Taku Matsushita

Ferromagnetic Transition of Pyrochlore Compound Yb2Ti2O7

R2Ti2O7 (R = Y and various rare earth elements) has pyrochlore type structure, which consists of two kinds of three-dimensional networks individually formed by the corner-sharing R4and Ti4-tetrahedra, respectively. Due to this structural characteristic, magnetic moments at the R sites are expected to be frustrated, if their nearest neighbor interaction is antiferromagnetic. For R = Tb, the value of Weiss temperature w is 19K, indicating the Tb3þ moments have antiferromagnetic nearest neighbor interaction and the system does not exhibit clear evidence for magnetic ordering. Previously, we investigated both the dynamical and static magnetic properties of Tb2Ti2O7 by means of neutron scattering on a single crystal. Based on results of measurements of the specific heat C and ac magnetic susceptibility , low temperature state of Tb2Ti2O7 was discussed in ref. 4, too. The frustration is also expected even for the system with the ferromagnetic nearest neighbor interaction, if the moments have strong uniaxial anisotropy, where each moment lies along the local principal axis corresponding to the line which connects the site with the center of gravity of the tetrahedron. (There are four principal axes along [111] and other crystallographically equivalent directions.) Such the situation can be found in R2Ti2O7 with R = Dy 5) and Ho, which are called ‘‘spin ice’’. For Yb2Ti2O7, w is equal to be 0:53K as shown in the inset of Fig. 1, indicating the nearest neighbor interaction between the Yb3þ moments is ferromagnetic. The electronic ground state of Yb3þ ion was reported to be a Kramers doublet with relatively small planar anisotropy, g? 1⁄4 4:27 and gk 1⁄4 1:70, where g? and gk are the g-values perpendicular to and along the local principal axis, respectively. Sengupta et al. reported that the system has uniaxial anisotropy, g? 1⁄4 0 and gk 1⁄4 3:4. A sharp peak of C–T curve was reported at 0.24K, indicating the existence of the phase transition. However, Hodges et al. did not observe magnetic reflection except the small angle diffuse scattring. In order to identify the specific heat anomaly at 0.24K, we have carried out neutron diffraction and other magnetic measurements on a single crystal of Yb2Ti2O7 down to 0.03K by using dilution refrigerator. Here, we report that the system exhibits ferromagnetic transition at TC 1⁄4 0:24K. We also discuss the low temperature behavior of the moments. A single crystal of Yb2Ti2O7 was grown by a floating zone (FZ) method. The magnetization M was measured by using a SQUID magnetometer. The method of the ac magnetic susceptibility is described in ref. 4. Neutron measurements were carried out by using the triple axis spectrometer HQR (T1-1) installed at the thermal guide of JRR-3 of JAERI in Tokai. The crystal was oriented with [hh0] and [00l] axes in the scattering plane. Figure 1 shows the M–H curves of Yb2Ti2O7 obtained at 5K with the magnetic fields along [001], [110] and [111], where the anisotropy of the curves is found to be relatively small. We calculated the M–H curves considering an anisotropic Kramers doublet and using a molecular field treatment of the ferromagnetic interaction with a coupling constant . By fitting the calculated curve to the data, the parameters are estimated to be 1⁄4 0:64 0:10T/ B, g? 1⁄4 3:9 0:2 and gk 1⁄4 2:6 0:4. Judging from the rather small differences among the M–H curves, the deduced anisotropy is surprisingly large, but at least much smaller than that reported in refs. 7 and 8. This can be understood as follows. Because Yb sites are divided into four sets with different local principal axes along [111] and three equivalent directions, the averaged anisotropy of the moments over these sets becomes very small, even though the anisotropy is rather large within each set of the Yb moments. The value of saturation magnetization estimated from the M–H curves is 1:8 B/Yb. The T-dependence of the real part of the ac magnetic susceptibility 0 of Yb2Ti2O7 measured with increasing T is shown in the inset of Fig. 2, where a clear anomaly has been observed in the T-dependence at 0.24K. The value of 0 at 0.24K is found to agree with the value of 1=4 N within the experimental error bar, where N is the demagnetization coefficient of the used sample. Because M=H is described as 0=ð1þ 4 0NÞ, which approaches 1=4 N as 0 ! 1, the result indicates that the system exhibits a ferromagnetic transition at TC 1⁄4 0:24K. At T 1⁄4 0:03K (

Extremely High Frequency Dependence of Two-Dimensional Superfluid Onset

We observed the frequency dependence of the superfluid transition of 4 He films adsorbed on planar gold up to a very high frequency of 180 MHz, using the overtone harmonic modes of a quartz crystal microbalance. The superfluid onset was observed at a temperature markedly higher than the Kosterlitz–Thouless (KT) transition temperature, the onset temperature in the low-frequency limit. The observed frequency dependence is surprisingly well reproduced by the dynamic theory close to the high-frequency condition where the vortex diffusion length in a period becomes as small as the vortex core diameter. We also observed that the superfluid vortex parameters depend strongly on the kind of substrate as well as on 4 He film thickness.

Observation of superfluidity in two- and one-dimensions

Even though there is no long-range-ordered state of a superfluid in dimensions lower than the three-dimension (3D) such as bulk 4He liquid, superfluidity has been observed for flat 4He films in 2D and recently for nanotubes of 4He in 1D by the torsional oscillator method. In the 2D state, in addition to the superfluid below the 2D Kosterlitz–Thouless transition temperature TKT, superfluidity is also observed in a normal fluid state above TKT, which depends strongly on the measurement frequency and the system size. In the 1D state of the nanotubes, superfluidity is directly observed as a frequency shift in the torsional oscillator experiment. Some calculations suggest a superfluidity of a 1D Bose fluid with a finite length, where thermal excitations of 2π–phase winding play the main role for superfluid onset of each tube. Dynamics of the 1D superfluidity is also suggested by observing the dissipation in the torsional oscillator experiment.

Quantum Spin State and Magnetization Plateaus in an S=1 Kagomé Heisenberg Antiferromagnet

The organic Heisenberg antiferromagnet m -MPYNN·BF 4 has a two-dimensional Kagome lattice of S = 1 dimers with a small trigonal distortion. This antiferromagnet indicates a nonmagnetic ground state with a gap of 0.2 K in zero field. To investigate the ground state of this quantum magnet, we measured the AC susceptibility and the magnetization as a function of the magnetic field. Magnetization plateaus in applied fields were sensitively observed from steep decrements in the AC susceptibility at low temperatures. They indicate characteristic behaviors to be expanded at finite temperatures. The magnetization curve indicates that the fractional plateaus are at 1/2 and 3/4 of the saturation magnetization. The observed plateaus are not commensurate with the unit cell of the Kagome lattice, suggesting a contribution of long-distance interactions.

Amorphous solid like heat capacity of 4He fluid films adsorbed on pores

In the nanopores of HMM-2 whose mean pore diameter is 2.7 nm, adsorbed 4He forms layers up to about two atomic layers. At low temperatures, the 4He films show properties of the Bose quantum fluid and superfluidity above about 1.4 layers. Below the coverage or above the superfluid transition temperature, 4He film is in the normal fluid state. The heat capacity of the normal fluid shows linear temperature (T) dependence. The T-linear coefficient of the heat capacity is about 5 μJ/(m2-K2). According to Andreevs idea originally developed for bulk helium liquids, the 4He fluid can be regarded as an amorphous solid with T-linear dependence of the heat capacity. Its coefficient is described as π2D0κB2/6, where D0 is a density of states and κB is the Boltzmann constant. The density of states is estimated from the density (coverage) dependence of the isosteric heat of sorption qst which was obtained from the vapor pressure data of adsorption. The estimated density of state well explains the observed magnitude of the T-linear coefficient of heat capacity.

Specific Heat of the Spin‐Gapped S=1 Kagomé Antiferromagnet m‐MPYNN⋅BF4 in Magnetic Fields

We have studied the specific heat of an organic compound m‐MPYNN⋅BF4‐(1/3)(acetone) in magnetic fields. This compound is a spin‐1 Kagome Heisenberg antiferromagnet and has a non‐magnetic ground state with a spin gap of 0.25–0.45 K in zero field. We observed that the specific heat has two maxima below about 3 K. The maximum due to short‐range ordering observed at T = 1.6 K in zero field shifts with the field, reflecting competition between the antiferromagnetic interaction and the Zeeman energy. A critical field of about 2 T is suggested by a minimum of the peak temperature. Another peak at 0.12 K does not shift until 4 T, which indicates that the peak is not related to the spin entropy.

Quantum State of 4He Confined in Nanocages of Na-Y Zeolite

We have studied the heat capacity of 4He adsorbed in Na-Y zeolite down to 70 mK. The Y-type zeolite has void cages 1.3 nm in diameter connected through narrow apertures 0.8 nm in diameter. After the first solid layer of adsorbed 4He is completed at 10.3 atoms/cage (about 37% of full pore), the pore apertures are considered to be so narrow that 4He adatoms in the second layer are confined in each cage at low temperatures, and form a cluster of several atoms. After the first layer completion, the low-temperature heat capacity isotherm has two peaks around 13.7 and 17.0 atoms/cage (about 50 and 63%), between which quantum-statistical differences from those of 3He appear. From the peaks in the heat capacity isotherm, the quantum region for 4He adatoms in Na-Y zeolite was determined.

Phase diagrams of 4He bose fluids formed in one-and three-dimensional nanopores

In the one-dimensional (1D) nanopores of FSM-16 (2.8 nm in diameter) and the 3D pores of HMM-2 (2.7 nm, and 5.5 nm in 3D period), the 4He films adsorbed on these nanopore walls show the properties of the Bose quantum fluid and superfluidity above 1.4 atomic layers at low temperatures. The boundary of the Bose fluid region was determined from the kink (peak) temperature TC of the heat capacity at each coverage n. The phase diagrams obviously show dependence on the 1D and 3D pore connections, respectively. In the 3D nanopores, the coverage (density) dependence of TC is well reproduced by the Bose-Einstein condensation temperature of the 3D ideal gas which is proportional to (n - nc)2/3, where nc is the onset coverage. In the case of the 1D pores (channels), TC is proportional to (n - nc) at 0.1 < TC < 1K. This TC is likely to correspond to the crossover temperature of the 2D ideal gas heat capacity from the constant heat capacity of the Boltzmann gas to the linear in T, with decreasing temperature. At TC, the thermal de Broglie wavelength of the free particle is still shorter than the pore diameter, while the thermal phonon wavelength is estimated to become longer than the diameter below TC, which indicates the 1D phonon state.

Vapor Pressure Measurement for 4He Films Adsorbed on 2D Mesoporous Hectorite

The vapor‐pressure measurement for adsorbed films is equivalent to the measurement of the chemical potential. By the measurement of 4He films adsorbed on two‐dimensional (2D) mesoporous Hectorite, we obtained the 2D isothermal compressibility, the isosteric heat, and the effective thickness deduced from the FHH model, mainly above a coverage of 15 μmol/m2. The compressibility shows two dips at n1 = 17.5±0.5 μmol/m2 and n2 = 22.7±0.5 μmol/m2 which correspond to the first layer completion and appearance of the quantum‐Bose‐fluid layer, respectively. For the quantum‐Bose‐fluid layer, the phonon velocity deduced from the compressibility is on the order of 100 m/s, and it reasonably agrees with that obtained from the 2D phonon heat capacity.

3He Fluid Formed in One‐Dimensional 1.8 nm Pores Preplated with 4He Layer

In one‐dimensional (1D) nanopores 1.8 nm in diameter preplated with 1.2 atomic layers of 4He, we have made 3He film tubes whose diameter is estimated to be about 1.0 nm. At a low 3He density, the heat capacity shows that of a 2D Boltzmann gas at high temperatures followed by a Schottky‐like peak at about 300 mK. This result can be understood in terms of dimensional crossover from 2D to 1D with decreasing temperature. The peak appears at a temperature about 0.3 times the energy gap between the ground state and the first excited states of the azimuthal motion in the 3He fluid tubes.