NMR and other magnetic resonance techniques in unstable magnets

This paper reviews and compares the use of nuclear magnetic resonance (NMR) and related hyperfine techniques [muon spin rotation (μSR) and, to a lesser extent, other methods] in the study of 4f and 5f magnetism in “unstable magnets”, i.e., intermediate-valent and heavy-fermion materials. In both NMR and μSR the features of interest are the spectral shape, the frequency shiftK (Knight shift in metals) and the spin-lattice relaxation rate 1/T ₁. For temperatures below the characteristic or “Kondo” temperatureT ₀ these experiments given evidence for (1) modification of the transferred hyperfine field [nonlinearK(χ)]. (2) spin fluctuations with a characteristic fluctuation rate ∼k _B T ₀/h, (3) strong energy-gap anisotropy (zeros of the gap along lines on the Fermi surface) in heavy-fermion superconductors, (4) spin-singlet Cooper pairing from the change in muon Knight shift in superconducting UBe₁₃, and (5) very weak static magnetism (10⁻¹–10⁻³ μ_B/f atom) in CeAl₃, CeCu₂Si₂, U_1−x Th _x Be₁₃ (x=0.033), and UPt₃. There is some controversy concerning the interpretation of 1/T ₁ well aboveT ₀ in UBe₁₃; the situation is reviewed.     

Phenomenological model of superconductivity in U1−xThxBe13

A phenomenological model taking into account the interaction between superconductivity and the coherence of Kondo screening is introduced. This model describes the main experimental data on UBe₁₃, including the behaviour of T_c in U_1−xTh_xBe₁₃ under ambient and elevated pressures.     

Recent applications ofμ+SR in magnetism: Novel magnetic features inheavy electron compounds

As an example for the power ofμ ⁺ SR-spectroscopy in solid state physics three applications to heavy electron systems, i.e. CeAℓ₃, U_1-x Th _x Be₁₃ and UCu₅ will be discussed. Each of these systems reveals very specific magnetic features of unusual characteristics which involve very small to extremely small magnetic moments and random or very short range magnetic order. This kind of small moment magnetic order can be studied relatively easily by μSR but will be hardly accessible by other methods such as neutron scattering. This paper is dedicated to Prof. G. zu Putlitz on the occasion of his 60th birthday     

A comparative study of the magnetic heavy-electron materials U2Zn17 and UCu5 by μ+SR

A systematic μ⁺SR study of the magnetic heavy-electron systems U₂Zn₁₇ and UCu₅ in the paramagnetic and in the magnetically ordered state is presented. In both systems the antiferromagnetic nature of the low-temperature phase could be at least partially confirmed, but the muon reveals significant differences with regard to the phase transition itself. UCu₅ behaves like a model-antiferromagnet showing a drastic increase of the relaxation rate both below and above T_N, two spontaneous frequencies in the ordered phase, and a Knight shift above T_N which scales with the bulk susceptibility. In contrast U₂Zn₁₇ shows a loss of μ⁺ asymmetry by 20% below T_N, which is independent of the external field but can be quenched in sufficiently strong longitudinal fields. No scaling of the Knight shift and the susceptibility was observed and no critical increase of the relaxation rate λ. Most astonishing is the strong and nonlinear field dependence of λ above and below T_N in both compounds. The absence of longitudinal relaxation demonstrates the static origin of λ.     

Muon spin relaxation and knight shift in the heavy-fermion superconductor UPt3

Positive muon spin relaxation experiments have been conducted on the heavy-fermion superconductor UPt₃ in both the normal and superconducting states for zero, transverse, and longitudinally applied magnetic fields. Below 6 K in zero applied field, the μ⁺ relaxation rate is approximately twice that expected from¹⁹⁵Pt nuclear dipolar relaxation alone. Transverse- and longitudinal-field measurements show that the observe relaxation rate depends on magnetic field and is quasistatic in origin. It is suggested that the onset of very weak (≈10⁻³ μ_B/U atom) magnetic ordering below approximately 6 K is responsible for the observed increase in the relaxation rate. μ⁺ Knight shift measurements in the normal state of UPt₃ show a temperature dependent shift K_μ which tracks the bulk susceptibility X. From the K_μ vs. X plot, a μ⁺ hyperfine field of approximately 100 Oe/μ_B is extracted.     

Magnetism and superconductivity in the ErBa2Cu3OA system

Transverse field μSR studies of the system ErBa₂Cu₃O_x with x=6.4, 6.53 and 7 reveal a split signal with each component displaying a distinct paramagnetic or Knight shift related to the Er 4f-moments. This implies the presence of transferred hyperfine fields even in the superconducting state.     

Composite spin-triplet superconductivity in an symmetric lattice model

The two-channel Anderson lattice model which has SU (2) ⊗ SU (2) symmetry is of relevance to understanding of the magnetic, quadrupolar and superconducting phases in U_1-xTh_xBe₁₃ or Pr based skutterudite compounds such as PrFe₄P₁₂ or PrOs₄Sb₁₂. Possible unconventional superconducting phases of the model are explored. They are characterized by a composite order parameter comprising of a local magnetic or quadrupolar moment and a triplet conduction electron Cooper-pair. This binding of local degrees of freedom removes the entropy of the non Fermi-liquid normal state. We find superconducting transitions in the intermediate valence regime which are suppressed in the stable moment regime. The gap function is non analytic and odd in frequency: a pseudo-gap develops in the conduction electron density of states which vanishes as |ω| close to ω = 0. In the strong intermediate valent regime, the gap function acquires an additional -dependence. Received 28 February 2002 / Received in final form 18 April 2002 Published online 9 July 2002     

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu_2.1Si₂, the relaxation rate of muon spins increases rapidly with decreasing temperature below T_C. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5T_C, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift K_μ in the normal (or paramagnetic) state of various heavy-fermion systems. K_μ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu₂Si₂, UPt₃ and CeAl₃, while more complicated signals are measured in CePb₃ and CeB₆. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.     

London field penetration in heavy fermion superconductors

We present results of a series of high resolution, low fielddc-magnetization measurements on the heavy fermion superconductors UPt₃, UBe₁₃, U_1–x Th _X Be₁₃ and CeCu₂Si₂, from which values of the magnetic penetration depth can be extracted. A study of the temperature variation reveals aT ² power law in all cases. This can not be reconciled with a BCS-like isotropic energy gap but may be explained by the presence of low energy quasiparticle states inside the gap. In the case of very pure superconductors, one such possibility is the assumption of point-nodes in the gap function. We argue, however, that an interpretation in terms of resonant impurity scattering in various anisotropic superconducting states is more likely to explain a broad range of experimental data. The results on differently oriented single crystals of UBe₁₃ and UPt₃ reveal no pronounced anisotropy related to the crystal lattice. Absolute values of atT=0 are deduced by a novel method in which the field is first screened out from the sample by means of an evaporated superconducting film (of lowerT _c ). Above this lowerT _c the sudden penetration of field into the sample can then be measured absolutely.     

Diamagnetism and muon knight shift in semimetallic and semiconducting BiSb single crystals

A series of single crystalline Bi_1−x Sb _x alloys (x=0,0.03, 0.14, 0.19, 0.37) covering both the semimetallic (0≤x≤0.07 orx≥0.22) and the semiconducting region (0.07≤x≤0.22) was examined using the stroboscopic μ⁺ SR method. The μ⁺ Knight shift, negative for all Sb concentrations, shows pronounced temperature dependences and large anisotropies. A scaling with the-negative-total magnetic susceptibility [1] is found in the semiconducting alloys. In detail, the isotropic part of the μ⁺ Knight shift is proportional to the isotropic part of the susceptibility, and the anisotropic Knight shift scales with the anisotropic susceptibility. Possible mechanisms leading to this relation are investigated.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.     

Heavy-ion irradiation of UBe13 superconductors

We irradiate the heavy fermion superconductors (U,Th)Be₁₃ with high-energy heavy ions. Damage from the ions affects both heat capacity and magnetization measurements, although much less dramatically than in other superconductors. From these data and from direct imaging, we conclude that the irradiation does not create the amorphous columnar defects observed in high-temperature superconductors and other materials. We also find that the damage suppresses the two superconducting transitions of U_0.97Th_0.03Be₁₃ by comparable amounts, unlike their response to other types of defects.     

μSR-Study of CeH2.7

Metallic CeH_2.7 shows a sizably increased electronic specific heat of γ=100 mJ/mol·K², compared to γ=0.04 mJ/mol·K² in LaH_2.7 at low tempratures, which could qualify it as another heavy electron system. μSR Knight shift and relaxation studies were started on a powderous CeH_2.7 sample in order to test this possibility further. It is found that the relaxation rate λ_T depends strongly on the applied field strength. These values indicate that the relaxation must be of electronic origin. Strong irreproducibilities at low temperature point to pronounced hysteretic features, which might be related to structural changes. The Knight shift shows a shallow peak around 150 K but no conspicious increase at low temperatures.     

237Np Mössbauer Investigations of (U1−x Np x )2Rh2Sn

Surprisingly, Np₂Rh₂Sn does not order magnetically whereas the uranium counterpart U₂Rh₂Sn orders antiferromagnetically at 24 K with a 5f moment μ _U ≈0.38μ _B . We have investigated the magnetic and electronic properties of (U_1−x Np _x )₂Rh₂Sn solid solutions. For x=0.25 and 0.5, the ordering temperature decreases to 11 K whereas the Np-rich compound (x=0.75) shows the onset of magnetic order around T≈6 K. The average Np magnetic moment amounts to 0.84 μ _B ,0.83μ _B and 0.25 μ _B respectively. The isomer shift slightly decreases, from −9.6 mm/s to −10.4 mm/s (versus NpAl₂) as x increases. The values of the quadrupole interaction parameter in the ordered and paramagnetic state suggest that Np moments are parallel to c for x=0.25 and then rotate to the basal plane for higher x. This revised version was published online in September 2006 with corrections to the Cover Date.     

μSR experiments in heavy electron systems

The salient features of heavy electron systems are reviewed and the advantages and disadvantages of the μSR technique for studying heavy electron properties are discussed. Three current areas of heavy electron physics are emphasized: the symmetry of the superconducting state, the interplay of magnetism and superconductivity, and the role of impurity substitutions in changing heavy electron properties. Experiments in (U, Th) Be₁₃, URu₂Si₂ and UPt₃ are discussed.     

Nuclear and muon hyperfine techniques in the study of heavy-fermion superconductors

Nuclear magnetic resonance and relaxation, and the related techniques of muon spin rotation and relaxation, have been used to study local spin polarization and quasiparticle excitations in the heavy-fermion superconductors CeCu₂Si₂, pure and thoriated UBe₁₃, and UPt₃. Measurements of nuclear and positive muon Knight shifts, linewidths, and spinlattice relaxation rates give some hints as to the nature of Cooper pairing in these exotic materials.     

Spin-lattice relaxation and Knight shift on protons in the hydrogen-doped superconducting system H0.2La1.8Sr0.2CuO4

Measurements of the spin-lattice relaxation rate and Knight shift on protons in hydrogen-doped superconducting H_0.2La_1.8Sr_0.2CuO₄ samples are performed in the temperature range 4.2–300 K. An anomalous behavior of the spin-lattice relaxation rate is observed at low temperatures T∼20 K. A model is constructed that explains the appearance of carrier-depleted regions in the bulk of the semiconductor on the basis of the formation of a charged defect (proton). Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 533–538 (10 April 1996)     

Anomalous anisotropies and field dependencies of the muon Knight shift and the relaxation rate in monocrystalline Bi

The angular dependence of the muon Knight shift,K _μ, and the muon relaxation rate in Bi at 11 K were measured in external magnetic fields up to 1 T. BothK _μ and the second moment,M ₂, are field dependent and involveP ₄ ⁰(cos θ) andP ₄ ³(cos θ) terms in the angular dependence. The Knight shift behaviour is discussed in terms of the dipole-dipole interaction and the de Haas-van Alphen effect, a consistent interpretation was not achieved in either case. The field dependence ofM ₂ is in complete contrast to the second moment calculations and points to a field dependent redistribution of the charge distribution around the interstitial site.