Magnetism and candidate muon-probe sites in RBa2Cu3O y

Key results of zero-field (ZF) and transverse-field (TF) muon-spin-relaxation (μSR) experiments on superconducting and insulating RBa₂Cu₃O _y (R123 _y , with R=Eu, Gd, Pr and Pr/Y:y=6, 7) are examined. The chemical behavior of the positive muon probe is addressed, and muon-oxygen bonding is shown to occur in all these cuprates. To explain magnetic fields at muon-probe sites in Pr _x Y_1−x Ba₂Cu₃O _y (0<=x<0.5,y=7 andx=0,y=6) samples, improvements on the reported magnetic structures from neutron diffraction are necessary. Cu magnetism in Pr123y (y=6,7) is observed belowT _N1, which is near RT. The magnetism seen belowT _N2 can be interpreted assuming an additional ordering in the Cutt-O chain layers. Alternatively, Pr ordering is also considered as the cause of the second phase transition. Considering the specific muon-probe location, a more detailed interpretation can be provided for the μSR parameters, measured in the normal and mixed states of these unconventional superconductors.     

Positive muon sites and possibility of anyons in the YBa2Cu3O x system

Possible positive muon sites in YBa₂Cu₃O _x were determined from the observedμ ⁺ hyperfine fields in antiferromagnetically ordered YBa₂Cu₃O _x and GdBa₂Cu₃O₇. After determining theμ ⁺ sites, the possibility of anyons or chiral spin ordering in the superconducting YBa₂Cu₃O₇ is discussed. Positive muon implanted in YBa₂Cu₃O₇ feel static magnetic fields of average 1.4G, which are explicable in terms of nuclear magnetic dipolar fields. Non observation of static local magnetic fields of electronic origin (the upper limit is the order of 0.1 G) means that anyons or chiral spin ordering might not exist in superconducting YBa₂Cu₃O₇.     

Dual features of magnetic susceptibility in superconducting cuprates: a comparison to inelastic neutron scattering

Starting from the generalized t−J−G model Hamiltonian, we analyze the spin response in the superconducting cuprates taking into account both local and itinerant spin components which are coupled to each other self-consistently. We demonstrate that derived expression reproduces the basic observations of neutron scattering data in YBa₂Cu₃O_6+y compounds near the optimal doping level.     

The superconducting properties of YBa2(Cu1−xMx)3O7 for M=Zn and Ni

Transverse and zero-field μSR measurements were made on YBa₂(Cu_1−xNi_x)₃O_7−y withx=0.1 and 0.2, and YBa₂(Cu_1−x Zn _x )₃O_7−y withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained, and the low temperature values of these are σ=3.2 μs⁻¹.1.6μs⁻¹, and 1 μs⁻¹ forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs⁻¹, 0.75 μs⁻¹, 0.65 μs⁻¹, and 0.4 μs⁻¹ forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made, but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect of scattering.     

Homogeneous VS. Inhomogeneous spin freezing in pure and au-dopedCuMn

Zero-field μSR provides clear evidence for a spatially inhomogeneous spin freezing in the spin glass systemCuMn. To test a spin glass with very different properties with respect to this characteristic, we investigatedCuMn samples doped with Au. The freezing process, as observed by μSR, was found unaffected.     

Interplays ofμSR,susceptibility and neutron studies on dilute-alloy spin glasses

Static spin polarization of Fe moments in a spin glassAuFe, determined by zero-fieldSR, is compared to an ac-susceptibility measurement below the cusp temperatureT _g, and a rather uniform amplitude of the static polarization is pointed out for frozen spins. Completely random orientation of frozen spins is revealed by neutron scattering in a dilute 1%CuMn, and an importance of comparing results of these different methods is demonstrated.     

Features of the superconducting state and structural disorder in ultrafine particles of the HTSC YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>

We study the reasons for which the compound YBa₂Cu₃O _y begins to lose its superconducting ability with a decrease in particle sizes to values of ∼0.1 μm. Our analysis of the results of structural and magnetic studies has allowed us to reveal changes in the parameters of the crystal structure and of the superconducting state in small particles of an HTSC and to show that the main cause of these changes is a special kind of a structural disorder peculiar only to small particles of YBa₂Cu₃O _y and is realized as a consequence of the need for nonequilibrium conditions during their synthesis.     

Local magnetism in superconducting YBa2Cu3O6+x

Oxygen-deficient YBa₂Cu₃O_6+x samples were investigated by the muon spin rotation technique in zero external field. In an intermediate oxygen concentration region we find strongly relaxing μSR signals indicating the existence of internal magnetic fields. The strongly relaxing signals were observed only in samples with superconducting transition temperatures below 50 K. As an interpretation of the data we suggest that magnetic ordering and superconductivity coexist in these samples within regions of extensions of a few lattice constants, but not necessarily on the same sites.     

μ+SR studies on superconducting YBa2(Cu1−xFex)3Oy system

Spin-glass like magnetic ordering of iron moments was observed in both orthorhombic and tetragonal YBa₂(Cu_1−xFe_x)₃O_y (x=0.08) by μ⁺SR measurements. In a “Tetra” sample, all the muons sense the superconducting transition at 60 K and magnetic ordering at around 15 K, while in an “Ortho” sample they reveal that two magnetically different parts exist in the sample: about 40% of the sample is superconducting withT _c ≈90K and the remaining part is magnetic withT _M≈33K. These phenomena can be explained in terms of clustering of the Fe atoms in the “Ortho” sample.     

μ− SR studies of oxide-superconductorsSR studies of oxide-superconductors

The negative muon spin rotation method (μ⁻ SR) has been applied to studies of electronic states at oxygen sites of oxide superconductors YBa₂Cu₃O₇, Nd_2−x Ce _x CuO_4−δ (x=0.15, oxygen reduced), LiTi₂O₄ and related oxide-insulators La₂CuO_4−δ, CuO, Cu₂O. The paramagnetic shifts of μ⁻ trapped at oxygen nuclei in these polycrystalline powder samples have been measured at 300 K. All the measured shifts are positive. In copper-oxides the paramagnetic shifts are of the order 10⁻³, while in LiTi₂O₄ is very small (8.4±3.34×10⁻⁵). In YBa₂Cu₃O₇, a fast μ⁻ spin relaxation timeT ₂ ^* (∼ 200 ns) has been observed; the reason for this is unknown and further studies are now in progress.     

μSR Study of the Unusual Magnetic Ordering in the Frustrated Antiferromagnet Zn(Cr x Ga1−x )2O4

μSR spectra on the spin frustrating spinel antiferromagnet Zn(Cr _x Ga_1−x )₂O₄ (x=0.9,1.0) have been measured. For x=1.0 compound, both the relaxation rate and the initial asymmetry showed distinct anomalies at the Néel temperature. The magnetic susceptibility for the x=0.9 compound was known to have a faint peak at around 12 K, whose origin was not clear so far. Our μSR study revealed that this temperature is the onset temperature of development of the magnetic correlation accompanied by appreciable spin fluctuations. This revised version was published online in September 2006 with corrections to the Cover Date.     

Tendencies toward nematic order in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6+δ</Subscript>: Uniform distortion <Emphasis Type="Italic">vs.</Emphasis> incipient charge stripes

Recent neutron scattering and transport data obtained on underdoped YBa₂Cu₃O_6+δ, with strong signatures of rotation symmetry breaking at low temperatures, point toward electron-nematic order in the charge sector. Such order may originate from a uniform distortion with d-wave symmetry or as a precursor of a uni-directional stripe phase. Here, we discuss whether the neutron scattering data can be linked to incipient charge stripes. We employ and extend a phenomenological model for collective spin and charge fluctuations and analyze the resulting spin excitation spectrum under the influence of lattice anisotropies. Our results show that the experimentally observed temperature-dependent magnetic incommensurability is compatible with a scenario of incipient stripes, the temperature dependence being due to the temperature variation of both strength and correlation length of the charge stripes. Finally, we propose further experiments to distinguish the possible theoretical scenarios.     

Anisotropy inc-axis oriented YBa2Cu3O7−δ

Muon spin relaxation (μSR) data taken at LAMPF on ac-axis oriented fine powder sample of YBa₂Cu₃O_7−δ (YBCO) embedded in epoxy are analyzed for relaxation rate anisotropy. Clear differences beyond simple magnetic field penetration depth anisotropy are observed forB‖c andB c. The low-temperature anisotropy ratio is consistent with oriented ceramic data. Small crystallite size and anisotropic flux pinning characteristics are suggested as the fundamental cause of the additional effects.     

Search for magnetic order in undoped and doped spin‐gap systems by μSR

We introduce our μSR investigations of spin‐gap systems, such as, (1) a 2‐leg spin‐ladder material SrCu₂O₃, (2) a Haldane material (S=1 spin‐chain) Y₂BaNiO₅, (3) a spin‐Peierls material CuGeO₃, (4) a spin‐chain# material Sr₆Ca₈Cu₂₄O₄₁. All of these antiferromagnetic spin systems are characterized by a spin‐gap between the singlet ground‐state and the triplet first excited states. In the above‐mentioned materials, we confirmed the absence of magnetic order down to milli‐Kelvin regime, supporting the non‐magnetic feature of the ground‐state. If a spin‐gap system is doped with charges and/or vacancies at the spin site, unpaired spins are induced out of the singlet ground‐state. In some materials, doping completely destroys the singlet ground‐state and induces a bulk magnetic order. We report μSR investigations of doped materials as well, which clarifies the existence/absence of a magnetic order upon doping. This revised version was published online in July 2006 with corrections to the Cover Date.     

A muon spin rotation study of hydrogen in YBa2Cu3O y

Superconducting YBa₂Cu₃O _y samples were doped with hydrogen and investigated by the muon spin rotation technique. For hydrogen concentrations above a thresholdx, which depends on the oxygen stoichiometry, we find a well defined precession signal in zero external field. This is a clear indication of magnetic ordering in these samples. In samples with a smaller hydrogen content no magnetic ordering was found. For these samples however, the depolarization rate σ(T→0) as measured in a transverse external field depends strongly on the hydrogen content. Our data are consistent with the assumption that hydrogen acts as an electron donor, filling the hole states in YBa₂Cu₃O _y .     

Spin gap systems: What can be measured by muon spin relaxation?

Muon spin relaxation (μSR) and nuclear magnetic resonance (NMR) are powerful probes of magnetism, which have been extensively applied to studies of spin gap systems. Comparison of results obtained with the two techniques gives complementary results, as each is sensitive to different aspects of spin gap magnetism. We discuss recent μSR measurements of the spin ladder compounds Sr _n?1Cu _n+1O_2n , pure and doped Haldane materials (Y_2?x Ca _x )Ba(Ni_1?y Mg _y )O₅, and doped spin Peierls compounds (Cu_1?x Zn _x )(Ge_1?y Si _y )O₃.     

Neutron scattering and μSR

The paper discusses the characteristics of neutron scattering andSR in order to find the collaborating works with both techniques. The discussions are made on four subjects, random spin systems, itinerant electron magnetism, surface and real time spectroscopy, with some detailed discussions on the cluster spin glass 88FeTiO₃-12Fe₂O₃ and itinerant ferromagnet MnSi, for which the collaboration has yielded the fruitful results.Finally I would like to thank T. Yamazaki, K. Nagamine and Y.J. Uemura for crucial discussions on the SR and Y. Endoh for discussions on the neutron scattering.     

The μSR study of the relaxation of Ho and Er magnetic moments in high-Tc 1-2-3 compounds

High temperature superconductors HoBa₂Cu₃O_7−δ (T _c ≅93 K), Ho_0.5Y_0.5Ba₂Cu₃O_7−δ (T _c ≅93 K) and ErBa₂Cu₃O_7−δ (T _c ≅95 K) were investigated by the zero-field μSR-technique. The muon spin depolarisation rate connected with the fluctuation frequency of rare-earth ion magnetic moments was measured. It was found that the samples with holmium show a fast increase of the muon spin depolarisation rate at temperatures below 20 K, while in ErBa₂Cu₃O_7−δ the depolarisation rate remains low in the whole temperature region studied (4.2 K-270 K). The sharp difference between the behaviours of the muon spin depolarisation rate may be explained by the difference between the ground state of Ho³⁺ and Er³⁺ ions in the crystalline field of the lattice.     

Zero-field μSR study of ErBa2Cu3Ox for various oxygen contentx

Results from zero-field μSR experiments are presented, performed on the high-T _c compounds ErBa₂Cu₃O_x for various oxygen contentx with 6≤x≤7 at temperatures between 40 mK and 300 K. The aim was to study the magnetic ordering behavior of the Cu moments and the Er moments, and its interplay with superconductivity.     

Frustration driven magnetic states of A-site spinels probed by <Emphasis Type="Italic">μ</Emphasis>SR

The normal A-site spinels MnAl₂O₄, FeAl₂O₄, CoAl₂O₄, as well as related mixed (Mn_0.5Fe_0.5Al₂O₄) and partially inverted (Fe_1.4Al_1.6O₄) spinels have been studied by μSR. The magnetic ions are subject to magnetic frustration by competing interactions. In all materials and at all temperatures the μSR spectra consist of two signals suggesting a bimodal distribution of the fluctuation rates of magnetic moments. A characteristic temperature T _M is found in each compound, representing either a magnetic phase transition into a long-range ordered state (MnAl₂O₄, Fe_1.4Al_1.6O₄) or the formation of a spin liquid phase (FeAl₂O₄, CoAl₂O₄, Mn_0.5Fe_0.5Al₂O₄). The magnetic ground state of MnAl₂O₄ shows coexistence of antiferromagnetic and spin liquid phases. In FeAl₂O₄ and CoAl₂O₄ long-range order is suppressed altogether, the ground state can be characterized as a fast relaxing spin liquid coexisting with a small fraction of paramagnetic spins. The partial replacement of Mn by Fe in Mn_0.5Fe_0.5Al₂O₄ prevents long-range order and leads to a spin liquid state in the low temperature limit. The partial occupancy of B-sites by magnetic ions in Fe_1.4Al_1.6O₄ strengthens the exchange coupling, allowing the formation of long-range magnetic order at a rather high temperature (~100 K). Magnetic phase diagrams are presented demonstrating that for the studied compounds the magnetic properties are determined by the degree of frustration.