Slow spin fluctuations

Figure 15 (a) The 4.2 K Mossbauer spectra of [(Fe(IV)=0)(TMC)(NCCH3)](0Tf)2 in acetonitrile recorded in (A) zero field and (B)a parallel field of 6.5 T. The solid line represents a spin Hamilton simulation with the parameters described in the text, (b) Mossbauer spectra of [Fe(lV)=(0)(TMCS)] recorded at temperatures and applied fields that are indicated. The solid lines represent spin Hamiltonian simulations with parameters described in the text. The spectra were simulated in the slow (at 4.2 K) and fast (at 30 K) spin fluctuation limit. The applied field was directed parallel to the observed y radiation. The doublet drawn above the topmost experimental spectrum (0 T, 4 K) represents a 7% Fe(ll) contribution from the starting complex. (From J. U. Rohde et al. (2003) Science 299 1037-1039. Reprinted with permission from AAAS)... 

Using the notions of spin-fluctuation theory, the approach to the magnetic instability can be understood as a critical slowing down of the fluctuations accompanied by a gradual decrease of TSF. The deviation from Curie-Weiss law should... 

This approximation will only be valid for 7 —> 0, as fluctuations are often visible as the sample is warmed towards 7m. Little is understood, however, about slow spin dynamics (i.e., within the iSR, but below the neutron time window) in ordered magnets. A theoretical treatment of spin lattice relaxation and its relation to jxSR for a Heisenberg ferromagnet has been given by Dalmas de Rentier and Yaouanc (1995). 

Y(Mn,Al)2. A means to reduce fhistration is to substitute some of the Mn ions (e.g., Y(Mni jAl t)2) since the strict tetrahedral exchange correlation is then partially broken. Substitution by Al also causes lattice expansion, which leads to some moment stabilization and in turn causes slowing down of spin fluctuations. The system enters a spin glass state at rather elevated temperatures Tg ss 50 K) for x = 0.06 and above (Motoya et al. 1991). pSR measmements on a sample with x = 0.1 clearly confirm spin glass order below Tg and also support the notion of slowed down spin fluctuations by a more Gaussian shape of the muon spin depolarization fimction at T Tg (Cywinski and Rainford 1994). 

ZF and LF-ftSR has now been reported by Dunsiger et al. (2000). The ZF relaxation function is root-exponential at all temperatures down to 0.025 K, indicative of a dilute spin system with substantial dynamics. This supports the idea of isolated islands nucleated around defects, but indicates only slowed fluctuations, not full freezing. The apparent spin fluctuation rate drops starting near 1 K (where bulk probes see effects they attribute to short-range magnetic order, Schiffer et al. 1994), but does not extrapolate to zero, and shows no effect around 0.14K. Thus p,SR sees no spin-glass transition. All of this is generally consistent with the neutron diffraction results. In LF at 0.1 K, the relaxation... 

At r > 5K, the muon spin relaxation rate becomes unmeasurably small (i.e., A < 0.004 (xs ). Taking the high-temperature value of the moment on Ce one arrives at a spin fluctuation rate in excess of 10 Hz. In particular, no effect on A could be seen around 10 K where susceptibility reaches a peak. This definitely proves that this peak is not connected to any magnetic transition, but signals the onset of the AFM spin correlations seen in the neutron measurements mentioned. [tSR, due to its different time window, responds only when the correlations have caused a substantial slowing down of spin fluctuations (i.e., at much lower temperatures). 

In summary, the work of Yaouanc et al. (1999b) finds no magnetic phase transition, only comparatively slow paramagnetic spin fluctuations persisting down to 40 mK coupled to a strongly reduced Yb moment. 

A preliminary report (Amato et al. 1998) presents ZF- and LF-pSR data down to 0.1K. The ZF spectra are characterized by nuclear-electronic double relaxation. The nuclear part can be suppressed in LF = 20 G. No magnetic transition was observed. Below 10 K, the electronic relaxation rate increases monotonically with decreasing temperature. Application of LF = 200 G also suppresses electronic relaxation, indicating rather slow dynamics of the spin system. From the field dependence of relaxation rate the spin fluctuation frequency was found to be V4f(r —> 0) 2.7 MHz. It appears that this is another case where spin correlations develop at low temperatures, but persistent slow spin dynamics prevent the formation of an ordered magnetic state (see CeNiSn in sect. 9.2 for comparison). 

Up to now, we have concentrated on the physics at zero kelvin. In this section, we extend the studies to finite temperatures and discuss finite temperature phase diagrams. The physics at finite temperatures is dominated by thermal fluctuations between low lying excited states of the system. These fluctuations can include spin fluctuations, fluctuations between different valence states, or fluctuations between different orbitally ordered states, if present. Such fluctuations can be addressed througih a so-called alloy analogy. If there is a timescale that is slow compared to the motion of the valence electrons, and on which the configurations persist between the system fluctuations, one can replace the temporal average over all fluctuations by an ensemble average over all possible (spatially... 

---