- Email: [email protected]
Magnetic properties of oxygen monolayers
Journal of Magnetism and Magnetic Materials 177-181 (1998) 719 720
~i ~[~ ~I]
ELSEVIER
Journalof magnetism and magnetic materials
Magnetic properties of oxygen monolayers Ibha
Chatterjee*
Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Calcutta 700064, India
Abstract
The magnetic properties of oxygen monolayer which is purely two-dimensional have been investigated by a phenomenological theory using Heisenberg model. The neutron diffraction data of the magnetic-order parameter agree fairly well with the theoretical results. The exchange parameter estimated from these experimental results are used to calculate the zero-field susceptibilities. As there are no such experimental data no comparison is possible. © 1998 Elsevier Science B.V. All rights reserved. K e y w o r d s . Localised model; Low-dimensional system; Magnetic ordering, antiferromagnet
Oxygen molecules physisorbed on graphite grow in a layer-by-layer fashion [1, 2] and the oxygen molecules on the graphite form an ideal two-dimensional (2D) lattice. 02 molecule has spin S = 1 and the interaction between them is Heisenberg-like and it is antiferromagnetic. It becomes a magnetic insulator in the condensed phase. So this is an ideal substance to study a 2D Heisenberg antiferromagnetic spin system. During the last few years investigations on this system have been performed from all corners. X-ray diffraction, neutron diffraction, susceptibility, heat capacity measurements and spectroscopic studies, to name a few such investigations. From structural studies it can be concluded that this system exists in different phases depending on temperature and oxygen coverage. There is a dilute phase (6) in which molecular axis is parallel to the graphite surface, whereas in dense phases (e and ~) the molecular axes are perpendicular to the graphite surface. There is a clear indication of magnetic phase transition [3] in the dense phase accompanied by a lattice distortion, a phase is antiferromagnetic with a deformed triangular lattice. The magnetic phase transition is evident from neutron diffraction experiment as well as from susceptibility measurements in presence of magnetic field [1-3]. The transition temperature is TN = 11.9 + 0.1 K. 02 molecule has spin S = 1 and it has magnetocrystalline anisotropy which splits the spin-triplet state into
a doublet and a singlet. This effect can be incorporated in the Heisenberg Hamiltonian by introducing a term DS~. The Heisenberg Hamiltonian describes the magnetic interaction between the 02 molecules physisorbed on graphite and it is purely two-dimensional. Since in two dimensions, correlation and fluctuation become important the magnetic properties are to be studied by a theory which goes beyond the mean-field theory. The correlated effective field theory developed by Lines [4] can be applied in this case to study the magnetic properties in both the ordered and the paramagnetic phases. Magneto-crystalline anisotropy has very little effect on the magnetic properties of oxygen monolayer and the relevant Hamiltonian is (1)
H = - 2 ~' Ji~Si'Sj, ij
where the spin S = 1. In correlated effective field theory fluctuation is introduced semiempirically by a temperature-dependent correlation parameter (c0 and it is determined self-consistently via the fluctuation dissipation theorem. In this theory a particular spin S}' is replaced by (S}') + A~)(S~'-(S~')) where A~) is related to ~. as }~j J i ) A i ) = ~ ' ~ J ~ ) and 7 corresponds to the spatial components. ~ is assumed to be same for all sites but different in different spatial directions. The correlated effective field Hamiltonian [4] then becomes H cEv : - ~ Ji'~:~;'(Si")2 - 2 ~ JI~)S~'((S~) - ~Y(Si')).
* Fax: +91 33 337 4637; e-mail: [email protected]. 0304-8853/98/$19.00 .~): 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 8 50-0
";,J
~'.i
(2)
720
1. Chattetjee /'Journal of Magnetism and Magnetic Materials 177 181 (1998) 719 720 1.2
-0.50 Th
1.0
"~
-0.40
• -0.35
~0.8 (n
-0.30
~0.6
~. -0.25 ._~ -0.20
o~
~
a ± - -
-0.45
0.4
-0.15 -0.10
rr 0.2
-0.05 0.C
i 2
0
6 8 10 12 Temperature(K)
4
i • 14 16
Fig. 1. Variation of magnetic-order parameter with temperature using .I = - 2.56 K.
45
Z± m
40 35 _~. 3O 25
20
~? o15
//
10 ./ ,~r ~
2
4
i
i
6
.
1'0 12 1 ' . 1 ; 1 ' 8 2 0
Temperature(K)
Fig. 2. Variation of susceptibility (Z) with temperature using J = 2.56 K.
~: is the temperature-dependent correlation parameter to be determined self-consistently [4, 5]. The correlated effective field theory as applied to the ordered and disordered magnetic phases are discussed in great detail in Refs. [5, 6] and has been successfully applied to a variety of magnetic substances. Recently, this method has been applied to a layered c o m p o u n d [7]. In this compound although magnetic interaction is confined within a layer, the compound is three-dimensional. But in the present investigation an attempt has been made to study the magnetic properties of oxygen monolayer which is purely two-dimensional. F r o m the neutron diffraction experiment [1] the temperature dependence of the staggered magnet±sat±on in the dense monolayer phase has been studied and compared with the theoretical results. As evident from Fig. 1, there is very good agreement with the experimental
0.00
4
6 10 12 114 1; Temperature(K)
1; 20
Fig. 3. Variation of correlation parameter (:0 with temperature using J = -- 2.56 K.
results shown by filled circles. The value of the exchange parameter is J = - 2.56 K. The magnetic susceptibility (g) is also calculated using the same J value and is shown in Fig. 2. As there is no experimental result no comparison can be made. The temperature dependence of the correlation parameter (~) is shown in Fig. 3. The anisotropy in ~ and Z are observed in the ordered phase and it is evident from the Hamilton±an (Eq. (2)). Fig. 1 shows a discontinuous change in the order parameter at T ~ 12 K, which is consistent with other measurements also. As discussed in an earlier paper [1], the results are very close to 2D Ising model calculation. 2D Ising model calculation by Onsager [8] is for S = ½ but oxygen monolayer corresponds to S = 1 and there is no exact calculation of 2D Ising model for S = 1. Therefore, the comparison of 2D Ising model calculation [1] is not very clear.
References
[1] Y. Murakami, I.N. Makundi, T. Shibata, H. Suematsu, M. Arai, H. Yoshizawa, H. Ikeda, N. Watanabe, Physica B 213&214 (1995) 233. [2] Y. Murakami, H. Suematsu, Phys. Rev. B 54 (1996) 4146. [3] H. Suematsu, Y. Murakami, J. Magn. Magn. Mater. 90&91 (1990) 749. [4] M.E. Lines, Phys. Rev. B 9 (1974) 3927. [5] I. Chatterjee, Phys. Rev. B 19 (1979) 3827. [6] N. Suzuki, T. Isu, K. Motizuki, Solid State Commun. 23 (1977) 319. [7] I. Chatterjee, Phys. Rev. B 51 (1995) 3937. [8] L. Onsager, Phys. Rev. 65 (1944) 117.
~i ~[~ ~I]
ELSEVIER
Journalof magnetism and magnetic materials
Magnetic properties of oxygen monolayers Ibha
Chatterjee*
Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Calcutta 700064, India
Abstract
The magnetic properties of oxygen monolayer which is purely two-dimensional have been investigated by a phenomenological theory using Heisenberg model. The neutron diffraction data of the magnetic-order parameter agree fairly well with the theoretical results. The exchange parameter estimated from these experimental results are used to calculate the zero-field susceptibilities. As there are no such experimental data no comparison is possible. © 1998 Elsevier Science B.V. All rights reserved. K e y w o r d s . Localised model; Low-dimensional system; Magnetic ordering, antiferromagnet
Oxygen molecules physisorbed on graphite grow in a layer-by-layer fashion [1, 2] and the oxygen molecules on the graphite form an ideal two-dimensional (2D) lattice. 02 molecule has spin S = 1 and the interaction between them is Heisenberg-like and it is antiferromagnetic. It becomes a magnetic insulator in the condensed phase. So this is an ideal substance to study a 2D Heisenberg antiferromagnetic spin system. During the last few years investigations on this system have been performed from all corners. X-ray diffraction, neutron diffraction, susceptibility, heat capacity measurements and spectroscopic studies, to name a few such investigations. From structural studies it can be concluded that this system exists in different phases depending on temperature and oxygen coverage. There is a dilute phase (6) in which molecular axis is parallel to the graphite surface, whereas in dense phases (e and ~) the molecular axes are perpendicular to the graphite surface. There is a clear indication of magnetic phase transition [3] in the dense phase accompanied by a lattice distortion, a phase is antiferromagnetic with a deformed triangular lattice. The magnetic phase transition is evident from neutron diffraction experiment as well as from susceptibility measurements in presence of magnetic field [1-3]. The transition temperature is TN = 11.9 + 0.1 K. 02 molecule has spin S = 1 and it has magnetocrystalline anisotropy which splits the spin-triplet state into
a doublet and a singlet. This effect can be incorporated in the Heisenberg Hamiltonian by introducing a term DS~. The Heisenberg Hamiltonian describes the magnetic interaction between the 02 molecules physisorbed on graphite and it is purely two-dimensional. Since in two dimensions, correlation and fluctuation become important the magnetic properties are to be studied by a theory which goes beyond the mean-field theory. The correlated effective field theory developed by Lines [4] can be applied in this case to study the magnetic properties in both the ordered and the paramagnetic phases. Magneto-crystalline anisotropy has very little effect on the magnetic properties of oxygen monolayer and the relevant Hamiltonian is (1)
H = - 2 ~' Ji~Si'Sj, ij
where the spin S = 1. In correlated effective field theory fluctuation is introduced semiempirically by a temperature-dependent correlation parameter (c0 and it is determined self-consistently via the fluctuation dissipation theorem. In this theory a particular spin S}' is replaced by (S}') + A~)(S~'-(S~')) where A~) is related to ~. as }~j J i ) A i ) = ~ ' ~ J ~ ) and 7 corresponds to the spatial components. ~ is assumed to be same for all sites but different in different spatial directions. The correlated effective field Hamiltonian [4] then becomes H cEv : - ~ Ji'~:~;'(Si")2 - 2 ~ JI~)S~'((S~) - ~Y(Si')).
* Fax: +91 33 337 4637; e-mail: [email protected]. 0304-8853/98/$19.00 .~): 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 8 50-0
";,J
~'.i
(2)
720
1. Chattetjee /'Journal of Magnetism and Magnetic Materials 177 181 (1998) 719 720 1.2
-0.50 Th
1.0
"~
-0.40
• -0.35
~0.8 (n
-0.30
~0.6
~. -0.25 ._~ -0.20
o~
~
a ± - -
-0.45
0.4
-0.15 -0.10
rr 0.2
-0.05 0.C
i 2
0
6 8 10 12 Temperature(K)
4
i • 14 16
Fig. 1. Variation of magnetic-order parameter with temperature using .I = - 2.56 K.
45
Z± m
40 35 _~. 3O 25
20
~? o15
//
10 ./ ,~r ~
2
4
i
i
6
.
1'0 12 1 ' . 1 ; 1 ' 8 2 0
Temperature(K)
Fig. 2. Variation of susceptibility (Z) with temperature using J = 2.56 K.
~: is the temperature-dependent correlation parameter to be determined self-consistently [4, 5]. The correlated effective field theory as applied to the ordered and disordered magnetic phases are discussed in great detail in Refs. [5, 6] and has been successfully applied to a variety of magnetic substances. Recently, this method has been applied to a layered c o m p o u n d [7]. In this compound although magnetic interaction is confined within a layer, the compound is three-dimensional. But in the present investigation an attempt has been made to study the magnetic properties of oxygen monolayer which is purely two-dimensional. F r o m the neutron diffraction experiment [1] the temperature dependence of the staggered magnet±sat±on in the dense monolayer phase has been studied and compared with the theoretical results. As evident from Fig. 1, there is very good agreement with the experimental
0.00
4
6 10 12 114 1; Temperature(K)
1; 20
Fig. 3. Variation of correlation parameter (:0 with temperature using J = -- 2.56 K.
results shown by filled circles. The value of the exchange parameter is J = - 2.56 K. The magnetic susceptibility (g) is also calculated using the same J value and is shown in Fig. 2. As there is no experimental result no comparison can be made. The temperature dependence of the correlation parameter (~) is shown in Fig. 3. The anisotropy in ~ and Z are observed in the ordered phase and it is evident from the Hamilton±an (Eq. (2)). Fig. 1 shows a discontinuous change in the order parameter at T ~ 12 K, which is consistent with other measurements also. As discussed in an earlier paper [1], the results are very close to 2D Ising model calculation. 2D Ising model calculation by Onsager [8] is for S = ½ but oxygen monolayer corresponds to S = 1 and there is no exact calculation of 2D Ising model for S = 1. Therefore, the comparison of 2D Ising model calculation [1] is not very clear.
References
[1] Y. Murakami, I.N. Makundi, T. Shibata, H. Suematsu, M. Arai, H. Yoshizawa, H. Ikeda, N. Watanabe, Physica B 213&214 (1995) 233. [2] Y. Murakami, H. Suematsu, Phys. Rev. B 54 (1996) 4146. [3] H. Suematsu, Y. Murakami, J. Magn. Magn. Mater. 90&91 (1990) 749. [4] M.E. Lines, Phys. Rev. B 9 (1974) 3927. [5] I. Chatterjee, Phys. Rev. B 19 (1979) 3827. [6] N. Suzuki, T. Isu, K. Motizuki, Solid State Commun. 23 (1977) 319. [7] I. Chatterjee, Phys. Rev. B 51 (1995) 3937. [8] L. Onsager, Phys. Rev. 65 (1944) 117.