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Pressure-induced magnetic ordering in KCuCl3
ARTICLE IN PRESS
Physica B 385–386 (2006) 450–452 www.elsevier.com/locate/physb
Pressure-induced magnetic ordering in KCuCl3 K. Kakuraia,, T. Osakabea, K. Gotob, A. Oosawac, M. Fujisawab, H. Tanakab a
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan c Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
b
Abstract KCuCl3 is a singlet ground state system with excitation gap D of 31 K. The magnetization measurements under applied hydrostatic pressure show the existence of the magnetic order above the critical pressure Pc ¼ 8.8 kbar. We report here on the first neutron diffraction observation of the pressure-induced antiferromagnetic ordering in KCuCl3 under hydrostatic pressure of 11 kbar. The magnetic structure will be discussed and compared with the pressure-induced magnetic order observed in TlCuCl3, an isostructural three dimensionally coupled dimer system. r 2006 Elsevier B.V. All rights reserved. Keywords: Quantum spin system; Singlet ground state; Magnetic structure
1. Introduction Recently the induced magnetic ordering in the singlet spin liquid ground state either by applied magnetic field, applied pressure or impurity doping is vividly discussed and investigated. Especially the possible interpretation of the quantum-phase transition in TlCuCl3 as a field or pressure driven Bose–Einstein condensation (BEC) attracted many experimental and theoretical investigations on this three dimensionally coupled dimer system [1–8]. KCuCl3 is isostructural to TlCuCl3. The main feature of the crystal structure belonging to the space group P21/c (a ¼ 4.029 A˚, b ¼ 13.785 A˚, c ¼ 8.735 A˚, b ¼ 97.31 for KCuCl3) is the double chain structure of edge-sharing octahedral CuCl6 along the a-axis, as illustrated in Fig. 1. The non-magnetic low-T susceptibility behaviour thus has been initially ascribed to the singlet ground state of an S ¼ 1/2 Heisenberg spin ladder. The subsequent neutron inelastic scattering experiments on the spin excitations first in KCuCl3 [9,10] and later on in TlCuCl3 [11,12] then clearly demonstrated that these systems should be regarded as weakly 3-D coupled antiferromagnetic (AF) dimer singlet ground state systems. The rather large gap energy Corresponding author. Tel.: +81 29 284 3523; fax: +81 29 282 5939.
E-mail address: [email protected] (K. Kakurai). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.237
of 31 K in KCuCl3 prohibited to studying the induced magnetic ordering in this substance so far in contrast to the daughter compound TlCuCl3 with a smaller gap energy of 7.7 K. Quite recently the susceptibility and magnetization measurements of KCuCl3 under applied pressure indicated the pressure-induced magnetic ordering with a critical pressure of Pc ¼ 8.8 kbar [13]. It is thus of great interest to study the magnetic structure of the pressure-induced ordering in KCuCl3 by means of neutron diffraction in comparison with the TlCuCl3 case. In this short paper we report the first observation of the magnetic Bragg peaks in KCuCl3 under applied hydrostatic pressure of 11 kbar. 2. Experiment The experiment was performed on TAS-1 spectrometer installed at JRR-3 M in JAEA, Tokai. The incident energy was Ei ¼ 14.7 meV and the collimation series of 600 -800 -800 800 were used. Double pyrolytic graphite filters are placed in the beam to suppress the higher-order contaminations. The KCuCl3 sample (0.2 cm3) was aligned with it’s a and c-axis in the scattering plane and placed into the pressure cell for neutron scattering developed by Prof. Onodera [14]. A mixture of Fluorinert FC70 and FC77 was used as the pressure-transmitting medium. The applied pressure of
ARTICLE IN PRESS K. Kakurai et al. / Physica B 385–386 (2006) 450–452
451
Fig. 1. (a) Crystal structure of KCuCl3. (b) Definition of angles a and y. Fig. 3. Integrated magnetic intensities at various Q positions. The vertical bars indicate the calculated intensities for the magnetic structure as described in the text.
Fig. 2. Temperature dependence of the maximum intensities at magnetic Bragg peaks.
11 kbar at low T was verified by measuring the lattice constant of the NaCl standard crystal mounted simultaneously in the pressure cell. Fig. 2 depicts the temperature dependence of the maximum intensity at (0 0 1) and (1 0 3). The critical temperature TN ¼ 6 K is clearly seen, below which the resolution limited magnetic Bragg peaks are observed. The inset of Fig. 2 shows an example of the (1 0 3) magnetic peak profile at T ¼ 1.3 K after the subtraction of the hightemperature scan at T ¼ 12 K. The residual temperatureindependent intensities, very small compared to the fundamental nuclear peaks at (h,0,l) with l ¼ even, above the critical temperature at the forbidden nuclear peak positions for l ¼ odd can most probably be ascribed to a impurity-induced small local distortion and hence have been subtracted from the low-T data to obtain the genuine magnetic contribution. The integrated intensities of magnetic Bragg peaks, normalized on the (0 0 1) magnetic intensity, are summarized in Fig. 3. These reciprocal points are equivalent to those positions, where the induced magnetic ordering in TlCuCl3 was generally observed [3,6,15]. We therefore fit the observed magnetic intensities
with the magnetic structure similar to that of the pressureinduced magnetic structure in TlCuCl3 [6]. The characteristics of the magnetic structure are the AF order within the dimer, ferromagnetic (FM) order along the chain direction and AF orientation of the spins in the nearest neighbour chains. The moment direction in the a–c plane is given by the angle a to the a-axis direction. The out-of-plane moment direction is expressed by the angle y from the b-axis direction, i.e. y ¼ 901 corresponds to the moment direction in the a–c plane (see the inset of Fig. 1). The calculated intensities with these two angles as fit parameters are indicated by the vertical bars in Fig. 3 for a ¼ (2973)1 and y ¼ (7479)1. One recognizes a good agreement with the observed intensities. This means that the ordered moments are almost in the a–c plane and tilted 291 from the a-axis. The magnitude of the ordered moment is evaluated as om4 ¼ gmBoS4 ¼ 0.45(2) mB at T ¼ 1.3 K by the comparison of the magnetic intensities with those of the nuclear reflections. These results clearly demonstrate that the spin gap in KCuCl3 is completely suppressed under the pressure of 11 kbar and the triplet states of the spin dimer orders at TN ¼ 6 K. The application of the hydrostatic pressure obviously increases the ratio of interdimer(J0 ) to intradimer(J) exchanges and reduces the excitation gap. When the critical value (J0 /J)c is reached at 8.8 kbar, the gap is totally suppressed and the system undergoes the pressure-induced quantum phase transition from non-magnetic singlet ground state to magnetic ground state. Because of the rather high critical pressure of KCuCl3 in contrast to that of TlCuCl3 (Pc0.4 kbar), the pressure dependence of the susceptibility clearly shows that the temperature of the susceptibility maximum Tmax decreases and the value of wmax increases with applied pressure [5]. This indicates that the intradimer exchange interaction J decreases, while the interdimer exchange J0 increases with applied pressure. The intradimer interaction J is a superexchange interaction and the angle of the path (Cu2+–Cl–Cu2+) can be thought to
ARTICLE IN PRESS 452
K. Kakurai et al. / Physica B 385–386 (2006) 450–452
change upon applying pressure. At the same time, the interdimer interaction J0 is enhanced by pressure, because the distances between dimers are contracting. The ordered magnetic structure is very similar to that of the field- and impurity-induced magnetic order in TlCuCl3. The small out-of-plane component indicated by the fit results may be already indicative of the spin reorientation as has been observed in TlCuCl3 under applied pressure [16]. The pressure-dependent experiments are required to investigate this aspect and are planned for near future. To summarize we have observed pressure-induced AF magnetic ordering by means of neutron diffraction in a weakly coupled dimer singlet ground state system KCuCl3 under hydrostatic pressure of 11 kbar and the magnetic structure with the ordered magnetic moment of /mS ¼ 0.45 mB has been determined. References [1] A. Oosawa, M. Ishii, H. Tanaka, J. Phys.: condens. matter 11 (1999) 265. [2] T. Nikuni, M. Oshikawa, A. Oosawa, H. Tanaka, Phys. Rev. Lett. 84 (2000) 5868.
[3] H. Tanaka, A. Oosawa, T. Kato, H. Uekusa, Y. Ohashi, K. Kakurai, A. Hoser, J. Phys. Soc. Jpn 70 (2001) 939. [4] Ch. Ru¨egg, N. Cavadini, A. Furrer, H.-U. Gu¨del, K. Kra¨mer, H. Mutka, A. Wildes, K. Habicht, P. Vorderwisch, Nature (London) 423 (2003) 62. [5] K. Goto, M. Fujisawa, T. Ono, H. Tanaka, Y. Uwatoko, J. Phys. Soc. Jpn 73 (2004) 3254. [6] A. Oosawa, M. Fujisawa, T. Osakabe, K. Kakurai, H. Tanaka, J. Phys. Soc. Jpn 72 (2003) 1026. [7] Ch. Ru¨egg, A. Furrer, D. Sheptyakov, Th. Stra¨ssle, K. Kra¨mer, H.-U. Gu¨del, L. Me´le´si, Phys. Rev. Lett. 93 (2004) 257201. [8] M. Matsumoto, B. Normand, T.M. Rice, M. Sigrist, Phys. Rev. B 69 (2004) 054423. [9] T. Kato, K. Takatsu, H. Tanaka, W. Shiramura, M. Mori, K. Nakajima, K. Kakurai, J. Phys. Soc. Jpn 67 (1998) 752. [10] N. Cavadini, W. Henggeler, A. Furrer, H.U. Gu¨del, K. Kra¨mer, H. Mutka, Eur. Phys. J B 7 (1999) 519. [11] N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.U. Gu¨del, K. Kra¨mer, H. Mutka, Phys. Rev. B 63 (2001) 172414. [12] A. Oosawa, T. Kato, H. Tanaka, K. Kakurai, M. Mu¨ller, H.-J. Mikeska, Phys. Rev. B 65 (2002) 094426. [13] K. Goto, T. Ono, H. Tanaka, Y. Uwatoko, Prog. Theor. Phys. (Suppl.) 159 (2005) 397. [14] A. Onodera, et al., Jpn. J. Appl. Phys. 26 (1987) 152. [15] A. Oosawa, M. Fujisawa, K. Kakurai, H. Tanaka, Phys. Rev. B 67 (2003) 184424. [16] A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, H. Tanaka, J. Phys. Soc. Jpn 73 (2004) 1446.
Physica B 385–386 (2006) 450–452 www.elsevier.com/locate/physb
Pressure-induced magnetic ordering in KCuCl3 K. Kakuraia,, T. Osakabea, K. Gotob, A. Oosawac, M. Fujisawab, H. Tanakab a
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan c Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
b
Abstract KCuCl3 is a singlet ground state system with excitation gap D of 31 K. The magnetization measurements under applied hydrostatic pressure show the existence of the magnetic order above the critical pressure Pc ¼ 8.8 kbar. We report here on the first neutron diffraction observation of the pressure-induced antiferromagnetic ordering in KCuCl3 under hydrostatic pressure of 11 kbar. The magnetic structure will be discussed and compared with the pressure-induced magnetic order observed in TlCuCl3, an isostructural three dimensionally coupled dimer system. r 2006 Elsevier B.V. All rights reserved. Keywords: Quantum spin system; Singlet ground state; Magnetic structure
1. Introduction Recently the induced magnetic ordering in the singlet spin liquid ground state either by applied magnetic field, applied pressure or impurity doping is vividly discussed and investigated. Especially the possible interpretation of the quantum-phase transition in TlCuCl3 as a field or pressure driven Bose–Einstein condensation (BEC) attracted many experimental and theoretical investigations on this three dimensionally coupled dimer system [1–8]. KCuCl3 is isostructural to TlCuCl3. The main feature of the crystal structure belonging to the space group P21/c (a ¼ 4.029 A˚, b ¼ 13.785 A˚, c ¼ 8.735 A˚, b ¼ 97.31 for KCuCl3) is the double chain structure of edge-sharing octahedral CuCl6 along the a-axis, as illustrated in Fig. 1. The non-magnetic low-T susceptibility behaviour thus has been initially ascribed to the singlet ground state of an S ¼ 1/2 Heisenberg spin ladder. The subsequent neutron inelastic scattering experiments on the spin excitations first in KCuCl3 [9,10] and later on in TlCuCl3 [11,12] then clearly demonstrated that these systems should be regarded as weakly 3-D coupled antiferromagnetic (AF) dimer singlet ground state systems. The rather large gap energy Corresponding author. Tel.: +81 29 284 3523; fax: +81 29 282 5939.
E-mail address: [email protected] (K. Kakurai). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.237
of 31 K in KCuCl3 prohibited to studying the induced magnetic ordering in this substance so far in contrast to the daughter compound TlCuCl3 with a smaller gap energy of 7.7 K. Quite recently the susceptibility and magnetization measurements of KCuCl3 under applied pressure indicated the pressure-induced magnetic ordering with a critical pressure of Pc ¼ 8.8 kbar [13]. It is thus of great interest to study the magnetic structure of the pressure-induced ordering in KCuCl3 by means of neutron diffraction in comparison with the TlCuCl3 case. In this short paper we report the first observation of the magnetic Bragg peaks in KCuCl3 under applied hydrostatic pressure of 11 kbar. 2. Experiment The experiment was performed on TAS-1 spectrometer installed at JRR-3 M in JAEA, Tokai. The incident energy was Ei ¼ 14.7 meV and the collimation series of 600 -800 -800 800 were used. Double pyrolytic graphite filters are placed in the beam to suppress the higher-order contaminations. The KCuCl3 sample (0.2 cm3) was aligned with it’s a and c-axis in the scattering plane and placed into the pressure cell for neutron scattering developed by Prof. Onodera [14]. A mixture of Fluorinert FC70 and FC77 was used as the pressure-transmitting medium. The applied pressure of
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451
Fig. 1. (a) Crystal structure of KCuCl3. (b) Definition of angles a and y. Fig. 3. Integrated magnetic intensities at various Q positions. The vertical bars indicate the calculated intensities for the magnetic structure as described in the text.
Fig. 2. Temperature dependence of the maximum intensities at magnetic Bragg peaks.
11 kbar at low T was verified by measuring the lattice constant of the NaCl standard crystal mounted simultaneously in the pressure cell. Fig. 2 depicts the temperature dependence of the maximum intensity at (0 0 1) and (1 0 3). The critical temperature TN ¼ 6 K is clearly seen, below which the resolution limited magnetic Bragg peaks are observed. The inset of Fig. 2 shows an example of the (1 0 3) magnetic peak profile at T ¼ 1.3 K after the subtraction of the hightemperature scan at T ¼ 12 K. The residual temperatureindependent intensities, very small compared to the fundamental nuclear peaks at (h,0,l) with l ¼ even, above the critical temperature at the forbidden nuclear peak positions for l ¼ odd can most probably be ascribed to a impurity-induced small local distortion and hence have been subtracted from the low-T data to obtain the genuine magnetic contribution. The integrated intensities of magnetic Bragg peaks, normalized on the (0 0 1) magnetic intensity, are summarized in Fig. 3. These reciprocal points are equivalent to those positions, where the induced magnetic ordering in TlCuCl3 was generally observed [3,6,15]. We therefore fit the observed magnetic intensities
with the magnetic structure similar to that of the pressureinduced magnetic structure in TlCuCl3 [6]. The characteristics of the magnetic structure are the AF order within the dimer, ferromagnetic (FM) order along the chain direction and AF orientation of the spins in the nearest neighbour chains. The moment direction in the a–c plane is given by the angle a to the a-axis direction. The out-of-plane moment direction is expressed by the angle y from the b-axis direction, i.e. y ¼ 901 corresponds to the moment direction in the a–c plane (see the inset of Fig. 1). The calculated intensities with these two angles as fit parameters are indicated by the vertical bars in Fig. 3 for a ¼ (2973)1 and y ¼ (7479)1. One recognizes a good agreement with the observed intensities. This means that the ordered moments are almost in the a–c plane and tilted 291 from the a-axis. The magnitude of the ordered moment is evaluated as om4 ¼ gmBoS4 ¼ 0.45(2) mB at T ¼ 1.3 K by the comparison of the magnetic intensities with those of the nuclear reflections. These results clearly demonstrate that the spin gap in KCuCl3 is completely suppressed under the pressure of 11 kbar and the triplet states of the spin dimer orders at TN ¼ 6 K. The application of the hydrostatic pressure obviously increases the ratio of interdimer(J0 ) to intradimer(J) exchanges and reduces the excitation gap. When the critical value (J0 /J)c is reached at 8.8 kbar, the gap is totally suppressed and the system undergoes the pressure-induced quantum phase transition from non-magnetic singlet ground state to magnetic ground state. Because of the rather high critical pressure of KCuCl3 in contrast to that of TlCuCl3 (Pc0.4 kbar), the pressure dependence of the susceptibility clearly shows that the temperature of the susceptibility maximum Tmax decreases and the value of wmax increases with applied pressure [5]. This indicates that the intradimer exchange interaction J decreases, while the interdimer exchange J0 increases with applied pressure. The intradimer interaction J is a superexchange interaction and the angle of the path (Cu2+–Cl–Cu2+) can be thought to
ARTICLE IN PRESS 452
K. Kakurai et al. / Physica B 385–386 (2006) 450–452
change upon applying pressure. At the same time, the interdimer interaction J0 is enhanced by pressure, because the distances between dimers are contracting. The ordered magnetic structure is very similar to that of the field- and impurity-induced magnetic order in TlCuCl3. The small out-of-plane component indicated by the fit results may be already indicative of the spin reorientation as has been observed in TlCuCl3 under applied pressure [16]. The pressure-dependent experiments are required to investigate this aspect and are planned for near future. To summarize we have observed pressure-induced AF magnetic ordering by means of neutron diffraction in a weakly coupled dimer singlet ground state system KCuCl3 under hydrostatic pressure of 11 kbar and the magnetic structure with the ordered magnetic moment of /mS ¼ 0.45 mB has been determined. References [1] A. Oosawa, M. Ishii, H. Tanaka, J. Phys.: condens. matter 11 (1999) 265. [2] T. Nikuni, M. Oshikawa, A. Oosawa, H. Tanaka, Phys. Rev. Lett. 84 (2000) 5868.
[3] H. Tanaka, A. Oosawa, T. Kato, H. Uekusa, Y. Ohashi, K. Kakurai, A. Hoser, J. Phys. Soc. Jpn 70 (2001) 939. [4] Ch. Ru¨egg, N. Cavadini, A. Furrer, H.-U. Gu¨del, K. Kra¨mer, H. Mutka, A. Wildes, K. Habicht, P. Vorderwisch, Nature (London) 423 (2003) 62. [5] K. Goto, M. Fujisawa, T. Ono, H. Tanaka, Y. Uwatoko, J. Phys. Soc. Jpn 73 (2004) 3254. [6] A. Oosawa, M. Fujisawa, T. Osakabe, K. Kakurai, H. Tanaka, J. Phys. Soc. Jpn 72 (2003) 1026. [7] Ch. Ru¨egg, A. Furrer, D. Sheptyakov, Th. Stra¨ssle, K. Kra¨mer, H.-U. Gu¨del, L. Me´le´si, Phys. Rev. Lett. 93 (2004) 257201. [8] M. Matsumoto, B. Normand, T.M. Rice, M. Sigrist, Phys. Rev. B 69 (2004) 054423. [9] T. Kato, K. Takatsu, H. Tanaka, W. Shiramura, M. Mori, K. Nakajima, K. Kakurai, J. Phys. Soc. Jpn 67 (1998) 752. [10] N. Cavadini, W. Henggeler, A. Furrer, H.U. Gu¨del, K. Kra¨mer, H. Mutka, Eur. Phys. J B 7 (1999) 519. [11] N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.U. Gu¨del, K. Kra¨mer, H. Mutka, Phys. Rev. B 63 (2001) 172414. [12] A. Oosawa, T. Kato, H. Tanaka, K. Kakurai, M. Mu¨ller, H.-J. Mikeska, Phys. Rev. B 65 (2002) 094426. [13] K. Goto, T. Ono, H. Tanaka, Y. Uwatoko, Prog. Theor. Phys. (Suppl.) 159 (2005) 397. [14] A. Onodera, et al., Jpn. J. Appl. Phys. 26 (1987) 152. [15] A. Oosawa, M. Fujisawa, K. Kakurai, H. Tanaka, Phys. Rev. B 67 (2003) 184424. [16] A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, H. Tanaka, J. Phys. Soc. Jpn 73 (2004) 1446.