NMR and EPR approaches to magnetic properties of
(TMTTF)2Br

Pawel Wzietek, Claude Bourbonnais, François Creuzet, Denis Jerome, Klaus

Bechgaard

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Pawel Wzietek, Claude Bourbonnais, François Creuzet, Denis Jerome, Klaus Bechgaard. NMR and EPR approaches to magnetic properties of (TMTTF)2Br. EPL - Europhysics Letters, 1990. hal-05000115

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NMR and EPR Approaches to Magnetic Properties of (TMTTF)₂Br.

P. WZIETEK(*)(**), C. BOURBONNAIS(*)(**), F. CREUZET(*)

D. JÉROME(*) and K. BECHGAARD(***)

(*) Laboratoire de Physique des Solides, Université de Paris-Sud
Bât. 510, 91405 Orsay, France

(**) Centre de Recherche en Physique du Solide, Université de Sherbrooke
Sherbrooke, Québec, Canada J1K

(***) H. C. Oersted Institute - DK-2100 Copenhagen, Denmark

(received 22 January 1990; accepted in final form 3 May 1990)

PACS. 74.70K – Organic superconductors.

PACS. 76.60E – Relaxation effects.

PACS. 71.45 – Collective effects.

**Abstract.** – We present ¹³C spin-lattice relaxation time and EPR susceptibility measurements on selectively enriched single crystals of (TMTTF)₂Br over a wide temperature domain. The divergence of T₁⁻¹ at T_N ≈ 15 K is associated with the antiferromagnetic transition and 3D critical effects. The EPR susceptibility and T₁⁻¹ are shown to satisfy 1D dynamic scaling for the existence of 1D paramagnons and antiferromagnetic correlations up to room temperature. Applied to bromide salt which undergoes a Mott-Hubbard localization under 100 K, our approach thus confirms the spin-charge separation predicted for the 1D correlated electron gas model. These findings are in close similarity with the behavior of T₁⁻¹ found previously in the 1D antiferromagnet (TMTTF)₂PF₆.

Recently, a lot of interest has been devoted to the study of electronic correlations in organic conductors by the use of nuclear relaxation rate measurements [1, 2]. This provides a local probe for studying the nature of the magnetic excitations and their evolution with temperature. In the Bechgaard salts series for example, the electronic contribution to the ⁷⁷Se and ¹³C relaxation is well known to be dominant [2]. In this case, the relaxation rate T₁⁻¹ is directly related to the imaginary part χ'' of the retarded transverse electronic susceptibility integrated over all wave vectors q [3]:

$$T_1^{-1} \propto T \int d^d q \chi''_{\perp}(q, \omega_N)/\omega_N, \qquad (1)$$

where ω_N is the nuclear Larmor frequency. As the relaxation mechanism only involves low-energy scattering processes, the main contributions to T₁⁻¹ come from uniform or ferro-(q=0) and antiferromagnetic (q=Q₀) spin fluctuations [1, 2] (Q₀ is the AF modulation
vector). These contributions have quite different dynamics and can be experimentally distinguished by their characteristic temperature profiles [2]. Dynamic scaling arguments applied to expression (1) have shown that the $T_1^{-1}$ ($q \approx 0$) and $T_1^{-1}$ ($q \approx Q_0$) parts are, respectively, proportional to the temperature-dependent uniform and staggered magnetic correlation lengths to some characteristic powers which depend on the dimensionality of spin fluctuations [2a]. It has been shown that the temperature dependence of $T_1^{-1}$ can be put in the form [2a]

$$T_1^{-1} \approx C_0 T(\chi_s(T)^{1/2(5-d)} + C'_1 T \xi_{AF}^{-\gamma/\nu+z-d}), \quad (2)$$

where $\chi_s(T)$ is the temperature-dependent magnetic susceptibility and $C_0, C'_1$ are positive constants. $\xi_{AF}$ is the AF correlation length and $\nu$ its critical exponent, $\gamma$ is the critical exponent of the staggered susceptibility and $z$ is the dynamical exponent for the scaling of the frequency. With this procedure, we have been able to characterize both the precursor and the critical temperature domains of several members of the selenide (TMTSF)$_2$X and sulfur (TMTTF)$_2$X series. This has been particularly illustrated for three prototype compounds: the spin-Peierls system (TMTTF)$_2$PF$_6$ [2a, d], the antiferromagnet (TMTSF)$_2$PF$_6$ [2a, c] and the superconductor (TMTSF)$_2$ClO$_4$ [2a]. Indeed, for all the three compounds, the observation of the scaling relation between $T_1^{-1}$ and $T \chi_s^2(T)$ has demonstrated that one-dimensional paramagnons give the dominant contribution to both $T_1^{-1}$ and $\chi_s(T)$ in the high-temperature domain. However, the antiferromagnetic part of the relaxation becomes clearly manifest at low temperature for all the compounds. In (TMTSF)$_2$PF$_6$, it even diverges at the Neel critical point [2c].

The case of (TMTTF)$_2$Br at ambient pressure is particularly interesting here since the ground state is antiferromagnetic with no lattice softening precursors, in contrast to (TMTTF)$_2$PF$_6$ [4-6]. Furthermore, the Mott-Hubbard charge localization occurs below the resistivity minimum near $T_c \approx 100$ K [4, 7, 8]. This compound appears thus to be intermediate between the strongly correlated (TMTTF)$_2$PF$_6$ ($T_c \approx 220$ K) and the itinerant antiferromagnet (TMTSF)$_2$PF$_6$ ($T_c < T_N \approx 12$ K).

Previous $^1$H NMR experiments performed by Creuzet et al. [7] have shown that $T_1^{-1}$ is singular at $T_N \approx 14$ K, confirming the magnetic nature of the ordered state. However, the proton NMR in these organic salts is not a good probe of the electronic behavior in the full paramagnetic domain because $T_1^{-1}$ is hugely enhanced by methyl group rotation effects [7]. Therefore, we have measured the $^{13}$C nuclei relaxation in order to discuss the nature and the temperature dependence of spin fluctuations in (TMTTF)$_2$Br. This work will then allow us to confirm the separation between charge and spin degrees of freedom, as predicted for 1D correlated systems.

The experiment has been performed on single crystals of (TMTTF)$_2$Br. We have used a 90% $^{13}$C enriched sample (on the central C-C bond of the TMTTF molecule). The measurements were carried out in the temperature range from 15 to 300 K at a fixed field of 56 kG. The $^{13}$C spectrum is made up of two well-resolved lines (assigned to the two nonequivalent carbon sites) separated by 100 p.p.m. at 300 K. The relaxation of each line is found to be exponential over a decade of magnetization. We have also performed an EPR experiment on the same sample in order to extract the temperature dependence of the uniform magnetic susceptibility in the temperature range (20 ÷ 300) K.

The temperature dependence of $T_1^{-1}$ is shown in fig. 1. In the vicinity of the magnetic transition at $T_N \approx 15$ K, the relaxation is strongly enhanced by antiferromagnetic critical fluctuations. For a 3D transition, using the Gaussian approximation for the AF part of (2) near $T_N$, that is $\gamma=1$, $z=2$, and $\xi_{AF} \propto (T - T_N)^{-\nu}$ with $\nu=1/2$ [9], we get: $T_1^{-1}(q \approx Q_0) \propto (T - T_N)^{-1/2}$. We have verified that for both NMR lines, such a power law divergence
<figure><img src="image_3.png" /><figcaption>Fig. 1. – Temperature dependence of the relaxation rate for two central carbon sites in (TMTTF)₂Br at 56 kG. The insert shows the power-law divergence of $T_1^{-1}$ near $T_N$.</figcaption></figure>

is observed below 25 K or so (see the insert of the figure). The error on the critical exponent is estimated to be of the order of 10%. In the paramagnetic domain, our results are similar to those obtained previously on proton up to 30 K: the relaxation rate is almost constant up to 60 K [7]. Above this temperature, $T_1^{-1}$ increases with T and the upward curvature appears to be a common feature of the nonordered phases of both (TMTTF)₂X and (TMTSF)₂X series. According to the scaling arguments presented in ref. [2a, c], the temperature dependence of $T_1^{-1}$ for a d = 1 antiferromagnet below $T_ρ$ is of the form

$$T_1^{-1} = C_0 T \chi_s^2(T) + C_1, \quad (3)$$

where $C_0$ and $C_1$ are positive constants. Here the $T_1^{-1}(2k_F) = C_1$ contribution can be easily obtained from (2) using the well-known results $ν = γ = z = 1$ for a d = 1 electron gas in strong-coupling domain ($T < T_ρ$) [2a, 7, 8]. Consequently, in order to confirm that the increase of the relaxation rate scales with the magnetic susceptibility, we present in fig. 2

<figure><img src="image_4.png" /><figcaption>Fig. 2. – Relaxation data of fig. 1 plotted vs. $χ_s^2 T$ interpolated from EPR measurements showing the scaling relation (3). In the insert: temperature dependence of the EPR susceptibility $χ_s$.</figcaption></figure>
the relaxation data of fig. 1 plotted vs. $T\chi_s^2$ using $\chi_s$ values interpolated from EPR measurements between $T \approx 30$ K ($T\chi_s^2 \approx 2.3$), where critical precursors are essentially inexistent and 290 K ($T\chi_s^2 \approx 4.3$). A relation of the form (3) can then be fitted fairly well. Although the experimental error of the EPR data does not allow us to extract the accurate relation between $T_1$ and $\chi_s$, this interpretation is based on the low-dimensional character of the electronic spectrum and the importance of Coulomb forces which are not new concepts for TMTSF and TMTTF families and are consistent with their low-temperature properties [8]. According to this, it should be stated once again that, as far as the TMTTF salts are concerned, relation (3) *cannot* be identified with the well-known Korringa result for a free-electron gas since the conductivity of these compounds shows a manifestly nonmetallic behaviour (see the insert of fig. 3 below). We wish to mention, however, that the contribution of Coulomb correlations to the susceptibility enhancement at high temperature is not necessarily related to the existence of a resistivity minimum. A detailed analysis of $\chi_s$ temperature and pressure dependence in both sulphur and selenide series will be presented in the forthcoming paper [10].

A constant contribution to $T_1^{-1}(C_1)$ which is visible in fig. 2 can be attributed to the one-dimensional antiferromagnetic part of the relaxation, as it was in $(TMTTF)_2PF_6$. We notice that this contribution is indeed constant in the whole temperature domain studied, while the minimum of resistivity occurs at $T_\rho \approx 100$ K ($T\chi_s^2 \approx 0.6$). Therefore, because the exponent $\gamma = 1$ prevails well above $T_\rho$, we suggest that transients to strong-coupling regime are present up to ambient temperature.

We have not performed a systematic study of the possible frequency dependence of $T_1$, which is actually one of the most direct methods to probe the dimensionality, but some experiments at lower field (34 kG) did not show any variation of the $^{13}$C relaxation time. Since the $^{13}$C relaxation rate is not influenced by molecular reorientation as are the proton $T_1$'s of the $CH_3$ groups, we consider that the field independence of the relaxation rate which is observed below 6 T sets a lower field limit for the $T_1$ dimensionality crossover [1, 2b]. This result is in fair agreement with the enhanced transverse coupling of the $(TMTTF)_2X$ series as compared to the charge transfer conducting salt TTF-TCNQ with a crossover field around 1 T [1].

The validity of the scaling analysis carried out simultaneously for the two carbon sites provides us with some additional information. First, it supports the hypothesis about the electronic origin of the relaxation. Indeed, the ratio $T_1^{-1}(q \approx 0)/T_1^{-1}(2k_F)$ is the same for both lines as is expected if the difference arises only from different hyperfine constants (note that the separation of the two lines is large enough to preclude any spin diffusion effect). The spin density calculations [11] for the TMTSF family have shown that such a distribution of the hyperfine field is possibly coming from a combined effect of the dimerization and of the anion interaction.

We also remark that the enhancement of $T_1^{-1} (q=0)$ due to correlations is the same for both lines. In models where the electron-electron interaction is represented by the «on-site» coupling, this parameter would then be a molecular rather than an atomic property. This is consistent with the fact that a single band scheme can be used as a good starting point, regardless of the actual band structure and electronic density distribution.

It is now instructive to compare our data with similar analysis performed for other compounds [2a, d]. In fig. 3, the fastest of the relaxation rates of $^{13}$C in $(TMTTF)_2Br$ is plotted vs. $T\chi_s^2$ (in the same units as in fig. 2), together with the $^{13}$C relaxation data in $(TMTTF)_2PF_6$ obtained under similar conditions [2d]. We note that the unique relaxation time reported in ref. [2d] is presumably due to spin diffusion effects (actually, these results were obtained at lower field and furthermore, the interaction with the fluorine nuclei can be quite important). Anyhow, a comparison is meaningful if we are only interested in the
<figure><img src="image_5.png" /><figcaption>Fig. 3. – Comparison of $T_c^{-1}$ ($q = 2k_F$) amplitudes (represented by $C_1$ constant in (3)) in (TMTTF)$_2$Br (triangles) and (TMTTF)$_2$PF$_6$ (squares, from ref. [2d]). The dashed line sketches the corresponding result in their selenide analogs (ref. [2a]). In the insert: longitudinal resistivity of TMTTF salts vs. temperature (ref. [4]).</figcaption></figure>

relative weights of the two different contributions to the relaxation. Although the uncertainty of EPR data does not allow an accurate determination of the AF part of the relaxation represented by $C_1$ in (1), the results presented in fig. 3 agree with the theoretical prediction, namely that its relative amplitude is gradually suppressed when the characteristic localization temperature $T_c$ is lowered. In fact, this is the amplitude of the $2k_F$ magnetic susceptibility in the strong-coupling domain ($T \le T_c$) which is responsible for the temperature-independent contribution $C_1$. Thus, comparing the two values of $T_c$ for both sulfur compounds (see the insert of fig. 3), it is natural to observe a lower value of $C_1$ for the bromide salt. This picture can be extrapolated to the high-temperature region for the TMTSF family (dashed line in fig. 3), where the resistivity minimum disappears (that is $T_c < T_N$). This implies a much lower value for the $2k_F$ susceptibility at high temperature with $C_1 \approx 0$. According to (2), a power law: $T_c^{-1}(2k_F) \propto T^{-\gamma+1}$ with $\gamma < 1$ in weak coupling [8] is expected, and $C_1$ will thus decrease rapidly with $T$ at low temperature. Therefore, as far as the AF correlations are concerned, the low-temperature AF characteristics of $T_c^{-1}$ under pressure (or the amplitude of $\chi(q \approx Q_0)$) should scale towards those of selenide series as $T_c \to 0$.

On the other hand, one should note that the enhancement of the spin susceptibility $\chi_s(T)$ with $T$ is essentially the same in both families at ambient pressure. It has already been shown that when pressure is applied to (TMTTF)$_2$Br, its critical behavior approaches the one of (TMTSF)$_2$PF$_6$ at 1 bar [12], while the $\chi_s$ enhancement becomes sizably reduced. In this respect, a quantitative analysis of $T_c^{-1}$ vs. $T$ in several members of both series under hydrostatic pressure has shown [10] that, as far as the uniform spin fluctuations are concerned, their amplitude for the sulfur series does not scale towards the one of selenides under pressure.

In conclusion, we have presented and analyzed the temperature dependence of $^{13}$C nuclear relaxation rate and spin susceptibility in (TMTTF)$_2$Br. Near $T_N$, our data confirm the existence of classical AF critical effects. At high temperature, the enhancement of $T_c^{-1}$ and $\chi_s$ reveals all the features known for other correlated metals and is shown to be due to paramagnetic excitations. It is then possible to extract the staggered part of the relaxation. A comparison with previous results for other members of TMTCF salts lead us to establish that, as far as the AF fluctuation amplitude is concerned, (TMTTF)$_2$Br takes some intermediate position between (TMTTF)$_2$PF$_6$ and the (TMTSF)$_2$X series.
We wish to acknowledge H. HURDEQUINT for allowing us to use the EPR spectrometer. One of us (CB) would like to thank the C.N.R.S. for chercheur associe position during his stay in Orsay. P. WZIETEK thanks the Canadian Institute of Advanced Research and the Centre de Recherche en Physique du Solide de l'Université de Sherbrooke for financial support during his stay at Sherbrooke. This work was also partially supported by ESPRIT contract n. 3121BRA.

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