- Email: [email protected]
High-frequency high-field ESR of quantum double spin chain systems KCuCl3 and TlCuCl3
Physica B 246—247 (1998) 545—548
High-frequency high-field ESR of quantum double spin chain systems KCuCl and TlCuCl 3 3 H. Tanaka!,*, T. Takatsu!, W. Shiramura", T. Kambe#, H. Nojiri$, T. Yamada%, S. Okubo&, H. Ohta%, M. Motokawa$ ! 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 # Department of Physics, Faculty of Science, Okayama University, Tsushimanaka, Okayama-shi, Okayama 700, Japan $ Institute for Material Research, Tohoku University, Katahira, Aoba-ku, Sendai 980-77, Japan % Department of Physics, Faculty of Science, Kobe University, Rokkodai, Nada-ku, Kobe 657, Japan & The Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-ku, Kobe 657, Japan
Abstract ESR measurements have been performed on KCuCl and TlCuCl in the frequency range up to 762 GHz and field 3 3 range up to 30 T at helium temperatures. The exchange network in the present systems is described as an S"1 2 Heisenberg spin ladder along the a-axis with an additional diagonal interaction. Both compounds have a singlet ground state with an excitation gap. In KCuCl , two kinds of transitions are observed between the ground state and the excited 3 triplet states. They correspond to the excitations at Q"(1, 0, 1) and (0.5, 0, 1) with the excitation energies D+640 and 1080 GHz, respectively. When the external field is increased, the frequency of the lowest branch with the zero-field gap D+640 GHz decreases linearly with a tendency toward zero at H +22 T. In TlCuCl , a transition from the singlet # 3 ground state to the excited triplet state is observed. The zero-field gap is determined as D+160 GHz. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: KCuCl ; TlCuCl ; ESR; High magnetic field; Double spin chain; Singlet ground state; Excitation gap 3 3
1. Introduction Recently the physics of spin-ladder systems has been of great interest. KCuCl and TlCuCl are 3 3 composed of the double chain of edge-sharing octahedra CuCl along the a-axis [1,2]. The exchange 6 * Corresponding author. Tel.: #81 3 5734 3541; fax: #81 3 5734 2702; e-mail: [email protected].
network in the double chain can be described as an S"1 Heisenberg spin ladder with an additional 2 diagonal interaction. The susceptibilities for three different external field directions in KCuCl and 3 TlCuCl exhibit broad maxima at 30 and 38 K, 3 respectively, and decrease exponentially to zero with decreasing temperature [2,3]. The result indicates that the ground state of the present systems is a spin singlet with an excitation gap, as predicted for Heisenberg spin ladder systems [4,5]. The singlet
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 2 - 4
546
H. Tanaka et al. / Physica B 246—247 (1998) 545—548
ground state was also confirmed by high-field magnetization measurements [6]. A transition from the 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 excita3 3 tion gap D was evaluated from the critical field as D/k "31.1 K for KCuCl and 7.5 K for TlCuCl . B 3 3 In order to investigate the magnetic excitations of the present systems, we carried out high-frequency high-field ESR measurements on the single crystals of KCuCl and TlCuCl . In this 3 3 note we report the results.
2. Experimental Single crystals of KCuCl and TlCuCl were 3 3 grown from a melt by the Bridgman method. ESR measurements were carried out in static magnetic fields up to 8 T and pulsed magnetic fields up to 30 T using FIR laser (404—762 GHz), Gunn oscillators (50—315 GHz) and klystrons (50—115 GHz). The magnetic fields were applied perpendicularly to the cleavage plane and in a direction parallel to the cleavage plane. The Miller indices of the cleavage planes have not been determined. In this letter we refer to the cleavage plane as CP.
3. Results and discussions Fig. 1 shows the high frequency ESR signals of KCuCl for H//CP. The data were collected at 3 4.2 K, where the susceptibility is almost zero [3]. Besides the sharp DPPH line, three kinds of welldefined resonance mode labeled as A, B and Pmodes, are observed. The ESR data obtained are summarized in Fig. 2. For KCuCl the value of the critical field is 3 H +22 T, when H//CP [6]. The paramagnetic res# onance P-mode is described by +u"gk H with B g"2.10. Its intensity becomes smaller as the temperature is lowered and the resonance field is lowered. This behavior is consistent with the fact that there is an excitation gap between the singlet ground state and the excited state. The P-mode corresponds to the transition between the excited
Fig. 1. High-frequency ESR signals of KCuCl observed at 3 4.2 K. The external field is parallel to the cleavage plane.
triplet states, when the resonance field is lower than the critical field H . # We see from Fig. 2 that the A- and B-modes correspond to the direct transitions from the singlet ground state to two triplet states with the excitation gaps D +640 GHz and D +1080 GHz. Both A B A- and B-modes split into three branches by the external field. Recently we have investigated the magnetic excitations in KCuCl by neutron inelas3 tic scattering experiments, and have determined the dispersion relation in the a*—c* plane [7]. The lowest excitation energy was found at Q"(1, 0, 1) to be 2.70 meV, which coincides with the zero field frequency of the A-mode. The excitation energy which coincides with the zero field frequency of the
H. Tanaka et al. / Physica B 246—247 (1998) 545—548
547
by +u"D !gk H, and the line width broadens B B out. For HoCP, the A- and B-modes were not clearly observed. Fig. 3 shows the ESR signals of TlCuCl for 3 H//CP obtained at 2 K in static magnetic fields. The susceptibility is almost zero at 2 K [2]. Three kinds of ESR modes, which we label u , u and 1 2 u -modes, are observed. Fig. 4 shows the frequency 3 versus field diagram obtained at 2.0, 4.2 and 5.0 K. The u and u -modes may correspond to the 2 3 transition between the excited triplet states. The notable mode is the u -mode with zero-field gap of 1 about 160 GHz. With increasing external field, its frequency decreases straightly toward zero at 6.1 T for 2.0 K, which coincides with the critical field observed by high-field magnetization measurements [6]. Thus, the u -mode corresponds to the 1 direct transition from the singlet ground state to an excited triplet state. From Fig. 4, we see that the Fig. 2. Frequency versus field diagram of KCuCl observed for 3 H//CP at 4.2 K. The external field is parallel to the cleavage plane.
B-mode was found at Q"(0.5, 0, 1). Thus we can say that the A- and B-modes correspond to the excitations at Q"(1, 0, 1) and (0.5, 0, 1). We notice in Figs. 1 and 2 that the A-mode splits into two close modes, A -mode (open rectangles) 1 and A -mode (filled rectangles), with the excitation 2 gaps D"632 and 641 GHz, respectively. Since the intensity of the A -mode is always larger than that 1 of the A -mode, the splitting is not due to the 2 instrumental problem such as the interference effect, but intrinsic to the present system. Since the Zeeman splittings of the A - and A -modes can be 1 2 described by the same g-factor, their origins are in the same spin site. The lowest branch of the A 1 mode can be clearly observed down to 50 GHz. When the external field is increased, its frequency decreases straightly with a tendency toward zero at 22 T, which coincides with the critical field H ob# tained by high-field magnetization measurements [6]. The intensity of the lowest branch of the A 2 mode becomes smaller with decreasing frequency, and it is hardly observed in the frequencies lower than 100 GHz. Above H , the resonance condition # of the B-mode deviates from the straight line given
Fig. 3. ESR signals of TlCuCl observed at 2.0 K. The external 3 field is parallel to the cleavage plane.
548
H. Tanaka et al. / Physica B 246—247 (1998) 545—548
TlCuCl is generally forbidden. We believe that the 3 antisymmetric Dzyaloshinsky-Moriya type interaction H which can exist in the present systems DM causes such excitations. The matrix elements of H between the singlet and the triplet states have DM non-zero values. Consequently, the ground state has a small amount of the triplet state component, and the ESR transition from the ground state to the excited state becomes possible.
References
Fig. 4. Frequency versus field diagram of TlCuCl observed for 3 H//CP at 2.0, 4.2 and 5.0 K.
critical field H estimated by extrapolating the u # 1 branch increases with increasing temperature. This behavior is also confirmed by high-field magnetization measurements [6]. The ESR excitation from the singlet ground state to the triplet state as observed in KCuCl and 3
[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] T. Kato, K. Takatsu, H. Tanaka, W. Shiramura, M. Mori, K. Nakajima, K. Kakurai, J. Phys. Soc. Jpn. 67 (1998) 752.
High-frequency high-field ESR of quantum double spin chain systems KCuCl and TlCuCl 3 3 H. Tanaka!,*, T. Takatsu!, W. Shiramura", T. Kambe#, H. Nojiri$, T. Yamada%, S. Okubo&, H. Ohta%, M. Motokawa$ ! 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 # Department of Physics, Faculty of Science, Okayama University, Tsushimanaka, Okayama-shi, Okayama 700, Japan $ Institute for Material Research, Tohoku University, Katahira, Aoba-ku, Sendai 980-77, Japan % Department of Physics, Faculty of Science, Kobe University, Rokkodai, Nada-ku, Kobe 657, Japan & The Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-ku, Kobe 657, Japan
Abstract ESR measurements have been performed on KCuCl and TlCuCl in the frequency range up to 762 GHz and field 3 3 range up to 30 T at helium temperatures. The exchange network in the present systems is described as an S"1 2 Heisenberg spin ladder along the a-axis with an additional diagonal interaction. Both compounds have a singlet ground state with an excitation gap. In KCuCl , two kinds of transitions are observed between the ground state and the excited 3 triplet states. They correspond to the excitations at Q"(1, 0, 1) and (0.5, 0, 1) with the excitation energies D+640 and 1080 GHz, respectively. When the external field is increased, the frequency of the lowest branch with the zero-field gap D+640 GHz decreases linearly with a tendency toward zero at H +22 T. In TlCuCl , a transition from the singlet # 3 ground state to the excited triplet state is observed. The zero-field gap is determined as D+160 GHz. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: KCuCl ; TlCuCl ; ESR; High magnetic field; Double spin chain; Singlet ground state; Excitation gap 3 3
1. Introduction Recently the physics of spin-ladder systems has been of great interest. KCuCl and TlCuCl are 3 3 composed of the double chain of edge-sharing octahedra CuCl along the a-axis [1,2]. The exchange 6 * Corresponding author. Tel.: #81 3 5734 3541; fax: #81 3 5734 2702; e-mail: [email protected].
network in the double chain can be described as an S"1 Heisenberg spin ladder with an additional 2 diagonal interaction. The susceptibilities for three different external field directions in KCuCl and 3 TlCuCl exhibit broad maxima at 30 and 38 K, 3 respectively, and decrease exponentially to zero with decreasing temperature [2,3]. The result indicates that the ground state of the present systems is a spin singlet with an excitation gap, as predicted for Heisenberg spin ladder systems [4,5]. The singlet
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 2 - 4
546
H. Tanaka et al. / Physica B 246—247 (1998) 545—548
ground state was also confirmed by high-field magnetization measurements [6]. A transition from the 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 excita3 3 tion gap D was evaluated from the critical field as D/k "31.1 K for KCuCl and 7.5 K for TlCuCl . B 3 3 In order to investigate the magnetic excitations of the present systems, we carried out high-frequency high-field ESR measurements on the single crystals of KCuCl and TlCuCl . In this 3 3 note we report the results.
2. Experimental Single crystals of KCuCl and TlCuCl were 3 3 grown from a melt by the Bridgman method. ESR measurements were carried out in static magnetic fields up to 8 T and pulsed magnetic fields up to 30 T using FIR laser (404—762 GHz), Gunn oscillators (50—315 GHz) and klystrons (50—115 GHz). The magnetic fields were applied perpendicularly to the cleavage plane and in a direction parallel to the cleavage plane. The Miller indices of the cleavage planes have not been determined. In this letter we refer to the cleavage plane as CP.
3. Results and discussions Fig. 1 shows the high frequency ESR signals of KCuCl for H//CP. The data were collected at 3 4.2 K, where the susceptibility is almost zero [3]. Besides the sharp DPPH line, three kinds of welldefined resonance mode labeled as A, B and Pmodes, are observed. The ESR data obtained are summarized in Fig. 2. For KCuCl the value of the critical field is 3 H +22 T, when H//CP [6]. The paramagnetic res# onance P-mode is described by +u"gk H with B g"2.10. Its intensity becomes smaller as the temperature is lowered and the resonance field is lowered. This behavior is consistent with the fact that there is an excitation gap between the singlet ground state and the excited state. The P-mode corresponds to the transition between the excited
Fig. 1. High-frequency ESR signals of KCuCl observed at 3 4.2 K. The external field is parallel to the cleavage plane.
triplet states, when the resonance field is lower than the critical field H . # We see from Fig. 2 that the A- and B-modes correspond to the direct transitions from the singlet ground state to two triplet states with the excitation gaps D +640 GHz and D +1080 GHz. Both A B A- and B-modes split into three branches by the external field. Recently we have investigated the magnetic excitations in KCuCl by neutron inelas3 tic scattering experiments, and have determined the dispersion relation in the a*—c* plane [7]. The lowest excitation energy was found at Q"(1, 0, 1) to be 2.70 meV, which coincides with the zero field frequency of the A-mode. The excitation energy which coincides with the zero field frequency of the
H. Tanaka et al. / Physica B 246—247 (1998) 545—548
547
by +u"D !gk H, and the line width broadens B B out. For HoCP, the A- and B-modes were not clearly observed. Fig. 3 shows the ESR signals of TlCuCl for 3 H//CP obtained at 2 K in static magnetic fields. The susceptibility is almost zero at 2 K [2]. Three kinds of ESR modes, which we label u , u and 1 2 u -modes, are observed. Fig. 4 shows the frequency 3 versus field diagram obtained at 2.0, 4.2 and 5.0 K. The u and u -modes may correspond to the 2 3 transition between the excited triplet states. The notable mode is the u -mode with zero-field gap of 1 about 160 GHz. With increasing external field, its frequency decreases straightly toward zero at 6.1 T for 2.0 K, which coincides with the critical field observed by high-field magnetization measurements [6]. Thus, the u -mode corresponds to the 1 direct transition from the singlet ground state to an excited triplet state. From Fig. 4, we see that the Fig. 2. Frequency versus field diagram of KCuCl observed for 3 H//CP at 4.2 K. The external field is parallel to the cleavage plane.
B-mode was found at Q"(0.5, 0, 1). Thus we can say that the A- and B-modes correspond to the excitations at Q"(1, 0, 1) and (0.5, 0, 1). We notice in Figs. 1 and 2 that the A-mode splits into two close modes, A -mode (open rectangles) 1 and A -mode (filled rectangles), with the excitation 2 gaps D"632 and 641 GHz, respectively. Since the intensity of the A -mode is always larger than that 1 of the A -mode, the splitting is not due to the 2 instrumental problem such as the interference effect, but intrinsic to the present system. Since the Zeeman splittings of the A - and A -modes can be 1 2 described by the same g-factor, their origins are in the same spin site. The lowest branch of the A 1 mode can be clearly observed down to 50 GHz. When the external field is increased, its frequency decreases straightly with a tendency toward zero at 22 T, which coincides with the critical field H ob# tained by high-field magnetization measurements [6]. The intensity of the lowest branch of the A 2 mode becomes smaller with decreasing frequency, and it is hardly observed in the frequencies lower than 100 GHz. Above H , the resonance condition # of the B-mode deviates from the straight line given
Fig. 3. ESR signals of TlCuCl observed at 2.0 K. The external 3 field is parallel to the cleavage plane.
548
H. Tanaka et al. / Physica B 246—247 (1998) 545—548
TlCuCl is generally forbidden. We believe that the 3 antisymmetric Dzyaloshinsky-Moriya type interaction H which can exist in the present systems DM causes such excitations. The matrix elements of H between the singlet and the triplet states have DM non-zero values. Consequently, the ground state has a small amount of the triplet state component, and the ESR transition from the ground state to the excited state becomes possible.
References
Fig. 4. Frequency versus field diagram of TlCuCl observed for 3 H//CP at 2.0, 4.2 and 5.0 K.
critical field H estimated by extrapolating the u # 1 branch increases with increasing temperature. This behavior is also confirmed by high-field magnetization measurements [6]. The ESR excitation from the singlet ground state to the triplet state as observed in KCuCl and 3
[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] T. Kato, K. Takatsu, H. Tanaka, W. Shiramura, M. Mori, K. Nakajima, K. Kakurai, J. Phys. Soc. Jpn. 67 (1998) 752.