- Email: [email protected]
Field dependence of magnetic ordering in Tb2Ti2O7
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e1007–e1008
Field dependence of magnetic ordering in Tb2Ti2O7 N. Hamaguchi*, T. Matsushita, N. Wada, Y. Yasui, M. Sato Department of Physics, Graduate School of Science, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
Abstract We have investigated the phase transition in magnetic field, for the pyrochlore compound Tb2 Ti2 O7 with strong geometrical frustration. The specific heat has been measured down to 0:15 K in magnetic fields up to 1:6 T: Temperatures of the transition to long-range order and the broad peak due to short-range ordering shift towards higher temperatures with increasing the applied magnetic field. The field dependence of the transition temperature suggests another long-range ordered phase above about 0:3 T: r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Kz; 75.40.Cx; 75.50.Ee Keywords: Tb2 Ti2 O7 ; Phase transition; Magnetic ordering; Geometrical frustration; Pyrochlore lattice; Specific heat
The pyrochlore rare earth titanates R2 Ti2 O7 have attracted much interest on the geometrical frustration for the magnetic ordering. For Ho and Dy titanates, ferromagnetic interactions with strong uniaxial anisotropy lead to the frustrated state ‘spin ice’ (for example see Ref. [1] and references therein). For antiferromagnetic Tb2 Ti2 O7 ; exchange and dipolar interactions have the same order of magnitude, and compete also with the anisotropy energy [2]. Thus the effect of frustration possibly appears in a different form from those of the other titanates. While intensive studies have been done for this titanate [2–8], the magnetic ground state of Tb2 Ti2 O7 was still unclear. The moments of Tb3þ have been considered to remain paramagnetic down to 70 mK from the mSR experiment [3]. On the other hand, recently we found that several magnetic phases exist in Tb2 Ti2 O7 at low temperatures [9]. For the lowest doublet of the Tb3þ moments, the short-range order grows below about 2 K; and shows peculiar properties with the residual magnetization below 1:5 K: The specific heats indicate that a second-order transition occurs at 0:4 K: In addition, the spin-glass state below 0:2 K is shown in the AC susceptibilities. *Corresponding author. Tel.: +81-52-789-2887; fax: +8152-789-2888. E-mail address: [email protected] (N. Hamaguchi).
To investigate the ordered phase between 0.2 and 0:4 K and the competing interactions therein further, we have measured the specific heats of Tb2 Ti2 O7 in magnetic field. We found that the frustration is suppressed by the magnetic field and another long-range ordered phase exists above 0:3 T: The single crystal sample of Tb2 Ti2 O7 were cut from a single crystal which was prepared by the floating zone method as reported in our previous paper [2]. The specific heat C was measured by the ordinary adiabatic heat pulse method down to 0:15 K; in zero field and magnetic fields up to 1:6 T: The T-dependence of C of Tb2 Ti2 O7 in zero field is shown by open circles in Fig. 1. The C–T curve has a broad peak around Ts ¼ 0:66 K due to short-range ordering. The form of the sharp peak at 0:37 K indicates that a second-order magnetic transition occurs at Tc ¼ 0:40 K: Here, we defined the transition temperature Tc as the midpoint of the C–T slope at the higher temperature side of the peak. The upturn of C below 0:2 K is attributed to the nuclear magnetism due to the hyperfine interaction of the order of 0:3 K [5]. The magnetic entropy was estimated to be almost zero below 0:15 K [9], in contrast to the residual entropy at T ¼ 0 for the spin ice systems. We have measured C in several magnetic fields along the ½1 1 0 direction of the single crystal. Field dependences of Tc and Ts are shown in Fig. 2. While both
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.451
ARTICLE IN PRESS N. Hamaguchi et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1007–e1008
e1008
1
8
6
T (K)
C (J K-1 mol-1)
0.8
4
0T 0.4 T 1T
2 H // [110] 0
0.6 0.4
Tc Ts
0.2
H // [110]
0 0
0.5
1
1.5
H (T) 0.5
1
T (K) Fig. 1. Temperature dependences of specific heats of Tb2 Ti2 O7 in some magnetic fields. The static fields are applied in the ½1 1 0 direction of the single crystal.
Tc and Ts shift towards higher temperatures with increasing the applied field, Tc rises steeply at about 0:3 T: The C in some fields are plotted in Fig. 1. They show that the transition peak becomes small around 0:3 T: These behaviors suggest that magnetic phase boundary exists around 0:3 T; and above 0:3 T another long-range ordered phase appears. Although the field direction is different, the antiferromagnetic order induced by the field has been observed in the neutron scattering experiments with the fields along the ½1 1% 1 direction [6]. The monotonic increase of Tc and Ts with the field implies that the applied field acts to cancel the spin frustration. Above 0:3 T; competitions among several interactions including the Zeeman interaction induce another long-range ordered phase. The magnetization
Fig. 2. Field dependences of the transition temperature Tc and the broad peak temperature Ts shown in Fig. 1. Lines are guides for the eye.
curve measurement in this temperature region can reveal properties of the ordered states further. We acknowledge T. Kurokawa for his technical support.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
S.T. Bramwell, M.J.P. Gingras, Science 294 (2001) 1495. Y. Yasui, et al., J. Phys. Soc. Jpn. 71 (2002) 599. J.S. Gardner, et al., Phys. Rev. Lett. 82 (1999) 1012. M. Kanada, et al., J. Phys. Soc. Jpn. 68 (1999) 3802. M.J.P. Gingras, et al., Phys. Rev. B 62 (2000) 6496. Y. Yasui, et al., J. Phys. Chem. Solids 62 (2001) 343. G. Luo, et al., Phys. Lett. A 291 (2001) 306. I. Mirebeau, et al., Nature 420 (2002) 54. N. Hamaguchi, et al., Phys. Rev. B, submitted for publication.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e1007–e1008
Field dependence of magnetic ordering in Tb2Ti2O7 N. Hamaguchi*, T. Matsushita, N. Wada, Y. Yasui, M. Sato Department of Physics, Graduate School of Science, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
Abstract We have investigated the phase transition in magnetic field, for the pyrochlore compound Tb2 Ti2 O7 with strong geometrical frustration. The specific heat has been measured down to 0:15 K in magnetic fields up to 1:6 T: Temperatures of the transition to long-range order and the broad peak due to short-range ordering shift towards higher temperatures with increasing the applied magnetic field. The field dependence of the transition temperature suggests another long-range ordered phase above about 0:3 T: r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Kz; 75.40.Cx; 75.50.Ee Keywords: Tb2 Ti2 O7 ; Phase transition; Magnetic ordering; Geometrical frustration; Pyrochlore lattice; Specific heat
The pyrochlore rare earth titanates R2 Ti2 O7 have attracted much interest on the geometrical frustration for the magnetic ordering. For Ho and Dy titanates, ferromagnetic interactions with strong uniaxial anisotropy lead to the frustrated state ‘spin ice’ (for example see Ref. [1] and references therein). For antiferromagnetic Tb2 Ti2 O7 ; exchange and dipolar interactions have the same order of magnitude, and compete also with the anisotropy energy [2]. Thus the effect of frustration possibly appears in a different form from those of the other titanates. While intensive studies have been done for this titanate [2–8], the magnetic ground state of Tb2 Ti2 O7 was still unclear. The moments of Tb3þ have been considered to remain paramagnetic down to 70 mK from the mSR experiment [3]. On the other hand, recently we found that several magnetic phases exist in Tb2 Ti2 O7 at low temperatures [9]. For the lowest doublet of the Tb3þ moments, the short-range order grows below about 2 K; and shows peculiar properties with the residual magnetization below 1:5 K: The specific heats indicate that a second-order transition occurs at 0:4 K: In addition, the spin-glass state below 0:2 K is shown in the AC susceptibilities. *Corresponding author. Tel.: +81-52-789-2887; fax: +8152-789-2888. E-mail address: [email protected] (N. Hamaguchi).
To investigate the ordered phase between 0.2 and 0:4 K and the competing interactions therein further, we have measured the specific heats of Tb2 Ti2 O7 in magnetic field. We found that the frustration is suppressed by the magnetic field and another long-range ordered phase exists above 0:3 T: The single crystal sample of Tb2 Ti2 O7 were cut from a single crystal which was prepared by the floating zone method as reported in our previous paper [2]. The specific heat C was measured by the ordinary adiabatic heat pulse method down to 0:15 K; in zero field and magnetic fields up to 1:6 T: The T-dependence of C of Tb2 Ti2 O7 in zero field is shown by open circles in Fig. 1. The C–T curve has a broad peak around Ts ¼ 0:66 K due to short-range ordering. The form of the sharp peak at 0:37 K indicates that a second-order magnetic transition occurs at Tc ¼ 0:40 K: Here, we defined the transition temperature Tc as the midpoint of the C–T slope at the higher temperature side of the peak. The upturn of C below 0:2 K is attributed to the nuclear magnetism due to the hyperfine interaction of the order of 0:3 K [5]. The magnetic entropy was estimated to be almost zero below 0:15 K [9], in contrast to the residual entropy at T ¼ 0 for the spin ice systems. We have measured C in several magnetic fields along the ½1 1 0 direction of the single crystal. Field dependences of Tc and Ts are shown in Fig. 2. While both
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.451
ARTICLE IN PRESS N. Hamaguchi et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1007–e1008
e1008
1
8
6
T (K)
C (J K-1 mol-1)
0.8
4
0T 0.4 T 1T
2 H // [110] 0
0.6 0.4
Tc Ts
0.2
H // [110]
0 0
0.5
1
1.5
H (T) 0.5
1
T (K) Fig. 1. Temperature dependences of specific heats of Tb2 Ti2 O7 in some magnetic fields. The static fields are applied in the ½1 1 0 direction of the single crystal.
Tc and Ts shift towards higher temperatures with increasing the applied field, Tc rises steeply at about 0:3 T: The C in some fields are plotted in Fig. 1. They show that the transition peak becomes small around 0:3 T: These behaviors suggest that magnetic phase boundary exists around 0:3 T; and above 0:3 T another long-range ordered phase appears. Although the field direction is different, the antiferromagnetic order induced by the field has been observed in the neutron scattering experiments with the fields along the ½1 1% 1 direction [6]. The monotonic increase of Tc and Ts with the field implies that the applied field acts to cancel the spin frustration. Above 0:3 T; competitions among several interactions including the Zeeman interaction induce another long-range ordered phase. The magnetization
Fig. 2. Field dependences of the transition temperature Tc and the broad peak temperature Ts shown in Fig. 1. Lines are guides for the eye.
curve measurement in this temperature region can reveal properties of the ordered states further. We acknowledge T. Kurokawa for his technical support.
References [1] [2] [3] [4] [5] [6] [7] [8] [9]
S.T. Bramwell, M.J.P. Gingras, Science 294 (2001) 1495. Y. Yasui, et al., J. Phys. Soc. Jpn. 71 (2002) 599. J.S. Gardner, et al., Phys. Rev. Lett. 82 (1999) 1012. M. Kanada, et al., J. Phys. Soc. Jpn. 68 (1999) 3802. M.J.P. Gingras, et al., Phys. Rev. B 62 (2000) 6496. Y. Yasui, et al., J. Phys. Chem. Solids 62 (2001) 343. G. Luo, et al., Phys. Lett. A 291 (2001) 306. I. Mirebeau, et al., Nature 420 (2002) 54. N. Hamaguchi, et al., Phys. Rev. B, submitted for publication.