Spin Density Wave and Superconducting Properties of Nanoparticle Organic Conductor Assemblies

PHYSICAL REVIEW B 91, 035437 (2015)

Spin density wave and superconducting properties of nanoparticle organic conductor assemblies

Laurel E. Winter,1,* Eden Steven,1,* James S. Brooks,1,† Shermane Benjamin,1 Ju-Hyun Park,2 Dominique de Caro,3,4 Christophe Faulmann,3,4 Lydie Valade,3,4 Kane Jacob,3,4 Imane Chtioui,3,4 Belen´ Ballesteros,5,6 and Jordi Fraxedas5,6 1Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA 2National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA 3CNRS, Laboratoire de Chimie de Coordination, 205 route de Narbonne, BP 44099, 31077 Toulouse Cedex 4, France 4Universite´ de Toulouse, UPS, INPT, 31077 Toulouse Cedex 4, France 5ICN2 - Institut Catala de Nanociencia i Nanotecnologia, Campus UAB, 08193 Bellaterra, Barcelona, Spain 6CSIC - Consejo Superior de Investigaciones Cientiﬁcas, ICN2 Building, 08193 Bellaterra, Barcelona, Spain (Received 3 November 2014; revised manuscript received 6 January 2015; published 27 January 2015)

The magnetic susceptibilities of nanoparticle assemblies of two Bechgaard salts (TMTSF)2PF6 and (TMTSF)2ClO4, have been studied vs temperature and magnetic ﬁeld. In the bulk these materials exhibit a spin density wave formation (TSDW = 12 K) and superconductivity (Tc = 1.2 K), respectively. We show from inductive (susceptibility) measurements that the nanoparticle assemblies exhibit ground-state phase transitions similar to those of randomly oriented polycrystalline samples of the parent materials. Resistivity and diamagnetic shielding measurements yield additional information on the functional nanoparticle structure in terms of stoichiometric and nonstoichiometric composition.

DOI: 10.1103/PhysRevB.91.035437 PACS number(s): 75.50.Tt, 75.30.Fv, 74.70.Kn

I. INTRODUCTION or electrocrystallization in the presence of stabilizing agents acting as growth inhibitors [9]. Additional refinements of Restricted geometries have been realized in many materials the synthesis conditions have produced a number of DA such as semiconductors and metals, and often the bulk organic superconductors where strong correlations between properties are modified when the size of a structure approaches the spectroscopic and crystallographic properties of the bulk the characteristic extent of the ground-state order parameter. materials and the nanoparticles have been established [10]. For instance, in semiconductor devices [1] or type-I elemental In light of these advances, the main purpose of the present metal superconductors like aluminum [2,3], the evolution work is to identify the low-temperature thermodynamic from an insulator to a metal or superconductor is observed ground states of the nanoparticle species. An example of the with increasing electron density or film thickness, and in nanocrystalline and nanoparticle structure of (TMTSF) ClO nanoparticles of tin [4] or lead [5,6] a modification of the su- 2 4 isshowninFig.1. High-resolution transmission electron perconducting properties is observed for sizes smaller than the microscope (HR-TEM) studies [10] show that single-crystal coherence lengths. The single-molecule magnet material Mn 12 constituent nanoparticles of approximately 3–5 nm in size (see acetate has also been produced as a thin film [7]. Although the Supplemental Material, Fig. 1 [11]) make up nanoparticles that film retains aspects of the more dramatic magnetic hysteresis TEM images show are on average about 10 times larger (e.g., effects seen in the bulk crystalline materials, modifications average cluster size of 34 nm). These nanoparticles form a fine such as an additional magnetic phase also appear. However, powder (assembly) with a random crystallographic orientation progress in the study of thin-film and nanoparticle geometries (see Supplemental Material, Fig. 2 [11]) that is then used for in the important class of organic superconductors, which are the characterization of the physical properties. predominantly charge-transfer organic salts with relatively We focus on the low-temperature and high-magnetic-field large donor and acceptor organic molecules, has remained properties of two new nanoparticle systems in the class of elusive. This is due to the reluctance of these materials to the Bechgaard salts [12]. The first is (TMTSF) PF (also, naturally form epitaxial layers on substrates; rather, the default 2 6 NP-PF ), which undergoes a spin density wave (SDW) and growth morphology, for instance, via electrocrystallization, 6 metal-insulator transition at T = 12 K, and the second is often the nucleation of small crystallites at arbitrary SDW is (TMTSF) ClO (also, NP-ClO ) which, due to the low orientations. Some progress has been made by evaporation 2 4 4 symmetry of the tetrahedral anion ClO , first undergoes and sublimation methods that produce small patches of ordered 4 an anion ordering transition at T = 24 K, followed by charge-transfer complexes on metallic substrates that can then AO a superconducting transition at T = 1.2K [13]. The main be measured by scanning probe methods [8]. Such sample c goal of the present work is to determine if the nanoparticle geometries and measurements present considerable challenges morphologies of these materials exhibit the same ground states and are not conducive to other characterization methods that as the bulk-single-crystalline materials. We will show that the can probe the ground-state thermodynamics of a nanostructure. ground-state properties of the nanoparticles compare favorably Recently dispersed nanoparticles of donor-acceptor (DA) with their bulk counterparts when the highly anisotropic organic conductors have been synthesized by either oxidation nature of the Bechgaard salt properties are taken into account [14]. (Bulk crystals form in needlelike morphologies where the most conducting axis is the a axis oriented along the *Corresponding authors: [email protected], esteven@ magnet.fsu.edu needle direction, the a-b plane constitutes a conducting layer, †Deceased September 27, 2014. and the c axis is the least conducting direction, normal to

(a) (b) (c) Average = 34 nm NP-ClO 70 FWHM = 12 nm 4 60 Gaussian Fit 50 40

Count (#) 30 4 20

ClO 10 0 10 20 30 40 50 60 Size (nm)

FIG. 1. (Color online) (TMTSF)2ClO4 nanoparticles. (a) Low-resolution TEM image of nanoparticles dispersed on a substrate. (b) HR-TEM image of nanoparticle structure: dashed envelope, approximate extent of the overall nanoparticle; circles, positions of constituent nanoparticles of 3–5 nm in size. (c) Size distribution of nanoparticles in (a). Nanoparticles of (TMTSF)2PF6 exhibit similar morphologies and size distributions. the layers.) However, an unambiguous demonstration of a Since the Bechgaard salts are highly anisotropic in terms possible alteration of the bulk ground-state properties when of their electronic structure and magnetic field effects [12], the nanoparticle size is less than the ground-state coherence a comparison of the electronic properties and susceptibility lengths will require further studies. of a randomly oriented assembly of nanoparticles (and therefore the constituent nanoparticles) with previous bulk- single-crystal measurements requires an average of the a-, b-, II. RESULTS AND DISCUSSION and c-axis properties. For this purpose, we assume that the For clarity in terminology in what follows, we note that electrical current path or applied magnetic field direction lies the objects on the order of 30–60 nm, as seen in the with equal probability along any of the three principle axes of lower-resolution TEM image [Fig. 1(a)], are referred to as each nanoparticle. This leads to a simple 1/3 contribution of the nanoparticles. These nanoparticles are made up of smaller property from each direction, averaged to allow a comparison entities, referred to as the constituent nanoparticles, with size with the corresponding nanoparticle assembly data. 3–5 nm, as seen from the HR-TEM image [Fig. 1(b)]. For susceptibility and inductive studies, the samples measured A. Spin-density wave transition in (TMTSF)2PF6 nanoparticles were encapsulated powders or assemblies (see Supplemental Material, Fig. 2 [11]) comprised of nanoparticles. For electrical We first discuss the electronic transport of the SDW transport measurements, nanoparticle assemblies were studied transition in the (TMTSF)2PF6 nanoparticle assembly. In in a four-terminal configuration. In the following sections powders, the nanoparticles tend to form a dense, intercon- measurements on the nanoparticle assemblies are presented nected assembly unlike that observed in crushed single-crystal in parallel with comparisons with bulk-single-crystal results. powders where the crystals are well dispersed and separated (Supplemental Material, Fig. 2 [11]). This indicates a strong interparticle interaction between nanoparticles (Supplemental Material, video 1 [11]). The source of this unusual mutual 4 attraction is not presently understood, but based on the sample 3 R SC ) 3 preparation, we do not believe there are residual solvents or R E = 2 meV 2 NP a stabilizing agents on the surface of the nanoparticles. We find Norm RModel 2 the assembly is electrically conducting, and the temperature- dependent resistance of the nanoparticle assembly was studied 10 Ln(R 1 using an adhesive stamp electrode method [15] and a lock-in E = 0.75 meV 6 0 a amplifier (SRS 830) in a four-probe configuration down to Norm 5

R cryogenic temperatures. As observed in Fig. 2, the SDW 4 0.08 0.12 0.16 0.20 transition (accompanied by a metal-insulator transition) occurs 3 1/Temp (1/K) at TSDW = 12 K, similar to that of the bulk single crystals. We 2 RSC note that in bulk single crystals, the temperature-dependent R = R Model S T dR/dT > RP resistance above SDW is metallic, i.e., 0, but the 1 nanoparticle assembly shows very little dependence of the 6 8 10 12 14 16 18 20 resistance above TSDW. However, below TSDW the activated component of the resistance rises quickly and is clearly Temperature (K) observable above the background. Notably, the activation energy (E )oftheNP-PF assembly FIG. 2. (Color online) Electrical transport in the (TMTSF)2PF6 a 6 nanoparticle (NP) assembly compared with single-crystal (SC) (c- is much lower compared to the case for a bulk single crystal axis) measurements. Upper inset: Comparison of Arrhenius activation (Fig. 2, upper inset). In the simplest case, this lower Ea can plots for the nanoparticle assembly and single crystals showing be assigned to the presence of nonstoichiometric contributions the lower activation energy for the nanoparticle assembly. Lower to the overall transport signal. If the electrical transport in insert sketch: Series (RS) & parallel (RP) model for the nanoparticle the NP-PF6 assembly (RNP) is purely stoichiometric, then assembly resistance. the activation energy should be close to that seen in a single

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(a) 1.95 (b) c 1.2

1.90 a 0.8 emu/mol) ave -4 1.85 0.4 (10 b 1.80 spin 0.0 3.0 T 5 10 15 20 25

emu/mol) Temperature (K) -4 1.75 1.5 T 1.0 T (c) (10 0.7 T 0.3 1.5

spin 1.70 0.5 T 0.3 T 0.2 NP 1.0 emu/mol) emu/mol) -4 1.65 0.1 T a -4 0.1 (10 b 0.5 (10

1.60 0.0 c NP,spin

0.0 SC,spin 8 12 16 20 0.5 1.0 1.5 2.0 2.5 3.0 Temperature (K) Field (T)

FIG. 3. (Color online) Magnetic properties of (TMTSF)2PF6. (a) Temperature and magnetic-field-dependent susceptibility of a randomly oriented (TMTSF)2PF6 nanoparticle assembly. The curves have been shifted to coincide with the 3-T data at 13 K to account for a systematic field-dependent background. (b) Single-crystal results for (TMTSF)2AsF6 fromRef.[16]fora-, b-, and c-axis orientations at 0.3 T. The solid line is a simple average of the susceptibility for all three directions [compare with 0.3-T data in Fig. 3(a)]. (c) Spin-flop behavior at 5 K [left axis: χNP = χNP (5 K, B) – χNP (5 K, 0.1 T)] compared with χb results for single-crystal (TMTSF)2AsF6 from Ref. [16] [right axis: χa, χb, χc], where we note that the field dependencies of χa and χc are negligible on this scale. crystal. However, if there are nonstoichiometric resistances in stoichiometric material) will be reduced by the presence of series (RS) and parallel (RP) to the stoichiometric resistance conduction through nonstoichiometric parallel pathways. It (RSC), then the temperature dependence of the transport will be also indicates the contribution of the stoichiometric resistance modified. We have used a simple series-parallel model (Fig. 2, becomes most evident below the SDW transition, where its lower inset) to describe the apparent suppression of Ea.Our resistance rises by orders of magnitude with respect to the model assumes that each nanoparticle in a compacted assembly nonstoichiometric material. is separated from the others by a thin, nonstoichiometric Next, we examine the magnetic susceptibility χ of the coating. Hence the coating will give rise to both series (RS) SDW transition in (TMTSF)2PF6 nanoparticles shown in and parallel (RP) resistances with respect to the stoichiometric Fig. 3(a). To study the magnetic properties, NP-PF6 powders resistance RSC. We further assume the nonstoichiometric of mass 63.8 mg were placed in a polycarbonate capsule resistances are constant with the temperature, and the stoichio- and measured in a commercial superconducting susceptometer metric resistance RSC follows the temperature dependence of (MPMS, Quantum Design) vs temperature and magnetic field. a bulk single crystal (which is small above TSDW, and rises The background signal from the polycarbonate capsule was rapidly below TSDW). For the analysis, we have normalized the measured independently. The spin susceptibility is obtained resistances to the data at 20 K and included a weighting ratio η, by subtracting the molecular diamagnetism [16] χmol = 3.5 × −4 which represents the portion of the total resistance that is due to 10 emu/mol of (TMTSF)2PF6 from the total susceptibility. parallel elements in the circuit. The model for the temperature For comparison [Fig. 3(b)], the most complete previous study dependence of the total resistance of the assembly is RModel = of the anisotropic susceptibility for a bulk single crystal (1 − η) × RS + η × [RSCRP/(RSC + RP)]. It provides an was in the isostructural material (TMTSF)2AsF6 (with nearly excellent fit to the experimental data (Fig. 2 upper inset), where identical properties) reported by Mortensen et al. [16]for we find η = 0.2, RS = 1, and RP = 19.1. This means that at the a, b, and c directions with respect to an applied field of most the stoichiometric contribution to the overall resistance H = 0.3 T. It was found that below TSDW = 12 K, χb dropped of the NP-PF6 assembly is 20% of RSC (in the limit that RP → rapidly, indicating antiferromagnetic order develops along the ∞). The rest is due to contributions that could originate from b axis. In contrast, χa and χc remain paramagnetic below TSDW. some combination of contact resistances between individual It was further found [Fig. 3(c)] that a magnetic field applied nanoparticles and/or nonstoichiometric material. along the b axis induces a spin-flop at Hsf ≈ 0.45 T, where χb The main results of this analysis are that for the self- then approaches χa and χc. adhering powdered nanoparticle assembly of (TMTSF)2PF6, From Figs. 2 and 3 it is clear that the (TMTSF)2PF6 electrical conductivity occurs via a combination of transport nanoparticle assembly exhibits qualitatively the same SDW through stoichiometric and nonstoichiometric material in ground state of a bulk single crystal, including the metal- effectively parallel and series pathways. This implies that insulator transition and the spin-flop behavior in magnetic the effective activation energy in the SDW state (of the field compared with a simple averaging argument based on

035437-3 LAUREL E. WINTER et al. PHYSICAL REVIEW B 91, 035437 (2015) bulk-single-crystal results. There is no apparent shift in the 0 ''-(ET) SF CH CF SO SDW transition temperature between the nano- and bulk 2 5 2 2 3 1.0 (Prozorov et al. f ) materials, indicating that the effective coherence length (ξ)of -100 NP - (TMTSF)2ClO4 the SDW order parameter is comparable to or smaller than the (This work - f ) 0.8 effective nanoparticle size (estimated from a simple BCS-type -200 SC - (TMTSF)2ClO4 argument to be ξ = ν /2πk T ≈ 10 nm). Qualitatively, (Gubser et al. F B SDW 0.6 in Fig. 3 there may be some functional differences in the ﬁeld

(kHz) -300 f (arb. units) and temperature dependence of the nanoparticle susceptibility - and in the higher spin-ﬂop saturation (1.5 T vs 0.45 T), but 0.4 -400 f at present we cannot make any signiﬁcant assignment of the 0.2 behavior to size effects. -500

0.0 B. Superconductivity and critical magnetic ﬁelds -600 0.0 0.2 0.4 0.6 0.8 1.0 in (TMTSF)2ClO4 nanoparticles T/Tc

We next turn our attention to the (TMTSF)2ClO4 nanoparti- FIG. 4. (Color online) A comparison between the change in cle system. Due to the low temperature of the superconducting − ∼ transition temperature (T = 1.2 K) in (TMTSF) ClO , which frequency ( δf ) for (TMTSF)2ClO4 nanoparticles (Tc 1.2K), c 2 4 the normalized average relative susceptibility (χ) of a bun- was below the 1.5-K limit of the MPMS, we used a high- dle of (TMTSF) ClO single crystals (T ∼ 1.1 K) by Gubser sensitivity inductive method in a dilution refrigerator in a 16-T 2 4 c et al. [21], and the averaged penetration depth change (f )of superconducting magnet to study the diamagnetic signal asso- β -(ET) SF CH CF SO (T ∼ 5.5K)[22] as a function of reduced ciated with the superconducting state. (The superconducting 2 5 2 2 3 c temperature T/Tc. magnet was swept through zero magnetic field to eliminate remnant field effects due to trapped flux in the solenoid.) The inductive method involves a tunnel diode oscillator (TDO) self- −δf are in qualitative agreement with previous susceptibility resonating LC circuit (L = inductor, C = capacitor) operating measurements performed by Gubser et al. [21] for a bundle with a frequency f and driven by a tunnel diode biased in the of aligned crystals (Fig. 4). The weak, sigmoidal nature negative resistance region [17,18]. Changes in the resonant of the temperature dependence of −δf in Fig. 4 does not frequency are directly proportional to any mechanism that correspond to the much stronger temperature dependence of γ −1/2 changes the effective inductance of a coil in which the sample a BCS-type model λ(T) = λ(0) × (1 − (T/Tc) ) , where is placed. In the case of a superconducting transition, this the exponent (typically between 1.5 and 4) depends on the occurs due to the diamagnetic response that effectively reduces nature of the superconducting order parameter. This is made the volume of the coil due to flux excluded from the sample, evident by comparison with another organic superconductor, leading to an increase in the resonant frequency. For this work, β -(ET)2SF5CH2CF2SO3 [22], where the rise in λ(T) (f in an assembly of NP-ClO4 of mass 7.385 mg (corresponding to Fig. 4) near Tc (∼5.5 K) is rapid. Due to the layered, anisotropic a sample volume of 3.1 mm3) was placed inside a nonmagnetic structure of organic superconductors, the orientation of the gelatin capsule with an approximate capsule volume of 18.08 sample in the inductor coil plays a significant role. Defining mm3, which was then placed inside of a 40-turn coil (L) with an the layers to lie in the a-b plane, for the oscillating magnetic 3 approximate length and volume of 4.6 mm and 23.68 mm ,re- field h perpendicular to the c axis, λ⊥(T) can be much larger spectively. The rms field (h) due to the measurement coil is es- and less temperature dependent than λ (T) for h parallel to the timated to be 0.04 Oe, well below the lower (Meissner) critical c axis. A simple averaging to find the contributions for the a, field Hc1 for T

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(a) (b)

FIG. 5. (Color online) Two scenarios for superconductivity in the nanoparticle assembly of (TMTSF)2ClO4. (a) Model of the nanoparticle assembly acting as a monolithic solid body in an inductive coil. (b) Visualization of magnetic ﬁeld penetration in a weakly interacting assembly of superconducting nanoparticles.

3 We find that Vs = 0.075 × Vcoil = 1.79 mm , which implies temperatures between 1.5 K and 33 mK. Shown in Fig. 6 that at 0.03 K, about 58% of nanoparticle material is su- are the normalized changes in the TDO frequency δfnorm, perconducting and shields the field. Therefore 42% of the which is normalized with respect to −δf at zero field for nanoparticle assembly volume is either penetrated by field or is the lowest temperature sweep (T = 33 mK, see Supplemental nonstoichiometric material. There are two different scenarios Material, Fig. 3 [11]), for increasing magnetic field for two of how the nanoparticle assembly can act: (a) the nanoparticles representative temperatures below Tc ∼ 1.2 K, where a are either electrically connected or Josephson coupled, acting quadratic field-dependent instrumental background present at as a monolithic solid body where the shielding currents appear all temperatures has been subtracted from the data. For T< at the periphery [Fig. 5(a)]; (b) as an assembly of weakly Tc, δfnorm increases rapidly with field. For comparison, we interacting nanoparticles [Fig. 5(b)] where the field easily show the normalized field-dependent changes in susceptibility penetrates, and the diamagnetic shielding arises from the sum data, χav = (2χ⊥ + χ )/3, averaged to estimate a random of individual superconducting nanoparticles [23]. orientation from Ref. [21] for two similar temperatures (ex- Scenario (a): If we assume that there is no nonstoi- panded view in lower inset). We find again a good qualitative chiometric material (i.e., rstoich. = rassem.), we may estimate how far the magnetic field penetrates into the nanoparticle assembly volume at low temperature, i.e., the effective change 1.0 in penetration depth λeff = λ(Tc) − λ(T = 0) by assuming λ(Tc) ∼ rassem. for a spherical sample shape of radius rassem. ≡ 3 1/3 ≡ 3 1/3 0.8 H*c2 (630 mK) H*c2 (33 mK) ( [ 4 πVassem.] ), and shielded sample radius rs( [ 4 πVs] ). 4 3 Using the relation π(rassem. − λeff) = Vs we find λeff ∼ 3 TDO fnorm 1.0 150 μm. If there is nonstoichiometric material, then λeff 0.6 630 mK 0.8 will be smaller. We note that λeff ∼ 150 μmisinthe 33 mK 0.6 range of values for the penetration depth reported for other (arb. units)

0.4 norm organic superconductors (λ⊥ ∼ 800 μm and λ ∼ 1 μmfor f

norm 0.4

f anisotropic β -(ET)2SF5CH2CF2SO3 [22]), and that it is Relative Susceptibility 0.2 significantly larger than the range of coherence lengths in 0.2 Gubser et al. (TMTSF)2ClO4 :80nm<ξ<2nm. 650 mK 0.0 Scenario (b): The nanoparticles act individually. Noting 35 mK 0.00 Field (T) 0.10 that the rms ac field h = 0.04 Oe Hc1, no vortex state 0.0 enters an individual nanoparticle, and since λ (microns) ξ ∼ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 nanoparticle size (nanometers), the presence of the field would Field (T) result solely in a reduced superconducting order parameter within the nanoparticle [24], and the diamagnetic response FIG. 6. (Color online) A comparison of the magnetic field de- would come from the sum of the nanoparticles in the assembly, pendence of the normalized changes in the TDO frequency δfnorm (normalized with respect to −δf at zero field for the lowest mimicking a bulk solid-body response. Previous work on Pb temperature sweep, 33 mK) compared with the normalized average nanoparticles indicates that even in a compacted state, the relative susceptibility χav = (2χ⊥ + χ )/3 obtained by Gubser et al. nanoparticles act as individual entities [5] and give rise to a [21] (inset: expanded low-field view). Estimates of the upper critical bulklike diamagnetic signal. Moreover, there is no suppression ∗ field Hc2 (arrows) are obtained from the field where the signal in Tc until the nanoparticle size is only about 10% of the bulk asymptotically merges with the constant background at higher field. coherence length. The randomly aligned nanoparticles exhibit a field dependence that is We next turn to the magnetic field dependence, deter- in qualitative agreement with the average response of aligned single mined systematically by isothermal magnetic field sweeps for crystals.

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material that we have modeled as a coating that in a 2.0 NP Assembly: nanoparticle assembly acts as both a series and parallel H* Average c2 conducting path with the stoichiometric material. It is likely H*c2 Fit that the (TMTSF)2ClO4 functional structure is similar. Hence 1.5 in the superconducting state, there are normal-state regions between any two superconducting centers, and this will reduce the Josephson coupling in the assembly. The relatively 1.0 (Tesla) large effective penetration depth λeff ∼ 150 μm may be a c2 SC (Murata et al.): manifestation of this, since the entire mass of the assembly is H 0 H a-axis 0.5 c2 taken into account when estimating the nanoparticle effective Hc2 c-axis volume, but only part of it actually goes superconducting and Hc2 b-axis contributes to the change in diamagnetic shielding below Tc. H average 0.0 c2 Based on the observations above, it is probable that 0.0 0.2 0.4 0.6 0.8 1.0 1.2 NP-ClO4 acts as isolated superconducting nanosized regions Temperature (K) below Tc. In this respect, previous work on Pb nanoparticles is instructive. Bulk Pb is a type-I superconductor with a critical FIG. 7. (Color online) A comparison between the upper critical temperature of Tc = 7.2 K, a coherence length ξ(0) ∼ 90 nm, field Hc2 reported on a single crystal (SC) of (TMTSF)2ClO4 for and a penetration depth λ(0) ∼ 40 nm. Li et al. [5] investigated each axis (broken lines) and their average (solid line) [25]and both the susceptibility and resistivity of nanoparticle powders ∗ our determination of Hc2 for the (TMTSF)2ClO4 nanoparticle (NP) of Pb (NP-Pb) for a variety of nanoparticle sizes between 86 assembly (solid circles). The uncertainty bars represent the range and 2 nm in capsules with a packing mass density of ∼7% of ∗ of Hc2 values based on determinations from all field sweep data the bulk (less than half of what we determined for our ClO4 at each temperature. The gray-scale dashed line is a polynomial capsule). They found that the T of NP-Pb did not decrease ∗ c guide-to-the-eye fit and indicates that Hc2 for the (TMTSF)2ClO4 until the particle size was less than 10% of the bulk coherence nanoparticle assembly is similar to that of Hc2 for single crystals length. Two important implications of this work are that the averaged over the three crystal directions. NP-Pb act individually and not as a connected system, and that the nanoparticles must be significantly smaller in size than the coherence length before size effects cause a significant change similarity between the magnetic-field-dependent susceptibility in the superconducting order parameter. of the nanoparticle assembly and bulk-single-crystal data. Quantitatively, the single-crystal susceptibility data shows a III. CONCLUSIONS slightly faster suppression of the diamagnetic shielding with field. The above experiments on nanoparticle Bechgaard salts, For higher fields δfnorm asymptotically approaches unity at and the implications provided by comparisons with previous different fields for different temperatures, which we interpret single-crystal studies, are subject to a number of uncertainties, ∗ as the onset of the upper critical field Hc2.Giventhe namely, the distribution of nanoparticle sizes, the random uncertainties in estimating asymptotic intercepts, we have orientation of the nanoparticles, and experimental parameters, ∗ determined the Hc2 onset vs temperature for our complete including the relatively high frequency used (15 MHz, the set of field sweep data from −2 T to 2 T (see Supplemental quasiparticle skin depth above Tc is δ = 15 μmintheTDO Material, Fig. 3 [11]). The results are plotted in Fig. 7, along probe). In spite of these complications, we find a remarkably with previous determinations of Hc2 by Murata et al. [25] strong correlation between the nano and bulk ground-state for the three crystal directions, and their averaged (solid line) properties, and the nanoparticle materials do indeed reflect ∗ contribution. Clearly, Hc2 of the NP-ClO4 assembly follows the intrinsic materials with nearly unperturbed transition closely the expectations for Hc2 of the bulk crystal. We note temperatures. Less clear is evidence for the nanosize effects that up to 16 T at 33 mK, there was no evidence for orbital on the temperature and magnetic field dependencies of the features associated with the field-induced SDW phases, nor ground states. Based on previous results on Pb nanoparticles, the rapid oscillations [26]. Since these effects are periodic in it may be necessary to significantly reduce the size of the inverse field for B c, they may average out due to the random (TMTSF)2ClO4 nanoparticles by an order of magnitude from nanoparticle orientations, although size effects may also play 30 to 3 nm. Indeed, this is the size of the constituent a role. nanoparticles that comprise a single nanoparticle [Fig. 1(b)]. Summarizing, the (TMTSF)2PF6 and (TMTSF)2ClO4 Future work will be needed to specifically address the effects nanoparticle systems are assemblies of organic charge-transfer of size on these constituent nanoparticles with, for instance, metal nanoparticles that exhibit, respectively, a SDW for- low-temperature scanning probe spectroscopy. mation and superconductivity. Our characterizations of their ground-state properties indicate a close correspondence to the ACKNOWLEDGMENTS bulk-single-crystal parent materials, and also give information about the functional description of the nanoparticle struc- This work is dedicated to the memory of Dr. James S. tures beyond spectroscopy and electron microscopy. Specif- Brooks. This work was supported by NSF-DMR Grants No. ically, the temperature-dependent resistance measurements 1005293 and No. 1309146, and the NHMFL is supported by on (TMTSF)2PF6 indicate the presence of nonstoichiometric NSF Cooperative Agreement No. DMR-1157490, the State of

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Florida, and the U.S. Department of Energy. Funding for the (LCC) was supported by the French Centre National de dilution refrigerator used for the 16-T experiment came from la Recherche Scientiﬁque (CNRS). I.C. thanks the French DOE NNSA SSAA Grant No. DE-NA0001979. Collaboration Ministere´ de l’Enseignement Superieur´ et de la Recherche within the European Associated Laboratory Trans-Pyren´ een´ (MESR) for a Ph.D. grant. L.W. and E.S. contributed equally (LEA) (Program: “de la Molecule´ aux Materiaux”)´ is appreci- to this work; L.W. measured NP-ClO4 and E.S. measured ated. Work done at the Laboratoire de Chimie de Coordination NP-PF6.

[1] E. Abrahams, S. V. Kravchenko, and M. P. Sarachik, Metallic lattice constants are 7.297, 7.711, and 13.522 A,˚ and the transfer behavior and related phenomena in two dimensions, Rev. Mod. integrals are 0.51, 0.52, and 1.73 meV. Phys. 73, 251 (2001). [15] E. Steven, E. Jobiliong, P. M. Eugenio, and J. S. Brooks, Note: [2] D. B. Haviland, Y. Liu, and A. M. Goldman, Onset of Adhesive stamp electrodes using spider silk masks for electronic superconductivity in the two-dimensional limit, Phys. Rev. Lett. transport measurements of supra-micron sized samples, Rev. 62, 2180 (1989). Sci. Instrum. 83, 046106 (2012). [3] K. Ohshima, T. Kuroishi, and T. Fujita, Superconducting [16] K. Mortensen, Y. Tomkiewicz, and K. Bechgaard, transition temperature of aluminum ﬁne particles, J. Phys. Soc. Antiferromagnetism in the organic conductor bis-

Jpn. 41, 1234 (1976). tetramethyltetraselenafulvalene hexaﬂuoroarsenate [(TMTSF)2 [4] S. Bose, A. M. Garcia-Garcia, M. M. Ugeda, J. D. Urbina, AsF6]: Static magnetic susceptibility, Phys. Rev. B 25, 3319 C. H. Michaelis, I. Brihuega, and K. Kern, Observation of shell (1982). effects in superconducting nanoparticles of Sn, Nat. Mater. 9, [17] W. A. Coniglio, L. E. Winter, K. Cho, C. C. Agosta, B. Fravel, 550 (2010). and L. K. Montgomery, Superconducting phase diagram and

[5] W.-H. Li, C. C. Yang, F. C. Tsao, and K. C. Lee, Quantum size FFLO signature in λ-(BETS)2GaCl4 from rf penetration depth effects on the superconducting parameters of zero-dimensional measurements, Phys.Rev.B83, 224507 (2011). Pb nanoparticles, Phys.Rev.B68, 184507 (2003). [18] G. J. Athas, J. S. Brooks, S. J. Klepper, S. Uji, and [6] S. Reich, G. Leitus, R. Popovitz-Biro, and M. Schechter, M. Tokumoto, Tunnel diode oscillator application to high sen- Magnetization of small lead particles, Phys. Rev. Lett. 91, sitivity de Haas-van Alphen and superconducting critical ﬁeld 147001 (2003). studies of anisotropic organic conductors, Rev. Sci. Instrum. 64, [7] J. Means, V. Meenakshi, R. V. A. Srivastava, W. Teizer, A. A. 3248 (1993). Kolomenskii, H. A. Schuessler, H. Zhao, and K. R. Dunbar, [19] J.-P. Savy, D. de Caro, L. Valade, J.-C. Coifﬁc, E. S. Choi, Films of Mn12-acetate deposited by low-energy laser ablation, J. S. Brooks, and J. Fraxedas, Evidence of anion-ordering in

J. Magn. Magn. Mater. 284, 215 (2004). (TMTSF)2ClO4 electrodeposited on silicon wafers, Synth. Met. [8] K. Clark, A. Hassanien, S. Khan, K. F. Braun, and S. W. 160, 855 (2010). Hla, Superconductivity in just four pairs of (BETS)2GaCl4 [20] J. P. Pouget, G. Shirane, K. Bechgaard, and J. M. molecules, Nat. Nano. 5, 261 (2010). Fabre, X-ray evidence of a structural phase tran- [9] D. de Caro, L. Valade, C. Faulmann, K. Jacob, D. Van Dorsselaer, sition in di-tetramethyltetraselenafulvalenium perchlorate

I. Chtioui, L. Salmon, A. Sabbar, S. El Hajjaji, E. Perez, [(TMTSF)2ClO4], pristine and slightly doped, Phys. Rev. B 27, S. Franceschi, and J. Fraxedas, Nanoparticles of molecule-based 5203 (1983). conductors, New J. Chem. 37, 3331 (2013). [21] D. U. Gubser, W. W. Fuller, T. O. Poehler, D. O. Cowan, [10] D. de Caro, C. Faulmann, L. Valade, K. Jacob, I. Chtioui, M. Lee, R. S. Potember, L. Y. Chiang, and A. N. Bloch, Mag- S. Foulal, P. de Caro, M. Bergez-Lacoste, J. Fraxedas, B. netic susceptibility and resistive transitions of superconducting

Ballesteros, J. S. Brooks, E. Steven, and L. E. Winter, Four (TMTSF)2ClO4, Phys. Rev. B 24, 478 (1981). molecular superconductors isolated as nanoparticles, Eur. J. [22] R. Prozorov, R. W. Giannetta, J. Schlueter, A. M. Kini, J. Inorg. Chem. 2014, 4010 (2014). Mohtasham, R. W. Winter, and G. L. Gard, Unusual temperature [11] See Supplemental Material at http://link.aps.org/supplemental/ dependence of the London penetration depth in all-organic β-

10.1103/PhysRevB.91.035437 for additional nanoparticle pho- (ET)2SF5CH2CF2SO3 single crystals, Phys. Rev. B 63, 052506 tos, videos, and data. (2001). [12] T. Ishiguro, K. Yamaji, and G. Saito, Organic superconductors, [23] S. Haddad, S. Charfi-Kaddour, and J.-P.Pouget, Inhomogeneous Organic Superconductors, 2nd ed. (Springer-Verlag, Berlin, superconductivity in organic conductors: The role of disorder 1998). and magnetic field, J. Phys.: Condens. Matter 23, 464205 (2011). [13] P. Alemany, J.-P. Pouget, and E. Canadell, Electronic structure [24] C. Kittel, Introduction to solid state physics, Introduction to and anion ordering in TMTSF2ClO4 and TMTSF2NO3:Afirst- Solid State Physics, 7th ed. (Wiley, New York, 1996). principles study, Phys.Rev.B89, 155124 (2014). [25] K. Murata, M. Tokumoto, H. Anzai, K. Kajimura, and [14] The anisotropic properties of (TMTSF)2 X are as follows [12] T. Ishiguro, Upper critical field of the anisotropic organic

for the a, b,andc axis, respectively. For (TMTSF)2ClO4 the superconductors, (TMTSF)2ClO4, Jpn. J. Appl. Phys. 26, 1367 lattice constants are 7.266, 7.678, and 13.275 A;˚ the transfer (1987). integrals are 250, 25, and 1.5 meV; the approximate coherence [26] S. Uji, T. Terashima, H. Aoki, J. S. Brooks, M. Tokumoto, lengths at zero temperature are 800, 300, and 20 A;˚ the critical S. Takasaki, J. Yamada, and H. Anzai, Rapid oscillations in

ﬁelds Hc1 (50 mK) are 0.2, 1, and 10 Oe; and the upper critical the organic conductor (TMTSF)2ClO4, Phys.Rev.B53, 14399 ﬁelds Hc2 (0 K) are 28, 21, and 1.6 kOe. For (TMTSF)2PF6,the (1996).

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