# NMR in the (BEDT)zX Organic Superconductors

Pawel Wzietek, Hadrien Mayaffre, Denis Jerome, Serguei Brazovskii

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Pawel Wzietek, Hadrien Mayaffre, Denis Jerome, Serguei Brazovskii. NMR in the (BEDT)zX Organic Superconductors. Synthetic Metals, 1997, 85, pp.1511. 10.1016/S0379-6779(97)80327-X. hal-05314527

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# NMR in the (BEDT)₂X Organic Superconductors

P. Wzietek, H. Mayaffre, D. Jérome and S. Brazovskii*

Laboratoire de Physique des Solides (CNRS),

Université de Paris-Sud, 91405 Orsay, France

*on leave from L.D.Landau Institute for Theoretical Physics, Moscow, Russia

## Abstract

We review recent NMR studies of a layered organic superconductor of the (BEDT)₂X family. First the normal state properties are discussed. The central issue is the importance of the interplay between antiferromagnetism and superconductivity in these materials demonstrated by the observation of a pseudogap developing prior to the superconducting transition. The use of high pressure to tune the amplitude of AF fluctuations enables us to draw a general phase diagram of the family. In the second part the NMR experiments in the superconducting state are presented. One of the fundamental questions addressed by these experiments is the symmetry of the order parameter related to the pairing mechanism. The most spectacular NMR measurements are those performed in the lock-in state, which give access to the density of superconducting excitations at low energy. These experiments suggest that the pairing state may be unconventional featuring an anisotropic superconducting gap, possibly with nodes.

**Keywords:** Organic superconductors, Superconducting phase transitions, Nuclear magnetic resonance spectroscopy

## 1. Introduction

Since the discovery of superconductivity in the BEDT-based salts, the number of these quasi two-dimensional organic superconductors has grown very rapidly and actually these materials are the largest part among about 50 organic superconductors [1, 2, 3]. These compounds, in spite of rather low critical temperatures (≈10 K) are very interesting as model materials for studying the mechanisms of superconductivity in the 2D superconductors. Particular place in this family is occupied by the so called κ-phases which have been most extensively studied and appear to be representative for a quite large class of materials. Especially, they display a lot of properties similar to those observed in the high temperature superconductors (HTSC): high conductivity anisotropy or interplay between magnetism and superconductivity. In this short review we concentrate on various aspects related to the application of the NMR and the electronic properties, and present some of recent results obtained on κ-(ET)₂Cu[N(CN)₂]Br [4, 5, 6, 7]. This representative member of the κ-(ET)₂X family is one of the best characterized up to date, it is also the 2D organic superconductor with the highest known T_c (12.6 K) at ambient pressure [8].

## 2. Electronic properties in metallic phase

There are various applications of the NMR in the normal phase: spin density distribution studies, structural peculiarities and their relation to metallic properties. A more exhaustive review can be found in [4], here we focus rather on the apparent non-metallic behaviours revealed by NMR and transport studies and which seem to be common to most κ-phase superconductors. For example, the resistivity often exhibits a maximum around 90 K and quite generally in the superconducting κ-phases a maximum of dR/dT occurs near 50 K and tends to vanish under pressure. The NMR investigation of the electronic properties involves mainly the ¹³C Knight shift and relaxation measurements in function of temperature and pressure. As the NMR properties of this nucleus are only determined by hyperfine interaction with conducting electrons, the Knight shift and relaxation reflects the evolution of the local static or dynamic susceptibility.

Fig.1 shows the temperature and pressure dependence of the Knight shift and spin-lattice relaxation rate in κ-(ET)₂Cu[N(CN)₂]Br. The variation of the spin susceptibility in high temperature region can be attributed to the lattice contraction, but below 50 K we observe a sharp
drop in the spin susceptibility which has been interpreted in
terms of a pseudo-gap in the density of states [9]. At 4 kbar
this pseudo-gap disappears and the compound exhibits a
more common metallic behavior in agreement with the ob-
servations made on the resistivity under pressure. [10]. The

<figure><img src="image_3.png" /><figcaption>Figure 1: (a)normalized Knight shift vs temperature at 1 bar (●) and 4 kbar (○); (b)1/T₁T vs temperature at different pressures: 1 bar (●), 1,5 kbar (△), 3 kbar (◦) and 4 kbar (○).</figcaption></figure>

1/T₁T data show a large peak which seems to be related
in some way to the decrease of the susceptibility: it occurs
near 50 K and is progressively spread out under pressure.
At higher temperatures the susceptibility becomes constant
and at the same time a Korringa-like behaviour is restored
for 1/T₁T.

The temperature profiles of 1/T₁T and Knight shift show
a rather striking similarity with those reported for some
HTSC materials and interpreted as the appearance of short
range antiferromagnetic correlations in the CuO₂ planes
leading to a pseudogap affecting the spin degrees of freedom
[11]. But unlike in HTSC, there are no evidences here
for spin-charge decoupling since there is strong correlation
between the relaxation rate and the resistivity which has
a peak near 90K. Remind also that the Fermi surface of
κ-(ET)₂Cu[N(CN)₂]Br is substantially different from that
of HTSC's since there is no van Hove singularity [5, 4]. On
the other hand, it was suggested that the observed effects

are related to the electron-electron interactions enhanced
by a partial nesting of the Fermi surface [5]. This is
because both nuclear relaxation and electron scattering are
sensitive to the imaginary part of the susceptibility χ''. In
RPA χ'' is renormalized by a factor (1 - Uχ''₀(⃗*ω*, ω_N))⁻²
and may become large because of the peak in χ''₀(⃗*ω*, ω_N)
at the nesting vector [12]. The importance of the Coulomb
repulsion has already been inferred from the observed strong
variation of the Knight shift under pressure (-6 %/kbar) [5].
The estimation based on RPA theory gives then U≈0.7 eV
which is comparable to the bandwidth W≈0.6 eV. More
elaborated Fermi Liquid theories introduce the notion of
pseudo-gap as a decrease of the effective density of states
at Fermi level [13, 14]. Such pseudo-gap developing at
low temperatures would affect the static and dynamic
susceptibility explaining thus both the drop of K and
peak in 1/T₁T [13, 14]. The disappearance of the spin
fluctuations under pressure, observed in the spin-lattice
relaxation rate, which is parallel to the reduction of the
pseudo-gap manifesting by the decrease of the Knight shift
meet the expectations of this theoretical model.

Following the example of a unified phase diagram for
1D conductors [15], we proposed an implementation of such
general *p*-*T* phase diagram for the *κ* phases. This is shown

<figure><img src="image_4.png" /><figcaption>Figure 2: General P-T phase diagram of the κ-(ET)₂X family.</figcaption></figure>

in Fig.2. The important feature of this phase diagram is the
proximity of antiferromagnetism and superconductivity as
already suggested by the observation of the relaxation peak
but finally confirmed by the discovery of the antiferromag-
netic ground state in κ-(ET)₂Cu[N(CN)₂]Cl [16, 17, 18].
The fact that when applying pressure this compound be-
comes superconducting reminds the properties of the phase
diagram of for the (TMTSF)₂X-(TMTTF)₂X family, how-
ever, unlike in 1D compounds, there is no dimensionality
crossover and although the nesting has a 1D character the
electron gas remain essentially two-dimensional for all tem-
peratures. On the other hand, the above phase diagram is
also similar to that of the underdoped YBa₂Cu₃Oₓ. In the
latter the doping which governs the carrier concentration is a
parameter analogous to pressure in our phase diagram. The
similarity with HTcs raises once again the question about
the nature of the antiferromagnetism in the 2D organics:
itinerant or localized?
### 3. ¹³C NMR in the superconducting state

In the superconducting state, the NMR relaxation can probe various types of fluctuations: superconducting excitations, localized electrons in the vortex cores, and motion of the vortex structure. An important achievement of the presented study is that all of these contributions could be properly separated, first choosing suitable NMR nuclei and furthermore using the properties of the lock-in state to separate the contributions due to normal electrons and superconducting excitations in the ¹³C relaxation [4, 6]. The ¹H NMR studies of the vortex state have been presented by Brazovskii et al. [19, 20], here we only present the ¹³C experiments.

There is still no general consensus on the mechanisms of superconductivity in quasi-two-dimensional organic superconductors. For example, the experimental results for the magnetic penetration depth are still controversial leading to differing conclusions as to the superconducting gap symmetry both isotropic s-wave and a more unconventional pairing have been proposed [21, 3]. The latter was motivated by the fact that pronounced electron correlations appear to be a common property for cuprate high-T_c or heavy fermion superconductors. On one hand the available studies of the temperature dependence of the superconducting gap and of the electromagnetic properties seem to exclude non conventional schemes such as local-pairing model, on the other hand there is no decisive arguments neither for BCS-type pairing nor for the pairing mechanism. ¹³C NMR is particularly adapted to probe the electronic properties, since the carbon atoms lie in the core of the conducting layers [4].

Below we discuss recent Knight shift and relaxation measurements made on κ-(ET)₂Cu[N(CN)₂]Br for two orientations of the crystal: field perpendicular (H₀//b) and parallel (H₀ in the (a-c) plane) to the conducting layers. The results obtained in a field perpendicular to the conducting layers are shown in Fig.3 (Knight shift) and Fig.4 (T₁).

<figure><img src="image_5.png" /><figcaption>Figure 3: Normalized Knight shift at 7.8 T in perpendicular (●) and parallel field (o).</figcaption></figure>

The observed field dependence of 1/T₁ and has been interpreted assuming the following scenario: in the mixed state there are two kinds of electronic spins interacting with ¹³C nuclei, those of normal electrons in the vortex cores and those of thermally broken superconducting pairs.

<figure><img src="image_6.png" /><figcaption>Figure 4: (T₁T)⁻¹ in perpendicular field.</figcaption></figure>

This field dependence is a signature of a relaxation due to "normal" electrons in the vortex cores: it merely reflects the variation of the vortex density with the field. A similar field dependence have been studied recently in HTSC [22, 23].

To interpret the curves of Fig.3 we have considered a simple model, with two different sources of relaxation [6]. The first (T₁) comes from normal electrons in the vortex cores and the second (T₁) involves pair excitations across the superconducting gap. Considering that all carbon nuclei belong to the same spin bath, we measure the total rate defined as:

$$ \frac{1}{T_1} = \frac{H_0}{H_{c2}} \frac{1}{n T_1} + \left(1 - \frac{H_0}{H_{c2}}\right)^{\frac{1}{s}} \frac{1}{s T_1} \quad (1) $$

where H₀ is the applied field and H₀H⁻¹ = 2πξ²₀H₀Φ⁻¹₀ is the total cross-section fraction of the vortex cores. The fitting of the experimental curves [6] yields H₀ = 10 T and ξ₀ = 60 Å. Note that other determinations of H₀ give usually higher values as they were derived from the zero temperature extrapolation of dH₀/dT near T₀.

We now turn to the measurements performed in parallel field and presented in Fig.3 (Knight shift) and Fig.5 (T₁). The first striking observation is the absence of any field dependence of the relaxation. This provides strong evidence for the absence of vortex pancakes in this configuration as is expected in the lock-in state [24]. The possibility of performing NMR measurements in the lock-in state is highly attractive since it gives the possibility to perform unique studies on the 2D superconductor: the Knight shift gives the spin susceptibility in the superconducting state and the relaxation rate probes the density of superconducting pair excitations. It was found (Fig.4) that the Knight shift tends towards zero at low temperature. This gives an evidence that the spin paring is singlet: in the triplet state, there should be no difference between the normal and superconducting spin susceptibility [25]. As for the relaxation rate, the first interesting observation is the absence of Hebel-Slichter peak. This can be explained as the influence of AF correlations in the case of an anisotropic gap [26, 27]. Probably the most valuable result of these studies was the discovery that (T₁)⁻¹ follows a T³ law below T₀.
<figure><img src="image_7.png" /><figcaption>Figure 5: ($T_1^{-1}$) in parallel field (no field dependence was detected in the range 5-8 T). The continuous line is the fit to the $T^3$ law.</figcaption></figure>

The data of Fig.5 show undoubtedly that such law is valid over a very wide range of temperature. There are different scenarios compatible with this observation. The model of Hasegawa et al [28] is based on an anisotropic gap with lines of zeros at the Fermi surface. Then the Hebel-Slichter peak is removed and that the relaxation rate follows a $T^3$ law at low temperature because of the linear density of states at low energy. This model was important because it gave a motivation for searching new types of pairing. In HTSC, the $T^3$ law has been observed several times [29, 23] and has been often interpreted as a signature of d-wave superconductivity. Indeed, theoretical calculations involving a d-wave pairing are in general in good agreement with the experimental results [27, 26, 30]. Nevertheless, a $T^3$ law can result as well from an anisotropic nodeless gap [23]. We estimated that if the gap is nodeless its anisotropy must be greater than 10 [6].

In summary, these results provide a solid experimental evidence for a very anisotropic (possibly with nodes in the gap) spin-singlet pairing in this class of 2-D superconductors. The possibility for non-conventional pairing in 2-D organic superconductors has been pointed out by Bulaevskii [3]. This pairing could bear some resemblance with the spin fluctuation mediated interchain interaction proposed for 1D superconductors [31].

**Acknowledgments.** S.B. acknowledges the hospitality of the LPS and the Laue-Langevin Institute as well as the support from the CNRS and from the Université Paris-Sud. H.M. thanks the Direction des Recherches, Etudes et Techniques.

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