Properties of Mn²⁺ and Π-Electron Spin Systems Probed by ¹H and ¹³C NMR in the Organic Conductor κ-(BETS)₂Mn[N(CN)₂]₃

Abstract

Properties of the spin systems of the localized 3d Mn²⁺ ions and the conduction π electrons in quasi-two-dimensional organic conductor κ-(BETS)₂Mn[N(CN)₂]₃ were accessed using ¹H and ¹³C NMR in order to find their relation to the metal-insulator transition which occurs at ∼23 K. The transition of the system into the insulating state is shown to be followed by localization of the π spins into a long-range ordered staggered structure of AF type. In contrast, the 3d Mn²⁺ electron spin moments form a disordered tilted structure, which may signify their trend to AF order, frustrated geometrically by the triangular arrangement of Mn in the anion layer. This result suggests that the MI transition in κ-(BETS)₂Mn[N(CN)₂]₃ is not the consequence of the interactions within the Mn²⁺ spins but due to the interactions within the π-electron system itself. Vice versa, it is more likely that the disordered tilted structure of the Mn²⁺ spins is induced by the ordered π-spins via the π-d interaction.

1. Introduction

NMR is a versatile tool for local-level investigation of magnetic properties in complex molecular systems. This technique uses nuclear spins to spy on the electron spin system by monitoring the local magnetic field created by electron spins at the nucleus site. Since NMR frequency is nucleus-specific, the experiment tuned to particular nucleus probes the electron spin system at the site of the corresponding atom within the crystal structure. In complex compounds incorporating more than one electron spin system (e.g., itinerant and localized electrons) such information helps to discriminate between the events developing within the electron subsystems and determine the interrelation between them.

Figure 1. (a) Side view (along ) of crystal structure of κ-(BETS)₂Mn[N(CN)₂]₃; (b) BETS molecule with ¹³C in positions of the central C = C bond; (c) Top view of schematic crystal structure of the conducting BETS layer. The circled pairs of lines represent (BETS)₂ dimers; (d) Side view of BETS dimer with site definition of the central C = C carbons; (e) Top view of the anion layer.

Figure 1. (a) Side view (along ) of crystal structure of κ-(BETS)₂Mn[N(CN)₂]₃; (b) BETS molecule with ¹³C in positions of the central C = C bond; (c) Top view of schematic crystal structure of the conducting BETS layer. The circled pairs of lines represent (BETS)₂ dimers; (d) Side view of BETS dimer with site definition of the central C = C carbons; (e) Top view of the anion layer.

The quasi-two-dimensional organic conductor κ-(BETS)₂Mn[N(CN)₂]₃ (BETS = C₁₀S₄Se₄H₈, bis-(ethylenedithio)tetraselenafulvalene) is an example of such compound (Figure 1). The system is metallic down to T_MI ~ 23K where it undergoes the metal-insulator (MI) transition [1,2]. Its conductivity is associated with π-electrons confined within the layers of dimerised organic BETS molecules, sandwiched between the insulating polymeric Mn[N(CN)₂]₃ anion layers, while the bulk magnetization is determined by Mn²⁺ (J = S = 5/2, L = 0) ions of the anion layers [3]. The static susceptibility in the metallic state is isotropic and obeys accurately the Curie-Weiss law. Below T_MI it becomes slightly smaller than the Curie-Weiss value, χ_cw (T), so that at T = 2K it makes 80%-85% of χ_CW, still essentially isotropic. This trend suggests that below T_MI the Mn²⁺ system tends towards antiferromagnetic (AF) order, which is however frustrated geometrically by triangular arrangement of Mn in the anion layer (Figure 1e). In the akin compound λ-(BETS)₂FeCl₄ with rectangular network of FeCl₄ units, the susceptibility governed by Fe³⁺ moments demonstrates below T_MI = 8K the distinctive features characteristic of a uniaxial Néel-type antiferromagnet with T_N = T_MI, which gave grounds to nominate the AF ordering within Fe³⁺ ions as driving force of the MI transition [4]. One can assume therefore that the AF interaction within the Mn²⁺ d-electron spins in the title compound may in a similar way cause localization of the conduction π electrons at T_MI due to strong π-d coupling presumably present in the system [5].

On the other hand, the MI transition is not only specific to quasi-two-dimensional organic conductors with magnetic anions: there are known non-magnetic compounds where the insulating state is attributed to strong electron correlations within the half-filled conducting band leading to Mott instability and electron localization [6]. Moreover, in some of them the electrons localize into the long-range AF structure (e.g., κ-(ET)₂Cu[N(CN)₂]Cl [7], β΄-(ET)₂X (X = ICl₂, AuCl₂) [8], where ET is isostructural to BETS but with sulphur on Se sites). Besides, recent experiments on λ-(BETS)₂FeCl₄ [9,10] have doubted the AF order in the Fe³⁺ spin system and its responsibility for the MI transition, stating that it is the π-electron system that orders antiferromagnetically and produces the MI transition, while the Fe³⁺ d-electrons remain in the paramagnetic state.

There is therefore a question if the magnetic interactions within Mn²⁺ moments in κ-(BETS)₂Mn[N(CN)₂]₃ are responsible for the MI transition, or it is a domestic affair of the conduction electrons as in some non-magnetic quasi-two-dimensional systems. To address this issue we have performed ¹H and ¹³C NMR measurements on κ-(BETS)₂Mn[N(CN)₂]₃ single crystals. For ¹³C NMR, the crystal with BETS molecules containing >99% of ¹³C isotope in the central C = C bond (Figure 1b) was used. Hydrogen atoms belonging to the ethylene groups at the terminals of BETS molecules (Figure 1a) are relatively close to the Mn sites and therefore are expected to provide information about the Mn²⁺ subsystem through dipolar fields induced by Mn²⁺ moments at hydrogen sites. ¹³C NMR on the carbons from the central C = C bond of the BETS molecule is known to be effective in probing the conduction π-electron spin system [11]. The two experiments combined together promise the complete description of the magnetic properties of the system.

2 Results and Discussion

2.1. ¹H NMR

Hydrogen sites located at the terminals of BETS molecules (Figure 1a) have negligibly small hyperfine coupling with conduction electrons [12], therefore the NMR frequency shift should be determined by the dipolar fields from the 3d Mn²⁺ ion electron spin moments (S_d = 5/2,g ≈ 2). For the arbitrary orientation of the magnetic field, the ¹H NMR spectrum will count 16 peaks: there are 8 inequivalent crystallographic hydrogen sites and two magnetically inequivalent orientations of the BETS dimer (Figure 1c). The BETS molecules within the dimer are inversion-symmetric to each other, thus magnetically equivalent.

Figure 2 shows ¹H NMR spectrum in κ-(BETS)₂Mn[N(CN)₂]₃ at T = 74 K in field H₀ = 7 T oriented at θ = 22°from towards direction. The spectrum is shown with respect to ¹v₀ = ¹γH₀, where ¹γ = 42.5759 MHz/T is the proton gyromagnetic ratio. For the chosen geometry , the two different orientations of the BETS dimer shown in Figure 1c become magnetically equivalent which reduces the total number of peaks to 8. Arrows in Figure 2 indicate the 8 peaks.

Figure 2. ¹H NMR spectrum in κ-(BETS)₂Mn[N(CN)₂]₃ at T = 74 K in field H₀ = 7 T oriented at θ = 22°from towards direction. The spectrum is shown with respect to ¹v₀ = ¹γH₀ .

Figure 2. ¹H NMR spectrum in κ-(BETS)₂Mn[N(CN)₂]₃ at T = 74 K in field H₀ = 7 T oriented at θ = 22°from towards direction. The spectrum is shown with respect to ¹v₀ = ¹γH₀ .

Figure 3 presents the angular evolution of ¹H NMR peak positions in κ-(BETS)₂Mn[N(CN)₂]₃ measured at 74 K in field H₀=7 T. The field is in the (a^*c)-plane, and the polar angle, θ, is reckoned from direction towards .

Figure 3. Angular evolution of ¹H NMR spectrum in the (a^*c) plane measured at 74 K in field H₀=7 T. Circles are the measured peak positions. Lines are model calculations using Equation 1.

Figure 3. Angular evolution of ¹H NMR spectrum in the (a^*c) plane measured at 74 K in field H₀=7 T. Circles are the measured peak positions. Lines are model calculations using Equation 1.

To model the observed proton spectrum one needs to sum up the dipolar fields, h_dip, created at the nucleus site by Mn²⁺ electronic spins, and take into account the sample geometry resulting in a demagnetizing field, h_D, and the Lorentz field, h_Lor, which is the mean field induced at the nucleus site by the bulk of the sample located outside the dipolar summation sphere [13].

For the magnetic field in the (a^*c)-plane, we model the spectrum as

(1a)

(1b)

(1c)

Here, γ_n = ¹γ; μ_Mn is the thermal average of the Mn²⁺ magnetic moment projection on the field direction, r_iis the length of the position vector from the proton site to the Mn site i, α_i is the angle between this vector and the field direction, V_Mn is the unit cell volume per Mn²⁺ ion, and N = N_┴ cos²θ + N_║sin²θ is the demagnetization factor.

Since the DC magnetization in κ-(BETS)₂Mn[N(CN)₂]₃ is determined by Mn²⁺ magnetic moments [3], we put in Equation 3 μ_Mn = M/N _A, where M is the measured DC magnetization per mole (3800 emu/mol at H₀= 7 T, T = 74 K) and N_A is Avogadro’s number. For our very thin-plate sample we assume the demagnetization factors N_┴ = 1, N_║ = 0. Crystallographic positions of Mn and H atoms required to calculate Equation 1b are available online from the CCDC library as mentioned in the Experimental Section. The sum in Equation 1a has been taken over ~ 200 Mn sites within ±20 Å to provide reasonable convergence.

The peak positions calculated using Equation 1 for each of the 8 inequivalent hydrogen sites are shown in Figure 3 by solid lines. The agreement between the calculated and the measured peak positions is clearly reasonable despite the absence of any fit parameters used in the calculations. This indicates that ¹H NMR frequency shift is determined by the dipolar fields from Mn²⁺ at the hydrogen site, at least at this field and temperature.

To check if this is true for all temperatures, we compare the temperature dependences of the DC magnetization and the ¹H NMR peak positions. Figure 4a,b show temperature dependences of, respectively, the molar DC magnetization normalized to the applied field, M/N, and the normalized frequency shift of the lowest-frequency peak in the spectrum measured in H ║ a^* geometry (θ = 0 in Figure 3), for the magnetic fields 1.4 and 7 T.

Figure 4. (a) Molar magnetization vs. temperature in H = 1.4 and 7 T; (b) Position of the lowest-frequency peak in ¹H NMR spectrum in geometry vs. temperature in H = 1.4 and 7 T; (c) Position of the peak for the temperature range 4-150 K, in function of the DC magnetization per Mn ion, μ_Mn = M/N_A, measured at the same temperatures and fields and expressed in terms of the Bohr magneton, μ_B. Open red circles and closed black circles correspond to the fields 1.4 and 7 T, respectively.

Figure 4. (a) Molar magnetization vs. temperature in H = 1.4 and 7 T; (b) Position of the lowest-frequency peak in ¹H NMR spectrum in geometry vs. temperature in H = 1.4 and 7 T; (c) Position of the peak for the temperature range 4-150 K, in function of the DC magnetization per Mn ion, μ_Mn = M/N_A, measured at the same temperatures and fields and expressed in terms of the Bohr magneton, μ_B. Open red circles and closed black circles correspond to the fields 1.4 and 7 T, respectively.

The right panel of Figure 4 depicts the plot of the proton frequency shift, v - ¹v₀, in function of the magnetization measured at the same temperatures and fields. The linearity of the data in Figure 4 demonstrates that for the whole temperature and field ranges covered in the experiment, the positions of ¹H NMR spectrum peaks are determined by the magnetic subsystem associated with Mn²⁺ moments, and can be utilized as Hall probes of the Mn²⁺ dipolar fields at hydrogen sites.

Figure 5a shows the evolution of ¹H NMR spectrum (H₀ = 1.4T parallel to ) with temperature. As can be seen, the frequency span of the spectrum increases with decreasing temperature while its shape is maintained down to ~20 K. At lower temperature the peaks broaden rapidly, which is more pronounced on the right-hand side of the spectrum. Figure 5b depicts the temperature dependence of the half width at half hight, , for the leftmost and the rightmost peaks in the spectrum. As one can see in Figure 5, the linewidth is relatively flat above T_MI ≈ 23 K (especially for the leftmost peak) and increases sharply below this temperature. Figure 5c demonstrates the plot of the linewidths in function of the DC magnetization. One can see in Figure 5c a crossover in the linewidth behavior at T_MI which is observed as an upturn from the linear M-dependence (shown by solid lines) obeyed at higher temperatures.

Figure 5. (a) Temperature evolution of ¹H NMR spectrum measured at H₀ = 1.4T parallel to ; (b) Temperature dependence of the half-linewidth of the leftmost (circles) and the rightmost (squares) peaks; (c) The leftmost and the rightmost peak half-linewidths in function of the DC magnetization. Solid lines extrapolate the linewidth behavior above 25 K to low temperatures. Dashed lines with numbers on top mark measurement temperatures.

Figure 5. (a) Temperature evolution of ¹H NMR spectrum measured at H₀ = 1.4T parallel to ; (b) Temperature dependence of the half-linewidth of the leftmost (circles) and the rightmost (squares) peaks; (c) The leftmost and the rightmost peak half-linewidths in function of the DC magnetization. Solid lines extrapolate the linewidth behavior above 25 K to low temperatures. Dashed lines with numbers on top mark measurement temperatures.

Since the ¹H NMR peak positions are highly anisotropic as can be seen in Figure 3, there is a number of trivial reasons for the peaks to be broadened, including sample imperfections on the macroscopic and local levels, as well as minor misalignment of the magnetic field from direction, as discussed in [14]. However, all of them should make the linewidth as linear in the magnetization as the peak position itself is (Figure 4c). The upturn of the linewidth M-dependence below T_MI ≈ 23 K (Figure 5c) indicates the onset of yet another broadening mechanism. Provided that the crystal lattice is intact, this should be related with local-level scatter of the dipolar fields from Mn²⁺ at the hydrogen site, for example, a variable from site to site tilt of the Mn²⁺ static moments. This site variation of the tilt is apparently random or incommensurate with the crystal lattice, because otherwise a splitting of ¹H NMR peaks would take place instead of the featureless broadening observed in the experiment (Figure 5a). The tilt of the Mn²⁺ moments emerging below T_MI, together with the deviation of the magnetization from the Curie-Weiss behavior [3], indicates apparently the tendency of the Mn²⁺ spin system towards the AF order. Frustrated geometrically by triangular arrangement of Mn in the anion layer (Figure 1e), Mn²⁺ system is resolved into a disordered (like spin-glass) or an incommensurate spin structure.

2.2. ¹³C NMR

The ¹³C NMR spectra were measured in κ-(BETS)₂Mn[N(CN)₂]₃ in the external field H = 7 T aligned perpendicular to at 45°to . For this experimental geometry, the metallic-state spectrum in theory is represented by four peaks arising from the two magnetically different orientations of the BETS dimers (Figure 1c) and nonequivalent(“inner” and “outer”) carbon sites of the central C=C bond within the dimer (Figure 1d) [15]. The dipolar interaction between ¹³C spins in the C=C bond, which in general provides another factor of two to the number of peaks, is nearly zero for this field orientation.

Figure 6. ¹³C NMR spectra measured in the external field H = 7 T aligned perpendicular to at 45° to . The spectra are shown with respect to ¹³v₀ = 74.946 MHz. (a) The spectrum at T = 50 K. Blue solid lines indicate positions of the resonance peaks calculated with the shift tensor of κ-(ET)₂Cu[N(CN)₂]Br [15]; (b) The evolution of the ¹³C NMR spectrum with temperature.

Figure 6. ¹³C NMR spectra measured in the external field H = 7 T aligned perpendicular to at 45° to . The spectra are shown with respect to ¹³v₀ = 74.946 MHz. (a) The spectrum at T = 50 K. Blue solid lines indicate positions of the resonance peaks calculated with the shift tensor of κ-(ET)₂Cu[N(CN)₂]Br [15]; (b) The evolution of the ¹³C NMR spectrum with temperature.

Unlike the magnetic ion-free quasi-two-dimensional ET-based conductors where the NMR peaks from magnetically nonequivalent ¹³C sites are usually well resolved, ¹³C spectrum in the metallic state of κ-(BETS)₂Mn[N(CN)₂]₃ for this field orientation is represented by a single featureless Gaussian-shaped line. The left panel in Figure 6 represents the spectrum taken at T = 50 K. Using the ¹³C NMR shift tensors obtained for κ-(ET)₂Cu[N(CN)₂]Br [15] (which is nearly the same as for κ-(ET)₂Cu[N(CN)₂]Cl [16]), for the given experimental geometry one expects a κ-(BETS)₂Mn[N(CN)₂]₃ sample to produce the resonance peaks at 2.7, 10.7, 22.7, and 40.8 kHz (with respect to ¹³v₀ = 74.946 MHz). Dipolar fields from Mn²⁺ moments provide additional shifts to the resonance frequencies, which can be calculated following Equations 3 using the values of Mn²⁺ moments known from the bulk magnetization measurements [3]. At T = 50 K the calculated dipolar fields from Mn²⁺ move the listed peaks to positions at 0.3, 7.7, 19, and 38.2 kHz. The calculated peak positions are shown by vertical lines in Figure 6a. One can see that the spectrum measured at 50 K covers fairly well the range of the calculated peak positions indicating that the ¹³C shift tensor in the title compound is not much different from that in κ-(ET)₂Cu[N(CN)₂]Br.

Evidently, the peaks from individual carbon sites in the metallic state of κ-(BETS)₂Mn[N(CN)₂]₃ are vastly broadened that merges them into a single line. Some broadening of ¹³C NMR peaks has been noticed in κ-(ET)₂Cu[N(CN)₂]Br and a number of reasons has been recruited to explain it [15], including spacial variation of the π-electron spin density due to precursors to Anderson localization or spin-density wave. For the sample reported here, the linewidth is expected broader than in non-magnetic compounds due to the presence of the anisotropic dipolar fields from Mn²⁺. For example, the same mechanism that creates the ¹H NMR linewidth (Figure 5b) will be responsible for ~10 kHz linewidth of the ¹³C peaks at carbon sites at 50 K. Anyway, more detailed analysis of the possible broadening mechanisms in the metallic state is beyond the scope of this communication.

The right panel in Figure 6 demonstrates the evolution of the ¹³C NMR spectrum with temperature. The single peak characteristic of the spectrum in the metallic state above T = 23K ≈ T_MI develops below this temperature into a broad symmetric pattern counting 5 pronounced peaks. Below T = 15 K the spectrum spans the range of nearly ± 1 MHz, which is huge compared to the spectrum width in the metallic state. This cannot result from the dipolar fields created by Mn²⁺: calculations show that fully polarized Mn²⁺ can provide a dipolar shift ranging from -12.5 to -19 kHz (depending on the carbon site) in 7 T field. Therefore the spectrum in the insulating state evidences enhancement of the electron spin density at carbon sites due to electron spins localized on the dimers of the BETS molecules. Moreover, several pronounced peaks are visible in the low-temperature spectrum, which infers a commensurate order of the localized spins. Finally, the symmetric shape of the spectrum indicates the staggered order, because antiparallel components of the staggered electron spins ( ) produce opposite local fields at carbon sites i and j: , where and are the nuclear and electron spin operators, respectively, and A is the hyperfine tensor. In turn, this signifies the AF exchange interaction between the localized spins. The staggered component of the spin magnetization lies apparently somewhere in the plane perpendicular to the magnetic field, since the anisotropic AF exchange term is usually much smaller than 7 T, the external field of this experiment.

The frequency range of the ¹³C spectrum in κ-(BETS)₂Mn[N(CN)₂]₃ at T = 5 K (Figure 6b) is of the same order of magnitude (~±1 MHz) as observed in the AF state of κ-(ET)₂Cu[N(CN)₂]Cl [16] and β΄-(ET)₂ICl₂ [17]. The magnitude of the electron spin magnetization of 0.5 μ_B and 1 μ_B per dimer, respectively, has been reported for these two compounds. Therefore in κ-(BETS)₂Mn[N(CN)₂]₃ this value should be within the same range since the hyperfine tensor here is expected to be similar, as the measurements in the metallic phase suggest.

More detailed and quantitative information about the spin structure of the localized πelectrons can hardly be derived at the moment. To do this one needs to know more or less exactly the hyperfine tensors for the central carbons in κ-(BETS)₂ Mn[N(CN)₂]₃, which in turn requires the value of the πspin susceptibility never reported so far (but probably accessible via ESR).

3 Experimental

The crystal structure of κ-(BETS)₂Mn[N(CN)₂]₃ is monoclinic with the space group P2₁/c and the lattice constants at 88 K a = 19.428 Å, b = 8.379 Å, c = 11.869 Å, β = 92.67°, and V = 1930.1 ų, with two formula units per unit cell. The conducting layers formed by BETS dimers in the (bc) plane are sandwiched between the polymeric Mn[N(CN)₂]₃ anion layers in the a direction (Figure 1a). The crystal structure is available at Cambridge Crystallographic Data Centre [18], CCDC 775974-775977, and has been discussed in details in earlier communications [1,2].

Crystals for ¹H NMR (with all natural-abundant carbon) were obtained by electrochemical oxidation of BETS in the mixture of solvents, 1,1,2-trichloroethane/ethanol (10:1 v/v), in the presence of Mn[N(CN)₂]₂ as electrolyte [1,2]. The ¹³C-enriched samples were synthesized by electrochemical oxidation of ¹³C-labeled BETS in benzonitrile/ethanol (10:1 v/v) in the presence of Ph₄PMn[N(CN)₂]₃ complex salt as electrolyte following the procedure reported in Reference [19]. ¹³C-enriched (>99%) BETS (Figure 1b) was synthesized with the use of ¹³C-enriched triphosgene (bis(trichloromethyl-¹³C₃)carbonate) according to the method described in literature [20].

The single crystals used in the ¹H NMR experiments had the dimensions a^* × b × c ~ 0.05 × 3 × 1 mm³. The dimensions of the crystal for ¹³C NMR were ~0.05 × 3 × 3 mm³. Crystallographic orientations of the crystals were X-ray defined. NMR spectra were acquired using standard spin-echo sequence with π-pulse length ≤2.5-3 μs. To cover broad spectra, Fourier-transforms of the acquired spin-echoes were collected at 150 kHz intervals and summed up.

4 Conclusions

We performed ¹H and ¹³C NMR measurements in κ-(BETS)₂Mn[N(CN)₂]₃ to find the relation between the MI transition and the properties of the spin systems of the localized 3d Mn²⁺ ions and the conduction πelectrons. We found that transition of the system into the insulating state is followed by localization of the πspins into a long-range ordered staggered structure of AF type. It should be emphasized here that this structure does not necessarily signify the conventional AF state but can be a field-induced effect in the presence of the Dzyaloshinskii-Moriya interaction, as it happens in κ-(ET)₂Cu[N(CN)₂]Cl [21].

In contrast, the Mn²⁺ spins do not order below T_MI but are likely to form a disordered tilted structure, which may signify their trend to AF order, frustrated geometrically by the triangular arrangement of Mn in the anion layer.

Our findings show that the MI transition in κ-(BETS)₂Mn[N(CN)₂]₃ is not the consequence of the interactions within the 3d Mn²⁺ electron spin system transferred to the conduction spin system by the π-d coupling, but is a result of the interactions within the π-electron system itself as in some magnetic ion-free quasi-two-dimensional charge-transfer salts. Vice versa, the observed formation of the disordered tilted structure in the Mn²⁺ electron spin system could be induced by the π-spin ordering via the π-d interaction. It has been reported in [3] that the susceptibility of κ-(BETS)₂Mn[N(CN)₂]₃ determined by the Mn²⁺ spin system depends on temperature as 1/ (T+θ)with θ ≈ 5.5 K. That means that the Mn²⁺ subsystem should remain paramagnetic down to T~θ, while in fact it deviates from the paramagnetic state at higher temperature T_MI ~23 K, suggesting the influence of the spin-ordered localization of π-electrons.