実験報告書様式（一般利用課題・成果公開利用）

MLF Experimental Report

提出日 Date of Report

課題番号 Project No.

装置責任者 Name of responsible person

2017A0185

Shinichi Itoh

実験課題名 Title of experiment

装置名 Name of Instrument/（BL No.）

Crystal field excitations of multiferroic β-Tb2(MoO4)3

BL１２

実験責任者名 Name of principal investigator

実施日 Date of ExperimentFumihito Shikanai

2017.11.09-2017.11.13

所属 Affiliation
Faculty of Education, Shimane University
試料、実験方法、利用の結果得られた主なデータ、考察、結論等を、記述して下さい。（適宜、図表添付のこと）
Please report your samples, experimental method and results, discussion and conclusions. Please add figures andtables for better explanation.
1. 試料 Name of sample(s) and chemical formula, or compositions including physical form.
β-Terbium molybdate, β-Tb2(MoO4)3. Ceramic samples of 122.57 g [φ4cm×4cm （ φ9mm×4cm×19 ） ] werewrapped in Al foil and set to a sample container (self-made) by Al wire. He gas was enclosed in an Al-can with thesample. We initially planned this experiments with a single crystal, however we could not perform it. Some highquality large single crystals were obtained by the days of the experiment, however we had no time to align the crystal
axis, because there was no device in our laboratory. Although it is an afterthought, byusing a large amount of ceramic sample advised by the responsible person, we could
capture the reliable data and the overall picture of the excitations of this material while
maintaining psychological margin during the experiment. ,2. 実験方法及び結果 （実験がうまくいかなかった場合、その理由を記述してください。）
Experimental method and results.

If you failed to conduct experiment as planned, please describe reasons.

The sample can was set to the 3K refrigerator. We measured the magnetic excitation levels at low temperature
focusing on the crystal field (CF) levels under 100 meV. The inelastic data (details and q-dependences of the levels)and temperature dependences of them were collected with various Ei using a high-resolution chopper spectrometer(HRC) in BL12 of J-PARC. Tb2(MoO4)3 (TMO) is in multiferroic phase in all the measurement temperature,
between the room-temperature and 3K, because there is no phase transition (ferroelectric phase transition 432 K,
antiferromagnetic phase transition 0.45 K). In this experiment, the benefit of multi Ei method is demonstrated, wecould obtain the data for eight kinds of Ei form 6 meV to 643 meV in a few long run measurements. Each data
includes a few levels which are particularly clear in it. This indicates aforte, high-resolution of the spectrometer HRC. Figure 1 shows inelastic
neutron scattering (INS) maps of TMO with Ei=26.3 meV at various
temperature. Nondispersive excitation levels are clearly observed 5, 7, 10,and 20 meV. These levels melt with increasing temperature while a quasielastic neutron scattering (QENS) spectrum appears. The data of Ei=8.14
meV simultaneously measured
1FIG.1 INS map of TMO Ei=26.3

2. 実験方法及び結果（つづき） Experimental method and results (continued)
meV simultaneously measured are shown in FIG.2. Intensity of QENS
spectrum increases with decreasing temperature and of which width decreases.
The result indicates that the magnetic moment of Tb3+ which precess random
at room temperature is integrated into the direction of the CF with decreasing
temperature. It is predicted that the QENS spectrum will disappear above
ferroelectric phase transition temperature 432K, and the magnetic moments
will be ordered below antiferromagnetic phase transition temperature 0.45 K,
although the temperature region were not measured in this experiment. The
relaxation time at 3-10 K is estimated as 40 ps. Inverse of relaxation times

FIG.2 Analytic results of QENS

obeys the Curie–Weiss law in temperature region above 100 K while the behavior in low temperature ischaracterized by the crystal field. However, itis necessary to perform more high-resolution
experiments to confirm them.
To determine the other levels of CF, the datawith various Ei were analysed (FIG. 3). The
positions of peaks founded in low Ei data (↓in FIG. 3) were fixed, and of which width andintensity to need to refine were refined. All thewidths were convoluted by that of elastic
peak, and the ratio of intensities were fixed toFIG.3 Analytical results of INS spectra at 3K.

those in low Ei as much as possible. This

analysis was repeated several times until convergence. The levels of 0.00, 3.52, 5.23, 7.12, 9.00,10.34, 18.7, and25.3 meV (blue dots in FIG. 3) were assigned as the CF levels from their q dependences. Levels at 62.2 and 78.7
meV are the Raman inactive modes of which near energies had reported as the CF excitations in Tb2Ti2O7, but theyshow opposite q dependence for those in TMO in FIG. 3. An excitation level 7F4 (J = 4 of Tb3+) can be found in thedata of Ei=642.8 meV. To assign 2J+1=13 CF levels to above obtained levels, the levels 0, 5.23, and 7.12 meV withstrong intensity, 18.7 and 25.3 meV with wide width were assumed as the double degeneracy. CF parameters wereobtained using the Hamiltonian HCF(C1) of which degree is up to the 2Jth order. HCF(C1) can almost be reproduced at
any level, but many candidates are obtained (FIG. 4). The parameters were refined after obtaining initial parametersfrom the Monte Carlo method. Because of the site symmetry at Tb3+ in TMO is C1, representation of all the crystal
filed levels are A. However, actual eigen states are classified into two states which include the state MJ=0 (red levelsin FIG.4) or not include it (blue levels in FIG.4). The levels belonging to the different representation can accidental
degenerate. Currently, we are calculating andconfirming the physical properties such as
magnetization and specific heat under amagnetic field from the level of FIG. 4. It is
predicted that there is another CF level below 1
FIG. 4 Candidates of the obtained crystal field levels

2

meV which is not measured this experiment.