MUON SPIN RELAXATION IN THE HEAVY FERMION SYSTEM

We report muon spin rotation/relaxation (µSR) measurements of the heavy fermion superconductor UPt 3 in external fields Hcnll2 We find that the muon Knight shift is unchanged in the superconducting state, consistent with odd-parity pairing (such as p wave). The transverse field relaxation is observed to be strongly field dependent, decreasing with increasing field. Below Tc the increase is barely detectable in an applied field of 4 kGllC. On the basis of the high field measurements, we estimate the low temperature penetration depth to be Ä.(T-0)>11000 A.

transverse field relaxation is observed to be strongly field dependent, decreasing with increasing field. Below Tc the increase is barely detectable in an applied field of 4 kGllC. On the basis of the high field measurements, we estimate the low temperature penetration depth to be Ä.(T-0)>11000 A.
There is a growing body of experimental evidence that shows that the heavy fermion system UPt 3 (Ref. 1) is a non-s-wave superconductor. Neutron scattering2 and heat capacity measurements detect strong spin fluctuations in the superronducting state, thougbt to favor anisotropic pairing (such as p or d wave). In addition, ultrasound velocity 3 and heat capacity 4 measurements have detected possible phase boundaries within the superconducting state. Tue existence of several superconducting phases has spurred the development of theories to identify the various states. In this vein, several authors 5 have suggested that UPt 3 possesses a multicomponent superconducting order parameter transforming according to a nonidentity representation of the hexagonal D 6 h group. There is still great uncertainty about the properties of UPt 3 : even the parity of the superconducting pair state has not been unambiguously determined.
Many properties of the superconducting state can reftect the underlying symmetry of the pairing. Among these are the spin susceptibility X and the magnetic field penetration depth Ä.. In an even parity (such as s wave) superconductor, the electrons are paired in states with opposite spin. Tue combined susceptibility of that pair is O; the measured spin susceptibility refiects that of the normal state electrons, approaching zero as the temperature approaches zero [following thc Yosida function Y(T)]. In odd parity superconductors, different susceptibilities are possible, depending on the pair wavefunction, and can be markedly different from the even parity case. For example, the triplet ABM and BW states of 3 He have susceptibilities XABMIXn = 1, XswlXn = j + ~Y(T), respectively, where Xn is the normal state susceptibility.
The magnetic field penetration depth A. describes the screening effects of the superconducting electrons. Its temperature dependence can also provide information about the pairing symmetry. 6 If there are nodes in the superconducting gap, characteristic of higher l pairing, thermal pair breaking will give rise to a power law temperature dependence in Ä.. By comparison, s-wave superconductors have no nodes in the gap, and as a result, the penetration depth shows little temperature dependence for T < T cf3.
Muon spin relaxation measurements are useful for deter.mining both A.(T) and X(T) simultaneously. 7 In a time differential µSR experiment, 100% spin polarized positive muons are injected individually into a specimen, where the m uon spins precess in the local magnetic field. Tue µ + decays (lifetime -r µ = 2.2 µs -1 ), emitting a positron, preferentially along the instantaneous muon spin direction. A histogram of positrons detected versus the time interval after implantation will exhibit the lifetime exponential decay superimposed on the muon spin polarization function. The "asymmetry," which is the ratio of the dilference and the sum of spectra from two opposing counters, is directly proportional to the muon polarization. Typically, in transverse field, the polarization function is given by where the frequency is given by the local field (J) = (rµ/21T')ß1oc and the relaxation rate u reftects the inhomogeneity in the local field. The local field can be different from the applied field due to a muon-conduction electron hyperfine interaction. The measured fractional shift in the muon precession frequency from this interaction is the sum of the muon Knight shift (Kµ,), Lorentz and demagnetizing shifts, and a diamagnetic shift in the superconducting state; and is given by
x (x10-J emu/mole) Comparing measurements of the muon Knight shift with those of the de susceptibility (both with the field applied along the c axis), we sec a similar temperature dependence; plotting K,,. vs X in Fig. 1, we obtain a linear relationship. Since the susceptibility in the basal plane displays a different temperature dependence, 1 we see that the muon K.night sbift reßects the susceptibility for fields along the c axis. The susceptibility x is largely due to the spin susceptibility xs; extrapolating to Xs = 0, we find Kµ.(Xs = 0) = + 0.13%. The slope of the K,,. vs x curve gives us a byperfine fi.eld of about -4.2 kG/µ 8 . This is substantially larger (and of opposite sign) than reported in previous measurements of polycrystalline UPt 3 , 8 which is not surprising in view of the strong anisotropy of X in UPt 3 .
Upon cooling through Tc :::::: 0.45 K, we see that there is no discemable change in K,,.. The measured shift, shown in Fig. 2(b), remains about -0.3%, of which about -0.12% comes from Lorentz and demagnetizing shifts ( which likc the Knight shift are proportional to X). Diamagnetic contn"butions to the shift [4nxd( 1 -n)] due to superconductivity are negligible since n is near to 1 in our geometry and Xd is small in high fields. We therefore conclude that the spin susceptibility is unchanged below Tc· This is in agreement with 195 Pt-NMR (Ref. 9) and induced moment form factor measurements. 10 In addition to measuring the frequency of the precession signal, we have simultaneously determined the relaxation rate u(T) for several fields <H112> up to 3.9 kG. The inhomogeneity in the local fields from the vortex lattice 11 13 Plotting the field dependence of the increase in tbe relaxation rate below Tc [inset of Fig. 2(a)], we see that there is a reasonably smootb decrease in u with increasing applied field. We expect that u should be field independent over a large range of fields between H c 1 and Hc2 (Refs. 11,12) in order to extract A.. If the measured inbomogeneity is fi.eld dependent it generally implies that the measured relaxation does not accurately reflect the penetration depth. In this case, the value of 11 000 A can only serve as a lower bound for the penetration depth, wbich may in fact be much longer.
There are several possible sources of increased broadening on low fields that could account for the enhanced relaxation. One of these is flux pinning, acting to prevent formation of a uniform fiux lattice. Zero field cooled measurements in 3.9 kG show greatly enhanced relaxation, characteristic of strong flux pinning. Other possible sources of low field broadening below Tc include proximity to Hc 1 and s hape-dependent inhomogeneities in the demagnetizing factor. 14 Ultrasound measurements 3 have detected an anomaly in UPt 3 around H = 12 kG (for HJIC). lt has been suggested that this anomaly indicates a phase boundary between different superconducting states. There is a possibility that our field-dependent relaxation may be related to this anomaly. However, we are prevented from accessing the feasibility of such an effect by a lack of theoretical understanding of the superconducting states of UPt 3 • Nevertheless, we note that all of these µ,SR measurements lie in the London limit, where we do not expect significant field dependence in the relaxation rate.
In conclusion, we find that the muon Knight shift is uncbanged in the superconducting state of UPt 3 , supporting the idea of odd-parity pairing. Although it is possible for spin orbit scattering to reduce changes in the Knight shift. ts we would argue the the long mean free path (/-1000 A in UPt 3 (Ref. 16)) suggests that scattering is not im.portant here.
We estimate that the low temperature penetration depth is in excess of 11 000 A, roughly consistent with the estimate from a Oux confinement measurement [A.(0)-19000 Ä.]. 17 Since the penetration deptb ...t o:: m*lns and the effective mass is large [e.g., cyclotron effective mass m-c = 25 -+ 90m, (Ref. 16)], we expect i1. to be rather large. The change below T" in relaxation rate is so small in high fields tbat is is not possible to discuss its temperature dependence in terms of different possible gap node structures.