Ⅲ-2. Atomic & Solid State Physics (Muon)

RIKEN Accel. Prog. Rep. 49 (2016)

Study of frustrated antiferromagnetic states by µSR
M. Abdel-Jawad,∗1 Y. Ishii,∗2 Y. Oshima,∗1 R. Kato,∗1 and I. Watanabe∗3
A series of organic salts, (Cation)[Pd(dmit)2 ]2(dmit=1,3-dithiole-2-thione-4,5-dithiolate) has a triangular exchange network of S = 1/2 units of moleculardimers1) . The strength of the spin frustration can becontrolled by the choice of the cation. In such triangular magnets, geometrical frustration is thought to play
an important role in determining the magnetic state, as
the antiferromagnetic (AF) transition temperature isfound to increase proportionally to the deviation fromthe almost regular triangular exchange networks. It
is thought that EtMe3 Sb[Pd(dmit)2 ]2 2) does not show
any AF order owing to strong spin frustrations. Theexchange interaction J in these materials is on the order of 200 to 300 K.
Recent longitudinal field (LF) µSR measurements
were performed on EtMe3 Sb[Pd(dmit)2 ]2 , a quantum
spin liquid (QSL) candidate. Preliminary analysis
suggests that the field dependence of √the muon relaxation rate, λ, is proportional to 1/ B in a field
range of 1 ≤ Bext ≤ 1000 G at low-temperatures.
Such behaviour is expected from one-dimensional (1D)
spin diffusion, a surprising result considering the quasi
two dimensional nature of the electronic structure ofPd(dmit)2 -based compounds.
To study how geometrical frustration affects the nature of the spin fluctuations, we have performed µSR
measurements on Et2 Me2 P[Pd(dmit)2 ]2 , a Mott insulator with an AF transition of 14 K. Analysis in theparamagnetic temperature region of the µSR spectra
was performed using the following formula:dependence of λ at 100 G, which peaks at 100 K andis dominated by 2D spin diffusion or 1D ballistic spin
motion. This 100 K maximum of λ at 100 G is interesting as it correlates with the thermoelectric power
maximum and the onset of the anomalous dielectric
constant5) of the same compound.

A(t) = A0 exp (−λt) × GKT (∆, HLF , t)Fig. 1. Dependence of the longitudinal relaxation rate
λ on the applied longitudinal field at 100 K in
Et2 Me2 P[Pd(dmit)2 ]2 . (Inset) Temperature dependence of the relaxation rate λ of Et2 Me2 P[Pd(dmit)2 ]2
at a zero field and a 100 G longitudinal field.

∗3Condensed Molecular Materials Laboratory, RIKEN
Shibaura Institute of Technology
RIKEN Nishina Center- 222 -λ(µs-1)

0.015

λ(µs-1)

0.01
0

100

ln(J10−210−31

10200T(K)/B).86∗210−10.05-0∗1ZF
100G0.1

B

where GKT (∆, HLF , t) is the Kubo-Toyabe function,
which is due to nuclear dipoles, and λ is the muon
depolarization rate, which describes the degree of electron spin fluctuation. ∆ values were determined withthe zero field (ZF) data and were assumed to be LFindependent.
Figure 1 shows that the LF dependence of λ at 100
K in Et2 Me2 P[Pd(dmit)2 ]2 is a combination of two different spin fluctuation motions. At low fields, λ follows
a power law LF dependence with an exponent of -0.86,
a value close to the -1/2 value expected from a spinon
1D spin diffusion motion, whereas at higher magneticfields a logarithmic dependence of λ emerges, indicative of a purely 2D spin diffusion or 1D ballistic spin
motion3,4) . The inset of Fig. 1 shows that the temperature dependence of λ at ZF, which is dominatedby the 1D spin diffusion motion, increases with decreasing temperature in contrast to the temperature

100

100
B(G)

300

J=2.

4T

1000

LF µSR measurements in Et2 Me2 P[Pd(dmit)2 ]2have shown that decreasing geometrical frustration on
the spin-liquid level not only increases the AF transition temperature but changes the nature of the spin
fluctuations from the purely 1D diffusion motion of aspinon. Further, LF µSR measurements are required
to properly quantify the ratio between the two different spin motions, their relation to charge transport,
and the degree of geometrical frustration.
References
1) K. Kanoda and R. Kato, Annu. Rev. Condens. Matter
Phys. 2, 167 (2011).
2) M. Yamashita et al., Science, 328, 1246 (2010).
3) F. L. Pratt et al., Phys. Rev. Lett. 96, 247203 (2006).
4) F. L. Pratt et al., Physica B 404, 585589 (2009).
5) M. Abdel-Jawad et al., Phys. Rev. B 88, 075139 (2013).