Spontaneous spin precession

Fig. 12. Top High-pressure cell (CuBe) used in the studies of rare-earth metals and intennetallic compounds up to 0.9 GPa (9 kbar). Bottom ZF-(xSR spectrum of FM gadolinium metal inside the CuBe high-fvessure cell. The oscillating signal (see also inset) is the spontaneous spin precession pattern of Gd. The Gaussian relaxation spectrum comes from muons stopped in the cell walls. After Schreier et al. (1997) and Kalvius et al. (20001).

At first, one might conclude that, due to the random orientation of Mdom> as found especially in an umnagnetized, polycrystalline magnet, a spontaneous spin precession signal is unobservable because the internal fields By taken over the whole sample are then randomly oriented as well. Fortunately, this is not so. We may approach the isotropic situation by assuming that exactly 1/6 of the field vectors point into each of the 6 cartesian directions +x,-x,+y,-y,+z,-z). The 1/3 of fields oriented along z will be parallel to the muon spin and do not induce precession. The 1/3 of field vectors oriented x will cause precession in the (y,z) plane, one half clockwise, the other half counter clockwise. 

Condition (ii) can be fulfilled in other crystal structures on occasion as well. An AFM state is usually a condition, since, as mentioned, the contact field will not vanish in a FM material (but is present only in conducting compounds). The important point is that in an AFM spontaneous spin precession can be absent although LRO of the spin system exists. The strict consequence of (ii) would be a non-depolarizing pSR signal in ZF. But in nearly all cases the field distribution (iii) exists and Lorentzian Kubo-Toyabe patterns are seen instead. It is important to realize that the width of the Lorentzian Kubo-Toyabe patterns is not simply connected to the size of the magnetic moments the concentration and nature of faults enters dominantly. A randomness of these faults (though probable) is not required since the muon positions woidd in any case be randomly distributed relative to them. We finally point out that the width of the field distribution is rather small (about 8 G for UAs) and in many cases not significantly different from that produced by nuclear dipoles. A distinction between the two can be cumbersome in some cases. 

Fig. 64. Left Contact fields for 7 — 0 derived from the spontaneous precession ftequencies for various RT2 intermetallics. The solid line suggests a hnear dependence on the magnetic moment of the 3d ligand. Also shown are the results for Fe and Co metal (Denison et al. 1979). Right Spontaneous spin precession frequency as a function of temperature in TmFe2. The solid line shows the temperature dependence of bulk magnetization normalized to V (0). From Barth et al. (1986a).

Puzzling are the results for DyD2.i3, which according to bulk data should behave like HoD2.i2- Above 10 K up to room temperature the pSR signal is reduced in amplitude, the asymmetry rising monotonically from 0.02 to 0.13. Below 10K a spontaneous spin precession signal with 90 MHz is found, but its intensity does not explain the... 

In the ordered state, part of the fast relaxing signal component exhibits spontaneous spin precession for T < 9 K (i.e., in the commensurate AFM state) with only moderate depolarization (A 2 p.s ). The saturation precession frequency is V f (0) 183 MHz, corresponding to an internal field of 1.35 T. These values are of the same magnitude as those in AFM Ho and Dy metals (see fig. 33), which verifies a muon position close to... 

Fig. 78. Temperature dependences of spontaneous spin precession signals in AFM UNiGa (single crystal). The dotted lines indicate transitions within the AFM state, the iiill line r resents the N6el temperature. After Prokes et al. (1995).

Gubbens et al. (1995b) concentrated on the behavior of relaxation rates both above and below 7n in the c geometry. These experiments were carried out at the ISIS pulsed facility, which precludes the observation of spontaneous spin precession patterns above the... 

Fig. 87. ZF j,SR spectrum of UO2 at 6.2 K (left) and temperature dependence of the spontaneous spin precession frequencies (right). From Kopmann et al. (1998).

Fig. 111. xSR spectroscopy of CePdSn in the AFM regime (a) ZF spectrum containing two spontaneous spin precession frequencies (b) temperature dependence of those frequencies. After Kalvius et al. (1995c). 

Fig. 123. Temperature dependence of the spontaneous spin precession ftequencies in the ZF spectra of magnetic CeBj. Solid and open symbols refer to different runs. From Feyeriietm et al. (1994c).

The X = 0.13 sample has Tn = 4.2 K. Below this temperature, a fast (Lorentzian) Kubo-Toyabe relaxation is seen (see fig. 130, left), but no spontaneous spin precession. The authors use a field distribution based on the known ISDW magnetic structure calculated by dipolar smns for the (0, 5, ) stopping site they prefer. This theoretical depolarization function is shown in fig. 130 (left) and agrees roughly (but not in detail) with the measured spectrum (the discrepancy becomes worse at lower temperatures), and supports the notion of ISDW magnetism. 

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