- Email: [email protected]
Magnetic anisotropy of the antiferromagnetically ordered free radical, p-Cl-BDPA
Volume 54A, number 3
PHYSICS LETTERS
8 September 1975
MAGNETIC ANISOTROPY OF THE ANTIFERROMAGNETICALLY O R D E R E D F R E E R A D I C A L , p-CI-BDPA H. OZAKI, H. OHYA-NISHIGUCHI Faculty of Science, Kyoto University, Kyoto, Japan
and J. YAMAUCHI Institute for Chemical Research, Kyoto University, U]i, Kyoto, Japan Received 21 May 1975 Revised manuscript ~eceived 7 August 1975 Magnetic torque of the antiferromagnetically ordered free radical, p-C1-BDPA, was measured. The b-axis is the easy axis and torque curves are in accordance with a simple two-sublattice model. Anisotropy fields are small; 6.5 Oe and 20Oe at OK.
An organic free radical is characterized by an unpaired electron with spin 1/2 in n-molecular orbitals, which exhibits very small anisotropy of the g-value in EPR experiments. In recent years a good deal of interest has arisen regarding the magnetic phase transition of such organic free radical crystals [ 1 - 3 ] . Because of the small intermolecular exchange interaction, the transition temperatures of these radicals lie down around 1K. In p-C 1-BDPA (1,3-bisdiphenylene-2-p-chlorophenyl allyl, C33H20C1), however, the antiferromagnetic phase transition takes place at relatively high temperature, 3.25 K [4]. We performed the magnetic torque measurements of p-CI-BDPA single crystal, in order to have information about the spin structure and anisotropy energy of the antiferromagneticaUy ordered electron spins in the delocalized molecular orbitals. p-CI-BDPA forms monoclinic crystals with the space group C2/C. The unit cell contains eight molecules and has the dimensions a = 32.9A, b = 9.30A, c = 15.1 A, = 101.0 °. The torque curves in the ordered state were accounted for by a two-sublattice model with collinear spin arrangement and by the anisotropy energy in the form of K 1o~2 + K272 (c~and 3' stand for direction cosines of the spin axis relative to the principal axes). In fig. 1, the torque curves in the a*b plane are shown. (a*-axis is the direction perpendicular to the bc plane.) When the Zeeman energy overcomes the anisotropy energy,
3100 0# 1~
1700 15oo
1250
v
f //~.\
II/f
llY ~ Ill ~
Vi
\ x \\\\
~\\
~\\\\
2 g i:9 ~°2
Fig. I. The torque curves in a*b plane at 2.16K. 1 8 5 0 O e is just below the criticalfield.
the spin axis deviates from the easy axis [5]. If the uniaxial anisotropy energy is much smaller than the exchange energy, the torque curves are expressed as follows.
X±- XII I sin 20 ] T=-~H 2 sin arctan c o s 2 ~ - H / H c ) 2 j , Hc2 -
2K1 , ×± - ×I~
where 0 is the angle of the external field relative to the easy axis, K 1 is the anisotropy energy constant, and H c is the critical field. The torque curve has a discontinuity when the critical field is applied along the easy axis. The torque curves in the a*b plane are in good agreement with the above formula. Hence, the b-axis 227
PHYSICS LETTERS
Volume 54A, number 3
H
XlO- 4
O~ egs emuIId
2O0O
~a~
150
IBOO 100 5O
o
1'
1600
%..
•
2
3
4
K
l:ig. 2. Temperature dependences of xA_- x Hand H c.
was found to be the easy axis. The temperature dependences of X ± - X II and H c are shown in fig. 2. These values extrapolated to OK are evaluated to be 150 X 10 . 4 cgsemu/mol, and 1500 Oe respectively. The anisotropy energy constant in this plane, K 1 , was also obtained by the use o f these values. K 1 at OK is 1.8 X 104 erg/mol, the corresponding anisotropy field H A being 6 . 5 0 e . The energy constant K 2 can be estimated from the torque curves in the bc plane. K 2 at OK was 6 × 104 erg/mol, giving the anisotropy field of 20 Oe. Since the bc plane contained both the easy axis, b-axis, and the hard axis, c-axis, the torque curves displayed abrupt
228
8 September 1975
changes due to spin flop out of the bc plane, which took place according to the critical hyperbola [5]. It should be noted that the anisotropy energy is very small in p-CI-BDPA. Because o r S = 1/2 and isotropic g-value, 2.0026, the anisotropy energy is considered to originate from the dipolar interaction. In addition to the large inter-molecular distances in this material, it seems to be responsible for this small anisotropy energy that the unpaired electron is delocalized over the whole molecular framework [6]. The authors wish to thank Prof. T. Takata for the use of the equipment and Prof. Y. Deguchi and Prof. M. Mekata for valuable discussions. References
[ 1 ] W. Duffy, Jr., J.F. Dubach, P.A. Pianetta, J.l:. Deck, D.L. Strandburg and A.R. Miedema, J. Chem. Phys. 56 (1972) 2555. [2] S. Saito, T. Sato, Phys. Lett. 44A (1973) 347. [31 M. Saint Paul, C. Veyret, Phys. Lett. 45A (1973) 362. [4] J. Yamauchi, J. Phys. Soc. Jap. 35 (1973) 2301. [5 ] T, Nagamiya, K. Yoshida and R. Kubo, Advance in Physics 4 (1955) 1. [6} K. Watanabe, J. Yamauchi, H. Ohya, Y. Deguchi and K. Ishizu, Chem. Lett. 1974 (1974) 489.
PHYSICS LETTERS
8 September 1975
MAGNETIC ANISOTROPY OF THE ANTIFERROMAGNETICALLY O R D E R E D F R E E R A D I C A L , p-CI-BDPA H. OZAKI, H. OHYA-NISHIGUCHI Faculty of Science, Kyoto University, Kyoto, Japan
and J. YAMAUCHI Institute for Chemical Research, Kyoto University, U]i, Kyoto, Japan Received 21 May 1975 Revised manuscript ~eceived 7 August 1975 Magnetic torque of the antiferromagnetically ordered free radical, p-C1-BDPA, was measured. The b-axis is the easy axis and torque curves are in accordance with a simple two-sublattice model. Anisotropy fields are small; 6.5 Oe and 20Oe at OK.
An organic free radical is characterized by an unpaired electron with spin 1/2 in n-molecular orbitals, which exhibits very small anisotropy of the g-value in EPR experiments. In recent years a good deal of interest has arisen regarding the magnetic phase transition of such organic free radical crystals [ 1 - 3 ] . Because of the small intermolecular exchange interaction, the transition temperatures of these radicals lie down around 1K. In p-C 1-BDPA (1,3-bisdiphenylene-2-p-chlorophenyl allyl, C33H20C1), however, the antiferromagnetic phase transition takes place at relatively high temperature, 3.25 K [4]. We performed the magnetic torque measurements of p-CI-BDPA single crystal, in order to have information about the spin structure and anisotropy energy of the antiferromagneticaUy ordered electron spins in the delocalized molecular orbitals. p-CI-BDPA forms monoclinic crystals with the space group C2/C. The unit cell contains eight molecules and has the dimensions a = 32.9A, b = 9.30A, c = 15.1 A, = 101.0 °. The torque curves in the ordered state were accounted for by a two-sublattice model with collinear spin arrangement and by the anisotropy energy in the form of K 1o~2 + K272 (c~and 3' stand for direction cosines of the spin axis relative to the principal axes). In fig. 1, the torque curves in the a*b plane are shown. (a*-axis is the direction perpendicular to the bc plane.) When the Zeeman energy overcomes the anisotropy energy,
3100 0# 1~
1700 15oo
1250
v
f //~.\
II/f
llY ~ Ill ~
Vi
\ x \\\\
~\\
~\\\\
2 g i:9 ~°2
Fig. I. The torque curves in a*b plane at 2.16K. 1 8 5 0 O e is just below the criticalfield.
the spin axis deviates from the easy axis [5]. If the uniaxial anisotropy energy is much smaller than the exchange energy, the torque curves are expressed as follows.
X±- XII I sin 20 ] T=-~H 2 sin arctan c o s 2 ~ - H / H c ) 2 j , Hc2 -
2K1 , ×± - ×I~
where 0 is the angle of the external field relative to the easy axis, K 1 is the anisotropy energy constant, and H c is the critical field. The torque curve has a discontinuity when the critical field is applied along the easy axis. The torque curves in the a*b plane are in good agreement with the above formula. Hence, the b-axis 227
PHYSICS LETTERS
Volume 54A, number 3
H
XlO- 4
O~ egs emuIId
2O0O
~a~
150
IBOO 100 5O
o
1'
1600
%..
•
2
3
4
K
l:ig. 2. Temperature dependences of xA_- x Hand H c.
was found to be the easy axis. The temperature dependences of X ± - X II and H c are shown in fig. 2. These values extrapolated to OK are evaluated to be 150 X 10 . 4 cgsemu/mol, and 1500 Oe respectively. The anisotropy energy constant in this plane, K 1 , was also obtained by the use o f these values. K 1 at OK is 1.8 X 104 erg/mol, the corresponding anisotropy field H A being 6 . 5 0 e . The energy constant K 2 can be estimated from the torque curves in the bc plane. K 2 at OK was 6 × 104 erg/mol, giving the anisotropy field of 20 Oe. Since the bc plane contained both the easy axis, b-axis, and the hard axis, c-axis, the torque curves displayed abrupt
228
8 September 1975
changes due to spin flop out of the bc plane, which took place according to the critical hyperbola [5]. It should be noted that the anisotropy energy is very small in p-CI-BDPA. Because o r S = 1/2 and isotropic g-value, 2.0026, the anisotropy energy is considered to originate from the dipolar interaction. In addition to the large inter-molecular distances in this material, it seems to be responsible for this small anisotropy energy that the unpaired electron is delocalized over the whole molecular framework [6]. The authors wish to thank Prof. T. Takata for the use of the equipment and Prof. Y. Deguchi and Prof. M. Mekata for valuable discussions. References
[ 1 ] W. Duffy, Jr., J.F. Dubach, P.A. Pianetta, J.l:. Deck, D.L. Strandburg and A.R. Miedema, J. Chem. Phys. 56 (1972) 2555. [2] S. Saito, T. Sato, Phys. Lett. 44A (1973) 347. [31 M. Saint Paul, C. Veyret, Phys. Lett. 45A (1973) 362. [4] J. Yamauchi, J. Phys. Soc. Jap. 35 (1973) 2301. [5 ] T, Nagamiya, K. Yoshida and R. Kubo, Advance in Physics 4 (1955) 1. [6} K. Watanabe, J. Yamauchi, H. Ohya, Y. Deguchi and K. Ishizu, Chem. Lett. 1974 (1974) 489.