue line) under a magnetic field $H=0.05$ parallel to sublattice A. All moments are in units of the Bohr magneton ${\mu }_B$ per V atom. Under a magnetic field, sublattice B does not develop its full moment due to the frustration from the magnetic field. The difference in spin ordering is depicted at the bottom of (c),(d). In the absence of an applied field, all spins (in black) order antiferromagnetically. When an external field (orange arrow) is applied along the A sublattice (red spins), the B sublattice (blue spins) is disordered. The calculated density of states (DOS) at $T=0.025$ is shown for the case of zero field (c) and $H=0.05$ (d), revealing how the magnetic field produces a closing of the AF gap, more pronounced for sublattice B (blue line) than for sublattice A (red line).