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 Report2018. 3. 13.

課題番号 Project No.

装置責任者 Name of responsible person

2017A0027

Dr. Kenji Nakajima

実験課題名 Title of experiment
Dynamical structure factors on S=1/2 triangular antiferromagnetic
system with bond randomness Cs2CuCl4-xBrx
実験責任者名 Name of principal investigator

装置名 Name of Instrument/（BL No.）

Toshio Ono

2017. 11. 10 – 2017. 11. 13.

BL 14
実施日 Date of Experiment

所属 Affiliation
Osaka Prefecture 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.
Cs2CuCl4 and Cs2CuBr4 are isomorphic and are spatially anisotropic S=1/2 triangular antiferromagnets. We areinvestigating the effects of the bond randomness on the triangular antiferromagnet using the mixture system
Cs2CuCl4-xBrx. On the present experiment, we have performed the inelastic neutron scattering for the sample with
x=3.4 which has antiferromagnetically ordered ground state. Three single crystals those were grown by slow
evaporation method were co-aligned so as to make the bc-plane is parallel to the scattering plane. The total massof the crystals used was 14g and a mosaic of the crystal is approximately ~1˚.

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.

h [r. l. u.]

600

Three co-aligned single crystals were cooled down to 0.3K using 3He refrigerator. In order to correct the fourdimensional scattering intensity I(Q,w), crystals were rotated 150˚ in the scattering plane with acquiring multiple
datasets. Measurements were also performed at T = 10K to check the temperature dependence of I(Q,w). Incident
neutron energies were chosen as 3.0, 5.6 and 13.7 meV using the multiple Ei chopper system [1].
Figure 1 shows the static structure foctor as a function of h and k. The intensity is energy integrated for ħ𝜔= [0.1, 0.1] meV. Measurements were carried out at 10 K (Fig. 1 (a)) and 0.3 K (Fig. 1 (b)). Antiferromagnetic phasetransition was observed at T = 0.6 K on the magnetic
0.4
Q = (H, K, 0)
ΔE = 0 meVmeasurement for the present sample. So that the0.20.0
reflections observed only at T = 0.3 K indicated by-0.2(a)T = 10 K
the black triangles should correspond to the-0.4
0.4
magnetic Bragg peaks. In addition to the nuclear
0.2
Bragg reflections expected for end member, such as0.0-0.2
h + k = even, weak reflection indicated by white
T = 0.3 K(b)-0.40.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
triangle was observed at Q = (0, 1, 0). The violation
k [r. l. u.]of the extinction rule might be caused by random Figure 1 Static structure factors in [hk0] plane measured at T = 10K(a) and 0.3K (b).
substitution of halogen ions. The position of500
300
200
100

h [r. l. u.]

400

Intensity [arb.units]01

2. 実験方法及び結果（つづき） Experimental method and results (continued)[1] K. Nakajima et al.: J. Phys. Soc. Jpn. 80 SB028 (2011).
[2] Z. Weihong et al.: Phys. Rev. B 59 14367 (1999).
[3] R. Coldea et al.: Phys. Rev. B 68 134424 (2003).
[4] R. Coldea et al.: Phys. Rev. Lett. 88 137203 (2002).
[5] T. Shimokawa et al.: Phys. Rev. B 92 134407 (2015).

2Intensity [arb. units.]

Energy [meV]

qobserved magnetic Bragg reflection was Q = (0. q, 0) with
0.70
q = 0.56(1). Within a classical treatment, the relationshipbetween q and the ratio of exchange interactions a = J2 / J10.65
are described as pq = arccos(-a/2) on the present system.
Where J1 and J2 are the exchange interactions shown in the0.60
x = 4.0
inset of Fig. 2. By applying the relation to the present result,present sample
a is obtained as a = 0.37. Weihong et al. studied the0.55
x=0quantum renormalization effects on the ground state and theexcitation
properties
ofanisotropic
triangular
0.50
Weihong et al.
antiferromagnet using the series expansion method [2].
Classical model
They obtained the relationship between q and a as shown
0.45
0.00.20.40.60.81.0
by a solid line in Fig. 2. When q is smaller than 2/3, aα = J2 /J1estimated from their theory is larger than that of classicalFigure 2 Static structure factors in [hk0] plane measured atmodel. Applying this relationship to the present T = 10K (a) and 0.3K (b).
experiment, we obtain a ~ 0.64 for the sample with x = 3.4.
3.0
Figure 3 shows a contour map of the excitation spectrum
Q = (0 k 0)
T = 0.3 Kalong (0 k 0) direction. Spin wave modes which is similar
2.53.0to those of end members were clearly observed. The dashed2.0
2.5
lines are the spin-wave dispersion relations of anisotropic
2.0
triangular antiferromagnetic model with a = 0.37 [3]. By
1.5
adjusting the amplitude of the model to the experimental
1.5
result, the exchange energy J1 can be estimated as J1 = 2.0
1.0
1.0± 0.1 meV. We should be noticed that the estimated J1 using
0.5
0.5
the classical model is enlarged by quantum renormalization
0.0
effect. For the sample with x = 0, Cs2CuCl4, J1 was found0.00.00.5
1.0
1.5
2.0
to be larger than the real magnitude of the interaction about
1.6 times [4].
k [r. l. u.]
Figure 4 is the scattering intensity as a function of energy Figure 3 Contour map the dispersion relation along [0 k 0]
direction. Dashed line indicates spin-wave dispersion
around Q = (0, k, 0) with k~0.76 measured at T = 0.3K. relation of anisotropic triangular antiferromagnet.
Excitation spectrum of present experiment which isindicated by red circles shows rather broad peak around 1.65 meV. Blue line is the result of the sample with x =4.0, Cs2CuBr4, measured with energy resolution DE ~ 1.7 meV which is almost equivalent to the presentexperiment. The line width of the spin-wave excitation of the present experiment is approximately 2 times larger
than that of x = 4.0. This result qualitatively reproduces the randomness effect on the line shape which is predicted
for triangular antiferromagnet by Shimokawa et al. [5].
As described above, the ground state and the dynamical structure factor of the present sample is identical to thoseof end member except for the magnitude of exchange interactions. This fact indicates that the halogen ion
substitution of the present system does not significantly
2.0
Present Experiment (ΔE~0.14meV)alter the fundamental properties as the anisotropic
x = 4.0 (IN6@ILL ΔE~0.17meV)
1.5
triangular antiferromagnetic system. By performing
Q = ( 0, ~0.76, 0)
T = 0.3 K
comparative study using the sample with more strong
1.0
randomness is essential to verify the random singlet state
0.5
which is theoretically expected.
0.001234Energy [meV]Figure 4 Measured scattering intensity at Q = (0, ~0.76, 0) as afunction of energy (red circles). Blue line denotes the result forthe sample with x = 4.0.