Collective magnetic excitations

The fluctuations of the magnetization direction around an easy axis, known as collective magnetic excitations, can be considered fast compared to the time scale of Mossbauer spectroscopy because there are no energy barriers between magnetization directions close to an easy direction, and the magnetic splitting in the 

Mossbauer spectrum is then proportional to the average value of the hyperfine field which is given by 

Numerous experimental studies have shown that the magnetic hyperfine field of magnetic nanoparticles varies linearly with temperature at low temperatures, in accordance with (6.23). This is in contrast to bulk materials for which the decrease in the hyperfine field with increasing temperature in accordance with spin wave 

---

MOssbauer Spectroscopy. Small, single domain, ferro- or ferri-magnetic particles can show both collective magnetic excitation (precession of the magnetic moment) and superparamagnetic (relaxa-... 

The results of these modeling studies are shown in Figures 2 and 3> The value of ic (anisotropy constant) was chosen so that the average particle radius determined from the reduction in the average hyperfine field splitting due to collective magnetic excitations... 

The interactions also suppress the collective magnetic excitations at low temperatures. Figure 6.17 shows the temperature dependence of the magnetic hyperfine... 

For Nd2Cu04, the R-Cu exchange interaction is a relevant quantity for the description of the low-energetic collective magnetic excitations. Collective excitations were studied... 

After presenting the sample preparation in Sect. 5.2, we give an introduction to the theoretical background in Sect. 5.3. In Sect. 5.4, we briefly review the electronic influence on structure and phase stability of crystalline Hume-Rothery phases. In Sect. 5.5, we discuss the properties of non-magnetic amorphous alloys of the type just mentioned. The electronic influence on structure (5.5.1) and consequences for the phase stability (5.5.2) are also discussed. Structural influences on the electronic density of states are shown in 5.5.3. Electronic transport properties versus composition indicate additionally the electron-structure interrelation (5.5.4), and those versus temperature, the influence of low-lying collective density excitations (5.5.5). An extension of the model of the electronic influence on structure and stability was proposed by Hdussler and Kay [5.21,22] whenever local moments are involved as, for example, in Fe-containing alloys. In Sect. 5.6, experimental indications for such an influence are presented, and additional consequences on phase stability and magnetic properties are briefly discussed. 

In addition to the studies cited above, Fourier Transform IR-spectrometers have been used for the study of magnetic excitations since the 1960s. Thus, collective excitations were observed in, among others, FeF2 [91, 92], Fe dithiocarbamate... 

Neutron scattering technique generally provides the most powerful probe of collective spin excitations. We recall that the cross section for magnetic neutron scattering from a system of N spins is given (Marshall and Lovesey 1971) by... 

In order to observe the collective magnetic properties experimentally one has to study proper substances with the help of inelastic neutron scattering. There are several model substances available which have been extensively investigated. TmSb is a model Van Vleck paramagnet with J(0)Ucni 0)< 1 so that the collective excitations are unimportant. PrjTl is a model system for an exchange induced Van Vleck ferromagnet (Tc=11.6K) with J(0) barely exceeding Jcrit(O), (/(0))//crit(0) = 1.014). 

---