Order quadrupolar

Fig. 13. Magnetic field vs. temperature phase diagram of single crystal PrFe4Pi2 with the magnetic fields applied along the (100) direction. The labels ODS and HFS refer to ordered state and heavy fermion state, respectively. The ordered state is probably due to quadrupolar ordering of the Pr 4f ground state. The solid and broken lines represent second-order and first-order phase boundaries, respectively (Aoki et al., 2002).

In Section 4.1 we will discuss the influence of crystalline electric fields on the magnetic properties and the phenomenon of orbital ordering (also called quadrupolar ordering or hidden order) of the 4f electrons in RNi2B2C compounds. In the following sections we will briefly report on the behavior of the individual RNi2B2C compounds from R = Ce to Yb. 

In HoBg, below Tq = 6.1 K, the Ho3+ quadrupole moments order in parallel (Yamaguchi et al., 2003). This is called ferroquadrupolar ordering (FQO). The cooperative phenomena AFQO and FQO are special types of quadrupolar order-... 

Figure 15.3 The decay of the so-called quadrupolar order as a function of the time interval t2 (quadrupolar order is created by a pulse at time tx, then relaxes during a time interval t2 before being observed via a third pulse). Data from three differently crosslinked PDMS networks are presented (M = 9700 g.mol"1 o, tetraallyloxyethylene-crosslinked (tetrafunctional) + crosslinked with bis(allyloxy)-3-[bis(allyloxymethyl]-2, 2-propylene oxide (hexafunctional) A tetravinylcyclosiloxane-crosslinked]. The longitudinal relaxation is plotted for comparison. Experimentally, the quadrupolar relaxation time T1Q equals about 1.33 T1Z...

The temperature dependence of the spectral spin diffusion and crossrelaxation was examined by Mueller et a/.287,288 with spin- and spin-1 systems. They showed that the diffusion rate can be strongly temperature dependent if it is motionally driven. It is therefore, unreliable to discriminate spin diffusion and chemical exchange by variable-temperature measurement of 2D exchange spectra. Mueller et al. suggested that the dependence of the polarization transfer rate on the spectral difference of the relevant resonances should be measured in a single crystal to safely distinguish the two different polarization transfer processes (see also ref. 289). They also explained satisfactorily why the relaxation of the quadrupolar order is much faster than the Zeeman order. This... 

Nevzorov AA, Trouard TP, Brown ME. Lipid bilayer dynamics from simultaneous analysis of orientation and frequency dependence of deuterium spin-lattice and quadrupolar order relaxation. Phys. Rev. E 1998 58 2259-2281. 

Figure 66. Tentative phase diagram of CO on boron nitride. The coverage n is given in units of the complete -v/s monolayer obtained from the top of the fluid to commensurate solid isotherm substep at low temperatures less than 62 K, (see Ref. 229). The phase diagram is based on adsorption isotherm data [229] indicated by filled dots at high temperatures and coverages, as well as on dielectric data [382] marked by filled diamonds. The various phases are denoted by the following abbreviations commensurate orientationally disordered solid, CD incommensurate orientationally disordered solid, ID fluid, F reentrant fluid, RF commensurate orientationally (quadrupolar) ordered solid, CO incommensurate orientationally (quadmpolar) ordered solid, lO commensurate orientationally and dipolar ordered solid, CDO incommensurate orientationally and dipolar ordered solid, IDO. Several coexistence regimes are indicated. The solid lines correspond to phase boundaries based on measured features, whereas the dotted lines are expected phase boundaries. (Adapted from Fig. 6 of Ref. 229 and from Ref. 382.)...

Jeener and Broekaert introduced, in 1%7, a three-pulse B,(r) sequence to measure the relaxation time Tm of the dipolar order of / = 1 spin systems in the presence of a conventional high Zeeman field, Bq, which is based on the decay time of the so-called Jeener echo . It was later extended by Spiess and Kemp-Harper and Wimperis to study in a similar way the quadrupolar order in / a 1 systems. The appearance of a Jeener echo depends upon the existence of interactions that are not averaged out by molecular motions on the considered time scale. The method has become of great importance in recent relaxation studies, in particular of liquid crystals because, in standard spin relaxation theories, it provides a power l means to separate and analyse the spectral densities / v) and /2) j. i4,is,2025 ggg... 

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