Hyperfine Interact (2016) 237:116 DOI 10.1007/s10751-016-1329-y

NMR study on the quasi one-dimensional quantum spinmagnet with ladder structure

Shohei Kobori1 ·Kazuki Matsui1 ·Hideki Kuwahara1 ·Takayuki Goto1 ·Xiao Zhang2 ·Yuki Nakano2 ·Sadafumi Nishihara2 ·Katsuya Inoue2 ·Takahiko Sasaki3

© Springer International Publishing Switzerland 2016

Abstract The two-legged spin ladder Cu(CO3)0.5(ClO4)(H2O)0.5(NH3)2.5 consists of arung formed by two Cu(II)’s and of a spacing molecule CO2−

3 between each two rungs. The

non-centrosymmetric shape of CO2−3 molecule brings a slight bond alternation along the leg,

and hence the system can be considered as an alternating spin chain, which is confirmed sofar by the temperature dependence of magnetic susceptibility. In order to investigate its spinstate at low temperatures, we have performed experiments of 1H-NMR, magnetization andspecific heat under wide range of magnetic field, and have found the critical diverging oflongitudinal relaxation rate 1/T1, the spectral broadening and the lambda-type anomaly inspecific heat at TN � 3.4 K, indicating the existence of long range magnetic order. In param-agnetic state well above TN, 1/T1 showed a power-law temperature dependence, suggestingthe realization of Tomonaga Luttinger liquid state.

Keywords Alternating spin chain · NMR · Tomonaga-Luttinger liquid

1 Introduction

Despite their simple Hamiltonian, one dimensional and quasi-one dimensional spin sys-tems possess a potential possibility to exhibit exotic phases at low temperatures, where the

This article is part of the Topical Collection on Proceedings of the International Conference onHyperfine Interactions and their Applications (HYPERFINE 2016), Leuven, Belgium, 3-8 July 2016

� Takayuki Gotogotoo-t@sophia.ac.jp

1 Physics Division, Sophia University, 7-1 Kioicho, Chiyodaku, Tokyo, 102-8551, Japan

2 Department of Chemistry, Hiroshima University, Higashi-hiroshima, 739-8526, Japan

3 Institute of Material Science, Tohoku University, 2-1-1 Katahira Aobaku, Sendai, 980-8577, Japan

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quantum fluctuation plays an important role. Among them, the alternating spin chain sys-tem, which is effectively described by a parameter of the alternating ratio of neighboringtwo exchange interactions, is expected to show a variety of phenomena. The ground statefor alternating spin chain system was theoretically investigated by Hida [2], who revealedthat there is no quantum critical point within the parameter space of alternating ratio from−1 (Haldane chain) to 1 (uniform antiferromagnetic chain). Nakamura has pointed out thatby introducing the bond-randomness the system may show a uniform ordered state (orderby disorder), which was experimentally confirmed in the bond-disordered F-AF alternatingsystem [3–5]. Further experimental surveys on the AF-AF’ alternating chain have suggestedthe possibility of the Bose-glass phase [6–8] which is the gapless state with a zero-criticaltemperature [9]. On the other hand, in alternating spin systems with the Dzyaloshinskii-Moriya (DM) vector alternation, the existence of field-induced spin excitation energy gaphas been reported [10].

Another important topic for the alternating spin chain system is the peculiarity of param-agnetic state. In one dimensional systems, condensation of magnons is strongly suppressed,and even at low temperatures spins stay in a critical state, where the spatial correlation func-tion becomes like x−2K . This is so-called Tomonaga Luttinger liquid (TLL), where manyphysical quantities are expected to show the power-law temperature dependence with anindex K , the Luttinger parameter [11]. The behavior of K is studied theoretically in detailfor alternating spin chains, and its detailed field-dependence was reported [12–15]. Experi-mental reports on magnetization or specific heat have reported the phase boundary of TLL,which locates adjacent to the ordered phase in H -T diagram [16–18]. However, the dataaccumulation of the Luttinger parameter K seems inadequate [19–21] until now to compareit with the theories.

The S = 1/2 quantum spin magnet Cu(CO3)0.5(ClO4)(H2O)0.5(NH3)2.5, which has beenrecently synthesized [1], possesses a two-legged spin ladder structure, belonging to thespace group of Pnma. There are two equivalent ladders in a unit cell. They run along a-axis(Fig. 1), and are well separated by intervening ClO4 molecules; the mean distance betweenladders is approximately 7.7 A. Between each two neighboring rungs on a ladder, thereexist non-centrosymmetric CO−2

3 molecules, which spatially modulate the exchange inter-action along the leg (Fig. 1), making the system equivalent to the alternating spin chain [1].By the temperature dependence of uniform susceptibility, our collaborators [1] have proventhat the system is well described as the alternating spin chain with two dominant exchangeparameters J3 = 7.26 and J4 = 4.42 K (Fig. 1), and that it shows no sign of magnetic orderdown to 2 K.

In order to investigate the ground state of this alternating spin chain system, we haveapplied 1H-NMR technique and measured the spectra and longitudinal nuclear spin relax-ation rate 1/T1 down to 2 K to find the existence of magnetic order at low temperatures.This conclusion is further supported by other experimental results of specific heat and mag-netization curve. In the paramagnetic region, the power-law behavior of 1/T1 was observed,and will be discussed in terms of the TLL state.

2 Experimental

The single crystal sample is obtained by the slow evaporation method [1]. The crystal istransparent-blue colored and has a shape of distorted hexagonal plate with an approximatesize 3×4×1 mm3. The longest edge of the hexagonal outline corresponds to the crystal a-axis. NMR spectra were obtained by conventional spin-echo method, where the amplitude

Hyperfine Interact (2016) 237:116 Page 3 of 7 116

5.40ÅÅ

3.3.71Å

4.43ÅÅ

a

Fig. 1 (left) Crystal structure with atomic labels, where N1, N2 and N3 make an NH3 molecule, and O6makes H2O. The distances between neighboring Cu’s are shown by arrows. (right) Schematic drawing ofladder structure, where tilted triangles show CO3 molecule. The denotation of J3, J4 and J5 of exchangeinteractions is after Ref [1]

of echo signal was recorded against the magnetic field which was ramped around 3 T. Thelongitudinal spin relaxation rate was measured by the saturation-recovery method with apulse train. 1/T1 was simply extracted by fitting the the observed time evolution of thenuclear spin magnetization to the single exponential function.

The uniform susceptibility, the magnetization curve, and the specific were measured byPPMS of Quantum Design Co. Ltd., under fields up to 8 T and in the temperatures down to2 K.

3 Results and discussion

Figure 2a shows typical spectral profiles at various temperatures. There observed two dis-tinct peaks A and B of 1H-NMR signal at lower and higher field sides, respectively. Judgingfrom the stoichiometric ratio of 15:2 for H2O and NH3 sites, shown in Fig. 1, the peak Bwith the larger amplitude was assigned to the latter site. We estimated the isotropic part ofhyperfine coupling constant AB � −0.353 T/μB by scaling the temperature dependences ofNMR shift and the uniform magnetization as shown in Fig. 2b. This value, which is slightlylarger than a rough estimation based on the classical dipole-dipole interaction between NH3and Cu, whose distance is approximately 2A, is quite adequate to let 1H-NMR be a goodmicroscopic probe for the magnetism of the system.

As the temperature was lowered, spectrum gradually broadened, and we evaluated theline width δH of peak B with the definition of half width at half maximum (Fig. 2a), whichallowed one to avoid an artifact due to the overlapping of the two peaks. The temperature

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(a) (b)

3.2 3.3H(T)

1.8K

7.0K

10K

3.0K

3.2K

Echo

Am

plitu

de (a

rb. u

nit) A B

H a-axis

δH

20 40 600

0.01

0.02

0

0.02

0.04

0.06

T (K)−Δ

HB(T

)

M(μ

B/C

u2+)

H⊥a-axis

ΔHB M

AB= −0.353 T/μΒ

3.25 T

Fig. 2 a Profile of spectra at various temperatures. The observed two peaks are denoted as A and B. Thevertical dashed line shows the zero-shift position. The definition of the line width δH for peak B is shown atthe bottom. b Temperature dependence of uniform susceptibility and the Knight shift for the peak B in theparamagnetic state

dependence of δH is plotted in Fig. 3a, where a distinct kink appeared at around TN =3.4K. In order to examine the steep increase below the kink temperature TN, we subtractedfrom the raw width δH the slowly-varying trend in the paramagnetic region just above TN,described effectively as the Curie-Weiss function with � � 4.8 K. Thus obtained effectivewidth δHeff is shown in the inset, the behavior of which strongly suggests the existence ofphase transition. The increase in δHeff at the lowest temperature is 0.012 T. If we simplyassume the collinear antiferromagnetic spin structure and the easy axis parallel with a, thesize of ordered moment is estimated to be anomalously small a value 0.034 μB. However,for its definitive argument, one needs further information, for there is a possibility of non-collinear spin structure, as will be discussed below.

We refer here a little bit the validity of the above subtracting function. Though the valueof � is comparable to J ’s and hence is considered to be quite reasonable, the temperaturedependence of this subtracting function is apparently different from that of the uniformsusceptibility [1], which takes a maximum at 4 K and decreases below it. This means thatthe increase in δH in the paramagnetic region above TN is driven by the development ofstaggered moment with short correlation length rather than the uniform alignment of spins.This can be confirmed by a diffuse scattering neutron experiments.

The occurrence of magnetic phase transition is further confirmed by a divergence in 1/T1due to a critical slowing down of spin fluctuation at TN, as shown in Fig. 3b. And also, thespecific heat C showed a lambda-shaped anomaly simultaneously at TN as shown in the insetof Fig. 4a. With these observations one can conclude that the second order phase transitiondoes take place. We note that the peak position in C, denoted as T ∗

N is slightly lower than theTN determined by NMR, which corresponds to the onset of the lambda-shape anomaly asshown in the inset of Fig. 4a. The specific heat under magnetic field shows that T ∗

N decreasesmonotonically with increasing field up to 8 T, where T ∗

N � 2.1 K. If one extrapolates it, T ∗N

may reach zero at 14(1) T, which coincides with the saturation field stated below.Next, we show in Fig. 4b the magnetization curve at 2 K for two different field direc-

tions. While M with H ⊥ a configuration increased monotonically with H , that with

Hyperfine Interact (2016) 237:116 Page 5 of 7 116

(a) (b)

2 3 4 5 60

0.005

0.01

T (K)δH

eff (

T)

TN =3.4 K

0 2 4 60

0.02

0.04

0.06

T (K)

δ H (O

e)

HWHM of peak-B H0=3.25 T

0 5 10 150

1

2

3

T (K)

1/T 1

(mse

c−1)

TN =3.4 K

1/T1∝Τ α

α = −0.080α = 3.0

3.271 T

0 1 2 3 410−2

10−1

100

τ (ms)

1 −

I(τ )

/I(∞

)

1.8 K

3.1 K

30 K

Fig. 3 a Temperature dependence of the line width δH of peak B, definition of which is shown in Fig. 1a.The vertical arrow shows TN =3.4 K, determined as the position of kink. The dashed curve is the Curie-Weissfunction fitted to the temperature dependence of δH in the paramagnetic state just above TN. The effectiveline width δHeff is obtained by subtracting this Curie-Weiss term from δH , and is shown in the inset. bTemperature dependence of the longitudinal nuclear spin relaxation rate T −1

1 of B-site. The solid and dashedcurves show the power law function T −3 and T −0.08 in the ordered state and paramagnetic state respectively.The inset shows typical relaxation curves

H ‖ a showed a small but distinct step �M = 0.026 μB at HSF = 1.15 T. In highfield region over HSF, there was no anisotropy in M up to 8 T. If we adopt the powder-averaged value of g-factor 2.20 [1], the saturation field is roughly estimated to be 14 T,which is comparable to the exchange parameters J ’s, and is quite reasonable. Although theobserved small step suggests the occurrence of a spin-flop transition for the field appliedparallel with the easy-axis of a, the low-field value of M/H for H ‖ a remains finite,that is, approximately 58 % of the higher-field value. This suggests that the spin structureat H < HSF is not of a simple antiferromagnetic type but of a non-collinear structure.In order to determine the structure, a neutron scattering experiment is necessary, and isplanned now.

Finally, we discuss the behavior of 1/T1 in the paramagnetic state, where it obeys powerlaw of T −0.08 in rather a wide temperature range between 5 and 20 K as shown in Fig. 3b.This behavior is apparently different from 1/T1 = const. of the isolated spin systems,and suggests the possibility of the TLL state. In this phase, the spin fluctuation of paral-lel and perpendicular components contribute through the anisotropic hyperfine interactionsuch as dipole-dipole interaction to 1/T1 as T 2K−1 and T 1/2K−1, respectively. At lowtemperatures, the term with the negative power law index must be dominant, indicatingthat 2K � 0.92 (1.09) if the parallel (perpendicular) component in the spin fluctuation isdominant.

So far, theoretical investigations on the alternating spin chain by the numerical diag-onalization method have been reported [12–15] for various alternation ratio and also forthe next-nearest neighbor interaction. For example ref. [13] reported that for the case ofalternation ratio 0.5, the index is estimated to be 2K � 1.5 and 0.76 for the parallel and per-pendicular fluctuations. In order to compare the observed result to the theory, detailed fielddependence of the index parameter must be measured, and that is now in progress.

116 Page 6 of 7 Hyperfine Interact (2016) 237:116

(a) (b)

0 2 4 6 80

1

2

3

H(T)

T N * (

K)

2 3 4 5 60

0.01

0.02

C (J

/K/g

)

T(K)

H=3T

TN*

0 2 4 6 80

0.2

0.4

0.6

H(T)M

(μB/C

u2+)

H a-axisH//a-axis

T = 2 K

0.026μB

HSF =1.15 T

Fig. 4 a Field dependence of T ∗N, determined by the specific heat C. The curve is for an eye-guide. The inset

shows a typical temperature dependence of C under field 3 T, where a definition of T ∗N as the peak top of λ-

shape anomaly is shown. TN determined by NMR is slightly higher than T ∗N, and points the onset temperature

of λ-shape anomaly. b M-H curves for field directions ⊥ a-axis and ‖ a-axis shown by dashed and solidcurves. The small jump at HSF =1.15 T and its jump width are shown by arrows

4 Summary

We have investigated the ground state and finite-temperature behavior of Heisenberg alter-nating spin chain Cu(CO3)0.5(ClO4)(H2O)0.5(NH3)2.5 by 1H-NMR. The evidence of theantiferromagnetic long-range ordering at TN = 3.4 K was pointed out from the spectralbroadening, 1/T1 divergence and λ-type anomaly in the specific heat. In paramagnetic state,the power-law type temperature dependence of 1/T1 ∝ T −0.08 was observed, indicating thepossibility of TLL state.

Acknowledgments This work was partly supported by JSPS KAKENHI Grant Number 26108713,15K05148 and 15H03700. It was also supported by the Sophia University Special Grant for AcademicResearch. This work was partly performed at High Field Laboratory for Superconducting Materials, Institutefor Materials Research, Tohoku University.

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