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High-field magnetization processes of quantum double spin chain systems KCuCl3, TlCuCl3 and NH4CuCl3
Physica B 246—247 (1998) 230—233
High-field magnetization processes of quantum double spin chain systems KCuCl , TlCuCl and NH CuCl 3 3 4 3 H. Tanaka!,*, W. Shiramura", T. Takatsu!, B. Kurniawan!, M. Takahashi#, K. Kamishima#, K. Takizawa#, H. Mitamura#, T. Goto# ! Department of Physics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan " Department of Physics, Faculty of Science and Technology, Sophia University, Kioi-cho, Chiyoda-ku, Tokyo 102, Japan # Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
Abstract High-field magnetization processes of S"1 double spin chain systems KCuCl , TlCuCl and NH CuCl have been 2 3 3 4 3 measured up to 39 T at helium temperatures using single crystals. A transition from a singlet ground state with an excitation gap to a gapless magnetic state occurs at H &20 and 6 T for KCuCl and TlCuCl , respectively. The # 3 3 excitation gap D is evaluated as D/k "31.1 K for KCuCl and 7.5 K for TlCuCl . Although the antiferromagnetic B 3 3 interactions in TlCuCl are stronger than those in KCuCl , which can be seen from the slope of the magnetization curves 3 3 above H , the excitation gap in TlCuCl is about a quarter of that of KCuCl . In contrast to KCuCl and TlCuCl , # 3 3 3 3 NH CuCl has a gapless magnetic ground state. It is found that NH CuCl undergoes five phase transitions in high 4 3 4 3 magnetic fields. Two wide plateaus are observed at a quarter and three quarters of the saturation magnetization. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: KCuCl ; TlCuCl ; NH CuCl ; High field; Magnetization process; Double spin chain; Singlet ground state; 3 3 4 3 Excitation gap; Plateau; Quantized magnetization
1. Introduction Recently, the physics of quantum antiferromagnetic systems has been attracting considerable attention. The feature of the crystal structure of KCuCl , TlCuCl and NH CuCl is the double 3 3 4 3 chain of edge-sharing octahedra CuCl along the 6 * Corresponding author. Tel.: #81 3 5734 3541; fax: #81 3 5734 2702; e-mail: [email protected].
a-axis [1,2]. The exchange network in the double chain is described as an S"1 Heisenberg spin 2 ladder with an additional diagonal interaction, or an alternating Heisenberg chain with a next-nearest-neighbor interaction [2,3]. For KCuCl and 3 TlCuCl , the susceptibilities for three different ex3 ternal field directions exhibit broad maxima at 30 and 38 K, respectively, and decrease exponentially to zero with decreasing temperature [2,3]. The result indicates that their ground states are spin singlet with excitation gaps, as predicted for
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Heisenberg spin ladders [4,5]. For NH CuCl , the 4 3 susceptibility of polycrystals displays a rounded maximum at about 4 K and decreases with decreasing temperature [2]. The ground state nature of NH CuCl has not been clear. In order to deter4 3 mine directly the excitation gap and to investigate the spin state in high magnetic fields, we carried out the high-field magnetization measurements on the single crystals. In this note we report the results.
2. Experimental Single crystals of KCuCl and TlCuCl were 3 3 grown from a melt by the Bridgman method. Single crystals of NH CuCl with a long prismatic shape 4 3 were obtahined by evaporating an ethyl alcohol solution containing NH Cl and CuCl at 60°C. 4 2 The crystals were shaped into rods, 3 mm in diameter and &5 mm in length, to fit a sample holder. High-field magnetization processes were measured by an induction method in pulsed magnetic fields up to 39 T. For KCuCl and TlCuCl , magnetic 3 3 fields are applied perpendicularly to the cleavage plane and in a direction parallel to the cleavage planes. The Miller indices of to the cleavage planes have not been determined. In this note we refer to the cleavage plane as CP. For NH CuCl , 4 3 measurements were carried out using both single crystal and powdered sample.
Fig. 1. Magnetization curves of KCuCl at 1.7 K for the ex3 ternal field H parallel and perpendicular to the cleavage plane. The inset shows dM/dH versus H.
3. Results and discussions Figs. 1 and 2 show the magnetization M and its field derivative dM/dH measured at 1.7 K for KCuCl and TlCuCl . A continuous transition can 3 3 be seen at H &20 T for KCuCl and H &6 T for # 3 # TlCuCl . The arrows in Figs. 1 and 2 denote the 3 transition fields H . The precise value of the critical # field in KCuCl is H "22.4 T for HECP and 3 # H "20.3 T for HoCP, while the value of H in # # TlCuCl is H "5.8 T for HECP and H "5.7 T 3 # # for HoCP. When the g-factor is anisotropic, the value of H depends on the external field direction. # We measured the g-factors of our samples by ESR, applying the external fields in the same directions as those for the magnetization measurements. The
Fig. 2. Magnetization curves of TlCuCl at 1.7 K for the ex3 ternal field H parallel and perpendicular to the cleavage plane. The inset shows dM/dH versus H.
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g-factors obtained are g "2.05 and g "2.29 , M for KCuCl and g "2.02 and g "2.04 for 3 , M TlCuCl . It is found that the magnetization 3 curves for HECP and HoCP normalized by the g-factors almost coincide [6]. Thus, the anisotropic behavior of H is attributed to the anisotropy of the # g-factor. The level crossing between the singlet ground state and the excited triplet state occurs at H which corresponds to the excitation gap at zero # field and, above H , the present systems are in # a gapless magnetic state. From the value of the critical field H , the excitation gap is evaluated as # D/k "31.1 K for KCuCl and 7.5 K for TlCuCl . B 3 3 Here the value of D for TlCuCl is evaluated from 3 the data obtained at 0.5 K. Although the maximum susceptibility temperature ¹ for TlCuCl is .!9 3 about 1.3 times as high as that for KCuCl , the 3 excitation gap in TlCuCl is a quarter of that in 3 KCuCl . From the slope of the magnetization 3 curve above H , saturation is expected to occur at # H &60 T for KCuCl and H &150 T for 4 3 4 TlCuCl . The saturation field H for TlCuCl is 3 4 3 more than twice as high as that for KCuCl , which 3 means that the antiferromagnetic interactions in TlCuCl are fairly strong compared with those in 3 KCuCl . The exchange network in the double 3 chain consists of three kinds of interactions, J , 1 J and J [2,3]. The results obtained mean that the 2 3 J , J and J interactions contribute to ¹ , D and 1 2 3 .!9 H in different ways. At present, the values of these 4 exchange parameters are not determined, so both the susceptibility and magnetization data are consistently explained. We also measured the temperature dependence of the critical field H . It is ob# served that the critical field increases with increasing temperature [6]. Fig. 3 shows the magnetization curve of NH CuCl at various temperatures. The external 4 3 field is applied along the double chain (a-axis). The magnetization curve of NH CuCl is different from 4 3 those observed in KCuCl and TlCuCl which 3 3 have a ground state of a spin singlet with an excitation gap. As seen from Fig. 3, the slope of magnetization curve near zero field is finite even at 0.5 K. This fact indicates that the ground state of NH CuCl is not a spin singlet with an excitation 4 3 gap, but magnetic.
Fig. 3. Magnetization curves of NH CuCl at four different 4 3 temperatures for the external field H parallel to the a-axis.
With decreasing temperature, the anomalies due to phase transitions become more and more distinct. We can see that NH CuCl undergoes five 4 3 transitions in high magnetic fields. In the data at 0.5 K, the phase transitions are detected at H "5.0 T, H "12.8 T, H "17.9 T, H " #1 #2 #3 #4 24.7 T and H "29.1 T. The magnetization satu4 rates at H . The notable feature of the magnetiz4 ation curve is two wide plateaus at a quarter and three quarters of the saturation magnetization M . 4 Two wide plateaus observed in NH CuCl 4 3 should be attributed not to the magnetic anisotropy, but to the quantum nature, because the magnetic anisotropy is negligibly small in the present system [6], and the two plateaus are also clearly observed in powdered sample. Recently, Oshikawa et al. [7] predicted that the magnetization curve for the quantum spin chain can have plateaus, and that the magnetization per site m is quantized as n(S!m)"integer at the plateaus, where n is the period of the ground state and S is the magnitude of
H. Tanaka et al. / Physica B 246—247 (1998) 230—233
spin. We apply the condition of plateaus to NH CuCl . The first and the second plateaus cor4 3 respond to m"1 and 3, because S"1. Thus the 8 8 2 period should be n"8. Since NH CuCl is the 4 3 double spin chain system, this result denotes that the period of the spin state at plateau is four times as large as the period of crystal lattice along the a-axis. It has been reported that NH CuCl under4 3 goes a structural phase transition at about 70 K [8,9]. Therefore, it is very probable that the unit cell is enlarged at low temperatures. The period of the Hamiltonian is determined by the period of the crystal lattice. The analysis of the crystal structure at low temperatures is needed to clarify the mechanism leading to the magnetization plateaus. Although m"1 satisfies the above condition with 4 n"8, no anomaly can be seen at the half value of M . 4
233
References [1] R.D. Willett, C. Dwiggins, R.F. Kruh, R.E. Rundle, J. Chem. Phys. 38 (1963) 2429. [2] K. Takatsu, W. Shiramura, H. Tanaka, J. Phys. Soc. Japan 66 (1997) 1661. [3] H. Tanaka, K. Takatsu, W. Shiramura, T. Ono, J. Phys. Soc. Japan 65 (1996) 1945. [4] K. Hida, J. Phys. Soc. Japan 64 (1995) 4896 and references therein. [5] E. Dagotto, T.M. Rice, Science 271 (1996) 618 and references therein. [6] W. Shiramura, K. Takatsu, H. Tanaka, K. Kamishima, M. Takahashi, H. Mitamura, T. Goto, J. Phys. Soc. Japan 66 (1997) 1900. [7] M. Oshikawa, M. Yamanaka, I. Affleck, Phys. Rev. Lett. 78 (1997) 1984. [8] A.M. Heyns, C.J.H. Schutte, J. Mol. Struct. 8 (1971) 339. [9] T. Kato, K. Takatsu, W. Shiramura, H. Tanaka, K. Iio, Read at Autumn Meeting of the Physical Society of Japan, Kobe, October, 1997.
High-field magnetization processes of quantum double spin chain systems KCuCl , TlCuCl and NH CuCl 3 3 4 3 H. Tanaka!,*, W. Shiramura", T. Takatsu!, B. Kurniawan!, M. Takahashi#, K. Kamishima#, K. Takizawa#, H. Mitamura#, T. Goto# ! Department of Physics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan " Department of Physics, Faculty of Science and Technology, Sophia University, Kioi-cho, Chiyoda-ku, Tokyo 102, Japan # Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
Abstract High-field magnetization processes of S"1 double spin chain systems KCuCl , TlCuCl and NH CuCl have been 2 3 3 4 3 measured up to 39 T at helium temperatures using single crystals. A transition from a singlet ground state with an excitation gap to a gapless magnetic state occurs at H &20 and 6 T for KCuCl and TlCuCl , respectively. The # 3 3 excitation gap D is evaluated as D/k "31.1 K for KCuCl and 7.5 K for TlCuCl . Although the antiferromagnetic B 3 3 interactions in TlCuCl are stronger than those in KCuCl , which can be seen from the slope of the magnetization curves 3 3 above H , the excitation gap in TlCuCl is about a quarter of that of KCuCl . In contrast to KCuCl and TlCuCl , # 3 3 3 3 NH CuCl has a gapless magnetic ground state. It is found that NH CuCl undergoes five phase transitions in high 4 3 4 3 magnetic fields. Two wide plateaus are observed at a quarter and three quarters of the saturation magnetization. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: KCuCl ; TlCuCl ; NH CuCl ; High field; Magnetization process; Double spin chain; Singlet ground state; 3 3 4 3 Excitation gap; Plateau; Quantized magnetization
1. Introduction Recently, the physics of quantum antiferromagnetic systems has been attracting considerable attention. The feature of the crystal structure of KCuCl , TlCuCl and NH CuCl is the double 3 3 4 3 chain of edge-sharing octahedra CuCl along the 6 * Corresponding author. Tel.: #81 3 5734 3541; fax: #81 3 5734 2702; e-mail: [email protected].
a-axis [1,2]. The exchange network in the double chain is described as an S"1 Heisenberg spin 2 ladder with an additional diagonal interaction, or an alternating Heisenberg chain with a next-nearest-neighbor interaction [2,3]. For KCuCl and 3 TlCuCl , the susceptibilities for three different ex3 ternal field directions exhibit broad maxima at 30 and 38 K, respectively, and decrease exponentially to zero with decreasing temperature [2,3]. The result indicates that their ground states are spin singlet with excitation gaps, as predicted for
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 2 6 ( 9 7 ) 0 0 9 8 3 - 6
H. Tanaka et al. / Physica B 246—247 (1998) 230—233
231
Heisenberg spin ladders [4,5]. For NH CuCl , the 4 3 susceptibility of polycrystals displays a rounded maximum at about 4 K and decreases with decreasing temperature [2]. The ground state nature of NH CuCl has not been clear. In order to deter4 3 mine directly the excitation gap and to investigate the spin state in high magnetic fields, we carried out the high-field magnetization measurements on the single crystals. In this note we report the results.
2. Experimental Single crystals of KCuCl and TlCuCl were 3 3 grown from a melt by the Bridgman method. Single crystals of NH CuCl with a long prismatic shape 4 3 were obtahined by evaporating an ethyl alcohol solution containing NH Cl and CuCl at 60°C. 4 2 The crystals were shaped into rods, 3 mm in diameter and &5 mm in length, to fit a sample holder. High-field magnetization processes were measured by an induction method in pulsed magnetic fields up to 39 T. For KCuCl and TlCuCl , magnetic 3 3 fields are applied perpendicularly to the cleavage plane and in a direction parallel to the cleavage planes. The Miller indices of to the cleavage planes have not been determined. In this note we refer to the cleavage plane as CP. For NH CuCl , 4 3 measurements were carried out using both single crystal and powdered sample.
Fig. 1. Magnetization curves of KCuCl at 1.7 K for the ex3 ternal field H parallel and perpendicular to the cleavage plane. The inset shows dM/dH versus H.
3. Results and discussions Figs. 1 and 2 show the magnetization M and its field derivative dM/dH measured at 1.7 K for KCuCl and TlCuCl . A continuous transition can 3 3 be seen at H &20 T for KCuCl and H &6 T for # 3 # TlCuCl . The arrows in Figs. 1 and 2 denote the 3 transition fields H . The precise value of the critical # field in KCuCl is H "22.4 T for HECP and 3 # H "20.3 T for HoCP, while the value of H in # # TlCuCl is H "5.8 T for HECP and H "5.7 T 3 # # for HoCP. When the g-factor is anisotropic, the value of H depends on the external field direction. # We measured the g-factors of our samples by ESR, applying the external fields in the same directions as those for the magnetization measurements. The
Fig. 2. Magnetization curves of TlCuCl at 1.7 K for the ex3 ternal field H parallel and perpendicular to the cleavage plane. The inset shows dM/dH versus H.
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H. Tanaka et al. / Physica B 246—247 (1998) 230—233
g-factors obtained are g "2.05 and g "2.29 , M for KCuCl and g "2.02 and g "2.04 for 3 , M TlCuCl . It is found that the magnetization 3 curves for HECP and HoCP normalized by the g-factors almost coincide [6]. Thus, the anisotropic behavior of H is attributed to the anisotropy of the # g-factor. The level crossing between the singlet ground state and the excited triplet state occurs at H which corresponds to the excitation gap at zero # field and, above H , the present systems are in # a gapless magnetic state. From the value of the critical field H , the excitation gap is evaluated as # D/k "31.1 K for KCuCl and 7.5 K for TlCuCl . B 3 3 Here the value of D for TlCuCl is evaluated from 3 the data obtained at 0.5 K. Although the maximum susceptibility temperature ¹ for TlCuCl is .!9 3 about 1.3 times as high as that for KCuCl , the 3 excitation gap in TlCuCl is a quarter of that in 3 KCuCl . From the slope of the magnetization 3 curve above H , saturation is expected to occur at # H &60 T for KCuCl and H &150 T for 4 3 4 TlCuCl . The saturation field H for TlCuCl is 3 4 3 more than twice as high as that for KCuCl , which 3 means that the antiferromagnetic interactions in TlCuCl are fairly strong compared with those in 3 KCuCl . The exchange network in the double 3 chain consists of three kinds of interactions, J , 1 J and J [2,3]. The results obtained mean that the 2 3 J , J and J interactions contribute to ¹ , D and 1 2 3 .!9 H in different ways. At present, the values of these 4 exchange parameters are not determined, so both the susceptibility and magnetization data are consistently explained. We also measured the temperature dependence of the critical field H . It is ob# served that the critical field increases with increasing temperature [6]. Fig. 3 shows the magnetization curve of NH CuCl at various temperatures. The external 4 3 field is applied along the double chain (a-axis). The magnetization curve of NH CuCl is different from 4 3 those observed in KCuCl and TlCuCl which 3 3 have a ground state of a spin singlet with an excitation gap. As seen from Fig. 3, the slope of magnetization curve near zero field is finite even at 0.5 K. This fact indicates that the ground state of NH CuCl is not a spin singlet with an excitation 4 3 gap, but magnetic.
Fig. 3. Magnetization curves of NH CuCl at four different 4 3 temperatures for the external field H parallel to the a-axis.
With decreasing temperature, the anomalies due to phase transitions become more and more distinct. We can see that NH CuCl undergoes five 4 3 transitions in high magnetic fields. In the data at 0.5 K, the phase transitions are detected at H "5.0 T, H "12.8 T, H "17.9 T, H " #1 #2 #3 #4 24.7 T and H "29.1 T. The magnetization satu4 rates at H . The notable feature of the magnetiz4 ation curve is two wide plateaus at a quarter and three quarters of the saturation magnetization M . 4 Two wide plateaus observed in NH CuCl 4 3 should be attributed not to the magnetic anisotropy, but to the quantum nature, because the magnetic anisotropy is negligibly small in the present system [6], and the two plateaus are also clearly observed in powdered sample. Recently, Oshikawa et al. [7] predicted that the magnetization curve for the quantum spin chain can have plateaus, and that the magnetization per site m is quantized as n(S!m)"integer at the plateaus, where n is the period of the ground state and S is the magnitude of
H. Tanaka et al. / Physica B 246—247 (1998) 230—233
spin. We apply the condition of plateaus to NH CuCl . The first and the second plateaus cor4 3 respond to m"1 and 3, because S"1. Thus the 8 8 2 period should be n"8. Since NH CuCl is the 4 3 double spin chain system, this result denotes that the period of the spin state at plateau is four times as large as the period of crystal lattice along the a-axis. It has been reported that NH CuCl under4 3 goes a structural phase transition at about 70 K [8,9]. Therefore, it is very probable that the unit cell is enlarged at low temperatures. The period of the Hamiltonian is determined by the period of the crystal lattice. The analysis of the crystal structure at low temperatures is needed to clarify the mechanism leading to the magnetization plateaus. Although m"1 satisfies the above condition with 4 n"8, no anomaly can be seen at the half value of M . 4
233
References [1] R.D. Willett, C. Dwiggins, R.F. Kruh, R.E. Rundle, J. Chem. Phys. 38 (1963) 2429. [2] K. Takatsu, W. Shiramura, H. Tanaka, J. Phys. Soc. Japan 66 (1997) 1661. [3] H. Tanaka, K. Takatsu, W. Shiramura, T. Ono, J. Phys. Soc. Japan 65 (1996) 1945. [4] K. Hida, J. Phys. Soc. Japan 64 (1995) 4896 and references therein. [5] E. Dagotto, T.M. Rice, Science 271 (1996) 618 and references therein. [6] W. Shiramura, K. Takatsu, H. Tanaka, K. Kamishima, M. Takahashi, H. Mitamura, T. Goto, J. Phys. Soc. Japan 66 (1997) 1900. [7] M. Oshikawa, M. Yamanaka, I. Affleck, Phys. Rev. Lett. 78 (1997) 1984. [8] A.M. Heyns, C.J.H. Schutte, J. Mol. Struct. 8 (1971) 339. [9] T. Kato, K. Takatsu, W. Shiramura, H. Tanaka, K. Iio, Read at Autumn Meeting of the Physical Society of Japan, Kobe, October, 1997.