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Magnetic properties of liquid oxygen in high magnetic fields
Physica B 155 (1989) 421-424 North-Holland, Amsterdam
MAGNETIC C. UYEDA’,
PROPERTIES
OF LIQUID
A. YAMAGISHI*,
OXYGEN
H. HOR13
IN HIGH MAGNETIC
FIELDS
and M. DATE3
‘College of General Education, Osaka University, Toyonaka, Osaka 560, Japan ‘The Research Center for Extreme Materials, Osaka University, Toyonaka, Osaka 560, Japan ‘Faculty of Science, Osaka University, Toyonaka. Osaka 560, Japan
Oxygen has a triplet ground state and it becomes a magnetic liquid below 90.2 K. The magnetic characteristics are related to the blue color of the oxygen. The absorption mechanism, magnetostriction and pair correlation in the liquid are investigated through magneto-optical measurements in high magnetic fields.
1. Introduction
‘A, ‘A,
The 0, molecule has received much interest in various fields of natural science. The molecule with triplet ground state has a magnetic moment and liquid and solid oxygen are considered to belong to the most fundamental materials in the research on magnetism. The liquid phase is found in the temperature range between 54.4 K and 90.2 K. The liquid is paramagnetic and the susceptibility obeys the Curie-Weiss law. The antiferromagnetic interaction between the molecules leads to a Weiss constant of 0 = - 40.6 K in the liquid phase. As is well known, liquid oygen shows a light blue color which arises from the absorption of the bimolecular optical transition between the ground 2(3_Zi) and excited 2(‘A,) states, where 2 before the parentheses means the bimolecular state [l]. An absorption is observed around 6290 8, and the phonon sideband is found at 576OA. It is noticed that the total spin angular momentum in the initial and final states of an 0, pair should be conserved in the electric dipole transition. As the final state of each 0, molecule is a spin singlet, the spins of the initial ground state in two 0, molecules should be antiferromagnetically coupled by the exchange interaction J(r), where r is the intermolecular distance. The process of optical transition is illustrated in fig. 1. When a high magnetic field is applied to the liquid, a decrease of the antiferromagnetic coupled pair is inferred and a reduction of the absorption intensity is 0921-4526/89/$03.50 0 (North-Holland Physics
Elsevier Science Publishers Publishing Division)
Fig. 1. Schematic
view of optical
absorption
process
in 0,.
expected. This effect can be observed as fieldinduced transparency of the liquid. The transparency increases with increasing magnetization and has a Curie-Weiss law like temperature dependence. A large magneto-volume effect due to the spin correlation in the liquid 0, is expected. This effect also contributes to the magnetization or transparency of the 0, liquid. This paper summarizes the experiments on the field-induced transparency in the liquid 0, reported in refs. 2 and 3 and shows that the mean field approximation is not adequate and that a quantitative explanation is obtained by the spinpair model.
2. Experimental
procedures
The new phenomenon of field-induced transparency in liquid 0, was observed at the High Magnetic Field Laboratory of Osaka University. The whole view of the field dependent absorption was observed by using a spectrometer with an optical multichannel analyzer (OMA) and a Xenon flash lamp as light source [4]. As shown in the insert of fig. 2, the spectra observed in a B.V.
--__ ,
L
,-L
100’3
500 MAGNETIC
Fig. 3. Field dependence 0,. Fig. 2. Transparency
of hqud
0,
in magnetic
FIELD
(kCeJ
of absorption
coefficient
m liquid
field.
camera system. The sample ing of the liquid nitrogen. pulsed field contain much noise but a decrease of the total absorption in high magnetic fields is found. To obtain the clear field dependence in the pulsed field. optical transparency was studied by using a He-Ne laser. The lasing wavelength (6328 A) of the laser is near the broad absorption peak of 6290 A and a large change in the transparency in a magnetic field H,, is expected. The experimental method is described in [2]. The result is shown in fig. 2 and the magnetic held dependence of the absorption coefficient k(H,,) is shown in fig. 3. As seen in fig. 3. a systematic deviation from the simple molecular held theory is found. The magneto-volume effect was observed in order to estimate the correction of the held-dependent transparency. Because of the slow response of the volume change, a superconducting magnet, which can generate magnetic fields up to 80 kOe, was used. The detailed method is described in [3] and the essential points are given here. The volume change in the field is small and the change is magnified by a thin capillary tube which is connected to the sample cell. The liquid level in the capillary tube is monitored by an optical periscope and a TV
3. Experimental
is cooled
by pump-
results and discussion
The bimolecular absorption occurs for the pairs with no resultant spins. Therefore, antiparallely coupled molecules with spins SI = + 1 and a couple of two SI = 0 molecules can contribute to the optical transitition. The normalized absorption coefficient is described by the population numbers N,, N and N,, for the ground S; = + 1. ~ 1 and 0 states. respectively. The normalized absorption coefficient is given by
(6,) + UWLl
k(H,,)ik((J) = [2N+(H,,)N
(2N, (O)N_ (0) + N,,(O)‘] .
,’ (1)
where a 0 in parentheses denotes the corresponding values at zero field 121. The N’s arc given by N, = Nexp(glCL,S,H,,,ik,,T)iZ, where
Z is the partition
function
(2) and
the sub-
C. Uyeda et al. I Magnetic liquid 0, in high jields
scripts
I = + 1, 0 and - 1 correspond to S, = + 1, ~ 1, respectively. H,,, calculated under the molecular field approximation is given by
0 and
K,,
= K, + 2Jz ( S; > l&Y% 1
(3)
where 2J is the exchange energy between two 0, spins. (S,) can be estimated from the CurieWeiss law [2] as 0,)
= 2g~+H,,i3k~(~
- 0) ,
where T is the temperature. Recently, we determined J(r) [5] as J(r) = J,, exp]a(r
--
(4)
the r dependence
r,,>l,
of
(5)
where J, = -3OK, r,, = 3.2A and F = -4.3Ai-‘. The thin broken line in fig. 3 shows the theoretical curve under the approximation. The deviation of the theoretical curve from the experimental data which is shown in the figure has inspired us to estimate the magneto-volume effect. The volume change due to the magnetovolume effect is given by the intermolecular potential. The potential U(r) is given by [3] U(r) = Uo[(a/r)12
- 2(air)‘]
- 2J(r)(
S,)’
,
(6)
where the first term in the parentheses is the Lennard-Jones potential and the second one is exchange energy [6]. The potential energy changes with variation of the magnetic moment which is proportronal to the applied field. This change induces a shift Ar of the minimum in the potential. The shift Ar is obtained from the condition of dlJ/dr = 0 and the volume change is written as AV/V,, = 3(Ar/a)
z= PHi
423
The constant p is evaluated as 2.7 x lo-” kOem2 by using the values of U,, = 100 K and a = 3.7 A. The experimental result of the field-dependent volume change is shown in fig. 4. The experimentally determined p of 3.5 x lo-’ kOe_’ is in fairly good agreement with the theoretical value. The experimental value gives a magnetovolume increase of 0.022% at 80 kOe and is much larger than the value in ferromagnetic Fe of 0.004% which is larger than the values in other usual ferromagnets. The volume increase leads to a reduction of the liquid density and the exchange field and makes the transparency increase. The correction of the magneto-volume effect is shown by the thin solid lines in fig. 3. The correction values, however, are still far from the observed values and other origins should be considered to explain quantitatively the field-induced transparency. In the molecular-field approximation, the 0, molecules experience a uniform mean field, but the model is less adequate to liquid in which the molecules have considerable pair correlation. Instead of the molecular field model, it is better to consider the spin pair coupling of two 0, molecules. The pair coupling of the S’ = 1 spins in 0, molecules gives three multiplets with total spin states S’ = 2, 1,O which have 5, 3 and 1 Zeeman levels, respectively. The energy gaps between S’ = 0 and 1 and between S’ = 1 and 2 are 2 J’ where J’ is the interand 4J’, respectively, molecular exchange energy. Only one singlet state with S’ = 0 is responsible for the optical
(7)
with p =
(J,,Eu/
12(/,,)[2gpB/3k,(
T
-
e)]’ Magnetic
x
ev[da
-
r,,)l
(8)
Fig. 4. Field dependence
Fteld
CkOe)
of magneto-volume
effect at 77 K.
424
c‘. Uyedu
et ul.
I Mugneiic
transition. The distribution over the many other levels in the spin pair state causes a reduction of the absorption. A preliminary estimate gives a good result, as shown by the thick dotted line in fig. 3. The detailed theory and discussions are given in ref. 7.
Acknowledgement The research is partly supported by a Grantin-Aid from the Ministry of Education, Science and Culture of Japan.
liquid
0,
in high fields
References [l) S.C. Tai and G.W. Robinson, J. Chem. Phys. 51 (1969) 3559. [2] C. Uyeda. A. Yamagishi and M. Date. J. Phys. Sot. Jpn. 55 (1986) 468. [3] C. Uyeda, A. Ydmagishi and M. Date, J. Phys. Sot. Jpn. 56 (1087) 3444. [4] H. Hori, in: High Field Magnetism, M. Date. ed. (NorthHolland, Amsterdam. 19X3), p. 289. [5] C. Uyeda, S. Sugiyama and M. Date. J. Phys. Sot. Jpn. 54 (1985) 1107. [6] T. Kihara and A. Koide. Adv. Chem. Phys. 33 (1975) 51. (71 C. Chiaki. A. Yamagishi and M. Date. submitted to J. Phys. Sot. Jpn.
MAGNETIC C. UYEDA’,
PROPERTIES
OF LIQUID
A. YAMAGISHI*,
OXYGEN
H. HOR13
IN HIGH MAGNETIC
FIELDS
and M. DATE3
‘College of General Education, Osaka University, Toyonaka, Osaka 560, Japan ‘The Research Center for Extreme Materials, Osaka University, Toyonaka, Osaka 560, Japan ‘Faculty of Science, Osaka University, Toyonaka. Osaka 560, Japan
Oxygen has a triplet ground state and it becomes a magnetic liquid below 90.2 K. The magnetic characteristics are related to the blue color of the oxygen. The absorption mechanism, magnetostriction and pair correlation in the liquid are investigated through magneto-optical measurements in high magnetic fields.
1. Introduction
‘A, ‘A,
The 0, molecule has received much interest in various fields of natural science. The molecule with triplet ground state has a magnetic moment and liquid and solid oxygen are considered to belong to the most fundamental materials in the research on magnetism. The liquid phase is found in the temperature range between 54.4 K and 90.2 K. The liquid is paramagnetic and the susceptibility obeys the Curie-Weiss law. The antiferromagnetic interaction between the molecules leads to a Weiss constant of 0 = - 40.6 K in the liquid phase. As is well known, liquid oygen shows a light blue color which arises from the absorption of the bimolecular optical transition between the ground 2(3_Zi) and excited 2(‘A,) states, where 2 before the parentheses means the bimolecular state [l]. An absorption is observed around 6290 8, and the phonon sideband is found at 576OA. It is noticed that the total spin angular momentum in the initial and final states of an 0, pair should be conserved in the electric dipole transition. As the final state of each 0, molecule is a spin singlet, the spins of the initial ground state in two 0, molecules should be antiferromagnetically coupled by the exchange interaction J(r), where r is the intermolecular distance. The process of optical transition is illustrated in fig. 1. When a high magnetic field is applied to the liquid, a decrease of the antiferromagnetic coupled pair is inferred and a reduction of the absorption intensity is 0921-4526/89/$03.50 0 (North-Holland Physics
Elsevier Science Publishers Publishing Division)
Fig. 1. Schematic
view of optical
absorption
process
in 0,.
expected. This effect can be observed as fieldinduced transparency of the liquid. The transparency increases with increasing magnetization and has a Curie-Weiss law like temperature dependence. A large magneto-volume effect due to the spin correlation in the liquid 0, is expected. This effect also contributes to the magnetization or transparency of the 0, liquid. This paper summarizes the experiments on the field-induced transparency in the liquid 0, reported in refs. 2 and 3 and shows that the mean field approximation is not adequate and that a quantitative explanation is obtained by the spinpair model.
2. Experimental
procedures
The new phenomenon of field-induced transparency in liquid 0, was observed at the High Magnetic Field Laboratory of Osaka University. The whole view of the field dependent absorption was observed by using a spectrometer with an optical multichannel analyzer (OMA) and a Xenon flash lamp as light source [4]. As shown in the insert of fig. 2, the spectra observed in a B.V.
--__ ,
L
,-L
100’3
500 MAGNETIC
Fig. 3. Field dependence 0,. Fig. 2. Transparency
of hqud
0,
in magnetic
FIELD
(kCeJ
of absorption
coefficient
m liquid
field.
camera system. The sample ing of the liquid nitrogen. pulsed field contain much noise but a decrease of the total absorption in high magnetic fields is found. To obtain the clear field dependence in the pulsed field. optical transparency was studied by using a He-Ne laser. The lasing wavelength (6328 A) of the laser is near the broad absorption peak of 6290 A and a large change in the transparency in a magnetic field H,, is expected. The experimental method is described in [2]. The result is shown in fig. 2 and the magnetic held dependence of the absorption coefficient k(H,,) is shown in fig. 3. As seen in fig. 3. a systematic deviation from the simple molecular held theory is found. The magneto-volume effect was observed in order to estimate the correction of the held-dependent transparency. Because of the slow response of the volume change, a superconducting magnet, which can generate magnetic fields up to 80 kOe, was used. The detailed method is described in [3] and the essential points are given here. The volume change in the field is small and the change is magnified by a thin capillary tube which is connected to the sample cell. The liquid level in the capillary tube is monitored by an optical periscope and a TV
3. Experimental
is cooled
by pump-
results and discussion
The bimolecular absorption occurs for the pairs with no resultant spins. Therefore, antiparallely coupled molecules with spins SI = + 1 and a couple of two SI = 0 molecules can contribute to the optical transitition. The normalized absorption coefficient is described by the population numbers N,, N and N,, for the ground S; = + 1. ~ 1 and 0 states. respectively. The normalized absorption coefficient is given by
(6,) + UWLl
k(H,,)ik((J) = [2N+(H,,)N
(2N, (O)N_ (0) + N,,(O)‘] .
,’ (1)
where a 0 in parentheses denotes the corresponding values at zero field 121. The N’s arc given by N, = Nexp(glCL,S,H,,,ik,,T)iZ, where
Z is the partition
function
(2) and
the sub-
C. Uyeda et al. I Magnetic liquid 0, in high jields
scripts
I = + 1, 0 and - 1 correspond to S, = + 1, ~ 1, respectively. H,,, calculated under the molecular field approximation is given by
0 and
K,,
= K, + 2Jz ( S; > l&Y% 1
(3)
where 2J is the exchange energy between two 0, spins. (S,) can be estimated from the CurieWeiss law [2] as 0,)
= 2g~+H,,i3k~(~
- 0) ,
where T is the temperature. Recently, we determined J(r) [5] as J(r) = J,, exp]a(r
--
(4)
the r dependence
r,,>l,
of
(5)
where J, = -3OK, r,, = 3.2A and F = -4.3Ai-‘. The thin broken line in fig. 3 shows the theoretical curve under the approximation. The deviation of the theoretical curve from the experimental data which is shown in the figure has inspired us to estimate the magneto-volume effect. The volume change due to the magnetovolume effect is given by the intermolecular potential. The potential U(r) is given by [3] U(r) = Uo[(a/r)12
- 2(air)‘]
- 2J(r)(
S,)’
,
(6)
where the first term in the parentheses is the Lennard-Jones potential and the second one is exchange energy [6]. The potential energy changes with variation of the magnetic moment which is proportronal to the applied field. This change induces a shift Ar of the minimum in the potential. The shift Ar is obtained from the condition of dlJ/dr = 0 and the volume change is written as AV/V,, = 3(Ar/a)
z= PHi
423
The constant p is evaluated as 2.7 x lo-” kOem2 by using the values of U,, = 100 K and a = 3.7 A. The experimental result of the field-dependent volume change is shown in fig. 4. The experimentally determined p of 3.5 x lo-’ kOe_’ is in fairly good agreement with the theoretical value. The experimental value gives a magnetovolume increase of 0.022% at 80 kOe and is much larger than the value in ferromagnetic Fe of 0.004% which is larger than the values in other usual ferromagnets. The volume increase leads to a reduction of the liquid density and the exchange field and makes the transparency increase. The correction of the magneto-volume effect is shown by the thin solid lines in fig. 3. The correction values, however, are still far from the observed values and other origins should be considered to explain quantitatively the field-induced transparency. In the molecular-field approximation, the 0, molecules experience a uniform mean field, but the model is less adequate to liquid in which the molecules have considerable pair correlation. Instead of the molecular field model, it is better to consider the spin pair coupling of two 0, molecules. The pair coupling of the S’ = 1 spins in 0, molecules gives three multiplets with total spin states S’ = 2, 1,O which have 5, 3 and 1 Zeeman levels, respectively. The energy gaps between S’ = 0 and 1 and between S’ = 1 and 2 are 2 J’ where J’ is the interand 4J’, respectively, molecular exchange energy. Only one singlet state with S’ = 0 is responsible for the optical
(7)
with p =
(J,,Eu/
12(/,,)[2gpB/3k,(
T
-
e)]’ Magnetic
x
ev[da
-
r,,)l
(8)
Fig. 4. Field dependence
Fteld
CkOe)
of magneto-volume
effect at 77 K.
424
c‘. Uyedu
et ul.
I Mugneiic
transition. The distribution over the many other levels in the spin pair state causes a reduction of the absorption. A preliminary estimate gives a good result, as shown by the thick dotted line in fig. 3. The detailed theory and discussions are given in ref. 7.
Acknowledgement The research is partly supported by a Grantin-Aid from the Ministry of Education, Science and Culture of Japan.
liquid
0,
in high fields
References [l) S.C. Tai and G.W. Robinson, J. Chem. Phys. 51 (1969) 3559. [2] C. Uyeda. A. Yamagishi and M. Date. J. Phys. Sot. Jpn. 55 (1986) 468. [3] C. Uyeda, A. Ydmagishi and M. Date, J. Phys. Sot. Jpn. 56 (1087) 3444. [4] H. Hori, in: High Field Magnetism, M. Date. ed. (NorthHolland, Amsterdam. 19X3), p. 289. [5] C. Uyeda, S. Sugiyama and M. Date. J. Phys. Sot. Jpn. 54 (1985) 1107. [6] T. Kihara and A. Koide. Adv. Chem. Phys. 33 (1975) 51. (71 C. Chiaki. A. Yamagishi and M. Date. submitted to J. Phys. Sot. Jpn.