Zero-field transitions

IV. PMDR AND MAGNETIC STUDIES A. Zero-Field Transitions... 

The technique of microwave-recovery provides crucial information about the substates involved in the ODMR transitions. For this experiment, Pd(2-thpy)2 is optically excited by a c. w. source. This leads to specific populations of the three triplet substates. At low temperature, they are thermally decoupled and thus emit according to their specific populations and their individual decay constants (e. g. see Sect. 3.1.3 and Table 2). In the microwave recovery experiment, the steady state conditions are perturbed by a microwave pulse being in resonance with the zero-field transition at 2886 MHz. Due to the microwave pulse, the populations of the two states involved are changed. Subsequently, one monitors the recovery of the emission intensity in time until the steady state situation is reached again. The microwave pulses have, for example, a duration of 20 ps and are applied repeatedly to enable a detection with signal averaging [61]. 

Fig. 5. Zero-field transitions observed by microwave phosphorescence double resonance in the lowest triplet state of ZnP. The lifetimes were obtained from MIDP experiments. Arrows indicate two radiative channels for the phosphorescence (adapted from Refs. 88, 89)...

Fig. III. 12. Zeeman multiplets of the 2i2—221 rotational transition of ethyleneoxide measured with AM = 0 (upper trace) and AM = 1 (lower trace) selection rule. The zero field transition frequency is marked by a dagger. The Stark lobes are pushed out of the frequency range shown in the figure by application of a sufficiently high square wave voltage to the Stark electrode...

Fig. 3a,b. a Transient nutation signal as probed for the zero-field transition at... 

MHz of [Rh(bpy)3](0104)3, in the phosphorescent triplet state, upon switching on the microwave power. The oscillations occur as the microwave pulse duration is increased. Photoexcitation is near 320 nm, detection is at 456 nm temperature is 1.4 K. b Optically detected echo amplitude decay for the 2320 MHz zero-field transition of [Rh(bpy)3] (0104)3 as obtained by applying a n/2-T-n-T-nl2 pulse sequence when increasing 2r... 

From magnetic resonance spectroscopy [49] it is well-known that IB effects are adequately circumvented by the tricks of a spin echo experiment. For instance, in a two-pulse echo experiment, IB effects are averaged out and one probes spin dephasing determined by time-dependent fluctuations characteristic of HB only (and not IB). More specifically, a nll-r-n microwave pulse sequence is applied, where the first nil pulse creates a coherent superposition state for which a la = 1 and the n pulse, applied at time r after the first pulse, generates a spin coherence (the echo) at time 2r after the initial pulse. The echo amplitude is traced with r. The echo amplitude decay time is characteristic of the pure dephasing dynamics. For phosphorescent triplet states it is possible to make the echo optically detectable by means of a final nil probe pulse applied at time f after the second pulse [44]. In Fig. 3b, the optically detected echo amplitude decay for the zero-field transition at 2320 MHz of... 

As shown in Fig. 3 a, spin coherence is manifested in the optically detected transient nutation signal for [Rh(bpy)3] (0)04)3 the phosphorescent triplet state. In this experiment, one observes that the phosphorescence intensity becomes modulated as the pulse length of microwave pulses, resonant with the D - transition, is gradually increased. The modulation is evidence that the micro-wave excitation induces a spin coherence in the ensemble of molecules in the photoexcited triplet state [44]. Moreover, from the transient nutation experiment one obtains the information about the duration of the pulses needed in a spin echo experiment. In the case of the example, the n/2 pulse is 100 ns and the 71 pulse has a length of 200 ns. Similarly, transient nutation signals for the other zero-field spin resonances could be obtained. The optically detected spin echo decay as measured for the D - j j zero-field transition for [Rhlbpylj](004)3... 

The three transitions between the three terms are referred to as zero-field transitions or the zero-field resonances. In an applied high-frequency field Bi cos rot, all three transitions are allowed. This follows immediately by computation of the transition matrix elements (g/UB/h)(Tu Bi S T > using Table 7.2 for example, the transition matrix element for the zero-field transition T -(- Tz (Fig. 7.5), the transition matrix element (Txl(BixSx+ BiySy+ Bi2S2) T2> is nonzero only for the y component. For this transition, Bi must thus have a component in the y direction. From Fig. 7.5, this becomes intuitively clear for this transition, aU the spins must process around the y axis. The other two zero-field transitions follow by cyclic permutations. 

The most precise measurements of the fine-structure parameters D and E have in fact been carried out using zero-field resonance. Figure 7.6 shows the three zero-field transitions in the Ti state of naphthalene molecules in a biphenyl crystal at T = 83 K. In these experiments, the absorption of the microwaves was detected as a function of their frequency [5]. The lines are inhomogeneously broadened and nevertheless only about 1 MHz wide. Owing to the small hnewidth of the zero-field resonances, the fine-structure constants can be determined with a high precision. This small inhomogeneous broadening is due to the hyperfine interaction with the nuclear spins of the protons (see e.g. [M2] and [M5]). For triplet states in zero field, the hyperfine structure vanishes to first order in perturbation theory, since the expectation value of the electronic spins vanishes in all three zero-field components (cf Sect. 7.2). The hyperfine structure of the zero-field resonances is therefore a second-order effect [5]. 

Fig. 7.26 Microwave-induced delayed phosphorescence. Above two superposed phosphorescence-intensity decays of quinoline in a durene crystal at T = 1.35 K and Bq = 0. The phosphorescing triplet component is Tz). The delayed phosphorescence signals, delayed in the first experiment by ca. 2 s and in the second by ca. 4 s, are produced by resonant 1000.5 MHz pulses, which saturate the zero-field transition Ty Tz at these times after the end of the UV excitation and thus...

A second direct optical-detection method for selective population and depopulation is microwave-induced delayed phosphorescence in zero field (Bq = 0) [25]. Figure 7.26 shows the phosphorescence intensity from quinoline in a durene (tet-ramethyl benzene) host crystal at T= 1.35 K as a function of the time after the end of the UV excitation. The phosphorescing zero-field component here is Tz). Its lifetime is considerably shorter than those of the other two zero-field components, from which furthermore no phosphorescence is emitted. If the zero-field transition... 

Table 1. Orientation of four pentacene molecules ( 4°) together with the transition energies of the two zero-field transitions. 0 denotes the angle between the individual molecular y axes of the different molecules. For comparison the corresponding data for the Oi and O2 ensembles are also included.

The change from the second-order nature of the transition observed at zero and low magnetic field to first order at high fields occurs at To 1.1 K = 0.48rc. This value should be compared with the estimate of 0.33 deduced from the Chandrasekhar-Clogston field of a d-wave order parameter and the orbital critical field obtained from extrapolating the behavior close to the zero-field transition to low temperatures. 

At extremely high fields the isotropic phase should be indistinguishable from the nematic one, even well above the zero field transition temperature, since the uniaxial order induced by a magnetic or ac electric field in the isotropic phase will be comparable with the nematic orientational order. However, such fields are hardly accessible, even with the pulse technique. Much stronger changes in order parameter may be achieved with ferroelectric transitions (see below). 

The Stark effect is usually used to modulate rotational lines to improve their detection. This is the basis of the Stark-modulation spectrometer (Fig. 2) discussed earlier. With this type of spectrometer both the Stark lines and the zero-field transitions are displayed. The Stark effect pattern can be a valuable aid in the assignment of rotational spectra, particularly for asymmetric tops. Specifically, by counting the number of Stark components, one can obtain an indication of the smaller J value involved in the transition. Another particularly important application of this effect is in the evaluation of very accurate electric dipole moments. These are determined by careful measurement of the displacement of the Stark components from the zero-field absorption line as a function of the applied field. The analysis of these Stark splittings by means of the appropriate expression allows... 

---