Nanostructured graphene for nanoscale electron paramagnetic resonance spectroscopy

Single-molecule magnets are clusters of magnetic ions or isolated ions embedded in a ligand shell. They are quantum systems that can be described by a single-spin Hamiltonian, with the spin of a single molecule, even when they are assembled in millimeter-size crystal. One main feature of SMMs is that they show magnetic bistability, due to an energy barrier to magnetization reversal. Once the molecules are magnetized by an external field and the field is removed, the barrier hinders magnetization reversal, yielding long relaxation times and hysteresis of the magnetization below a temperature termed the blocking temperature, T_B. For most SMMs the blocking temperature is on the order of a few Kelvins. Magnetic bistability was first discovered in [Mn₁₂ O₁₂ (O₂CCH₃)₁₆ (H₂O)₄] · 4H₂O · 2CH₃CO₂H in 1993 [15]. This SMM has a core of twelve magnetically coupled manganese ions (Mn₁₂) [16] and its relaxation time that can be years below 2 K [15, 17]. Several SMMs have been discovered after Mn₁₂, including those containing just one paramagnetic center, single-ion magnets (SIMs) [18], that are simpler to synthesize and model theoretically. Very recently, the synthesis of dysprosocenium metallocene SMMs yielded hysteresis of the magnetization below strikingly high blocking temperatures, 60 K [19, 20] and 80 K [21].

For a transition-metal-based SMMs with spin S, the degeneracy of the 2S + 1 magnetic states −S ≤ m_s ≤ S is lifted by the combined action of geometric distortion and spin–orbit coupling, so that states with the same ∣m_s∣ but opposite orientation are degenerate. This interaction is present also in the absence of an external magnetic field and it is represented by the zero-field splitting parameter D. The magnitude of this parameter determines the splitting of the energy levels according to E(m_s) ∼ Dm_s², where D is negative and m_s = ± S are degenerate ground states separated by an energy barrier Δ ∼ ∣D∣S² for integer spin or Δ ∼ ∣D∣(S² −1/4) for half-integer spins [22]. Increasing the spin of the molecule seems at first sight to be an obvious route to increasing the barrier to magnetization reversal and increasing the blocking temperature, but it was shown that with increasing S, D decreases [23]. However, the barrier height is not the only parameter that controls the blocking temperature. The magnetization of the molecule can also switch due to quantum tunnelling, even when the thermal energy is much less than the barrier height. Therefore, achieving high blocking temperatures requires careful design of the molecule and the ligand shell [24, 25].

SMMs are usually studied in the form of bulk crystals or powder pellets. Typical characterization techniques include traditional magnetometry, to measure the hysteresis of the magnetization, and HF-EPR, to measure the energy spacing of the electronic states m_s and to extract the parameters characterizing the molecules (including D) from fits to the spectra. In recent years there has been increased interest in the study and control of a small number of molecules, down to monolayer and few-layer thickness, to take full advantage of their nanometer-scale size. Although there have been demonstrations of monolayer SMMs that maintained their magnetic hysteresis, such as Fe₄ complexes grafted on gold surfaces [26, 27], for some SMMs, such as Mn₁₂, the magnetic hysteresis was suppressed when they were reduced to a monolayer [28]. It turns out that the interaction of the molecules with the surface on which they are deposited may reduce the energy barrier Δ compared to bulk samples, possibly due to structural deformations that depend on the SMMs shape. In addition, a given molecule may show magnetic hysteresis when grafted on some surfaces but not others. This is the case for bis(phthalocyaninato)terbium(III) (TbPc₂) SMMs, showing magnetic hysteresis when grafted on Ag(100) capped with MgO, but no hysteresis when grafted directly on Ag(100) [29]. One possible explanation is that the MgO layer better preserves the SMM electronic structure by reducing hybridization and reducing tunnelling of the magnetization through the barrier [29]. It is therefore extremely important to be able to characterize few-layer samples on different substrates to understand their interactions with the substrates and optimize their magnetic properties by chemical tailoring of the ligands. Unfortunately, the characterization of few-layer SMM is mainly limited to one tool, namely XMCD, because traditional magnetometers and conventional EPR instruments are not sufficiently sensitive for such small samples. Below we will show that graphene quantum dot bolometers have the potential to expand characterization techniques for SMMs deposited on surface with HF-EPR spectroscopy for the characterization of samples as thin as monolayers.

The graphene quantum dot bolometers are fabricated using the procedure described in our previous work [11, 30]. Presently, they are patterned from large-area epitaxial graphene grown on SiC, using a metallic mask, as shown in the diagram in figure 1. The mask is removed in the last step of the process by aqua regia, leaving the graphene fully exposed. Our previous work showed that the fabrication process modifies the graphene doping and quality [31]. The aqua regia is a strong hole dopant and affects the charge carrier density, while the metal sputtering induces defects in the graphene. These defects affect the electron cooling mechanism, yielding the counterintuitive result of enhancing the device performance [31]. At the end of the process, the graphene has a bowtie shape, with the quantum dot in the middle connected to triangular source and drain electrodes, as shown in figure 1. The diameter of the dots varies from 30 to 100 nm and the area of the whole graphene bowtie varies from 20 to 100 μm², depending on the distance of the metal contacts connected to the bowtie and the angle of the triangular parts of the bowtie.

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The quantum dot forms a nano-constriction that opens a quantum confinement gap in graphene. As a result, the graphene resistance shows a strong temperature dependence, as high as 100 MΩ K⁻¹ at temperatures below 10 K, due to thermal activation of the electronic current over the quantum confinement gap. When the graphene is irradiated, the electron temperature increases in the whole graphene area, the device resistance decreases and a photovoltage can be measured. The strong temperature dependence of the resistance is due to thermal activation of the electrical current over an energy barrier that is inversely proportional to the dot diameter [11]. This simple device design yields detectors with electrical responsivity as high as 10¹⁰ V W^-1 and noise equivalent power below 2 × 10⁻¹⁶ W Hz^−0.5 at 2.5 K [11, 12, 31]. These figures of merit are based on the absorbed power and the absorbed power can be measured directly from the bolometer current–voltage characteristics [11, 12].

We can assess whether the quantum dot bolometers are sufficiently sensitive for spectroscopy of monolayer samples by estimating the power absorbed by a monolayer of SMMs covering the graphene area. As an example, we consider the Fe₄ complex [Fe₄^III(acac)₆(Br-mp)₂] with ground spin state S = 5 (Hacac = acetylacetonate, Br-mpH₃ = Br-CH₂-C(CH₂OH)₃) [32]. The energy spacing between m_s = 4 and m_s = 5 is equivalent to the energy of a 92.4 GHz photon (or 0.380 meV). Assuming that under continuous-wave irradiation the rate of photon absorption is limited by the relaxation time T₁, we can estimate the absorbed power from a single SMM, P_1M, as the ratio of the photon energy matching the energy level spacing to the relaxation time. By using T₁ ∼ 1 μs (at 4.3 K) [32], we find P_1M ∼ 6 × 10⁻¹⁷ W. If a monolayer of SMMs covers the whole graphene area, about 20 μm² for the smallest bowties, for an approximate SMM size of 1 nm, we estimate 2 × 10⁷ SMMs covering the graphene and absorbing about 1.2 nW. This power is much higher (by at least two orders of magnitude) than the smallest absorbed power that we can measure with the graphene quantum dots [11, 12, 31], therefore power absorption from monolayer SMMs will cause a change in the power absorbed by the graphene quantum dots that should be easily measurable.

Successful deposition of SMMs on substrates (and specifically on graphene) is a key milestone toward the goal to use graphene quantum dots for in situ spectroscopy of monolayer SMMs. Previous work on the deposition of SMMs on surfaces mainly used dropcasting [26, 28] or evaporation methods [29, 33, 34]. A common challenge of these deposition methods is the need to preserve the chemical structure of the molecule during the process. Dropcasting is done from a solution of SMMs in a solvent such as dichloromethane. Typically, this method does not provide samples with uniform thickness across the substrate and it very often causes so-called coffee-ring effects. Evaporation in vacuum yields better uniformity, but the SMM temperature needs to be carefully controlled, so that it is not raised above the decomposition temperature of the molecules. As an example, we describe our tests on deposition methods of a cobalt-ferrocene dimer (CFD), with formula [Br₂Co(P(C₆H₅)₂C₅H₄)Fe], or [Co(dppf)Br₂]. The spin S = 3/2 of this SMM is due to three unpaired electrons on the Co²⁺ ions. Although there are some previous studies of its bulk properties [35], this CFD SMM has not yet been characterized as thin layers. We tested three deposition methods. The first method was based on a modified Langmuir–Schaefer deposition and tested using few-layer graphene (FLG) as a deposition surface [36]. Briefly, FLG was first deposited on a silicon substrate coated with SiO₂ from a suspension of graphene nanosheets in N-methyl-2-pyrrolidone [36]. The FLG-coated substrate was then immersed in a container filled with deionized water. A solution of CFD in chloroform was then carefully deposited onto the water and formed a film on the surface of the water. Two movable barriers were used to compress the molecules into a layer, the water was carefully pumped out and the layer of molecules was collected on the FLG-coated substrate. Figure 2(b) shows an AFM image of the molecules deposited with this method. This deposition method could achieve good uniformity on large-area substrates, but the deposited molecules lumped into large (a few hundreds of nm in size) crystals. Although the HF-EPR spectrum of the deposited molecules (shown in figure 2(a)) had resonance peaks close to the frequencies expected for bulk samples, the peaks were broader and the noise was higher.

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As discussed below, the presence of water likely affected the molecules at the surface of the crystal. Moreover, due to the sample morphology, mainly the bulk of the crystals rather than the surface contributed to the EPR signal. Basically, an accurate SMM characterization of surface molecules was not possible with this deposition method. The second method involved dropcasting dichloromethane solutions of different concentrations of this SMM. We found that this molecule was strongly affected by the presence of moisture and did not retain the Raman and UV-visible spectral signatures that we had measured for bulk samples. When the dropcast was done in a glovebox with dry nitrogen, the molecule retained its spectral features but its distribution on the substrates was non-uniform and showed 'coffee ring' effects.

The third deposition method was evaporation of the molecules in vacuum (10⁻⁵ Torr), using a dedicated vacuum chamber that allowed control of the temperature of the molecules. Figure 2(b) shows a sample with a 80 nm layer of CFD SMMs on a Si/SiO₂ substrate, obtained after a 4 h deposition at 215 °C. For depositions below 220 °C, the SMMs preserved their Raman and UV-visible spectral signatures, suggesting that thermal evaporation may be the best method to obtain a uniform, thin layer of CFD SMMs.

Tests of depositions to obtain thinner layers are underway.

Our previous work on graphene hot-electron bolometers was based on photodetection without a magnetic field applied. However, HF-EPR requires characterization with magnetic field of up to several Teslas. Since the conductance of graphene can be affected by magnetic field (e.g. due to the formation of Landau levels [37–39]), it is important to test the effect of an applied magnetic field on the photoresponse of graphene quantum dot bolometers. Figure 3(a) shows the current–voltage characteristics (source-drain current as a function of source-drain voltage) of a graphene quantum dot bolometer with the radiation off (black curve) and irradiated with a continuous wave source at 100 GHz (green), without an applied magnetic field, at a temperature of 15 K. We note that the current–voltage characteristic is nonlinear due to heating effects from the bias current [11]. The power absorbed from the THz source is about 2.4 pW, showing that even at temperatures above 10 K, the bolometers can resolve values of absorbed power that are much smaller than the power absorbed by a SMM monolayer. Although the bolometer responsivity drops when the operating temperature increases, the value is still as high as 10⁸ V W^-1 at 80 K for small diameter (less than 50 nm) quantum dots [11]. When an external magnetic field is applied, the response does not change noticeably, up to the maximum field of 7 T (red curve). Figure 3(b) shows a signal proportional to the source-drain current measured with a lock-in technique, using irradiation through a chopper at 11 Hz, at a fixed source-drain voltage. In the red regions the radiation was fully blocked and the signal dropped. The measurements show that the photoresponse at 15 K is almost independent of the magnetic field up to 7 T. We note that while the field was ramped there were small changes of the sample temperature, within 75 mK. Such variations of the sample temperature did not cause any measurable change of the sample resistance (the temperature had to be changed by at least 100 mK to cause a measurable change of sample current). We tested the graphene quantum dot bolometers in a cryostat with a larger maximum field and at lower temperature (1.5 K) and found that the photoresponse is independent of the magnetic field up to 15 T [40]. This can be understood by considering that the quantum confinement gap in the dots is dominated by the charging energy, which does not depend on the magnetic field, making the graphene quantum dot bolometers ideal detectors for HF-EPR measurements.

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To test the operation of graphene quantum dots for HF-EPR spectroscopy, we decorated the graphene with powder of Mn₁₂, as shown in the optical image in figure 4(b), and we measured the SMM absorption as a function of frequency at zero magnetic field. Here the powder was simply dropped dry (not in solution) on the samples. Mn₁₂ is the archetypal SMM and its properties have been widely studied. Mn₁₂ has a ground state spin of S = 10. The frequency domain magnetic resonance (FDMR) spectrum of a bulk sample in figure 4(a) shows absorption peaks for transitions between the lowest energy levels, ∣m_s ∣ = 10 and ∣m_s ∣ = 9 and ∣m_s ∣ = 9 and ∣m_s ∣ = 8, occurring in the range 200–350 GHz. Similar absorption peaks are measured with the decorated graphene quantum dot bolometer, using the ratio of the photoresponse measured from the bolometer decorated with molecules to the photoresponse measured from the bare bolometer, without molecules. Unfortunately, the THz source used for the measurements in figure 4(b) was a backward wave oscillator (quasi-optical source QS2, Microtech Instruments Inc.), that was not suitable for a careful analysis of the lineshapes [41], but these resonant absorption peaks could clearly be measured, even for this much smaller amount (compared to the measurements of figure 5(a)) of SMMs. We can roughly estimate the number of molecules in the cluster overlapping with the graphene bolometer from the optical image in figure 4(b). The area of the cluster is about 10 × 5 μm². We measured the height of clusters with similar size by using SEM imaging and found that it was always below one micrometer, typically a few hundreds of nanometers. We use the upper bound of one micrometer for the height of the cluster to obtain a cluster volume of 5 × 10⁻¹⁷m³. By assuming that the size of the Mn₁₂ SMM is about 1.5 nm, yielding a volume of 3.4 × 10^-27 m³ for a single SMM, we estimate that the cluster contains less than 1.5 × 10¹⁰ SMMs. We note that the bolometer used in this measurement is not coupled to an antenna. There is a large impedance mismatch between the high resistance of the bolometer and the characteristic impedance of free space, therefore the coupling between the incident radiation and the detector (decorated with SMMs or bare) is very weak. The signal can be enhanced by a few orders of magnitude by using an antenna to reduce the impedance mismatch and to focus the THz radiation on the detector. Nevertheless, even without optimizing the coupling to the THz radiation, we estimate that the bolometer can detect less than 1.5 × 10⁹ spins (if we take in account a signal-to-noise ratio of about 10) at 4 K. The Mn₁₂ powder did not stay on the sample when a magnetic field was applied, therefore measurements in magnetic field will require different deposition methods, where the Mn₁₂ molecules are anchored to the surface.

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However, since previous work showed that Mn₁₂ SMMs are not suitable for surface deposition [28], in future experiments we will focus on different SMMs, with smaller size and possibly with smaller deformation when deposited on a substrate, similar to those discussed in the previous section. We nevertheless performed test measurements of Mn₁₂ powder pellets in magnetic field using the graphene bolometer. Figure 5 shows three absorption spectra as a function of magnetic field, at fixed frequencies, 300 GHz (where the absorption peak occurs at zero magnetic field), 310 GHz and 317 GHz, respectively. The absorption peaks for the m_s ±10 to m_s ± 9 transition occur at values of magnetic fields that match the peak values calculated with EasySpin, a MATLAB-based computational package [42]. The values obtained from the simulations are indicated by the vertical dashed lines in figure 5.