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A New Mechanism for Electron Spin Echo Envelope Modulation ͒ John J

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A New Mechanism for Electron Spin Echo Envelope Modulation ͒ John J THE JOURNAL OF CHEMICAL PHYSICS 122, 174504 ͑2005͒ A new mechanism for electron spin echo envelope modulation ͒ John J. L. Mortona Department of Materials, Oxford University, Oxford OX1 3PH, United Kingdom Alexei M. Tyryshkin Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 Arzhang Ardavan Clarendon Laboratory, Department of Physics, Oxford University, Oxford OX1 3PU, United Kingdom Kyriakos Porfyrakis Department of Materials, Oxford University, Oxford OX1 3PH, United Kingdom S. A. Lyon Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 G. Andrew D. Briggs Department of Materials, Oxford University, Oxford OX1 3PH, United Kingdom ͑Received 21 January 2005; accepted 18 February 2005; published online 2 May 2005͒ Electron spin echo envelope modulation ͑ESEEM͒ has been observed for the first time from a coupled heterospin pair of electron and nucleus in liquid solution. Previously, modulation effects in spin-echo experiments have only been described in liquid solutions for a coupled pair of homonuclear spins in nuclear magnetic resonance or a pair of resonant electron spins in electron paramagnetic resonance. We observe low-frequency ESEEM ͑26 and 52 kHz͒ due to a new mechanism present for any electron spin with SϾ1/2 that is hyperfine coupled to a nuclear spin. In ͑ ͒ ͑ ͒ our case these are electron spin S=3/2 and nuclear spin I=1 in the endohedral fullerene N@C60. The modulation is shown to arise from second-order effects in the isotropic hyperfine coupling of an electron and 14N nucleus. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1888585͔ I. INTRODUCTION electron spins with different Larmor frequencies͒ results in no modulation effects from this mechanism: The heterospin Measuring the modulation of a spin echo in pulsed coupling energy changes its sign upon application of the re- magnetic-resonance experiments has become a popular tech- focusing pulse ͑because only one spin flips͒, and the magne- nique for studying weak spin-spin couplings. It is used tization is thus fully refocused at the time of echo formation, extensively in the fields of chemistry, biochemistry, and in the same way as in the presence of any other inhomoge- materials science, both in liquids and solids, using nuclear neous magnetic fields. magnetic resonance ͑NMR͒ and electron para- A second electron spin echo envelope modulation ͑ES- magnetic resonance ͑EPR͒.1–3 Two distinct mechanisms EEM͒ mechanism, which does apply to coupled pairs of for spin-echo modulation have been identified in the litera- heterospins, has also been identified.2,3 This mechanism re- ͑ ture. quires anisotropic spin-spin interactions e.g., AzzSzIz ͒ In the first mechanism, a pair of spins, S and I, are +AzxSzIx and is therefore restricted to solids or high- coupled through an exchange or dipole-dipole interaction, viscosity liquids. The modulation arises as a result of ជ ជ “branching” of the spin transitions created by the refocusing J·S·I or J·SzIz, and the echo modulation arises for nonselec- tive refocusing pulses, which flip both coupled spins. The pulse. The resonant spin S precesses with a Larmor fre- magnitude of the echo signal oscillates as cos͑Jt͒, where t is quency that is different before and after the refocusing pulse, the interpulse delay time.4 This is most commonly observed and therefore accumulates an additional phase, which causes ͑␻ ͒ ␻ for coupled pairs of homonuclear spins,5 though it is also oscillations in the echo signal, as cos Ikt , where Ik is the known for pairs of coupled electron spins with identical or spin transition frequency of the nonresonant spin I. The am- similar Larmor frequencies.6,7 plitude of the oscillations depends on the magnitude of the ជ ជ anisotropic hyperfine component. It should be emphasised that a similar coupling, J·S·I, In this paper we demonstrate that contrary to previous between unlike spins ͑including coupling between hetero- belief, echo modulation effects can also be observed for a nuclear spins, hyperfine coupling between electron and heterospin pair coupled by a purely isotropic spin interaction, nuclear spins, and electron-electron coupling between two and we thus identify a new ESEEM mechanism. Our het- erospin pair is the endohedral fullerene N@C60 in CS2 ͒ a Electronic mail: [email protected] solution, with electron spin S=3/2 interacting through an 0021-9606/2005/122͑17͒/174504/7/$22.50122, 174504-1 © 2005 American Institute of Physics Downloaded 18 Nov 2005 to 129.67.85.146. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 174504-2 Morton et al. J. Chem. Phys. 122, 174504 ͑2005͒ ͑ ͒ FIG. 1. a EPR spectrum of N@C60 in CS2 at room temperature. Each line ͑ ͒ in the triplet signal is labeled with the corresponding projection MI of the FIG. 2. a Two-pulse ESE decays for N@C60 in CS2 at 190 K measured at 14 N nuclear spin. ͑b–d͒ Zoom-in for each line showing details of the line- the central MI =0 and the high-field MI =−1 hyperfine components of the are due to a hy- EPR spectrum. ͑b͒ The Fourier transform ͑FT͒ of the oscillatory echo decay ͒ء shape structure. The small satellite lines ͑marked with 13 perfine interaction with the natural abundance of C nuclei on the C60 cage. at MI =−1. Measurement parameters: microwave frequency, 9.67 GHz; microwave power, 0.5 ␮W; modulation amplitude, 2 mG; modulation frequency, 1.6 kHz. frequency units͒ is ជ ជ isotropic hyperfine coupling ͑a·S·I,a=15.8 MHz͒ to the nuclear spin I=1 of 14N. The isotropic hyperfine coupling ជ ជ H = ␻ S − ␻ I + a · S · I, ͑1͒ lifts the degeneracy of the electron-spin transitions, 0 e z I z leading to a profound modulation of the echo intensity at about 52 kHz. We shall show that this third modulation ␻ ␤ ប ␻ ␤ ប mechanism is only effective in high-spin electron systems where e =g B0 / and I =gI nB0 / are the electron and ͑ Ͼ ͒ 14 S 1/2 . The N@C60 molecule has an exceptionally long N nuclear Zeeman frequencies, g and gI are the electron ͑ ␮ ͒ ␤ ␤ electron-spin dephasing time T2 =210 s , enabling the ob- and nuclear g-factors, and n are the Bohr and nuclear ប servation of this low-frequency ESEEM for the first magnetons, is Planck’s constant, and B0 is the magnetic time. field applied along the z axis in the laboratory frame. Each ͓ ͑ ͒ ͔ hyperfine line marked in Fig. 1 a with MI =0 and ±1 in- volves the three allowed electron-spin transitions ⌬ II. MATERIALS AND METHODS MS =1 within the S=3/2 multiplet. These electron-spin transitions remain degenerate for M =0, as seen in Fig. 1͑c͒, 8 I High purity endohedral N@C60 was prepared, dissolved but split into three lines ͑with relative intensities 3:4:3͒ for in CS to a final concentration of 1ϫ1015–2ϫ1015/cm3, ͑ ͒ ͑ ͒ 2 MI = ±1, as seen in Figs. 1 b and 1 d . This additional split- freeze-pumped in three cycles to remove oxygen, and finally ting of 0.9 ␮T originates from the second-order hyperfine sealed in a quartz EPR tube. The samples were 0.7–1.4-cm corrections a2 /␻ =26 kHz, and its observation is only long, and contained approximately 5ϫ1013 N@C spins. e 60 possible because of the extremely narrow EPR linewidth Pulsed EPR measurements were done at 190 K using an Ͻ0.3 ␮TinN@C . Similar second-order splittings have X-band Bruker Elexsys580e spectrometer, equipped with a 60 ͑ ͒ been reported for the related spin system of endohedral nitrogen-flow cryostat. In the two-pulse Hahn electron spin 31 ͑ ͒ ␲ ␶ ␲ ␶ ␲ fullerene P@C60, which has S=3/2 coupled with echo ESE experiments, /2− − − −echo, the /2 and 10 ␲ pulse durations were 56 and 112 ns, respectively. Phase I=1/2. ͑ ͒ cycling was used to eliminate the contribution of unwanted Figure 2 a shows two-pulse echo decays measured at free-induction decay ͑FID͒ signals. the central MI =0 and the high-field MI =−1 hyperfine lines. The decay is monotonic for MI =0 and has an exponential ͑ ␶ ͒ ␮ dependence exp −2 /T2 with T2 =210 s. However, the ͑ decay is oscillatory for MI =−1 and also for MI =+1, III. RESULTS AND DISCUSSION not shown͒—the Fourier transform of the decay reveals two Figure 1͑a͒ shows the continuous-wave EPR spectrum of peaks at frequencies 26 and 52 kHz, as seen in ͑ ͒ N@C60 in CS2 at room temperature. The spectrum is Fig. 2 b . These frequencies correlate closely to the splitting centered on the electron g-factor g=2.0036 and comprises of 26 kHz found in the EPR spectrum in three lines, resulting from the hyperfine coupling to 14N.9 Figs. 1͑b͒ and 1͑d͒, indicating that the two effects have the The relevant isotropic spin Hamiltonian ͑in angular same origin. Downloaded 18 Nov 2005 to 129.67.85.146. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 174504-3 Electron spin echo envelope modulation J. Chem. Phys. 122, 174504 ͑2005͒ ␻ We shall use the spin-density operator formalism to de- Hamiltonian, correct to second order in a/ e, becomes rive the modulation effects for the spin system S=3/2, I=1. The spin-density matrix after our two-pulse echo experiment is given by 0000 3␦ 0 00 2 H = S ͑␻ + a͒ − I ␻ − , ͑4͒ ␴͑␶͒ ͑ x x͒ ␴ ͑ x x͒† ͑ ͒ 0 z e z I 002␦ 0 = U␶R2U␶R1 · 0 · U␶R2U␶R1 .
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