Spin density wave and superconducting properties of nanoparticle organic conductor assemblies

The magnetic susceptibilities of nanoparticle assemblies of two Bechgaard salts ${\left(\mathrm{TMTSF}\right)}_2{\text{PF}}_6$ and ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$, have been studied vs temperature and magnetic field. In the bulk these materials exhibit a spin density wave formation $(T_{\text{SDW}}=12\mathrm{K})$ and superconductivity $(T_{\text{c}}=1.2\mathrm{K})$, 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.

Figure 1

${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$ 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 ${\left(\mathrm{TMTSF}\right)}_2{\text{PF}}_6$ exhibit similar morphologies and size distributions.

Figure 2

Electrical transport in the ${\left(\mathrm{TMTSF}\right)}_2{\text{PF}}_6$ nanoparticle (NP) assembly compared with single-crystal (SC) ($c$-axis) measurements. Upper inset: Comparison of Arrhenius activation plots for the nanoparticle assembly and single crystals showing the lower activation energy for the nanoparticle assembly. Lower insert sketch: Series ($R_{\text{S}}$) & parallel ($R_{\text{P}}$) model for the nanoparticle assembly resistance.

Figure 3

Magnetic properties of ${\left(\mathrm{TMTSF}\right)}_2{\text{PF}}_6$. (a) Temperature and magnetic-field-dependent susceptibility of a randomly oriented ${\left(\mathrm{TMTSF}\right)}_2{\text{PF}}_6$ 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 ${\left(\mathrm{TMTSF}\right)}_2{\text{AsF}}_6$ from Ref. [16] for $a$-, $b$-, 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]. (c) Spin-flop behavior at 5 K [left axis: $\Delta {\chi }_{\text{NP}}={\chi }_{\text{NP}}$ (5 K, B) – ${\chi }_{\text{NP}}$ (5 K, 0.1 T)] compared with ${\chi }_{\text{b}}$ results for single-crystal ${\left(\mathrm{TMTSF}\right)}_2{\text{AsF}}_6$ from Ref. [16] [right axis: ${\chi }_{\text{a}}$, ${\chi }_{\text{b}}$, ${\chi }_{\text{c}}]$, where we note that the field dependencies of ${\chi }_{\text{a}}$ and ${\chi }_{\text{c}}$ are negligible on this scale.

Figure 4

A comparison between the change in frequency ($-\delta f$) for ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$ nanoparticles ($T_{\text{c}}$ $\sim 1.2\text{K}$), the normalized average relative susceptibility ($\Delta \chi$) of a bundle of ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$ single crystals ($T_{\text{c}}\sim 1.1\text{K}$) by Gubser et al. [21], and the averaged penetration depth change ($\Delta f$) of ${\beta }^{\prime \prime }{\text{-(ET)}}_2{\text{SF}}_5{\text{CH}}_2{\text{CF}}_2{\text{SO}}_3$ ($T_{\text{c}}$ $\sim 5.5\text{K}$) [22] as a function of reduced temperature $\mathrm{T}/T_{\text{c}}$.

Figure 5

Two scenarios for superconductivity in the nanoparticle assembly of ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$. (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.

Figure 6

A comparison of the magnetic field dependence of the normalized changes in the TDO frequency $\delta f_{\text{norm}}$ (normalized with respect to $-\delta f$ at zero field for the lowest temperature sweep, 33 mK) compared with the normalized average relative susceptibility ${\chi }_{\text{av}}=(2{\chi }_{\perp }+{\chi }_{\parallel })/3$ obtained by Gubser et al. [21] (inset: expanded low-field view). Estimates of the upper critical field ${\text{H}}_{\text{c}2}^{*}$ (arrows) are obtained from the field where the signal asymptotically merges with the constant background at higher field. The randomly aligned nanoparticles exhibit a field dependence that is in qualitative agreement with the average response of aligned single crystals.

Figure 7

A comparison between the upper critical field ${\text{H}}_{\text{c2}}$ reported on a single crystal (SC) of ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$ for each axis (broken lines) and their average (solid line) [25] and our determination of ${\text{H}}_{\text{c}2}^{*}$ for the ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$ nanoparticle (NP) assembly (solid circles). The uncertainty bars represent the range of ${\text{H}}_{\text{c}2}^{*}$ values based on determinations from all field sweep data at each temperature. The gray-scale dashed line is a polynomial guide-to-the-eye fit and indicates that ${\text{H}}_{\text{c}2}^{*}$ for the ${\left(\mathrm{TMTSF}\right)}_2{\text{ClO}}_4$ nanoparticle assembly is similar to that of ${\text{H}}_{\text{c2}}$ for single crystals averaged over the three crystal directions.