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We investigated a three-dimensional frustrated 3d-electron magnet on a pyrochlore-like lattice Ni2(OH)3Cl with s = 1 by means of 1H-NMR measurements. Previous specific heat measurements reported that this material shows a phase transition at 4.0 K and also has an anomaly at around 20 K. Our 1H-NMR measurement in 0.73 T has demonstrated that both the spin-lattice relaxation rates T1−1 and the spectra show clear evidences of a magnetic long-range ordering below 4.0 K. However, they do not show any anomalies at 20 K. By contrast the width of the 1H-NMR spectra in 4.3 T starts to deviate from linearity to the magnetization below 20 K, which suggests that the magnetic anisotropy is induced by the magnetic field. In addition, T1−1 starts to decrease below 20 K, which indicates the suppression of spin fluctuation. We discuss the unusual spin state below 20K.

A pyrochlore lattice is a three-dimensional corner-sharing network of tetrahedra. Spin systems on pyrochlore lattices exhibit several exotic magnetic properties, such as spin ice, spin liquid and order by disorder, due to macroscopic degeneracy caused by geometrical frustration, depending on whether the interactions are ferromagnetic or antiferromagnetic, whether the spin system is classical or quantum, the symmetry of the spin space and the kinds of additional interactions. We survey the magnetic behavior of spin systems on pyrochlore lattices and present nuclear-magnetic-resonance (NMR) studies on the quantum Heisenberg antiferromagnets consisting of magnetic 3d transition metal ions Cu 2 (OH) 3 Cl and Ni 2 (OH) 3 Cl with spin 1/2 and 1, respectively. Cu 2 (OH) 3 Cl exhibits successive phase transitions at 18.1 and 6.4 K. The NMR spectra and spin–lattice relaxation rates indicate curious static and dynamic properties that appear to conflict. The coexistence of freezing and quantum fluctuation of spins a...

27Al NMR measurements of an intermetallic compound PrPtAl were performed to study the unusual properties above TC (5.8 K). A distinct enhancement of relaxation rate below 50 K was observed. This suggests that ferromagnetic ordering in this singlet ground state magnet is mainly driven by the development of the so-called central peak rather than softening effect of the magnetic excitations.

1H NMR measurements of 3d electron three-dimensional frustrated systems, Co2(OH)3Cl with s = 3/2 and Cu2(OH)3Cl with s = 1/2 have been performed. The relaxation rates T-11 of both compounds suggest the development of spin correlations at much higher temperatures compared with the magnetic transition temperatures. The temperature dependence of T-11 below 6 K of both compounds indicates the magnetic ordering and the existence of magnon excitations. The estimated magnon energy gaps are 13 K and 27 K for Cu2(OH)3Cl and Co2(OH)3Cl, respectively, which are consistent with the inelastic neutron experiments. The intermediate phase between TN1 = 18.1 K and TN2 = 6.4 K for Cu2(OH)3Cl shows the conflicting behaviors which are the coexistence of the freezing of the moments and the paramagnetic spin dynamics. The partial freezing and the time scale of spin dynamics should be crucial to understand these frustrated systems.

11B NMR and magnetic susceptibility measurements have been performed in order to investigate the spin dynamics of a triangular-lattice XY antiferromagnet UNi4B. In this compound, the partially ordered state appears below TN = 20 K with a peculiar vortex-like structure. Magnetic susceptibility shows that TN is slightly lower than the round maximum of the magnetic susceptibility suggesting the two dimensional character of this compound. The temperature dependence of the relaxation rate T-11 above TN is well reproduced by the theoretical model that were discussed in the Kosterlitz-Thouless-Berezinskii transition. Thus the temperature dependence of T-11 suggests that the spin dynamics in UNi4B above TN is dominated by the motion of the unbound vortices.

The family of layered organic salts X[Pd(dmit)2]2 are Mott insulators and form scalenetriangular spin-1/2 systems with antiferromagnetic exchange interactions J. Among them, EtMe3Sb[Pd(dmit)2]2 has a nearly regular-triangular spin system with J = 220-250 K. Our previous study proposed that a quantum spin-liquid state is realized in this system because this system was revealed to have neither spin ordering/freezing nor an appreciable spin gap down to 1.37 K. In the present study, to confirm the absence of spin ordering/freezing in the low-temperature limit, we cooled this system down to 19.4 mK, which is 4 orders of magnitude smaller than J, and measured 13C-NMR spectra. The obtained spectra do not show any critical broadening. Therefore, it is concluded that the spin system of EtMe3Sb[Pd(dmit)2]2 does not have spin ordering/freezing in the low-temperature limit; that is, the spin system is in a quantum-fluctuating spin state.

Nuclear magnetic relaxation rate T−11 of 27Al has been measured down to 30 mK in heavy-fermion antiferromagnet CePdAl. Below T N , T −1 1 does not show any anomalies which are ascribed to the second-phase transition observed by previous neutron diffraction measurements. Korringa relation is observed below 0.4 K showing that one-dimensional Ce chains in this compound are in heavy-fermion states.

A triangular antiferromagnet UNi4B experiences a partially disordered state, in which two-thirds of U 5f moments order in a vertex-like structure and one-third of U 5f moments remain paramagnetic. Magnetization and NMR measurements of UNi4B have been performed to study the dynamical properties of U magnetic moments in the partially disordered state. The value of the effective moment above TN derived from the fitting of the Curie–Weiss law suggests a significant crystal field splitting and the Kondo effect. The Weiss temperature was also estimated to be −28 K, which suggests that the exchange interaction is antiferromagnetic. Furthermore, the exchange interaction estimated from the relaxation rate T1−1 above 50 K is 18 K, which is close to the Weiss temperature. These results suggest that the dominant interactions between U moments are antiferromagnetic in the basal plane. The relaxation rate T1−1 decreases abruptly below TN down to 15 K and is almost constant between 10 and 15 K. In the same temperature range, the magnetic susceptibility still increases with decreasing temperature. However, the effective moment estimated below TN is almost the same as that above TN. This shows that there are anomalous fluctuations below TN which cannot be explained by the simple model.

Jarosite, KFe 3 (OH) 6 (SO 4 ) 2 , is a typical example of a classical frustrated antiferromagnet with s = 5/2 Fe 3+ ions on the Kagome lattice, and a metallic complex, [Cu 3 (titmb) 2 (CH 3 CO 2 ) 6 ]·H 2 O, abbreviated as Cu-titmb, is considered to be a candidate material for a quantum frustrated magnet with s = 1/2 on the Kagome lattice. Jarosite has a Weiss temperature of -530 K and shows magnetic ordering below 65 K due to weak anisotropy. The magnetic structure in the ordered phase has been determined, using neutron scattering and NMR, to be a q = 0 type 120° spin structure with + chirality. The nuclear spin-lattice relaxation rate T -1 1 and the spontaneous magnetization indicate the existence of the spin wave in the ordered phase. A small number of substitutions or deficiencies induce successive phase transitions, which represent two-dimensional ordering on the Kagome planes and three-dimensional ordering between the planes. For the quantum spin magnet, Cu-titmb, the nuclear spin relaxation at low temperatures shows the existence of anomalous low-lying excited states in the magnetic field. The relaxation rates at high temperatures give much smaller exchange interaction compared to the value estimated from the specific heat. Several interesting properties, such as double peaks of the specific heat, a 1/3 magnetization plateau for the pulse field and a ferromagnetic transition at 56 mK have been reported. We review the experimental results of Cu-titmb.

Powder neutron-diffraction measurements of the frustrated kagomelattice antiferromagnets Na- and K-jarosites (AFe3(OH)6(SO4)2: A = Na and K) were carried out. The determined magnetic structure at 10 K is the so-called q = 0 structure and found to be different from one reported previously for K-jarosite. The intensities of magnetic reflections show slow decreasing with increasing temperature near TN and seem to imply successive phase transitions observed in a recent NMR study.

55Mn NMR in CsMnI3 was investigated at 1.3 K to study the spin structure in a triangular lattice Heisenberg antiferromagnet. It was found that the rotation of the triangular spin plane around the c-axis survives below TN2 with canting angle 56.6° and induces the frequency pulling in 55Mn NMR.

In order to clarify the magnetic properties of an Yb-monopnictide YbAs from a microscopic point of view, nuclear magnetic resonance and relaxation studies on 75 As have been carried out at low temperatures down to 20 mK. The NMR spectra between 0.4 and 0.6 K indicate that paramagnetic and the antiferromagnetically ordered regions coexist. Below 0.2 K, the spin-lattice relaxation rate 1/T 1 shows Fermi-liquid-like behavior given as 1/T 1 T = 2.9(s K) −1 . From these results, it is concluded that YbAs is a heavy-fermion compound which undergoes an anomalous antiferromagnetic transition.

Nuclear magnetic relaxation measurements of pnictogen atoms in Yb-monopnictides (YbN, YbP, YbAs, YbAs0.8Sb0.2, YbSb) have been carried out to investigate the spin fluctuations of 4f electrons systematically. Estimated 4f fluctuation rates (τ−14f) of all Yb-monopnictides have almost the same temperature dependence. τ−14f increases monotonously with T½-like law. However, from YbAs to YbSb through YbAs0.8Sb0.2, the absolute value of the fluctuation rate showed a remarkable increase. This suggests that the dynamical properties of YbSb are significantly different from other Yb-monopnictides.

Spin dynamics in the antiferromagnetic ring Fe10 has been studied by means of magnetic susceptibility and 1 H-NMR experiments. The spin–lattice relaxation rate 1/ T 1 above 40 K reflects the spin fluctuations in the continuous energy levels of the spin states, while the rate below 40 K indicates the development of antiferromagnetic correlations and discrete energy levels. Especially the experimental rates below 4 K can be expressed by an exponential function of the temperature with an energy gap between the singlet ground state and the triplet excited state. The field dependence of the low-lying energy levels was clearly revealed by the 1/ T 1 measurements. On the other hand, the spin–spin relaxation rate 1/ T 2 is dominated by the temperature-independent fluctuations of the nuclear dipolar fields and a small contribution proportional to 1/ T 1 , and is consistent with the spectral widths.

An antiferromagnet on a Kagome lattice is a strongly frustrated spin system. In hexagonal compounds RFe3(OH)6(SO4)2[R=NH4, Na], Fe3+ ions form the Kagome lattice in thec-plane with the antiferromagnetic interaction. Successive phase transitions were found around 60 K by means of susceptibility and NMR measurements. The temperature range of the intermediate phase is about 5 K. NMR spectra of1H and23Na have structures and give information about the magnetic structures in each phase.

Nuclear spin relaxation time of a triangular lattice Heisenberg antiferromagnet CsNiBr3 has been measured to investigate the magnetic fluctuation in the frustrated system. The two-magnon process due to a swinging motion of the triangular spin structure in a plane containing the c-axis contributes the relaxation in the ordered phase.

The NMR spectrum and the relaxation time of 87 Rb in the triangular lattice antiferromagnet RbNiCl 3 have been measured between 0.5 and 60 K. Spins form triangular structure with a fan-out angle larger than 60° in the ordered phase. This is attributed to the unequal interchain interactions.

The proton spin-lattice relaxation time T 1 in the Haldane-gap system, Ni(C 2 H 8 N 2 ) 2 NO 2 (ClO 4 ) was measured down to 0.5 K. The development of antiferromagnetic short range order was not found even at low temperatures. A relaxation process of activation type with an energy gap of 11 K has been observed.

The longitudinal and transverse relaxation times of 133Cs were measured in the ordered phase of CsCoCl3. From an analysis of fluctuating internal field at the Cs nuclei, the experimental results were interpreted in terms of the spin inversion caused by the propagation of domain-wall pair in the Co2+ chain.

Nuclear spin-lattice relaxation properties of hcp solid 3He with 4He impurities have been studied. At temperatures below the exchange plateau region, three kinds of relaxation time were observed. To analyze the data, a phenomenological four-bath model was developed, the four baths being the Zeeman bath, the phonon bath, an “X-bath,” and a “Y-bath.” The X-bath consists of the exchange bath and a part of the 4He-4He elastic interaction bath. The Y-bath is the main part of the elastic interaction bath. We measured the concentration dependence of the energy constants of all the baths, as well as the temperature and concentration dependences of the three kinds of relaxation time. The relaxation behavior corresponding to the process between the X-bath and the Y-bath could not be expressed by a single exponential function of time and the relaxation rate was strongly dependent on the concentration. This process may be related to the internal thermal equilibrium process within the elastic interaction bath. The impurity-dependent relaxation time between the X-bath and the phonon bath had a temperature dependence of T −n with n = 7.4±0.3.

Helium-3 nuclear spin relaxation times T 1, T 2, and T 1ϱhave been measured for 3He-4He solid mixtures at the exchange plateau region (~0.5K). The 3He concentrations X 3of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm3/mole in hcp phase. The spectral density function J(Ω) for dipolar field fluctuations was determined in the low-frequency branch from T 1ϱmeasurements and in the high-frequency branch from conventional T 1measurements. It was found that J(Ω) is given by J(ω) = cJ(ω)|3−4 + (1−c)J(ω)|3−3, where J(Ω)|3−4 is the spectral density function due to the 3He-4He tunneling motions, and J(Ω)|3−3 is that due to the 3He-3He tunneling motions. Using the Torrey theory, the correlation frequency of the 3He-4He tunneling motions was evaluated from T 1ϱdata, and was found to be in good agreement with Landesman 's theory.

The nuclear spin-lattice relaxation time T 1 of 87 Rb in the singlet-ground-state easy-plane antiferromagnet RbFeCl 3 has been measured at the temperatures above and below T N ≈2.5 K with the external field applied both along and perpendicularly to the hard c -axis. From the analysis based on the dynamical correlated-effective-field approximation, it is found that the trend of the divergence of T 1 -1 in the paramagnetic phase around T N is closely related to the remarkable softening of the magnetic excitation for the K-point mode (\(\bm{q}=\bm{q}_{0}\)) via the in-plane component of the static susceptibility χ (\(\bm{q}_{0}\)).

The successive magnetic phase transitions ( T N1 and T N2 ) and magnetic properties of CsNiCl 3 , a Heisenberg antiferromagnet on the triangular lattice, have been investigated by means of the nuclear magnetic resonance of 133 Cs. In the low temperature phase ( T < T N2 ), the 120° structure of Ni 2+ spins was confirmed by the angular dependence of NMR spectra. In the intermediate phase ( T N2 < T < T N1 ), the observed angular dependences of NMR spectra can not be explained by the simple component disorder model which has been proposed previously. We interpret the NMR results in the intermediate phase by the component disorder model with the quasi-degeneracy. It was found that the quasi-degeneracy due to the freedom of rotation of the 120° spin structure in the a c -plane survives beyond T N2 down to about 3 K.

Solitons in one-dimensional magnetic systems have recently been receiving considerable interest. The soliton behaves like a free particle when the mean free path λ is much longer than the inverse of the soliton density ns (“coherent model”). On the contrary, if the condition nsλ TN2 has been shown by the experiments of ESR [2] and neutron scattering [3].

The proton spin relaxation times in TMMC ( T N = 0.84 K ) were mea sured in the temperature range 4.2–0.4 K. The experimental results suggest that the relaxation mechanism below T N is the magnon-scattering process characterized by weak interchain coupling and energy gap due to small in-plane anisotropy.

The nuclear spin-lattice relaxation time T1 of 133Cs in CsCoCl3·2H2O doped with magnesium with concentration of 2.5% has been measured to study the dynamical behaviors of the soliton (propagative domain-boundary) in ID Ising-like antiferromagnetic system, The experimental results for Ho//c-axis suggest an effect of the impurity on the soliton motion. The temperature dependence of T1 for Ho// a-axis exhibits quite similar features to those for the pure crystal: There appears (T1)min. We show that the diffusive-soliton model gives a good explanation of these experimental results.

Succesive phase transitions (TN1 and(>) TN2) and magnetic properties of a Heisenberg antiferromagnet on the triangular lattice, CsNiCl3, have been studied by NMR of is 133Cs. In the low temperature phase (TN2) the 120° structure of Ni moments in the ac-plane was confirmed by angular dependences of NMR spectrums. In the intermediate phase (TN2N1) the angular dependences of NMR spectrums were not explained by the component disorder model which has been proposed. We propose a new model that sublattice switching occurs in this phase. We have also observed an expansion of the temperature region of the intermediate phase due to the impurity of Co2+.