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Cold neutron scattering measurement on haldane gap in NDMAZ
Journal of Physics and Chemistry of Solids 60 (1999) 1141–1143
Cold neutron scattering measurement on haldane gap in NDMAZ T. Kajitani*, K. Takayama, Y. Ono Department of Applied Physics, Tohoku University, Sendai 980-8579, Japan
Abstract NDMAZ; Ni(dmpn)2N3ClO4, dmpn C5H14N2 is one of the closely related materials of a typical Haldane gap material NENP; Ni(en)2NO2ClO4, en C2H8N2 both of which have almost isolated pseudo-one-dimensional Ni 21(S 1)2X chains with X NO2 (NENP) and N3(NDMAZ), respectively. The Haldane gap energy was measured using a TOF type cold neutron spectrometer, AGNES, at temperatures from 4 to 100 K in the vicinity of the reciprocal lattice point, 001/2. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Organic compounds; B. Chemical synthesis; C. Neutron scattering; D. Magnetic properties
1. Introduction Haldane gap [1,2] has been observed in the S 1 onedimensional (1D) Heisenberg antiferromagnets generally. One of the typical observation was reported for the pseudo-1D compounds, AgVP2S6 [3,4] and Ni(C2H8N2)NO2ClO4; NENP [5]. These systems have well separated pseudo-ID metal cation and counter anion chains and do not exhibit long range magnetic ordering in the low temperature range. The Haldane gap, D , which is the energy difference between the singlet ground state and the first excited triplet state in the magnetically isotropic systems. The gap energy has been estimated as D 6 2uJuS exp 2pS theoretically [1,2]. Here, J is the inter-chain exchange interaction constant. The equal time correlation function of spins in the S 1 1D system is found to decay exponentially and being inversely proportional with the inter-chain distance [1,2,6]. The gap energy has been estimated by the computer simulation as 0.411 uJu [7]. The title compound Ni(dmpn)2N3ClO4 with dmpn (2,2dimethyl-1,3-propanediamine) C5H14N2 being abbreviated as NDMAZ was synthesized and identified as one of the typical S 1 pseudo-1D system, similar to NENP by Yamashita et al. [8] Fig. 1 shows a perspective view of its partial structure. The structure consists of nickel plus dmpn molecules and interconnecting N3 ions, by which –Ni–N3 – Ni–N3 – chains are realized parallel to the c-axis. Each chain is separated by ClO4 counter anions (not drawn). The crystal * Corresponding author.
has a monoclinic unit cell, space group C2, with a ˚ , b 8.152 A ˚ , c 6.098 A ˚ and b 98.278 at 18.860 A room temperature. The crystal structure is similar to NENP, which has –Ni–NO2 –Ni–NO2 – chains also separated by ClO4. The magnetic susceptibility, x , versus temperature dependency of NDMAZ was successfully measured by Takeuchi et al. [9], showing typical x –T curve of the ‘Haldane material’, slightly increasing with decreasing temperature from the ambient, but decreasing rapidly below 50 K. Based on the x –T curve, three physical quantities g, J and D , were determined as g 2.21, J 270.6 K and D 22 K, respectively. g corresponds to the spectroscopic splitting factor, i.e. the Lande´’s g-factor. The magnetization versus magnetic field dependency up to 30 T at 4.2 K was also observed. It was found that no magnetization appeared in the field below 14 T, but began to increase linearly beyond the critical magnetic field at HT 14 T. The gap energy of D gmBHT 20.8 K was thus estimated. The present study is aimed to obtain the Haldane gap energy, D , by the cold neutron scattering experiment.
2. Experimental Relatively large NDMAZ single crystals were synthesized by Takayama, one of the authors of the present paper, following a similar chemical procedure adopted for the NENP synthesis. Single crystals were grown from a saturated water solution. The synthesis as well as the growth of NDMAZ was not easy relative to NENP. The maximum
0022-3697/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00059-1
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T. Kajitani et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1141–1143
Fig. 1. Pseudo-1D chain of Ni(dmpn)2N3(ClO4).
volume of NDMAZ single crystals was about 2 mm 3. The quality of the grown crystals was examined by the powder and the single crystal X-ray diffraction measurements at temperatures from the ambient to 120 K and the magnetic susceptibility measurement using a SQUID magnetometer at temperatures down to 4 K. Cold neutron scattering measurement was carried out using a TOF-type spectrometer AGNES [10]. The mono˚ was chromatized cold neutron radiation with l 4.22 A used throughout the measurement. The dynamical structure factor, S q; v, of NDMAZ single crystal was mostly observed at the reciprocal point 001/2 (p ) at temperatures from 4 to 100 K. Oriented and bunched five 1–2 mm 3 NDMAZ single crystals were used for the cold neutron measurement. The neutron scattering intensities were collected by many neutron counters implemented in the scattering angles between 10 and 1308. The energy resolution of the apparatus is 0.12 meV (FWHM) in the vicinity of the elastic peak.
3. Results The lattice parameters of the synthesized NDMAZ, a ˚ , b 8.173(3) A ˚ , c 6.111(4) A ˚ and b 18.903(24) A 98.26(7)8, are determined by the single crystal X-ray
diffraction, consistent with the literature values [8]. The lattice parameter versus temperature dependency shows linear contraction from the ambient temperature to 160 K, but the b- and c-axis lengths begin to contract rapidly below 160 K. NENP shows a similar non-linear thermal contraction of the c-axis below 160 K. The magnetic susceptibility versus the temperature curve was measured for NDMAZ powder specimen. The values of J 265.8 K and g 2.1 are deduced from the x –T curve from 300 to 43 K by fitting with the function used previously [9]. These values are in reasonable agreement with the literature values of J 270.6 K and g 2.21 [9] assuming x T / e2D=kT . The Haldane gap energy, D 14.8 K, is also estimated from the same curve measured at temperatures from 23 to 5 K. This value is appreciably smaller than the literature value of D 21.6 K [9]. The cold neutron scattering measurement was carried out in the a* × c* reciprocal plane. Since the Haldane gap energy was estimated as D 20.8–22 K (1.79–1.90 meV) [8,9], the energy focus point at the 001/2 point was set at DE 6 22.0 meV being observable at 2u 15–208. Fig. 2 shows a scattering angle dependent scattering intensities at 4.2 K. Each spectrum corresponds to the scattering intensities obtained in 24 h by neutron counter groups at 2u 10–148 (A), 15–208 (B), 21–248 (C) and 25–308 (D), respectively. The scattering intensities observed by five
T. Kajitani et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1141–1143
Fig. 2. Scattering intensities observed in the angles of 2u 10–148 (A), 15–208 (B), 21–248 (C) and 25–308 (D) at 4.2 K.
neutron counters belonging to each group were added to obtain better data statistics. The central peak is due to the elastic scattering. Low energy transfer peaks with DE 21.7–2.0 meV are exhibited in the A–C spectra. The peak at DE 21.75 meV in the B-spectrum corresponds to the excitation at 001/2 or its adjacent area. The inelastic peaks in the A- and C-spectra are situated at slightly higher energy transfer side, i.e. DE 21.8 and 21.9 meV, respectively, obtained from the reciprocal area at 001/2 ^ d with d 6 0.1, an indication of the dispersion relationship of the excitation. Fig. 3 represents the temperature dependent change of the inelastic scattering spectra obtained by the B counter group situated at 2u 15–208 at temperatures from 4.2 to 100 K. The 21.75 meV peak was observed at 4.2 K only. This means that the excitation at DE 21.75 meV is highly temperature dependent and may be masked by the thermal excitation at temperatures from 10 to 100 K. 4. Discussion It is natural to assume that the observed low energy, DE 21.75 meV, excitation at 001/2 reciprocal point or its adjacent area is due to the opening Haldane gap, as the energy value is close enough to the estimated value [8], the peak intensity is highly temperature dependent and a dispersion relationship was suggested. The gap energy corresponds to the energy difference between the singlet ground state and the excited doublet state D xy, which is a part of the triplet state split by the single ion anisotropy term, DS2z , as in NENP [11]. 5. Conclusion The direct observation of Haldane gap, D xy, at 001/2
1143
Fig. 3. Temperature dependence of the scattering intensities observed by the B-neutron counter group situated at 2u 15–208.
reciprocal point or its adjacent area was successfully accomplished by the use of TOF-type cold neutron spectrometer, AGNES. Observed gap energy, D xy 1.75 meV (20.3 K), has reasonable agreement with the previously estimated value [8,9].
Acknowledgements Financial support by the grant-in-aid from the Ministry of Science, Sports and Culture is gratefully appreciated.
References [1] F.D.M. Haldane, Phys. Lett. 93A (1983) 464. [2] F.D.M. Haldane, Phys. Rev. Lett. 50 (1983) 1153. [3] H. Mutka, C. Payen, P. Molenie, J.L. Soubeyroux, P. Colombet, A.D. Taylor, Phys. Rev. Lett. 67 (1991) 597. [4] H. Mutka, C. Payen, P. Molenie, J.L. Soubeyroux, P. Colombet, A.D. Taylor, Physica B 180–181 (1992) 197. [5] L.P. Regnault, I. Zaliznyak, J.P. Renard, C. Vettier, Phys. Rev. B 50 (1994) 9174. [6] I. Affleck, J. Phys. Condens. Matter 1 (1989) 3047. [7] O. Golinelli, Th. Jolicoeur, R. Lacaze, Phys. Rev. B 45 (1992) 9798. [8] M. Yamashita, K. Inoue, T. Ohnishi, H. Miyamae, T. Takeuchi, T. Yoshida, Synth. Met. 71 (1995) 1961. [9] T. Takeuchi, T. Yoshida, K. Inoue, M. Yamashita, T. Kumada, K. Kido, S. Meral, M. Verdaguer, J.P. Renard, J. Mag. Mag. Mat. 140–144 (1995) 1633. [10] T. Kajitani, K. Shibata, S. Ikeda, M. Kohgi, H. Yoshizawa, K. Nemoto, K. Suzuki, Physica B 213–214 (1995) 872. [11] L.P. Regnault, I. Zalizuyak, J.P. Renard, C. Vettier, Phys. Rev. B 50 (1994) 9174.
Cold neutron scattering measurement on haldane gap in NDMAZ T. Kajitani*, K. Takayama, Y. Ono Department of Applied Physics, Tohoku University, Sendai 980-8579, Japan
Abstract NDMAZ; Ni(dmpn)2N3ClO4, dmpn C5H14N2 is one of the closely related materials of a typical Haldane gap material NENP; Ni(en)2NO2ClO4, en C2H8N2 both of which have almost isolated pseudo-one-dimensional Ni 21(S 1)2X chains with X NO2 (NENP) and N3(NDMAZ), respectively. The Haldane gap energy was measured using a TOF type cold neutron spectrometer, AGNES, at temperatures from 4 to 100 K in the vicinity of the reciprocal lattice point, 001/2. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Organic compounds; B. Chemical synthesis; C. Neutron scattering; D. Magnetic properties
1. Introduction Haldane gap [1,2] has been observed in the S 1 onedimensional (1D) Heisenberg antiferromagnets generally. One of the typical observation was reported for the pseudo-1D compounds, AgVP2S6 [3,4] and Ni(C2H8N2)NO2ClO4; NENP [5]. These systems have well separated pseudo-ID metal cation and counter anion chains and do not exhibit long range magnetic ordering in the low temperature range. The Haldane gap, D , which is the energy difference between the singlet ground state and the first excited triplet state in the magnetically isotropic systems. The gap energy has been estimated as D 6 2uJuS exp 2pS theoretically [1,2]. Here, J is the inter-chain exchange interaction constant. The equal time correlation function of spins in the S 1 1D system is found to decay exponentially and being inversely proportional with the inter-chain distance [1,2,6]. The gap energy has been estimated by the computer simulation as 0.411 uJu [7]. The title compound Ni(dmpn)2N3ClO4 with dmpn (2,2dimethyl-1,3-propanediamine) C5H14N2 being abbreviated as NDMAZ was synthesized and identified as one of the typical S 1 pseudo-1D system, similar to NENP by Yamashita et al. [8] Fig. 1 shows a perspective view of its partial structure. The structure consists of nickel plus dmpn molecules and interconnecting N3 ions, by which –Ni–N3 – Ni–N3 – chains are realized parallel to the c-axis. Each chain is separated by ClO4 counter anions (not drawn). The crystal * Corresponding author.
has a monoclinic unit cell, space group C2, with a ˚ , b 8.152 A ˚ , c 6.098 A ˚ and b 98.278 at 18.860 A room temperature. The crystal structure is similar to NENP, which has –Ni–NO2 –Ni–NO2 – chains also separated by ClO4. The magnetic susceptibility, x , versus temperature dependency of NDMAZ was successfully measured by Takeuchi et al. [9], showing typical x –T curve of the ‘Haldane material’, slightly increasing with decreasing temperature from the ambient, but decreasing rapidly below 50 K. Based on the x –T curve, three physical quantities g, J and D , were determined as g 2.21, J 270.6 K and D 22 K, respectively. g corresponds to the spectroscopic splitting factor, i.e. the Lande´’s g-factor. The magnetization versus magnetic field dependency up to 30 T at 4.2 K was also observed. It was found that no magnetization appeared in the field below 14 T, but began to increase linearly beyond the critical magnetic field at HT 14 T. The gap energy of D gmBHT 20.8 K was thus estimated. The present study is aimed to obtain the Haldane gap energy, D , by the cold neutron scattering experiment.
2. Experimental Relatively large NDMAZ single crystals were synthesized by Takayama, one of the authors of the present paper, following a similar chemical procedure adopted for the NENP synthesis. Single crystals were grown from a saturated water solution. The synthesis as well as the growth of NDMAZ was not easy relative to NENP. The maximum
0022-3697/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00059-1
1142
T. Kajitani et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1141–1143
Fig. 1. Pseudo-1D chain of Ni(dmpn)2N3(ClO4).
volume of NDMAZ single crystals was about 2 mm 3. The quality of the grown crystals was examined by the powder and the single crystal X-ray diffraction measurements at temperatures from the ambient to 120 K and the magnetic susceptibility measurement using a SQUID magnetometer at temperatures down to 4 K. Cold neutron scattering measurement was carried out using a TOF-type spectrometer AGNES [10]. The mono˚ was chromatized cold neutron radiation with l 4.22 A used throughout the measurement. The dynamical structure factor, S q; v, of NDMAZ single crystal was mostly observed at the reciprocal point 001/2 (p ) at temperatures from 4 to 100 K. Oriented and bunched five 1–2 mm 3 NDMAZ single crystals were used for the cold neutron measurement. The neutron scattering intensities were collected by many neutron counters implemented in the scattering angles between 10 and 1308. The energy resolution of the apparatus is 0.12 meV (FWHM) in the vicinity of the elastic peak.
3. Results The lattice parameters of the synthesized NDMAZ, a ˚ , b 8.173(3) A ˚ , c 6.111(4) A ˚ and b 18.903(24) A 98.26(7)8, are determined by the single crystal X-ray
diffraction, consistent with the literature values [8]. The lattice parameter versus temperature dependency shows linear contraction from the ambient temperature to 160 K, but the b- and c-axis lengths begin to contract rapidly below 160 K. NENP shows a similar non-linear thermal contraction of the c-axis below 160 K. The magnetic susceptibility versus the temperature curve was measured for NDMAZ powder specimen. The values of J 265.8 K and g 2.1 are deduced from the x –T curve from 300 to 43 K by fitting with the function used previously [9]. These values are in reasonable agreement with the literature values of J 270.6 K and g 2.21 [9] assuming x T / e2D=kT . The Haldane gap energy, D 14.8 K, is also estimated from the same curve measured at temperatures from 23 to 5 K. This value is appreciably smaller than the literature value of D 21.6 K [9]. The cold neutron scattering measurement was carried out in the a* × c* reciprocal plane. Since the Haldane gap energy was estimated as D 20.8–22 K (1.79–1.90 meV) [8,9], the energy focus point at the 001/2 point was set at DE 6 22.0 meV being observable at 2u 15–208. Fig. 2 shows a scattering angle dependent scattering intensities at 4.2 K. Each spectrum corresponds to the scattering intensities obtained in 24 h by neutron counter groups at 2u 10–148 (A), 15–208 (B), 21–248 (C) and 25–308 (D), respectively. The scattering intensities observed by five
T. Kajitani et al. / Journal of Physics and Chemistry of Solids 60 (1999) 1141–1143
Fig. 2. Scattering intensities observed in the angles of 2u 10–148 (A), 15–208 (B), 21–248 (C) and 25–308 (D) at 4.2 K.
neutron counters belonging to each group were added to obtain better data statistics. The central peak is due to the elastic scattering. Low energy transfer peaks with DE 21.7–2.0 meV are exhibited in the A–C spectra. The peak at DE 21.75 meV in the B-spectrum corresponds to the excitation at 001/2 or its adjacent area. The inelastic peaks in the A- and C-spectra are situated at slightly higher energy transfer side, i.e. DE 21.8 and 21.9 meV, respectively, obtained from the reciprocal area at 001/2 ^ d with d 6 0.1, an indication of the dispersion relationship of the excitation. Fig. 3 represents the temperature dependent change of the inelastic scattering spectra obtained by the B counter group situated at 2u 15–208 at temperatures from 4.2 to 100 K. The 21.75 meV peak was observed at 4.2 K only. This means that the excitation at DE 21.75 meV is highly temperature dependent and may be masked by the thermal excitation at temperatures from 10 to 100 K. 4. Discussion It is natural to assume that the observed low energy, DE 21.75 meV, excitation at 001/2 reciprocal point or its adjacent area is due to the opening Haldane gap, as the energy value is close enough to the estimated value [8], the peak intensity is highly temperature dependent and a dispersion relationship was suggested. The gap energy corresponds to the energy difference between the singlet ground state and the excited doublet state D xy, which is a part of the triplet state split by the single ion anisotropy term, DS2z , as in NENP [11]. 5. Conclusion The direct observation of Haldane gap, D xy, at 001/2
1143
Fig. 3. Temperature dependence of the scattering intensities observed by the B-neutron counter group situated at 2u 15–208.
reciprocal point or its adjacent area was successfully accomplished by the use of TOF-type cold neutron spectrometer, AGNES. Observed gap energy, D xy 1.75 meV (20.3 K), has reasonable agreement with the previously estimated value [8,9].
Acknowledgements Financial support by the grant-in-aid from the Ministry of Science, Sports and Culture is gratefully appreciated.
References [1] F.D.M. Haldane, Phys. Lett. 93A (1983) 464. [2] F.D.M. Haldane, Phys. Rev. Lett. 50 (1983) 1153. [3] H. Mutka, C. Payen, P. Molenie, J.L. Soubeyroux, P. Colombet, A.D. Taylor, Phys. Rev. Lett. 67 (1991) 597. [4] H. Mutka, C. Payen, P. Molenie, J.L. Soubeyroux, P. Colombet, A.D. Taylor, Physica B 180–181 (1992) 197. [5] L.P. Regnault, I. Zaliznyak, J.P. Renard, C. Vettier, Phys. Rev. B 50 (1994) 9174. [6] I. Affleck, J. Phys. Condens. Matter 1 (1989) 3047. [7] O. Golinelli, Th. Jolicoeur, R. Lacaze, Phys. Rev. B 45 (1992) 9798. [8] M. Yamashita, K. Inoue, T. Ohnishi, H. Miyamae, T. Takeuchi, T. Yoshida, Synth. Met. 71 (1995) 1961. [9] T. Takeuchi, T. Yoshida, K. Inoue, M. Yamashita, T. Kumada, K. Kido, S. Meral, M. Verdaguer, J.P. Renard, J. Mag. Mag. Mat. 140–144 (1995) 1633. [10] T. Kajitani, K. Shibata, S. Ikeda, M. Kohgi, H. Yoshizawa, K. Nemoto, K. Suzuki, Physica B 213–214 (1995) 872. [11] L.P. Regnault, I. Zalizuyak, J.P. Renard, C. Vettier, Phys. Rev. B 50 (1994) 9174.