structural fluctuations and magnetic excitations in the spin-peierls system cugeo3

ELSEVIER Physica B 234-236 (1997) 528-533

Structural fluctuations and magnetic excitations in the spin-Peierls system CuGeO3

L.P. Regnault D~partement de Recherche Fondamentale sur la Mati~re Condenske, SPSMS/MDN CEA-Grenoble, 38054 Grenoble Cedex 9, France

Abstract

A review of recent experimental results obtained by neutron diffraction and inelastic neutron scattering on the inorganic spin-Peierls compound CuGeO 3 is proposed. As the spin-Peierls scenario results from the interplay between lattice and magnetic fluctuations, we will focus on both aspects of the problem. With CuGeO3, most of the theoretical predictions have been very quantitatively verified. In this article, we will describe the most relevant results which have been obtained in zero field and at low fields. However, there remains unsolved questions which we will discuss briefly.

Keywords: Spin-Peierls system; One-dimensional system; Quantum effects; Inelastic scattering

1. Introduction

Since the pioneering work of Hase et al. [1] in 1993 and the large amount of work which has followed, the quasi-one-dimensional inorganic germanate CuGeO3 is now undoubtedly con- sidered as one of the best prototypical example of the spin-Peierls (SP) system. Basically, if one con-

. 1 siders a spln-i linear antiferromagnetic Heisenberg chain for which the spin-lattice interactions are sizable, the coupled system undergoes below a characteristic temperature Tsp (called the spin-Peierls transition temperature) a lattice distortion from a uniform (U) high-temperature phase to a dimerized (D) low-temperature phase [2]. This remarkable dynamical magneto-elastic phenom- enon gives rise to a rather universal phase diagram as a function of temperature (T) and field (H) [3]. The progressive dimerization of the lattice which occurs at Tsp has important consequences on both the magnetic and structural properties. First, the

ground state at T = 0 is predicted to be a non- magnetic (singlet) ground state, well separated from the first excited (triplet) states by an energy gap A ~ 1.76kTsp (BCS-like, directly related to Tsp). The presence of this gap implies the existence of exponential dependence in the thermal behavior of e.g. z(T) or C(T), which can be checked experi- mentally. Under an applied magnetic field, the SP system undergoes a new first order phase transition at a specific value Hc ~ 0.84A/g/~a [4, 5], above which a more conventional magnetic system is re- covered. This "intermediate" (I) phase is predicted to be a soliton-lattice phase, characterized by an incommensurate (IC) propagation vector ksp(H) = ksp(0) __+ 6ksp (H) function of field [6-8]. Above Hc, the lattice distortion can be schematically viewed as a staking of dimerized regions regularly spaced by a 3D array of solitons each carrying a spin value ½ [8]. The cell parameter L of the soliton lattice (representing two times the intersoliton distance) is directly related to the shift from commensurability

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i .P. Regnault / Physica B 234-236 (1997) 528-533 529

6ksp and the magnetization M, following the simple relation: 6ksp(H) ~ 2nIL(H) oc M(H).

All these features have been more or less seen in CuGeO3 from different techniques. In this paper, we will summarize the main findings obtained from neutron scattering. Despite an apparently good quantitative agreement with the standard SP model, some points (mainly concerning the lattice properties around Tse) are still unsolved. They will be briefly reviewed and discussed here.

2. Structural distortions and fluctuations

Germanate CuGeO3 crystallizes within an ortho rhombic structure of space group Pbmm. The lattice parameters at room temperature are: a = 4.81/~, b = 8.83/~ and c = 2.95 A. The crystal- lographic structure can be described as a stacking of CuO2 chains and GeO4 chains sharing one oxygen atom (both running along the c axis). More importantly, the Cu-O-Cu bonding angle is very near 90 °, a value which should imply a strong sensitivity of the intrachain magnetic coupling to distortions of the CuO/groups.

The specificity of CuGeO3 has been immediately recognized from the quite intriguing behavior of the magnetic susceptibility at low temperatures [1]. The two most remarkable features concern the rapid (exponential) drop of z(T) which is observed below 14 K and the departure from the Bonner- Fisher prediction giving the temperature depend-

. 1 ence of the magnetic susceptibility for the spin 5 U-chain. This behavior has been ascribed to the occurrence of a SP transition at Tsp ~ 14 K. The first evidence of the existence of dimerization superlattice peaks below Tsp were obtained from X-ray [9] and electron diffraction [10] experiments. Neutron diffraction measurements have confirmed the presence of nuclear satellites at the scattering vectors (Qa +_ ½, Qb, Qc +_ ½) with Qb odd [9, 11] and even [11], a fact which indicates that the propagation vector of the structural distortion is

1 1 ksp = (5, 0, 5). Fig. 1 shows a typical scan across the satellite reflection (½, 3, ½) which gives a clear evidence for a resolution-limited superlattice peak at a commensurate (C) position.

<:5

o E

Z

1400

1200

1000

8OO

6O0

4O0

200,

-0.04 -0.02 0 0.02 q (r.l.u.)

o CuGeO 3 Q=( 1/2+q/6,3+q, 1/2+q/6) -

\

0.04

Fig. 1. Longitudinal elastic scan across the (12, 3, ½) superlattice peak.

An accurate determination of the structural distortion in the D-phase has been obtained from neutron diffraction measurements [11,12]. Ac- cording to these results, the largest atomic displacements are observed for the Cu-atoms (moving mainly along the c-axis) and O(2)-atoms (moving mainly in the (a, b) planes), however with very small amplitudes. From the analysis of the integrated intensities of a series Of satellite reflections, the following values of relative displacements have been deduced: U~cu/C ~ 0.002, u~(2)/a ~ 0.0018 and u~(2)/b ~ 0.008, which confirm quantitatively their weakness. The resulting structural distortion can be described as an alternating rotation of the GeO4 groups, which induces positive and negative displacements of Cu-atoms along the chain axis [11, 12].

The transition at Tsp comes with pretransitional structural fluctuations which have been clearly observed by X-ray diffraction up to at least 40 K, but almost absent in neutron diffraction. In addition (and despite careful measurements), no phonon softening has been detected in CuGeO3 so far. These negative results may be attributed either to the weakness of the relevant structural fluctuations (roughly proportional to (u)ZT) or to the nature of the phase transition itself, which could be of order-disorder type instead of displacement-type (i.e. without phonon softening but associated with a phonon damping at Tsp). We will come back to this point later.

Magnetization [13] and X-ray diffraction [14] measurements allowed an accurate characteriza- tion of magnetic and structural properties above

530 L.P. Regnault I Physica B 234-236 (1997) 528-533

1200 CuGeo.~TSio.oo30 s

~" 1000 , / ~ ~ A6~ ° Q=(I/2,3,QL) o o L \o / k o

/ v \ ~' \ / \ - - -o-- . H = 1 2 T

z 200 0

0

0 ' '

0.48 0.49 0.50 0.51 0.52 QL (r.l.u.)

! 1 Fig. 2. Elastic scan along the chain direction across the (-~, 3, 3) satellite at 11.5 T and 12 T showing the rapid appearance of the incommensurability above Hc ~ 11.7 T.

the critical field (which amounts to about 12.5 T in CuGeO3). As expected from the standard SP model, X-ray measurements under field up to 13 T have nicely confirmed the IC nature of the I-phase and the existence of a soliton lattice above Hc [14]. Recent neutron diffraction measurements on a slightly (0.3%) Si-doped sample (for which Hc ~ 11.7 T is slightly reduced) have also given an unambiguous evidence for a splitting of the superlattice peaks above Hc. Fig. 2 illustrates the rapid appearance of the incommensurability above the critical field, which is well documented by the emergence of a two-peak structure when crossing the transition line. From the value of the incommensurability of the wave vector at 12T, 6ksp ~ 0.0075 r.l.u., one deduced an intersoliton distance of about 65 intrachain distances. The soliton width (estimated from the third-harmonic intensity) amounts to about 15 intrachain distances, in agreement with the X-ray determination. More details can be found in the paper by Grenier et al., this issue.

3. Magnetic excitations and fluctuations

As mentioned in the introduction, the progressive dimerization which takes place below Tsv indu-

ces at least two characteristic features: a singlet ground state and the opening of a gap in the magnetic excitation spectrum at "q = rt", the antiferromagnetic point. The existence of the singlet ground state has been unambiguously demon- strated from NQR measurements of the spin- lattice relaxation time T1 on the Cu-sites. The experimental data 1-15] show a rapid decrease of 1/TI, characteristic of a vanishing of all magnetic components at co ~ 0, as T ~ 0. Quasi-elastic neutron scattering experiments also revealed the absence of magnetic scattering at low energy. The gap has been directly observed from INS experiments [16, 17]. Fig. 3 shows a typical energy scan per- formed in the vicinity of the antiferromagnetic point kay = (0, 1,½), using the three-axes spectrometer IN14 installed on a cold guide at ILL (fixed kf = 1.5 A- 1). Quite unambiguously, a well defined and narrow peak is observed, which demonstrates the presence of an energy gap A ~ 1.95 meV in the excitation spectrum, d and Tsp verify the relation 2A/kTsa ~ 3.32, which is very close to the BCS value.

The dispersion relation of magnetic excitations along the chain axis has been determined in the full Brillouin zone [17]. Fig. 4 summarizes the results which were obtained. In a first approximation, the experimental data were analyzed within the

L.P. Regnault / Physica B 234-236 (1997) 528-533 531

1500

O o , I

II t - O

E ~ looo e -

o

500 .=_ t -

O

z 0 0.5

'' '' i . . . . i . ' ' ' I' '' 'I .... i . . . . I . . ''

C u G e O 3 Q=(0 ,-1 .O25, O.5) T=2.7 K H=0

,)

. . . . . • • • a l a , i , i i I I ' ' I I I I ' l

1 1.5 2 2.5 3 3.5 4 Energy (meV)

Fig. 3. Energy scan at the scattering vector Q = (0, - 1.025, ½) showing the spin gap in zero field.

20

15 > Q E

v >, 10

Q~ t--

,,, 5

0

i i i i

CuGeO 3 T=1.8 K

/ H = 0 '

0:3'0:4'0.5 qc (r.l.u.)

Fig. 4. Dispersioncurveofmagneticexcitat ions along the chain axis (full Brillouin zone).

• 1 framework of the spin- 5 alternating antiferromagnetic chain, expected to describe correctly the dimerized state at T ~ 0. For this model, the dispersion relation is given by the following relation [18]:

og(qc) ,~ x / A 2 + (¢02M -- AZ)sinZ(27zqcc), (1)

where ~0M (15.6meV in CuGeO3) represents the maximum energy of the excitation spectrum. Both A and tOM are functions of the two alternating exchange constants J1 and J] -- :~J1. The neutron data are reasonably reproduced by using the ex- pression 271~10.6meV and 6 = l - c t / l + c t ,~ 0.04 (solid line in Fig. 4). The latter value is

~ 140 O

E 120

g loo 0

8O .g- ~ 60 C

~ 40 e -

~ 20 , - i

~ 0 z 0

, ' I . . . . l ' ' ' ' I I ' ' ' i ' ' ' ' l . . . . i . . . . I ' ' ' '

CuGeO 3 Q=(0,-0.95,0.5) T=2.5 K

~, H=12 T

• • el,

"" "% .-.,. "-:. ¢

I .... i ~IIII~, .... i . . . . . . . i ...i

0.5 1 1.5 2 2.5 3 3.5 4 Energy (rneV)

Fig. 5. Energy scan at the scattering vector Q = (0, - 0.95, ½) and for a field of 12 T (applied along the chain axis) showing the splitting of the triplet excited states into three distinct modes.

consistent with the weakness of atomic displacements deduced from the neutron diffraction experiments. In addition, a relatively strong dispersion of magnetic excitations is observed along the b axis [16, 17], which can be understood from the existence of sizable antiferromagnetic interchain interactions along this direction (typically one got a ratio Jb/Jc "~ 0.1, which show quantitatively the poor 1D character of this compound). Indeed, a puzzling problem in CuGeO3 is to understand why the long range magnetic ordering is not found with such values of interchain couplings.

From the SP theory, the excited states are expected to be triplets. In the presence of the field, the gap should split into three distinct components with energies A _, A o and A + displaying quasi- linear dependence below Ho according to the relations:

A + (H) ~ A +_ gpBH, (2a)

Ao(H) ~ A. (2b)

INS experiments in high magnetic field (up to 12 T) have confirmed the splitting of the gap and the theoretically predicted linear dependences. Fig. 5 shows an energy scan carried out on the IN12 spectrometer (CRG-ILL) in the vicinity of the antiferromagnetic point for a temperature T = 2.5 K and a field H -- 12 T. These data reveal without any ambiguity the existence of three well defined peaks centered at 0.45, 1.95 and 3.45 meV with

532 L.P. Regnault / Physica B 234-236 (1997) 528-533

3 , 5 , , , i , , , i , , , i , , , J . , ,

, , ,

0 20 40 60 80 1 O0 H (kOe)

Fig. 6. Field dependence of gaps at "q = 7t" in field applied perpendicular to the chain axis. The solid lines correspond to the theoretical prediction given by Eq. (2).

1 1 intensity ratios 3" 1 • ~, respectively• This confirms that the excited states are triplets. The field depend- encies of the three gaps [17] at "q = n" (in a field perpendicular to the chain axis) are reported in Fig. 6. In the field range which has been explored, we observed essentially quasi-linear variations which are understood from the quasi-isotropy of the spin system. It is only in the vicinity of Hc that the lowest energy gap drops rapidly to zero (the magnetic system is expected to be gapless in the IC phase), without strong pretransitional effects• This is again in agreement with the occurrence of a first order C-IC phase transition.

4. Discussion and conclusion

Another puzzling result concerns the quite un- usual temperature dependence of the magnetic susceptibility which was observed above the SP transition temperature. As previously mentioned, z(T) is far from obeying the prediction of the simple

• 1 spin- 5 U-chain. Recent theoretical calculations [19, 20] have emphasized the possible role of next- nearest neighbors intrachain exchange couplings J2 in explaining the rounded shape of g(T). According to these calculations, a ratio as large as J2/J1 ~ 0.2 could account for the experimental data (taking 2J1 ~, 12 meV and a very small alternation parameter 6 ~ 0•03). Such a relatively large value of J2/J1 is in fact not at all inconsistent with our neutron data [17] concerning the dispersion relation of magnetic excitations along the chain (og(qc)) and the wave vector dependence of the energy integrated intensity (S(qJ). Although with a large uncertainty in the determination of this ratio, a sig- nificantly better agreement with the neutron data can be achieved by taking a value J2/J1 ~ 0.17. The strength of J2, by inducing additional quantum disorder (in fact spontaneous dimerization), could counterbalance the relatively strong interchain couplings existing in CuGeO3 [16, 17], restoring the singlet ground state and the spin gap. This explanation could also account for the anomalous nature of the transition, especially the absence of phonon softening. Quite obviously, more experimental as well as theoretical work is needed to clarify this crucial point.

The experimental investigation of CuGeO3 has allowed a precise verification of most of predictions of the SP system (dimerization, singlet ground state, gap, critical field, incommensurability .... ). However, the most crucial point (the dynamical interplay between spins and phonons) has not been established in this material. In the standard scenario, the structural distortion at Tsp is expected to be driven by a soft phonon mode. However, such a feature has not been observed so far in CuGeO3, so that the question on the validity of the standard approaches remains open. A first improvement of the theory would imply in going beyond the mean- field approximation and taking into account the structural fluctuations, still present in CuGeO3 above Tsp, as shown from X-ray diffraction.

Acknowledgements

It is a pleasure to thank my coworkers J.E. Lorenzo, B. Grenier, M. AYn, B. Hennion, G. Dhalenne and A. Revcolevschi. Discussions with J.P. Boucher and J.P. Renard were appreciated•

References

I-1] M. Hase, I. Terasaki and K. Uchinokura, Phys. Rev. Lett. 70 (1983) 3651.

[2] E. Pytte, Phys. Rev. B 10 (1974) 2039. [-3] M.C. Cross and D.S. Fisher, Phys. Rev. B 19 (1979) 402. I-4] J.W. Bray, Solid State Commun. 26 (1978) 771. [5] M.C. Cross, Phys. Rev. B 20 (1979) 4606.

L.P. Regnault / Physica B 234-236 (1997) 528-533 533

[-6] M. Fujita and K. Machida, J. Phys. Soc. Japan 53 (1984) 4395.

[-7] A.I. Buzdin and S.V. Polonskii, Sov. Phys. JETP 66 (1987) 422.

[-8] M. Fujita and K. Machida, J. Phys. C 21 (1988) 5813. [-9] J.P. Pouget, L.P. Regnault, M. Ain, B. Hennion, J.P.

Renard, P. Veillet, G. Dhalenne and A. Revcolevchi, Phys. Rev. Lett. 72 (1994) 4037.

[10] O. Kamimura, M. Terauchi, T. Tanaka, O. Fujita and J. Akimitsu, J. Phys. Soc. Japan 63 (1994) 2467.

[-11] K. Hirota, D.E. Cox, J.E. Lorenzo, G. Shirane, J.M. Tran- quada, M. Hase, K. Uchinokura, H. Kojima, Y. Shibuya and I. Tanaka, Phys. Rev. Lett. 73 (1994) 736.

[,12] M. Braden, G. Wilkendorf, J. Lorenzana, M. Ain, G.J. Mclntyre, M. Behruzi, G. Heger, G. Dhalenne and A. Revcolevschi, Phys. Rev. B 54 (1996) 1105.

[,13] M. Hase, I. Terasaki, K. Uchinokura, M. Tokunaya, N. Miura and H. Obara, Phys. Rev. B 48 (1993) 9616.

E14] v. Kiryukin, B. Keimer, J.P. Mill and A. Vigilante, Phys. Rev. Lett. 76 (1996) 4608.

E15] J. Kikuchi, Y. Yasuoka, M. Hase, Y. Sasago and K. Uchinokura, J. Phys. Soc. Japan. 63 (1994) 872

[,16] M. Nishi, O. Fujita and J. Akimitsu, Phys. Rev. B 50 (1994) 6508.

[17] L.P. Regnault, M. Ain, B. Hennion, G. Dhalenne and A. Revcholevschi, Phys. Rev. B 53 (1996) 5579.

[,18] J.C. Bonner and H.W.J. B16te, Phys. Rev. 13 25 (1982) 6959.

[,19] G. Castilla, S. Chakraverty and V.J. Emery, Phys. Rev. Lett. 75 (1995) 1823.

[20] S.Haas and E. Dagotto, Phys. Rev. B 52 (1995) R14 396.

structural fluctuations and magnetic excitations in the spin-peierls system cugeo3

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