# Metal-Insulator transition investigation in V2O3 by nuclear magnetic resonance and relaxation

Denis Jerome, A. L Kerlin, H. Nagasawa

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Denis Jerome, A. L Kerlin, H. Nagasawa. Metal-Insulator transition investigation in V2O3 by nuclear magnetic resonance and relaxation. Solid State Communications, 1973. hal-04990856

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Distributed under a Creative Commons Attribution 4.0 International License
METAL-INSULATOR TRANSITION INVESTIGATION IN V₂O₃ BY NUCLEAR MAGNETIC RESONANCE AND RELAXATION*

A.L. Kerlin†, H. Nagasawa‡ and D. Jerome

Laboratoire de Physique des Solides§, Université Paris-Sud, Centre d'Orsay, 91405 - Orsay, France

(Received 2 July 1973 by P.G. de Gennes)

The high temperature metal-insulator transition in pure V₂O₃ has been investigated by nuclear magnetic resonance and relaxation. The relaxation rate in the range 160–320 K was found to satisfy the Korringa relaxation and at temperature above 550 K to be constant as expected for a para-magnetic insulator. In the intermediate temperature range the high field resonance line shape showed broadening which we interpret as due to the coexistence of a metallic and an insulating phase.

THE EXISTENCE of a first-order, high temperature metal-insulator (M-I) transition in (V₁-xCrₓ)₂O₃ as a function of composition has been well established.¹ However, in pure V₂O₃, the previous measurements of X-ray and resistivity¹,³ do not give a definite picture for the high temperature of metal-insulator transition besides the description of a gradual change of the electronic properties.

In order to study the nature of the transition in V₂O₃ from a microscopic level as well as the electronic structure of the metallic and insulating states, we have used the technique of NMR over a broad temperature range. We report measurements of the spin-lattice relaxation rate of V⁵¹ in V₂O₃ between 160 and 840 K and the resonance line shape at high magnetic fields between 300 and 600 K.

Metallic phase (160–320 K)

There are no static magnetic moments in the M phase and therefore the observed temperature

<figure><img src="image_3.png" /><figcaption>FIG. 1. The experimental values of (1/T₁) for V⁵¹ in V₂O₃ as a function of temperature.</figcaption></figure>

dependent susceptibility should be described by narrow band temperature dependent Pauli-paramagnetism. In the M state, a Korringa-like nuclear spin-lattice relaxation rate would be expected from the 3d bands. The expected relaxation rate can be generally expressed as

$$ \frac{1}{T_1} = \left(\frac{1}{T_1}\right)_{\text{core polarization}} + \left(\frac{1}{T_1}\right)_{\text{Orbital}} + \left(\frac{1}{T_1}\right)_{\text{s}} + \left(\frac{1}{T_1}\right)_{\text{dipole}} \quad (1) $$

<footnote>* Work supported by CNRS-ATP and DRME contracts.</footnote>

<footnote>† CNRS-NSF Postdoctoral Fellow</footnote>

<footnote>‡ Permanent address; Department of Physics, Tokyo University of Education, Tokyo, Japan.</footnote>

<footnote>§ Associated to the CNRS.</footnote>
<table><caption>Table 1. Temperature dependence of the enhancement factor and densities of states of metallic V₂O₃ obtained by analysis of the relaxation rate</caption><thead><tr><th></th><th>160</th><th>200</th><th>240</th><th>280</th><th>320</th></tr></thead><tbody><tr><td>T(K)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>(1/T₁T) (sec<sup>-1</sup>K<sup>-1</sup>)</td><td>113.2</td><td>102.8</td><td>92.6</td><td>86.4</td><td>82.9</td></tr><tr><td>K(α)</td><td>0.51</td><td>0.51</td><td>0.50</td><td>0.51</td><td>0.52</td></tr><tr><td colspan="6">Stoner type long range electron-electron interaction<sup>7</sup></td></tr><tr><td>1/(1-α)</td><td>1.40</td><td>1.40</td><td>1.41</td><td>1.40</td><td>1.39</td></tr><tr><td>n<sub>d</sub>(E<sub>f</sub>) (state/eV)</td><td>10.1</td><td>9.6</td><td>9.2</td><td>8.9</td><td>8.4</td></tr><tr><td colspan="6">δ function-like short range electron-electron interaction<sup>6,7</sup></td></tr><tr><td>1/(1-α)</td><td>3.45</td><td>3.45</td><td>3.57</td><td>3.45</td><td>3.33</td></tr><tr><td>n<sub>d</sub>(E<sub>f</sub>) (state/eV)</td><td>4.12</td><td>3.92</td><td>3.64</td><td>3.60</td><td>3.51</td></tr><tr><td colspan="6">modified electron-electron interaction<sup>8</sup></td></tr><tr><td>1/(1-α)</td><td>2.27</td><td>2.27</td><td>2.33</td><td>2.27</td><td>2.23</td></tr><tr><td>n<sub>d</sub>(E<sub>f</sub>) (state/eV)</td><td>6.26</td><td>5.94</td><td>5.74</td><td>5.46</td><td>5.16</td></tr></tbody></table>

The experimental results of the magnetic susceptibility³ and the Knight shift measurements⁴,⁵ showed no contribution from s electrons. The dipole term was estimated to be small compared to the orbital term. Therefore we neglect the last two terms of equation (1). The relaxation rate due to the spin and the orbital term can be given as

$$ \frac{1}{T_1} = \frac{4\pi kT}{\hbar} \left(\frac{\gamma_n}{\gamma_e}\right)^2 K_{c.p.}^2 \left\{ F_{c.p.}(c) + F_{orb}(c) \left(\frac{H_{h.f.}^{orb}}{H_{h.f.}^{c.p.}}\right)^2 \right\} K(\alpha) \quad (2) $$

where $F_{c.p.}(c)$ and $F_{orb}(c)$ are the core polarization and orbital factors² arising from the symmetry of the *d* bands. These are given in the following equations as a function of the fraction *c* of $\Gamma_5$ orbitals in the *d* bands.

$$ F_{c.p}(c) = \frac{1}{3}c^2 + \frac{1}{2}(1-c)^2 $$

$$ F_{orb}(c) = \frac{2}{3}c(2 - \frac{5}{3}c) $$

$K(\alpha)$ is the enhancement parameter of the Korringa constant due to the electron-electron interaction introduced by Moriya⁶ and discussed latter by several authors.⁷ $H_{h.f.}^{c.p.}$ is the hyperfine field due to the spin polarization of inner core electrons by the magnetic

moments of outer *d* electrons, and $H_{h.f.}^{orb}$ is the hyperfine field due to the orbital magnetic moment. From analysis of the Knight shift and the susceptibility in metallic V₂O₃, these fields were estimated to be -140 kOe/μB and 395 kOe/μB respectively.⁴ $K_{c.p.}$ is the Knight shift due to the inner core polarization and is given as a fraction of the Pauli paramagnetic susceptibility of the *d* bands³,⁴ $\chi d(T)$ or the enhancement factor $1/1 - \alpha$ and density of state $n_d(E_f)$.

$$ K_{c.p.}(T) = \frac{H_{h.f.}^{c.p.}}{N\mu_B} \chi_d(T) = \frac{H_{h.f.}^{c.p.}}{N\mu_B} \frac{2\mu_B^2}{1-\alpha} n_d(E_f) \quad (5) $$

In the case of V₂O₃ at temperatures higher than 160 K (above the antiferromagnetic phase), each V³⁺ ion is located at the center of an octahedron of oxygens. The ligand field splitting is much larger than any interaction between the V³⁺ ions, so two electrons occupy the $\Gamma_5$ orbitals.⁹ Therefore we can expect that *c* is unity in equations (3) and (4).

By using our measurements of the spin-lattice relaxation rate (Fig. 1)* in conjunction with the previously reported measurements of the Knight shift⁵ and magnetic susceptibility,³ the temperature dependence of the density of states was obtained from equations (2) and (5) and is given in Table 1. The enhancement factor $1/(1-\alpha)$ as well as $K(\alpha)$ were
<figure><img src="image_4.png" /><figcaption>FIG. 2. Temperature dependence of the V⁵¹ NMR dispersion derivative spectra in V₂O₃. The measurements were made at a fixed frequency of 30 MHz. The vertical lines indicate our theoretical estimate of the position and intensity of the metallic and insulating lines. The metallic phase is shown on the high field side. The amplitudes of the traces are not scaled.</figcaption></figure>

found to be temperature independent below 320 K. This implies that the Korringa relation is valid in metallic V₂O₃. The densities of states given in Table 1 appear consistent with the electronic specific heat measurements¹⁰ of Ti doped V₂O₃ at low temperatures.

It is interesting to note that the observed relaxation rate shows a rapid increase with increasing temperature between 320 and 540 K and saturates at temperatures above 540 K. Later we will discuss the NMR results in this temperature region.

### Insulating phase

The flattening of the relaxation rate at high temperature means that there are no more conduction electrons at the Fermi level and V₂O₃ becomes an insulator on a microscopic level. In the insulating state, localized moments — whose existence is inferred from the Curie–Weiss susceptibility³ — should contribute to the nuclear relaxation. The fluctuating paramagnetic moments cause the hyperfine field to fluctuate and thus produce the relaxation rate.¹

$$ \frac{1}{T_1} = \frac{1}{T_2} = \sqrt{2\pi} \left(\frac{A}{\frac{1}{2}\hbar}\right)^2 \frac{S(S+1)}{3\omega_{ex}} \quad (6) $$

From the K-χ diagram,⁵ the hyperfine coupling constant A/ħ in the insulating state is estimated to be 1.0 × 10⁹ sec⁻¹. Using S = 1, ω<sub>ex</sub> = 3kT<sub>c</sub>/2ħ {ZS(S + 1)}¹/² = 1.8 × 10¹³ sec, we obtain T₁ = T₂ = 10 µsec; the comparison with the observed relaxation time (T₁)<sub>obs</sub> = 20 µsec is rather satisfactory.

### Intermediate region

In the temperature range between 300 and 550 K the measured susceptibility is nearly constant³ whereas the Knight shift increases monotonically.⁴,⁵ This results in the anomaly in the K-χ diagram.

We observed the NMR dispersion mode¹² line shape of V⁵¹ nuclei in V₂O₃ at high magnetic fields of 26.8 kG between 300 and 600 K and found the broadening in the resonance lines as shown in Fig. 2.** These results show the coexistence of the metallic phase and the insulating phase in this intermediate temperature range. The percentage of the metallic phase vaires with temperature. Based upon this microscopic evidence of the coexistence of two phases, we can easily estimate the percentage of the metallic state by comparison of the observed susceptibility and the susceptibilities extrapolated from low temperature (metallic phase) or high temperature (insulating phase) to this intermediate temperature
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FIG. 3. The solid lines represent the experimental resonance line shift of the M and I phases; the dashed lines are their respective extrapolations. The dot-dash line represents the estimated temperature dependence of the percentage of metallic phase.

range. Using the experimental results of Menth,³ we calculate the expected percentage of metallic phase as a function of temperature as shown in Fig. 3.

Since the frequency shift is proportional to χ in the insulating and metallic phase, we can estimate the frequency shift for each phase by extrapolating χ₁ and χM on the K-χ diagram of Gossard et al.⁵ The results are shown in Fig. 3. In the intermediate region the calculated differences in line position of the two phases are small, so the highest fields available were used to observe the broadening. The expected resonance field and the estimated relative intensity are in good agreement with the observed results (Fig. 2).**

It is important to notice that the observed relaxation rate below 320 K satisfies quite well the Korringa relation, a characteristic of metals. On the

other hand, the behavior of the high temperature relaxation rate reflects directly the localized character of the 3d electrons on every atomic side in the insulating phase. This is a nontrivial result because in V₂O₃ the transition between a Korringa-like relaxation and a localized electron spin relaxation is not accompanied by a sharp discontinuity, of the lattice parameter.¹ We are thus led to believe that we face a genuine electronic phase transition which occurs under continuous variation of the atomic volume.

The high temperature region of V₂O₃ could thus be described by the Mott-Hubbard¹³ picture in which the activation energy of the carriers is due to the electrons correlation rather than to Bragg scattering. Since the free carrier relaxation rate is negligible compared to the relaxation due to the fluctuation of the localized moments, the Hubbard gap must be somewhat larger than kT.

In the intermediate region the coexistence of the M and I phases was observed by study of the NMR at high magnetic fields. Based upon these experimental facts, we believe that the observed temperature independent susceptibility in this temperature region originates from the mixing of the susceptibility of the two phases. Therefore, the apparent anomaly in the K-χ diagram is interpreted successfully. An extended paper on this subject will be published in near future.

*Acknowledgements* – We would like to acknowledge Dr. J. Galy and M. Sénégas who provided us with the sample and G. Delplanque for his assistance in the preparation of the experiment.

## REFERENCES

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2. YAFET Y. and JACCARINO V., *Phys. Rev.* 133, A1630 (1964).

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*Note added to proof.*

* Spin-lattice relaxation times were measured with approximately 180-90° pulse sequence. The amplitude of the 90° pulse was measured with a boxcar integrator as a function of the interval between the 180° and 90° pulses. The rotating component of the pulsed r.f. magnetic field was typically 120 gauss.

** Our very recent measurements show that the line shapes change as a function of time in the intermediate temperature region after the sample reaches thermal equilibrium. We find that after 12 hours at a given temperature, the line shapes became symmetric. This leads us to believe that the kinetics of the M-I phase transition in pure V₂O₃ is slow. The results given in this work for NMR spectrum probably exhibit nonequilibrium behavior since the sample was kept for no more than 2 or 3 hours at a given temperature.

Des expériences de résonance magnétique nucléaire et de relaxation nucléaire ont été effectuées à haute température dans V₂O₃. On trouve que la vitesse de relaxation suit la loi de Korringa entre 160 et 320 K. Audessus de 550 K, la vitesse de relaxation devient indépendante de la température comme c'est le cas dans un isolant paramagnétique. Un élargissement de la raie de résonance en champ fort est observé dans le domaine des températures intermédiaires. Cet élargissement est interprété par la coexistence des phases isolantes et métalliques.