Phase-memory times

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

The main advantage of tlie tln-ee-pulse ESEEM experiment as compared to the two-pulse approach lies m the slow decay of the stimulated echo intensity detemiined by T, which is usually much longer than the phase memory time Ty that limits the observation of the two-pulse ESE. 

Carotenoids incorporated in metal-substituted MCM-41 represent systems that contain a rapidly relaxing metal ion and a slowly relaxing organic radical. For distance determination, the effect of a rapidly relaxing framework Ti3+ ion on spin-lattice relaxation time,and phase memory time, Tu, of a slowly relaxing carotenoid radical was measured as a function of temperature in both siliceous and Ti-substituted MCM-41. It was found that the TM and 7) are shorter for carotenoids embedded in Ti-MCM-41 than those in siliceous MCM-41. 

By spin-spin relaxation, the nuclei relax to equilibrium among themselves (i.e. precession occurs without phase coherence). The vectors dephase (Fig. 1.5 (b) - Fig. 1.5 (a)), and the components of transverse magnetization, Mx and My, decay to zero as a result (transverse relaxation). The spin-spin relaxation time T2 is thus also referred to as the phase memory time or the transverse relaxation time. 

The time constant tc is also called a phase-memory time, since it is related to the time for local fields to lose phase coherence (coupling) and decay to zero. 

The electron spin echo of Ag°(B) has a very short phase memory time but relatively strong aluminum modulation can be identified. However, the phase memory time is too short to carry out a quantitative analysis of the modulation. This also precludes us from getting analyzable modulation from deuterated adsorbate molecules in a three pulse echo experiment. So the data is insufficient to locate Ag°(B) in the zeolite lattice without additional information. 

Eigure 12.5 presents TR ESR and ET ESR spectra obtained under photolysis of DAR (Scheme 12.1). One can observe a broadened signal of benzoyl radical in the ET ESR (or a signal of much lower apparent intensity). The intensity of the signals in CW TR ESR is determined by polarization, longitudinal (spin lattice) relaxation time Ti and by the rate of chemical disappearance of r. The intensity of signals in ET ESR is determined by polarization, and phase memory time Tm, which includes Ti, transverse (spin-spin) relaxation time T2, and a rate of chemical disappearance of r. Broad ESR components have short Tm, and they are difficult to observe. Broadening of components in spin adducts is ascribed to a hindered rotation around a Cp bond or cis-trans isomerization (Scheme 12.4). ... 

For a two-pulse (90° - t - 180°), or primary echo experiment, the integrated intensity of the spin echo, which occurs at time t after the 180° pulse, is measured as a fimction of increasing t from the probe s dead-time ( 100 ns) to a time where the echo amplitude has decayed to a few percent of its initial amplitude (2-8 ps for most powder samples). A two-pulse ESE decay envelope for the type-1 Cu(II) site of a multi-copper oxidase, Fet3p, is shown in Figure 1(a). The data show an overall decay characterized by a phase memory time, Tm or T, of < 1.0 ps. Superimposed on this decay are echo modulations that arise ft om hyperfine coupling to the N nuclei of two histidyl imidazole ligands and the protons of the snrronnding matrix. 

Highly oriented poly acetylene. 257 4.3.4 Phase memory time Tm and ... 

Phase memory time and motional narrowed width (yc 2r) ... 

Figure 6.37. The teinperature dependence of the motional narrowed secular width (y7 2 ) (O) [6,82] and the phase memory time Tm (taken at X-band) in irans- CD), obtained by (I) Shiren et al ( ) [159-161] and (2) Isoya ( ) [193], The solid curve shows typical behaviour for (yTj ) 4- A// p...

K is shown in Fig. 3b. The signal fits a monoexponential decay function with a characteristic phase memory time of Tm= 3.1 0.2 ps. Table 4 summarizes the... 

Table 4. Phase memory time ([is) and homogeneous line width Tjj in brackets (kHz) as determined for the zero-field ODMR transitions of [Rh(thpy)2(bpy)]+, [Rh(thpy)(phpy)(bpy)]+, [Rh(phpy)(thpy)(bpy)]+, Rh(bpy) +, and Rh(phen) +. Asterisk means spin echo was not detected...

Although EPR lines of MNMs are generally inhomogeneously broadened, a lower limit of can still be obtained from the linewidth. This approach yielded values in the range of 10 ° to 10 s, including 0.2 ns [121], 0.5 ns [120], 2 ns [107], and 10 ns [114]. Pulse EPR measurements (Sect. 3) revealed that phase memory times can fortunately be much longer than these estimates. 

The spin-spin relaxation T2, or the experimentally determined phase memory time Tm, is a parameter of interest in molecular magnetism, because it is the time available for a quantum computation. It was recognized several years ago that MNMs may be used to implement quantum bits [137, 138]. There are currently essentially three proposals for using MNMs for quantum information processing [21, 139, 140]. The first is an elaborate scheme to use high-spin MNMs, such as... 

Phase memory times in solids are usually determined by the Hahn or primary echo sequence, 7i/2-T-7i-T-echo, by variation of t [144]. For quantum computation... 

Use of a surfactant allows solubilization of the polyoxometalate cluster K6[Vi5As6042(H20)] 8H20 (V15) in the organic solvent chloroform. Spin echo measurements revealed a phase memory time of Tm = 340 ns, which was attributed to resonances in the 5 = 3/2 excited state of the cluster [166]. No quantum coherence was detected in the pair of 5 = 1/2 ground states [151]. By measurement of the z-magnetization after a nutation pulse, and a delay to ensure decay of all coherences, Rabi oscillations were observed. From the analysis of the different possible decoherence mechanisms, it was concluded that decoherence is almost entirely caused by hyperfine coupling to the nuclear spins. 

The 5 = 5 ground state of the high spin cluster Fe4 possesses a negative axial ZFS with D = —0.342 cm [165]. As a consequence the zero-field energy gap between the Ms = 5 and Ms = 4 is 92 GHz, which is close to the fi-equency employed in a W-band EPR spectrometer (94 GHz). This fact was exploited in pulsed W-band EPR studies on frozen toluene solutions of Fe4 in zero external field [152], where a phase memory time of Tyi = 307 ns at T = 4.3 K was found in Hahn-echo measurements. The echo decay in an external field of 0.373 T shows ESEEM due to hyperfine coupling to protons. Interestingly, measurements on the protonated compound in deuterated toluene show ESEEM due to coupling to... 

Measurements of the quantum coherence are usually performed in dilute systems to prevent decoherence due to fluctuating intermolecular magnetic-dipolar electron-electron interactions. In SMMs these fluctuations can also be frozen out at low temperatures, below the blocking temperature of the magnetization. A singlecrystal study on Feg made use of this fact and, indeed, phase memory times of up to 712 ns were observed at 1.27 K [153]. Raising the temperamre to 1.93 K results in a drastic reduction of Tm to 93 ns. Simulations showed that electron spin-electron spin interactions can account quantitatively for this behavior. A second decoherence process was identified from these simulations, with a decoherence time of about 1 ps, which was attributed to hyperfine-induced decoherence. 

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