実験報告書様式（一般利用課題・成果公開利用）（ ※本報告書は英語で記述してください。ただし、産業利用課題として採択されている方は日本語で記述していただいても結構です。 ）MLF Experimental Report

提出日 Date of Report
June, 15 2017

課題番号 Project No.

装置責任者 Name of responsible person

2016B0023

Kenji Nakajima

実験課題名 Title of experiment
Exploring magnetic excitations in fully frustrated dimerized
quantum magnet
実験責任者名 Name of principal investigator

装置名 Name of Instrument/（BL No.）

Hidekazu Tanaka

AMATERAS (BL14)
実施日 Date of Experiment
February 3-6 and 10-13, 2017

所属 Affiliation
Tokyo Institute of technology
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.
Ba2CuSi2O6Cl2 and Ba2NiSi2O6Cl2

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.

A new series of two-dimensional (2D) dimerized antiferromagnets Ba2MSi2O6Cl2 (M = Co [1], Cu [2], Ni [3]),abbreviated hereafter as BMSOC, attracts recent attention owing to their intriguing quantum phenomena. The 2D
magnetic network is illustrated in Fig. 1 where J and Jij represent intradimer and interdimer exchangeinteractions, respectively. The ground state of BMSOC is a nonmagnetic singlet with a finite gap to the excitedstate. When magnetic field exceeding the critical field Hc is applied, magnetic excitations, magnons, are mapped
onto the boson lattice. Magnons move to the neighboring site with amplitude proportional to J11+J22-J12-J21.
When J11+J22 =J12+J21, the interdimer interactions are fully frustrated and hence the hopping of magnons
becomes completely suppressed.
It was reported that BCoSOC, which is described by an effective spin S = 1/2
XXZ model, exhibits a sharp stepwise magnetization plateau at one-half of thesaturation value Ms [1]. Recent inelastic neutron scattering measurements haveshown that the magnetic excitations are completely dispersionless. These results
provide evidence that the frustration of interdimer interactions is almost perfectand hence, above Hc, magnons form a periodic array regarded as a Wigner
crystal. Similar conclusion might be drawn for the S =1 analog BNiSOC where Fig. 1: 2D magnetic network
the magnetization process is stepwise with plateaus at (1/4)Ms and (1/2)Ms [3]. in Ba2MSi2O6Cl2. J and Jij
represent intradimer andOn the other hand, BCuSOC undergoes an XY antiferromagnetic ordering at Hcinterdimer exchange interabove which the magnetization continuously increases with increasing field [2],actions, respectively.
characteristic of the weak frustration, i.e. J11+J22 ≠J12+J21.
In this project, we measured magnetic excitations of BCuSOC and BNiSOC single crystals using acold-neutron diskchopper spectrometer AMATERAS (BL14) installed at J-PARC, Japan. For both themeasurements, the wave vector ki of incident neutron was first set to be parallel to the c* axis. The scatteringdata1

2. 実験方法及び結果（つづき） Experimental method and results (continued)
were collected by rotating the sample around the a- (or b-) axis to clarify excitation spectra in a wider
momentum-energy space. The intensities along the c* direction are integrated assuming that the interlayer
exchange interactions are negligibly small. The measurements were carried out mainly at the base temperature of
0.3 K and 4 K for BCuSOC and BNiSOC, respectively, which are sufficiently smaller than their gap energies.
Figure 2(a) shows the excitation spectra of BCuSOC for (h, 0) at 0.3 K with the incident neutron energy Ei =5.9 meV. In contrast to the case of BCoSOC, a dispersive excitation with the width of ~1 meV is observed. The
lowest excitation energy of 1.7 meV is comparable to the gap energy of 20.4 K [2]. The dispersive behavior isalso found for (0, k) while the excitation spectrum along the c* direction is almost flat, indicative of the goodtwo-dimensionality. Together with the reported magnetization process with magnetization slope above Hc, wecan conclude that the frustration of interdimer interactions is weak in BCuSOC. As the dispersion curve exhibits
minima at Γ point, J11+J22 < J12+J21 is probably realized. Interestingly, the scattering intensities become
significantly decreased at 2.6 meV, which is close to J = 28.1 K [2]. The gap-like feature with the splitting widthof 0.2 meV is found at 2.6 meV, independently of Q and of Ei. This result could be explained by the presence ofunequal interdimer interactions, which can produce a band gap at the energy corresponding to the J value. Since
this scenario is not applicable for the crystal structure of Cmca determined at room temperature [2], further
experiments such as low temperature X-ray measurements are necessary.
Figure 2(b) shows the excitation spectra of BNiSOC for (h, 0)
at 4 K with Ei = 9.9 meV. Almost dispersionless four excitations
are observed. Although the reason why the excitation spectra
constitute two similar excitations both at ~5 meV and ~7 meVhave not been identified yet, these two energies probably relate toexcitation gaps from the singlet ground state to the first andsecond excited states, respectively. In fact, the former and latter
gaps are deduced to be 5.6 meV and 9.6 meV, respectively [3].
The present result provides evidence that interdimer interactions
are strongly frustrated in BNiSOC, consistent with the reported
stepwise magnetization process [3]. It is of interest that the twoexcitations at ~ 5 meV and the other two excitations at ~ 7 meV
are intense when both h and k are integers and half-integers,respectively. It is noted that the similar lattice periodicity of thescattering intensities was found in the excitation spectra of
BCoSOC where the two excitations with Q-dependent scattering
intensities can reasonably be explained by the presence of
unpaired spin dimers [4].
Fig. 2: Energy-momentum maps of the neutron scattering intensityfor Qa = (h, 0) in (a) Ba2CuSi2O6Cl2 at T = 0.3 K with Ei = 5.9 meVand (b) Ba2NiSi2O6Cl2 at T = 4 K with Ei = 9.9 meV. The scattering
data were collected by rotating the samples around the a- (or b-) axis.
The intensities along the c* direction are integrated.

References[1] H. Tanaka, N. Kurita, M. Okada, E. Kunihiro, Y. Shirata, K. Fujii, H. Uekusa, A. Matsuo, K. Kindo, and H. Nojiri,
J. Phys. Soc. Jpn. 83, 103701 (2014).
[2] M. Okada, H. Tanaka, N. Kurita, K. Johmoto, H. Uekusa, A. Miyake, M. Tokunaga, S. Nishimoto, M. Nakamura,M. Jaime, G. Radtke, and A. Saúl, Phys. Rev. B 94, 094421 (2016).
[3] M. Koike, Master's thesis, Tokyo Institute of Technology (2017).
[4] N. Kurita et al., in preparation.
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