1H-NMR Study on the Magnetic Order in the Mixture of Two Spin Gap
  Systems (CH3)2CHNH3CuCl3 and (CH3)2CHNH3CuBr3
untitled
1H-NMR Study on the Magnetic Order  
in the Mixture of Two Spin Gap Systems 
(CH3)2CHNH3CuCl3 and (CH3)2CHNH3CuBr3 
Keishi Kanada1, Takehiro Saito1, Akira Oosawa1, Takayuki Goto1 
and Takao Suzuki1,2   
1Department of Physics, Faculty of Science and Technology, Sophia University 
7-1 Kioicho, Chiyodaku Tokyo 102-8554 
2Advanced Meson Science Laboratory, RIKEN 
2-1 Hirosawa, Wako, Saitama 351-0198 
 (Received   ) 
The antiferromagnetic ordering in the solid-solution of the two 
spin-gap systems (CH3)2CHNH3CuCl3 and (CH3)2CHNH3CuBr3 has 
been investigated by 1H-NMR.  The sample with the Cl-content 
ratio x=0.85 showed a clear splitting in spectra below TN=13.5 K, 
where the spin-lattice relaxation rate T1−1 showed a diverging 
behavior.  The critical exponent of the temperature dependence of 
the hyperfine field is found to be 0.33. 
KEYWORDS: disordered spin-gap systems, NMR, magnetic order 
1.  Introduction 
In classical spin systems, disorder destroys magnetic order by cutting off the correlation 
between neighboring spins.  However, in quantum spin systems, where the magnetic order is 
instabilized by the quantum spin fluctuation, disorder often brings the non-trivial effect to 
their ground state.  A low number of holes drastically destruct the antiferromagnetic order in 
parent phase of high-TC cuprates through frustration effect.1)  In spin liquid systems 
represented by CuGeO3, disorder induces an unpaired spin among singlet dimer and brings a 
static magnetic order to the disordered state.2) 
The title compounds of (CH3)2CHNH3CuCl3 and (CH3)2CHNH3CuBr3 abbreviated as 
IPA-CuCl3 and IPA-CuBr3 are isostructural spin gap systems with a non-magnetic ground 
state.  Both the mechanism and the magnitude of the gap are quite different in the two 
systems. In the Cl-system, which was discovered to have a ladder-like magnetic structure 
based on an inelastic neutron experiment5), the neighboring two S=1/2 spins on the rung 
interact ferromagnetically to form effective S=1 spins at low temperatures.  The interaction 
among these integer spins is weak and antiferromagnetic, so that the ground state is gapped 
one as Haldane conjectured6).  In a Br-system, the interaction between the two neighboring 
spins is antiferromagnetic, so that they form a singlet dimer state at low temperatures.  The 
spin excitation gaps of these two systems have been reported to be 18 and 98 K based on 
magnetization experiments7-9).   The former was re-examined in the neutron experiment and 
reported to be 13.9 K5).  The aim of this paper is a microscopic investigation on the ground 
state of the solid solution of the two spin gap systems. 
Manaka et al. have been working intensively on the macroscopic measurements in 
IPA-Cu(ClxBr1-x)3, and they report that the system becomes gapless only within the limited 
region x=0.44-0.87, where a magnetic order occurs at low temperatures9,10).  However, a 
microscopic investigation on the spin state has not been conducted except for our preliminary 
result by µSR11).  In this paper, we report the existence of an antiferromagnetic phase 
transition in IPA-Cu(ClxBr1−x)3 (x=0.85) through the use of 1H-NMR spectra and the 
spin-lattice relaxation rate. 
2. Experimental 
Evaporation method was utilized to grow single crystals of IPA-Cu(ClxBr1−x)3 (x=1 and 
0.85).  An isopropanol solution of isopropylamine hydrochloride, copper(II) chloride 
dihydrate, isopropylamine hydrobromide, copper (II) bromide was placed in a bowl, which 
was maintained at 30(±0.1)°C, and in an atmosphere of flowing nitrogen gas during an entire 
period of crystal growth, approximately two months.  A typical size of the obtained crystals 
was around 3×5×10mm with a rectangular shape as was reported in a previous paper 9).  The 
content of Cl, x=0.85(5) was determined using the ICP method for three tiny fragments 
chipped off from different points of the crystal.  Macroscopic quantities of obtained crystals, 
the specific heat and the susceptibility were measured by PPMS and MPMS manufactured by 
Quantum Design Co Ltd.  The uniform susceptibility of x=0.85 showed a kink at around 
12K, below which it steeply decreased for H⊥C and slightly increases for H⊥A.  The 
specific heat also showed a small but distinct cusp at the same temperature.  The sample x=1 
showed no anomalies in neither of the two quantities.  These results are consistent with 
reports by Manaka 9,10). 
1H-NMR measurements were performed using a 4K cryogen-free refrigerator set in a 6T 
cryogen-free-superconducting magnet.  The spectra were measured by recording a spin-echo 
amplitude simultaneously ramping up or down the magnetic field.  The spin-lattice 
relaxation rate T1−1 was measured by the saturation-recovery method with a pulse train.  
Relaxation curves were traced until the difference of the nuclear magnetization from its 
saturation value becomes one percent. 
3.  Results and Discussion 
Figure 1 shows the field-swept spectra of the two samples x=0.85 and 1.0 at various 
temperatures under the field around 3T.  At high temperatures both the samples show a sharp 
paramagnetic resonance line.  The width around 18K is approximately 200 and 80 Oe for 
x=0.85 and 1.0 respectively.  As the temperature decreases, the x=1.0 sample maintains a 
sharp width, and only the x=0.85 sample shows a drastic splitting in the peak below TN=13.5 
K.  This temperature coincides with that for an anomaly in 0χ  and the specific heat.  Five 
distinct peaks overlap each other at the lowest temperature of 4 K.  
These multiple peaks in spectra correspond to the inequivalent proton sites exposed to a 
hyperfine field produced by the antiferromagnetically-ordered spins.  Ten inequivalent 
proton sites are in the unit cell, and these proton sites have different distances from the nearest 
Cu site, varying from 3.3 to 6.8 Å.  They should feel different hyperfine fields from the 
ordered moment and should contribute to each split peak.  Actually, observed peak 
separations around 300 Oe are comparable with the estimation by the classical dipole-dipole 
interaction between electronic and nuclear spins.  Though we are still in the process of 
conducting a detailed site assignment, which requires measurements of spectra involving 
various directions of the field, we conclude that the spin structure is simple antiferromagnetic 
rather than incommensurate or glass-like.   
Recently, Nakamura numerically investigated the disordered bond-alternating spin chain 
to report that an antiferromagnetic state is more stable than a glass-like state expected in a 
classical point of view4).  He pointed out that the emergence of Néel state is totally to due the 
quantum effect.   In our previous µSR report11), we have pointed out that in the sample with 
x=0.95 which belongs to the gapped region, the antiferromagnetic spin fluctuation is 
anomalously enhanced at low temperatures.  This fact suggests that the magnetic instability 
is inherently present in the gapped sample. 
Figure 2 shows the dependence on the temperature of a peak separation H∆ , which is 
defined as the distance between the positions at 20% of maxima of the left most and right 
most peaks, and is considered to be a good measure for the magnitude of the staggered 
moment and hence of the order parameter.  The dependence of H∆  on temperature is aptly 
described by the scaling function ( )βN1 TT− , where β  is a critical exponent estimated 
from data fitting to be 0.33, the value of which is close to the value of 0.327 which is 
expected 3D-Ising model16), and is consistent with our report by µSR11).  The reason for the 
appearance of dimensionality of the universality class is 3D, simply because the phase 
transition in 1D-spin systems must be set off by the weak interaction paths that runs three 
dimensionally in the system. 
In previous paper11), we have explained the appearance of the Ising-type universality 
class in terms of D*, an effective single-ion anisotropy that appears at low temperatures 
owing to the formation of effective S=1 spins in ferromagnetic dimers.  However, an 
existence of effective S=1 spins12-14) are proved only in the pure system of x=1.0 but the 
disordered system x=0.85 containing both ferromagnetic and antiferromagnetic dimers.  It is, 
therefore, not self-evident whether or not the disordered system has a universality class 
identical to the pure system.  According to Harris criterion15), the disorder does not affect the 
universality class only for those systems with the negative critical exponent of the specific 
heat α, which does not hold in the present case. 
Therefore, the universality class of x=0.85 sample should be determined carefully 
through experiments.  Generally, in the presence of finite magnetic anisotropy D, the 
universality class of the spin system with Heisenberg interaction J shows a crossover from the 
isotropic Heisenberg class to Ising-like one as temperature getting closer to TN, at the 
temperature defined as 1~φ−t
, where t  is the reduced temperature, and 1<φ , the 
crossover index16).  The critical exponent is expected to show simultaneously the gradual 
change from 0.367 of 3D-Heisenberg to 0.327 of 3D-Ising.  However, as is clear in Fig. 2, 
the value of β, the gradient of the fitting line, shows a further decrease from 0.33 as the fitting 
temperature region is expanded.   We conclude that our previous interpretation of the 
observed β to be the Ising model arisen from D* is possibly be misleading.  The reason of 
appearance of β=0.33 experimentally confirmed by both µSR and NMR is still open question 
at this stage, and must be resolved in the future both theoretically and experimentally. 
Figure 3 shows the dependence of the spin-lattice relaxation rate 11
−T  on temperature.  
In a ordered state, 11
−T  was measured on a left most peak.  There was no significant 
difference in 11
−T  on any peaks except for the center peak which bears rather a lower 
relaxation rate.  While 11
−T  of the gapped sample (x=1.0) decreases exponentially as the 
temperature decreases, reflecting the gapped ground state, the gapless sample (x=0.85) shows 
diverging behavior around NT .  This clearly demonstrates the fact that the observed phase 
transition is a second order one.  In the vicinity of the second order phase transition, the 
fluctuation in the magnetic field shows a critical slow down and enhances NMR- 11
−T , a 
measure for the Fourier component of the Larmor frequency in the fluctuation.  The 
dominant q-component of the fluctuation is considered to be located at far apart from zero, 
that is, possibly, around π=q .  The reason for this is the uniform susceptibility that probes 
the fluctuation around q=0 shows no diverging behavior around NT . 
The scaling plot of 11
−T  in the temperature region both above and below NT  is shown 
in Fig. 4, where the dynamical critical exponent was obtained by fitting ( )nTT N1− to the 
observed temperature dependence as n=1.0(4) for NTT <  and 0.5(4) for NTT > .  The 
latter value above TN coincides with that for the classical 3D localized spin system.  The 
universality class belongs to the three dimensional one, for which the same argument as that 
on β stated above holds.   
In conclusion, we investigated 1H-NMR on a bond-disordered spin-gap system 
IPA-Cu(Cl0.85Br0.15)3.  The existence of an antiferromagnetic long-range order was clearly 
demonstrated by peak splitting in the spectra and by the divergence of 11
−T .  The critical 
exponent was obtained from the temperature dependence of hyperfine field to be β=0.33, 
which is close to the value expected for the 3D-Ising model. 
Acknowledgment 
We thank Dr. H. Manaka and Prof. T. Ohtsuki for their valuable advice, and Dr. K. Noda 
at Kuwahara Lab., Sophia University for his assistance with specific heat measurements using 
PPMS.  We also thank Prof. T. Nojima at the Center of Low Temperature Science of Tohoku 
Univ. for his assistance with magnetization measurements using MPMS.   This work was 
supported by the Kurata Memorial Hitachi Science and Technology Foundation, Saneyoshi 
Scholarship Foundation and by a Grant-in-Aid for Scientific Research on priority Areas “High 
Field Spin Science in 100T” (No.451) from the Ministry of Education, Culture, Sports, 
Science and Technology (MEXT). 
1) Y. Kitaoka, S. Hiramatsu, K. Ishida, T. Kohara, K. Asayama: J. Phys. Soc. Jpn. 56, 3024 
(1987) . 
2) M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura and H. Obara: Phys. Rev. Lett. 71, 4059 
(1993) . 
3) M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher: Phys. Rev. 40, 546 (1989). 
4) T. Nakamura: Phys. Rev. B71, 144401 (2005). 
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5) T. Masuda, A. Zheludev, H. Manaka, L.-P. Regnault, J.-H. Chung and Y. Qiu: Phys. Rev. 
Lett. 96, 047210 (2006).  
6) F. D. Haldane: Phys. Rev. Lett. 50, 1153 (1983). 
7) H. Manaka, I. Yamada, and K. Yamaguchi: J. Phys. Soc. Jpn. 66, 564 (1997). 
8) H. Manaka and I. Yamada: J. Phys. Soc. Jpn. 66, 1908 (1997). 
9) H. Manaka, I. Yamada and H. Aruga Katori: Phys. Rev. B63, 104408 (2001); In early 
papers of Manaka, three surfaces of the crystal were referred as A, B and C-plane in 
ascending order of area.  Recent neutron experiment by Masuda has revealed that b*-axis is 
perpendicular to C-plane, and c-axis, A-plane. 
10) H. Manaka, I. Yamada, H. Mitamura and T. Goto: Phys. Rev. B66, 064402 (2002). 
11) T. Saito, A. Oosawa, T. Goto, T. Suzuki and I. Watanabe: Phys. Rev. B74, 134423.  
12) H. Manaka, I. Yamada, M. Hagiwara and M. Tokunaga: Phys. Rev. B63, 144428 (2001). 
13) H. Manaka,I. Yamada: Physica B284-288, 1607 (2000). 
14) H. Manaka,I. Yamada: Phys. Rev. B62, 14279 (2000). 
15) A. B. Harris: J. Phys. C 7, 1671 (1974). 
16] J. Cardy: “Scaling and Renomalization in Statistical Physics” (Cambridge U. P. 1996). 
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−0.05 0 0.05
H−1γ/ν0 (T)
18.0K x=0.85(gapless)
x=1.0 (gapped) 15K
Fig. 1 1H-NMR spectra of x=0.85 and 1.0 at various temperatures.  The gyromagnetic ratio 
of 1H, 42.5774MHz/T is denoted as 1γ. 
0 5 10 15
Temperature (K)
TN=13.5K
0.01 0.05 0.1 0.5 1
H⊥C x=0.85 (gapless)
1−T(K)/TN
 β=0.33
∆H~ (1−|T |/TN)
 -12-
Fig. 2 Dependence of the splitting width ∆H on the temperature, definition of which is shown 
in Fig. 1.  The curve shows the scaling function ( )βN1 TT− , where =NT 13.5 K and 
33.0=β  are determined by data fitting. 
0 10 20 300
Temperature (K)
  x=0.85   
(gapless)
  x=1
(gapped)
0 1.0 2.0
0 10 20
Delay (msec)
↑ 3.7K
↓ 14K
Fig. 3  Dependence of the spin-lattice relaxation rate 11
−T  on temperature of gapped (x=1.0) 
and gapless (x=0.85) samples with the field direction H⊥C and H⊥B respectively.    The 
inset shows typical relaxation curves for the x=0.85 sample. 
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0.05 0.1 0.5 1
1−|T |/TN
x=0.85 (gapless)
T <TN    1.0  
T >TN    0.5
−1~ (1−|T |/TN)
Fig. 4 Scaling plot of 11
−T  against the reduced temperature N1 TT− .  The dynamical 
critical exponent was obtained from data fitting (dashed lines).
