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Crystals 2012, 2(3), 1116-1135; doi:10.3390/cryst2031116
Abstract: 1H and 195Pt NMR are used to probe the spin ½ anion chain in the quasi-one-dimensional conductor Per2[Pt(mnt)2], which exhibits nearly simultaneous charge density wave (CDW) and spin-Peierls (SP) transitions at low temperatures (Tc ~ 8 K). Below Tc the [Pt(mnt)2] chain forms a spin-singlet state that is evident in 1H NMR spectra and spin relaxation (1/T1) rates; however minority unpaired Pt spins may remain in the SP ground state. With increasing magnetic field, the SP and CDW order parameters decrease in unison, indicating they are coupled up to a critical field Bc ~ 20 T. Above Bc, the spin singlet evolves into a spin-polarized configuration. The 195Pt NMR signals vanish as either Tc or Bc are approached from within the SP ground state, suggesting the hyperfine field of the Pt nucleus is significantly stronger than at the proton sites. Simulations yield a consistent picture of the angular, temperature, and magnetic field-dependent spectral features.
Two-chain quasi-one-dimensional conductors in the series Per2[M(mnt)2] (Per = perylene; M = Au, Pt, Pd, Co, etc.) have long been studied due to the unique nature of their parallel, interacting chain structure . Here stacks of planar perylene donors with pi-overlapped orbitals yield a highly one dimensional, electrically conducting chain in parallel with stacks of [M(mnt)2] acceptors (Figure 1a). The former exhibits a Peierls (CDW-charge density wave) transition at low temperatures, and the latter exhibits spin-Peierls (SP) transition in the case where there is a localized d-electron spin on the [M(mnt)2] site for M = Pt, Pd, etc. A remarkable feature of the compounds with spin on the [M(mnt)2] site is that these two transitions appear to be nearly, or even exactly coincident at a temperature Tc, giving rise to the still open question of how the order parameters couple, and which one drives the other [2,3].
The subject of the present work is the compound Per2[Pt(mnt)2] with a localized spin ½ on the Pt site, with the emphasis on using NMR to probe the behavior of the spin chain in the paramagnetic and SP phases. An overview select physical properties of Per2[Pt(mnt)2] are shown in Figure 2. Specific heat , electron spin resonance , and electrical transport [7,8] indicate a common transition in the range Tc ~ 6 to 8 K, and diffuse X-ray studies , although not below 10 K, indicate the onset of dimerization in the [Pt(mnt)2] chains. (In compounds such as M = Pd with a higher transition temperature, X-ray measurements clearly show tetramerization in the perylene chains and dimerization in the [Pd(mnt)2] chains at Tc , and internal consistency among the different measurements and compounds Per2[M(mnt)2] indicate this should also be the case for Per2[Pt(mnt)2]). The periodicities of the CDW and SP chains, qPer = π/2b and qPt = π/b, are approximately commensurate with b, the lattice constant along the chains.
In recent years there have been extensive studies of electrical transport in Per2[Pt(mnt)2] in magnetic fields where the resistance of the sample yields information about how the CDW ground state changes with field and temperature , and B-T phase diagrams have been produced that show the CDW is suppressed at high magnetic fields (~20 T at 1 K), but a new type of insulating state appears at higher fields [4,13]. Since similar studies of the spin-zero isostructural compound Per2[Au(mnt)2] show that significantly larger fields (~30 T at 1 K) are necessary to suppress the conventional CDW ground state , one can reasonably ask what role the spin −½ chain plays in altering the B-T phase diagram, and if and how the spin and conducting chain order parameters couple. Since electrical transport is not directly sensitive to the magnetic structure in the [Pt(mnt)2] chains, proton (1H) and platinum (195Pt) nuclear magnetic resonance (NMR) over a broad range of temperature and magnetic field has been employed to try to elucidate these questions.
In this Review, we first survey the relevant results of previous NMR studies. We next present results of 1H NMR spectra which provide important information about B-T phase boundaries, and the behavior of the spin chains in the paramagnetic and spin-Peierls states. One important result is the observation that the CDW and SP order parameters remain coupled up to the critical field (~20 T) at low temperatures (see also ). Simulations of the spectra are described that yield a consistent picture of the angular, temperature, and magnetic field-dependent spectral features in terms of an effective dipole moment that is temperature and magnetic field-dependent. The 1H spin-relaxation data are then presented. These results show evidence for a minority concentration of unpaired spins in the spin-Peierls state, the effects of which are suppressed with increasing field. We next present the results of 195Pt NMR which is only measurable within the SP-CDW phase boundary. Unlike the 1H NMR, in this case the 195Pt nuclear spin of interest is on the same site as the d-electron spin, and this has a dramatic effect on the spectra and the relaxation rates. Finally, we put our results in the context of the problems of competing order parameters, and make conclusions and suggestions for future work. Additional details of the 195Pt and 1H studies are given in the Theses of Lumata  and Green  respectively.
The primary thrust of the work reported here concerns NMR (both spectra and spin-relaxation) on single crystal Per2[Pt(mnt)2] with a focus on the high magnetic field (2 to 33 T) dependence of the SP-CDW phases at low temperatures, and also on the spectra over broad range of temperature above the SP-CDW ground state. Earlier however, a milestone in the understanding of the magnetic properties of the Per2[Pt(mnt)2] system in the higher temperature paramagnetic phase is the work of Bourbonnais et al.  which addressed the temperature dependence of the 1H spin relaxation rate 1/T1 at 0.855 T from room temperature to ~ 4.2 K in a powdered sample. This group also measured 1/T1 in the zero-spin anion analogue Per2[Au(mnt)2], and combined with results of the magnetic susceptibility (χ) and electron spin resonance (ESR) data, affirmed the following:
(1) The susceptibility is Curie-Weiss like at higher temperatures (T > 20 K) in the paramagnetic state. The parameters are kBTSP0 ~ Θ ~ J/kB ~ ΔkB ~ 20 K. From a Curie-Weiss law fit to χ(T), the effective number of Bohr magnetons p = g[J(J + 1)]1/2 is about 1.87 , (close to the value p = 1.73 for g = 2, and J = ½). Since a dimerization driven solely by a one-chain spin-lattice effect has the criterion kBTSP0 << J, the fact that Tc ~ 8 K (i.e., is so high) is anomalous, and the origin of the SP state is not clear. Hence the proximity of the CDW order parameter may “aid” the formation of the SP state, as discussed below.
(2) In the paramagnetic state, the 1H spin-relaxation rate in Per2[Pt(mnt)2] is dominated by the transverse dipolar coupling between the Pt spins and the proton sites, and follows the relationship 1/T1~Tχ(T) down to about 20 K (see also Section 4). Therefore at high temperatures in the Curie limit where χ(T) = C/T, 1/T1 is independent of temperature. The conclusion was that, in comparison with Per2[Au(mnt)2], the 1H signal is primarily affected by the Pt spins. This opens the door to using 1H NMR to monitor the spin configuration of the SP state in the [Pt(mnt)2] chain vs. field and temperature, even though the protons sit at the periphery of the perylene molecule, at distances of 4.8 Å or more from the Pt sites. As we will see later, the situation for NMR on the 195Pt sites is very different.
Recently, we reported  the correspondence of the 1H NMR spectra and spin-relaxation rates to the B-T phase diagram of Per2[Pt(mnt)2] below 10 K in fields up to 26 T. The key results of this study were that the NMR spectral line shapes underwent fundamental changes passing from the low temperature—low magnetic field singlet SP-CDW insulating ground state to the high temperature paramagnetic, metallic phase, and/or into the high magnetic field phase. By monitoring the field and temperature where the characteristic, narrow line seen in the spin singlet state started to evolve into the broader, multiple peaked spectrum characteristic of the paramagnetic state, an estimate of the SP phase boundary could be determined, and compared with previous determinations based on electrical transport. The conclusions of this work were that the formation of the CDW state is necessary to induce the SP transition, which otherwise would not form, and that the two order parameters remain coupled at least until the low temperature critical field of Bc ~ 20 T is reached (Figure 1b).
3. 1H NMR Spectra and the SP Phase Boundary
3.1. Angular Dependent Spectra
Proton spectra vs. field direction are shown in Figure 3 at 7 T for 4.16 K and 11.45 K (in this work, the field is always directed in the a-c crystallographic plane).
For high symmetry field directions within the SP-CDW phase (4.16 K < Tc), only one spectral line is evident, but as the sample is rotated in field additional spectral components appear for some directions. This effect may arise from the existence of minority unpaired spins as described in Section 4. Above the phase boundary (at 11.45 K > Tc) multiple peaks appear even along high symmetry directions, and the total linewidth is about twice that at 4.16 K; with rotation above Tc, the linewidth and the multiple peak features increase significantly. In this work we take the transition between the single and multiple peak spectra along a high symmetry direction as the indication of the transition between the singlet and paramagnetic phase with either increasing temperature or magnetic field, as discussed in the following sections.
3.2. Temperature Dependent Spectra
Proton spectra at 14 T along a high symmetry direction are shown in Figure 4a from 3.5 to 170 K.
At high temperatures, there are multiple lines and with decreasing temperature the overall linewidth broadens until about 20 K, below which linewidth decreases and the spectrum collapses to a single line at the lowest temperature. In Figure 4b the first moment <m> (which is proportional to the shift Δν/ν0) and the root of the second moment <m2>1/2 (which is proportional to the linewidth) are shown vs. temperature, as computed from the data. There is a distinct change of slope in both moments at the transition Tc between 6 and 7 K; likewise Tc is evident as a sharp transition from a multiple to a single line in Figure 4c, the latter taken as an estimate of the onset of the SP phase (similar results and analysis for 7 T are shown in Reference ). The results of Figure 4 yield additional information about the hyperfine field seen at the proton sites due to the Pt spins. First, for 170 > T > 20 K, there is a direct correspondence between the paramagnetic susceptibility and the shift of individual peaks in the multiple peak spectrum (Figure 4c) and in <m2>1/2 (Figure 4b). However, the temperature dependence of <m> is relatively small, and difficult to determine above 20 K, but at temperatures below 20 K approaching and entering the SP ground state, it shifts significantly and approaches a constant by 3.5 K. By referencing the change in the first moment at 20 K to the low temperature value, i.e., Δν/ν0 = (ν(20 K) – ν(3.5 K))/ν(3.5 K), and using the susceptibility data of Reference , we find the hyperfine coupling constant at 20 K is Ahf = 56 Oe/µB, based on the relationship K = Ahf χ(T)/µBNA where K = Δν/ν0 and NA is Avogadro’s number. The shift K upon entering the low temperature ground state (for fields ≤ 14 T) is uniform with increasing field (or frequency), and scales with field, i.e., Δν/ν0 = ΔH/H = constant ~ 40 ppm. This is consistent with the loss of hyperfine field in the SP spin-singlet ground state. The linewidth of the proton NMR line in the SP spin-singlet state is about <m2>1/2 = 7.8 gauss. Like the low temperature shift in Δν/ν0 (20 K > 3.5 K), the linewidth does not appear to be strongly field-dependent up to 14 T. The maximum proton-proton hyperfine field for a separation of about 2.5 Å is about 1 gauss, so the broadening of the line in the SP ground state may arise from factors other than just isolated proton contributions.
In Figure 5 temperature dependent spectra above the main SP ground state (B > Bc) at 22 T are presented for temperatures from 2.9 to 17.55 K. The multiple peak spectra are characteristic of the paramagnetic phase. In comparison with similar spectra in incommensurate systems such as CuGeO4  or (TMTTF)2PF6 , aside from some minor changes in one of the spectral feature P3 in Figure 5b and 1/T1 near 5 K in Figure 5c, we find no apparent signature of a transition from an undimerized to an incommensurate (U-I) phase in Per2[Pt(mnt)2]. Although this may simply be due to the highly commensurate nature of the SP and CDW structure in this material, we currently do not have a full answer as to why the U-I phase boundary, which is seen in the other cases, is not present here.
3.3. Magnetic Field Dependent Spectra
The evolution of the proton spectra at low temperatures (3.1 K) up through the critical field is shown in Figure 6a. The data is a combination of superconducting, resistive magnet, and Hybrid magnet experiments. At low fields, the single line characteristic of the spin singlet SP phase remains relatively unchanged until about 14 T where it starts to shift to lower frequency. This is the same Δν/ν0 shift (~40 ppm) seen in the crossing of the phase boundary for the temperature dependent data at 14 T. Between 19 and 20 T, the line splitting (see arrows) characteristic of a transition to a paramagnetic phase is evident. Taken together, the spectral splitting in both the temperature dependent and field dependent data provide the B-T phase boundary of the SP phase for comparison with that obtained for the CDW phase from transport studies as shown in Figure 1b.
Above 14 T, <m2>1/2 begins to broaden with increasing field, and in Figure 6b a comparison is made with magnetic torque data . Here the implication is that the spin-Peierls singlet ground state is being broken, and field-induced unpaired spins begin to dominate the magnetic properties. A connection to the increase in the effective dipole moment (circles in Figure 6b) with increasing field is discussed in the next section.
3.4. Computed 1H Spectra in the Paramagnetic Phase
We have used a simple dipolar model to estimate the 1H NMR spectra in the paramagnetic phase of Per2[Pt(mnt)2] outside the SP phase boundary. The input into the model includes a real-space representation of the positions of the proton and platinum atoms in the crystal structure, using a 3-D crystal array with approximately 410 unit cells, derived from a standard cif file in xyz (Cartesian) format (Figure 1a). We use the standard vector dipolar expression to find the magnetic field due to a Pt site:
Bij(rij) = [(3µeff·rij)(rij/rij) − µeff]/rij3 (1)
where rij is the vector distance between a proton at position i and a Pt spin at position j; and µeff is the effective Pt electron moment in the solid state. In this expression, we assume the paramagnetic moment is always directed along the applied field, i.e., µeff//Bext, and that only the component of the dipole field parallel to the applied field Bij·Bext/Bext contributes to the resonance. Each proton, due to the many inequivalent positions in the crystal, will contribute one component to the total spectrum at frequency ωi = 2πγ∑jBij·Bext/Bext (neglecting Lorentz and demagnetization terms). The time-dependent signal from the ensemble will then be:
S(t) = ∑i exp(−iωit) exp(−βit) (2)
where βi is the damping factor at proton site i. S(t) can be Fourier transformed to obtain the frequency dependent spectrum, i.e.,
A(ω) = ∫−∞∞ ∑i exp(−iωit) exp(−βit) dt (3)
which can be integrated, under the assumption that βi = β is the same at all proton sites, as:
A(ω) = ∑i βi/[(ω − ωi)2 + β2] (4)
Implicit in the formulation above is the angular dependence of the spectrum with respect to the field and crystalline axis directions, as well as the temperature and magnetic field dependence of the spectrum through µeff. In Figure 7a, we compute the angular dependent spectrum for µeff = 0.04 µB and β = 15 kHz, corresponding to Figure 3a for 4.16 K: although the experiment is in the SP ground state, the small values of µeff and β represent the presence of minority unpaired spins in the crystal lattice, and therefore the spectrum will have multiple peaks with field rotation. In Figure 7b we have computed the temperature dependent spectrum for magnetic field Bsim along a high symmetry axis θ = 67° (see Figure 1a), based on a maximum effective moment µeff = 0.15 µB at 20 K, weighted by the temperature dependent susceptibility at 7 T. The computed spectrum, adjusted for the Boltzmann factor T−1, has the qualitative features of the experimental spectrum shown in Figure 4a. In Figure 7c the magnetic field dependence of the paramagnetic spectrum (again for θ = 67°) is shown at constant temperature, where we have modeled the field dependence in terms of an increase of µeff with field by matching the simulation linewidths with the experimental linewidths from Figure 6a for selected fields. For comparison we have plotted these simulation µeff values vs. magnetic field in Figure 6b, where we find the scaling to be very consistent with the linewidth and magnetic torque data. It is clear that at high fields (of order 50 to 60 T) µeff will eventually approach the full Bohr magneton µB in a fully polarized state.
The calculation shows that: (i) the multiple peaks in the paramagnetic phase are due to the in-equivalent proton sites; (ii) even in the SP state at low temperatures there are residual features of multiple peaks in the spectra indicating that the spin-singlet dimerized state may not be complete, which is consistent with the findings of 1/T1 and χ that suggest that there are still unpaired spins at low temperatures as discussed in the next section; (iii) the larger the effective moment is, the more pronounced the multiple peaks are, and the broader the linewidth.
4. Magnetic Field and Temperature Dependent 1H Spin-Relaxation Rates 1/T1
The nuclear spin relaxation rate 1/T1 yields information complementary to the spectra. In Figure 8 the spin relaxation rate vs. temperature for increasing magnetic field is shown in terms of the Korringa relationship for a metal 1/T1T = constant, giving a convenient point of reference for the temperature dependence of the relaxation data.
We note that over the narrow range of temperature above Tc where the data extend, one cannot discriminate between 1/T1 ~ Tχ(T), the Korringa relationship, or other possible dependences of 1/T1 on temperature (see also inset of Figure 9a and discussion below). The data in Figure 8 show some unusual features. First is the rise in 1/T1T at or below the temperature Tc. This rise eventually is suppressed above 10 T. This feature is not apparent in, for instance, the case of CuGeO4 where for NQR measurements, 1/T1 drops monotonically with temperature, and shows a “dog-leg” type feature at the undimerized to dimerized (U-D) phase boundary . (However, in magnetic field, NMR does show some deviation from the NQR data in the CuGeO4 transition region.) The correspondence between the field dependent data in Figure 8 and the B-T phase boundary is not as clear as it is for the spectral line shape changes, due in part to the anomalous rise in 1/T1 at lower fields below Tc. Above 10 T however, the anomalous rise is suppressed, and the SP phase transition is more apparent where a “dog-leg” feature (dashed line) moves to lower temperature with increasing field. Second, at lower temperatures the slope of 1/T1T drops monotonically in temperature for all fields below the critical field of 20 T. However, the slope in the low temperature limit is not monotonic in field, and reaches a minimum in the range 7 to 10 T. Above the critical field, in the high field phase region, the behavior of 1/T1T shown for 22 T is clearly very different.
The non-monotonic field dependence of the low temperature 1/T1 data is best examined by plotting 1/T1 directly against T (Figure 9a), where, for comparison, we also juxtapose susceptibility data at available corresponding magnetic fields (Figure 9b).
For a given temperature below 3 K, 1/T1 decreases with increasing field up to 10 T, but above 10 T it begins to increase. Correspondingly, in the susceptibility data we note that in addition to the drop in χ(T) due to the onset of the SP gap, there is a “Curie tail” at low temperatures which diminishes with increasing field. These results indicate the presence of two opposite, field-dependent mechanisms that manifest themselves in χ and 1/T1. The field dependent paramagnetic susceptibility for a spin −½ system is described by the Brillouin function, where for J = ½ simplifies to
χp(T) = (NpµB/B) tanh(x) (5)
(See Kittel : here Np is the number of paramagnetic spins and x = µBB/kBT and p = g(J(J + 1) is implicit). The Curie tail may be ascribed to a population (Np) of unpaired spins. The so called “impurities” Curie tail corresponding up to about 3% of the total spin population has been always found in different Per2[Pt(mnt)2] samples to a larger or smaller extent. This tail is common in 1D spin chain systems (e.g., [21,22]) and it believed to correspond to defects (missing molecules) or staking defaults of any kind, rather than impurities. In the present case it is the anions [Pt(mnt)2] which remain unpaired. This has been confirmed by EPR  which shows in single crystals that this tail corresponds to a signal with g-values typical of [Pt(mnt)2]−. Following Bourbonnais et al.  the contribution to the susceptibility from the Pt spins (NSP) involved in the dimerization will be only from those spins excited across the effective spin-Peierls gap Δ. Treating these spins also as a paramagnetic contribution as in Equation (5) leads to the following expression for χsp(T) below TSP-CDW:
χsp(T) = (NSPµB/B) tanh(x)exp(− Δ/kBT) (6)
Therefore, the total susceptibility below TSP-CDW may be written as:
χ(T) = χsp(T) + χp(T) (7)
The data in Figure 9b below Tc ~ 7 K were fitted accordingly to Equations (5–7) and yielded the following fitting parameters, namely Nsp/N ~ 97.5% and Np/N ~ 2.5% (where N = Nsp + Np), and Δ/kB = 18.3 ± 1.1, 17.2 ± 0.71, and 15.9 ± 0.34 K for magnetic fields 3.06, 4.59, and 5.35 T respectively.
We next turn attention to the temperature and field-dependent spin relaxation data in Figure 9a, where below 3 K 1/T1 is thermally activated. We note that the relationship 1/T1 ~ Tχ(T) is not valid below about 20 K as shown in the Figure 9a inset. In the mean field description, and supported by previous transport studies , the effective spin Peierls gap follows the general relationship:
Δ(B) = Δ(0)*(1 − (B/Bc)2) (8)
where Bc is the upper critical field; and Δ(0) is the gap for B = 0. (Δ(B) is also temperature dependent near the phase boundary, but we have neglected this in the present analysis which focuses on the data in the low temperature limit) Following a simple model for the relaxation rate of the spin-Peierls system 1/T1SP in terms of an activated behavior with energy Δ(B) we would expect the relationship:
1/T1SP = Г exp(−Δ(B)/kBT) (9)
where Г is an intrinsic inverse lifetime . Since the slopes of 1/T1 vs. T below 3 K are activated, and proportional to an effective energy gap, the fact that they are not monotonic in field implies the interplay of two, field dependent energy gaps that influence 1/T1. Indeed, only above 10 T does Equation (9) appear to be operative. Recalling the implied presence of unpaired spins from the low temperature, field dependent Curie tail, we may further add to the total relaxation rate a paramagnetic term:
1/T1P = П exp(−pµBB/kBT) (10)
Here П represents the inverse lifetime of the paramagnetic background, and in this case the Zeeman energy pµBB, where p is an effective Bohr magneton number, plays the role of the energy gap. Hence the total relaxation rate is:
1/T1 = 1/T1P + 1/T1SP (11)
By inspection, it is evident that Equation (10) will dominate the behavior of 1/T1 when the Zeeman energy (i.e., field) is low, and that as the Zeeman energy increases with field, eventually the mean field SP gap which decreases with field will determine 1/T1 (Equation (9)). We found that a fit of Equation (11) to the data is difficult, since the parameters Г and П have, in addition to the Zeeman and SP gap, some field and temperature dependence. To obtain a general description of 1/T1, we have used the effective expression:
1/T1 = W exp(−Δeff/kBT) (12)
where W is an effective inverse lifetime to derive an effective activation energy Δeff over the entire field range below Bc by fitting the 1/T1 data. We note that Δeff ~ pµBB/kB in the low field limit, and Δeff ~ Δ(B) in the high field limit.
This is evident in Figure 10a where there is a crossover from Zeeman to mean-field gap behavior at around 10 T. Returning now to Equations (8–11), we may fit the field dependence of 1/T1 at a constant temperature of 3 K with the parameters pµBeff = 1.4 µB (dashed line in Figure 10a) and a field dependent mean field gap with Δ(0)/k = 12 K (solid line in Figure 10a), as shown in Figure 10b. Due to the many parameters and experimental uncertainties, this “two-spin” model analysis is only semi-quantitative, but captures the main features of the spin relaxation behavior at constant temperature below Bc. We close this section by noting that near 20 T, 1/T1 shows evidence for a phase transition (Figure 10b). It is possible that features associated with sub-phases in the high field state seen in transport and magnetization  may appear in 1/T1 (such as the dip between 20 T and 25 T, but more detailed work will be needed to resolve this. The increase at higher fields above 25 T may be the result of an increase in paramagnetic spins due to the further destruction of the spin-singlet chains, which may still be breaking down above the critical mean field Bc.
5. 195Pt NMR below the SP-CDW Phase Boundary: Relaxation and Spectral Features
We initiated our study of the SP chain behavior in Per2[Pt(mnt)2] with 195Pt NMR (γ = 9.14894 MHz/T). A fundamental difference between 1H NMR described above and 195Pt NMR is that in the latter case, the NMR nucleus is at the center of the electronic orbital that gives rise to the dipolar field. In the former case, the NMR nuclei (protons) are separated on average by about 10 Å from the d-electron spins.
This became evident in a preliminary study of the spin-relaxation time, shown in Figure 11a. Here, we note that in the SP phase 1/T1 is on average 1000 times faster on the Pt nuclear site than on the proton site; and in this study 1/T1 was too fast to measure in the paramagnetic state at higher temperatures. Our results on 195Pt NMR were therefore restricted to low temperatures, and as shown below, also to fields below 20 T. The angular dependence on a single crystal (Figure 11b—rotation in the a-c plane) for 14.774 T at 1.63 K indicated a hyperfine field anisotropy of about 740 ppm, substantially larger than that for 1H NMR shown in Figure 3a, which is only about 8.5 ppm. The attenuation of the spectral amplitude for certain directions may arise from the anisotropy in Bc , coupled with the severe attenuation of the 195Pt NMR signal near Bc as discussed below. To obtain better signal-to-noise in the high field studies (the relative NMR sensitivity of 195Pt to 1H is down by 0.00335), we used assemblies of small single crystals with approximate alignment of the b-axis perpendicular to the magnetic field and arbitrary a- and c-axis orientation. This is shown by the highly asymmetric spectral line shape in Figure 12a that is expected to be the combined result of the anisotropic critical field Bc, and hyperfine fields for a randomly-aligned multi-crystalline sample. Most importantly, the spectral amplitude vanishes with increasing temperature in a manner much faster than the conventional Boltzmann 1/T behavior. A similar feature is seen in the magnetic field dependence in Figure 12b, where again the signal vanishes quickly as the upper critical field Bc is reached. We note that attempts to find again a 195Pt line at low temperatures well above 20 T (i.e., 30 T) were unsuccessful. It is possible that until the d-electron spins are fully polarized at much higher fields, the distribution in hyperfine fields at the Pt nuclear site will remain too large to observe an NMR signal.
The rapid attenuation of the 195Pt spectral intensity near the SP-CDW phase boundary was the main reason for switching to 1H NMR; this was the only way to probe the SP behavior through the phase transitions. The origin of the 195Pt NMR attenuation may arise from several factors, either in the switching of the hyperfine field to another value far away from the measuring frequency, or by an increasing spatial or temporal fluctuation in the hyperfine field. By inspection Figure 12a,b, it appears that the first moment shifts to lower frequencies as the phase boundary is approached (in T or B), which is consistent with what is seen for 1H NMR. However, since the signal attenuates so quickly, it is difficult to say anything about the line shape and/or the second moment, and spin-relaxation rates become highly uncertain near the phase boundary. If it is assumed that the spectrum of d-electron spin fluctuations is the same for both H and Pt, then the easiest estimate of the ratio of the relaxation rates (at the same temperature and field) at the two sites is their nuclear proximity R to the nearest Pt d-electron spin, i.e.,
T1 (1H)/T1(195Pt) ~ R6(H-Pt)/R6(Pt-Pt) (13)
Assuming a nearest neighbor [1/R3]2 dipolar interaction term between an NMR nucleus and the Pt electronic spin. Comparing a proton at a distance of 10 Å from a Pt electronic spin to a Pt nucleus at a distance of 4 Å from a neighboring Pt electronic spin, the ratio of relaxation rates is only a factor of 240. To get a ratio of order 1000, the effective Pt-Pt distance R (Pt-Pt) would need to be about 3 Å, less than the nearest neighbor Pt-Pt distance of 4.125 Å. This implies that the Pt relaxation and spectra are probably strongly influenced by the hyperfine interactions between each Pt nucleus and its own on-site [Pt(mnt)2]− spin. Even though the Pt orbital is d-like in symmetry, more than half of its spin density is distributed over the [Pt(mnt)2]− anion . We may roughly estimate a lower bound on the hyperfine coupling by considering the shift in the spectral position from 1.74 K to 4.2 K in Figure 12a, using the value for χ at 4.2 K. Here we find Ahf ~ 3700 Oe/µB, again a value significantly higher than that for the proton sites.
A summary of the field dependences of the 195Pt spectral amplitudes and the relaxation rates 1/T1 at high magnetic fields near Bc are shown in Figure 13. Although divergences in the relaxation rates may be expected as the phase boundary Bc is approached, the rapidly vanishing signal precluded any definitive determinations. Since the ratio of the relaxation rates of 195Pt to 1H is about 1000, scaling the 1H data in Figure 10b would put 1/T1 ~ 1.5 (ms)−1 = 1500 s−1 at Bc ~ 20 T, which seems plausible, base on the range of 1/T1 values in Figure 13.
6. Experimental Section
All studies were carried out with a standard NMR spectrometer using spin-echo methods. Both superconducting (17 T), resistive (31 T), and Hybrid (45 T) magnets were used with an interchangeable probe that allowed top-tuning and sample rotation in standard helium cryostats. For the 1H measurements, a single crystal (5 × 0.1 × 0.05 mm3) was used in a micro-coil with an estimated filling factor of 50%. For the 1H studies, the NMR coil was Teflon-coated silver wire, affixed to a Teflon platform on a rotation probe to avoid background proton signals. The long b-axis of the crystal was collinear with the coil, and perpendicular to the magnetic field. Single crystal rotation was in the a-c plane. For the 195Pt measurements, with the exception of one angular dependent study on a single crystal, multiple small crystals were used to enhance the signal-to-noise factor, where only alignment of the b-axis perpendicular to the field was possible, and with no preferred a- or c-axis orientation. A standard insulated copper wire coil was used for these measurements. To validate the simulation code used in Section 3.4, the angular-dependent proton spectrum in the metal-organic framework [(CH3)2NH2]Mn(HCOO)3 was computed (discarding the disordered [(CH3)2NH2] cation in the center of the framework), agreeing well with an independent simulation in Reference .
We have used 1H NMR spectra and spin-relaxation rates (1/T1) to track the behavior of the spin ½ chain in Per2[Pt(mnt)2] over a broad range of temperature and magnetic field. Below the spin-Peierls transition (T < Tc), the linewidth and 1/T1 indicate the formation of a spin-singlet state, but features in magnetic field dependence of the susceptibility and 1/T1 show the presence of a minority paramagnetic spin population. These minority spins arise from unpaired spins in the [Pt(mnt)2] anions, and we find their effects are not observable above 10 T due to the increase in the Zeeman energy. In parallel, for T < Tc, with increasing magnetic field the majority spins in the singlet state begin to break down, and the effective spin-Peierls gap decreases. Hence above 10 T, the breaking of the spin chain begins to dominate the behavior of 1/T1. Near and above the critical field Bc, we find that the spectra progressively broaden with magnetic field in a manner consistent with the increase in the effective moment µeff of the dipole interaction, and follow a similar trend seen in torque magnetization studies, and also simulations of 1H NMR spectra. We estimate it would take about 60 T to fully recover µB in the dipole interaction. In contrast, the 195Pt spectra are only observable deep in the SP ground state due to the close proximity of the d-electron moment to the 195Pt nucleus (same atom and nearest neighbor). Hence with increasing temperature, the relaxation rate quickly becomes too fast to measure, and with increasing magnetic field, the breaking of the spin-singlet state creates strong variations in the local hyperfine fields and quickly broadens and shifts the spectral lines.
The signatures of the onset of the SP ground state, based on all NMR spectra and spin relaxation data taken in this study, is that the full SP state appears to form below the CDW transition seen in transport measurements, at least at low magnetic fields. However, at high fields, the two order parameters appear to be coupled more closely. Since NMR is a dynamic probe ω ≠ 0, and transport is essentially ω = 0, it is possible that the two methods are affected by different aspects of the transitions as the order parameters develop below Tc. For example, similar differences in apparent phase boundaries have been observed in the case of the field-induced spin density wave phases of (TMTSF)2ClO4 . Nevertheless, the study presented here is consistent with the notion that the CDW ground state formation is a necessary condition to drive the formation of the SP ground state, and the commensurability of the two order parameter periodicities (2:1) most likely promotes this interaction.
To go beyond the present study, a more detailed investigation of 1H NMR spectra and 1/T1 in the range 20 to 45 T will be needed to resolve features associated with subphases in the high field state. This presents a challenge since GHz range NMR spectroscopy with sufficient power is necessary to overcome the demands on bandwidth due to the increasing linewidths at very high magnetic fields.
This work was supported in part by NSF DMR-0602859 and 1005293 (JSB), by FCT (Portugal) PTDC/FIS/113500/2009 (MA), by NSF DMR-0804625 (SEB), and performed at the National High Magnetic Field Laboratory (supported by NSF DMR-0654118, by the State of Florida, and the DOE).
J.P. Pouget has kindly directed our attention to Figure 5 of his work (Reference ) where the inverse structural susceptibility associated with the b*/2 fluctuations is plotted vs. temperature. Here, the inverse Curie Weiss-like behavior extrapolates to Tsp more clearly than in Figure 2c in the present paper.
Conflict of Interest
The authors declare no conflict of interest.
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