- Email: [email protected]
Magnetic behavior of 3He films
Physica B 169 (1991) North-Holland
177-182
Magnetic H.
Godfrin”3b,
behavior R.E.
of “He films
Rappb’”
and
H.J.
Lauter”
“Insritut Laue-Langevin, 156X 38042 Grenoble Cedex. France hCNRS-CRTBT, 166X 38042 Grenoble Cedex, France ‘I.F.- UFRJ. Cid. Univ.. CP 68528 Rio de Janeiro 21944, Brazil The invited
talk was given
by H. Godfrin.
Recent studies of the magnetic properties of ‘He films have revealed a very rich behavior, directly connected to the theories of two-dimensional Fermi liquids and solids. The experimental database and the associated theories are reviewed in this article.
I. Introduction There is considerable current interest in the behavior of thin films of 3He adsorbed on solid substrates. This review article will concentrate on the nuclear magnetic properties of a few two-dimensional “He magnetic systems, the structure of which is known; we shall refer to the original publications in the case of more complex or insufficiently characterized systems.
2. Adsorbed
3He
The introduction of exfoliated graphite substrates by the Nancy group and the measurements performed on helium films by the Seattle group opened a new field of research in surface physics. Presently, the experimental database covers most of the phase diagram of 3He films adsorbed on graphite. Solid, liquid, commensurate phases and coexistence regions have different signatures in NMR, neutron scattering, heat capacity or adsorption isotherm measurements. As shown in fig. 1, there is a good general agreement between these results. Solids are Contact address: H. Godfrin, Grenoble Cedex, France, GODFRINGFRILL.
CNRS-CRTBT 166X 38042 tel. 7688 1156, BITNET:
by neutron-diffraction peaks, characterized Curie-like nuclear magnetization, low heat display low magcapacity; liquids, conversely, netization, high heat capacity, and do not give rise to detectable diffraction signals. At very low magnetic exchange interactions temperatures, yield large effects in the magnetization and in the heat capacity, which are also well correlated with the structural phase transformations. Basically, the phase diagram (fig. 2) has been determined by high-temperature heat capacity data [l], identification of structural phases has been improved by recent heat capacity work [2] and neutron scattering [3], the nuclear magnetic properties have been determined by NMR magnetization data [4], which provide also the sign of the interactions (ferro or antiferromagnetism), and by heat capacity, which is more sensitive to the magnitude of the exchange parameters. However, despite the good agreement suggested by fig. 1 the discrepancy between coverage scales used in different laboratories is presently on the order of 5%.
3. Two-dimensional
Fermi fluids
Two-dimensional Fermi sub-monolayer coverages,
fluids are found at low at partially filled sec-
178
H. Godfrin
et al.
I Magnetic
behavior
of .‘He films
M
3mK
A A
&&+1D
CP
1st layer
0
0
+
o+-=+xx
++
+
o 0
0.08
0.06
A
2.5 mK
4.6
32
1.6
0.0
C’
”
”
”
I”’
/
“‘A
11.2
6.4
5.6
2.6
0.0
0.00
0.10
0.20 Coverage
0.30
0.40
(atoms/AZ)
Fig. 1. From top to bottom: isotherms of magnetization times temperature (41 at 3, 5 and 30 mK (+: all temperatures 30 mK), layer density measured [3] by neutron scattering (note the splitting around 0.18 A-‘). and heat capacity isotherms 5, 50 and 200 mK [2] are shown as a function of coverage.
below at 2.5,
H. Godfrin et al. I Magnetic behavior of 3He films
179
but here the coexistence region between the liquid and the commensurate phase is the dominant feature. Novel results on the susceptibility of multilayers of 3He have been obtained on Nucleopore [6] and more recently on Grafoil [5] substrates preplated with 4He. Well-defined steps are observed on the low-temperature magnetization of the liquid. This effect is similar to that expected for free Fermions in a box [7] of finite thickness. Similar steps are also observed in the heat capacity of thick 3He films adsorbed on Grafoil
0.10
P’ 0.04
PI. 4. Nuclear temperature
(K)
Fig. 2. Phase diagram [l, 21 of 3He on graphite. for the first and the second layer. F: fluid; R: registered; S: incommensurate solid.
ond layer coverages, and in the third layer. The first layer fluid coexists with a spurious phase (about 2% of a monolayer), and the corrugation of the graphite potential gives rise to single particle band effects. The second layer fluid seems in principle to be more suitable for a quantitative investigation. The experimental results follow the trend expected for a Fermi liquid: the magnetization is Curie-like above 1 K, and reaches a plateau at low temperatures; the heat capacity is constant at high temperatures, and decreases linearly in the low-temperature regime. Heat capacity [l, 21 has been used to determine the effective mass, which displays a much larger variation than in the three-dimensional liquid. An interesting feature has been observed in both the first and the second layer: the heat capacity extrapolates to a finite value at zero temperature, and an anomaly appears at about 3 mK [2]. Magnetization measurements covering the low-temperature regime have been performed on the second layer with pure 3He films at Grenoble [4], and with a 4He first layer at London [5]; typical degeneracy effects are observed. This is also the case for sub-monolayer 3He films [5],
ferromagnetism
As shown in fig. 1, the dominant feature in the low-temperature (3 mK) magnetization isotherm is the large excess magnetization for coverages around 0.23 atoms/A’ (“ferromagnetic peak”). The magnetization exceeds the free spin value expected for all the 3He atoms contained in the experimental cell. This demonstrates that strong ferromagnetic interactions occur among the 3He atoms located in the vicinity of the substrate. Measurements at a coverage of 0.233 A-’ performed down to sub-mK temperatures [4] showed a dramatic increase of the magnetization (note the logarithmic scale in fig. 3) well described for T > J by the exact high-temperature series expansion of the Heisenberg Hamiltonian; this allowed to deduce a value of J = 2.1 mK at this coverage. For T < J an exponential divergence of the magnetization was found, confirming theoretical predictions based on the Heisenberg model. Heat capacity data [2] are shown in fig. 4. The discrepancy between these data and the high-temperature series expansion is due in part to an incomplete solidification of the second layer and to the possible existence of an ordered phase at low magnetic fields, similar to that observed [8] in confined geometries for the very low field magnetization. Finally, results presented at this conference on 3He films adsorbed on 4He-preplated Grafoil [5] display a very similar magnetic behavior. The Heisenberg description of the nuclear fer-
H. Godfrin et al. I Magnetic behavior of ‘He films
180
aware of the existence of any better “model system” for the 2D ferromagnetic Heisenberg Hamiltonian. l-
B, =14.21mT
$1 Z
5. Nuclear
10-30-
“0
4
Temperature
(mK)
Fig. 3. Magnetization of the second layer of ‘He adsorbed on graphite. at the ferromagnetic peak coverage (0.23 A-‘) and very low temperatures [4]. Solid line: high-temperature series expansion of the 2D Heisenberg ferromagnet. 200
160
N t.c:: 80 u
o0
5
10
15
20
T (mK) Fig. 4. Heat capacity measured (21 around the ferromagnetic peak. Lines correspond to the series expansions of 2D Heisenberg ferromagnet.
romagnetic interactions around the “ferromagnetic peak” represents very well the temperature variation of the magnetization at moderate fields, and also provides a reasonably good model for the heat capacity at temperatures above a possible low field transition. We are not
antiferromagnetism
At coverages around 0.18 A ’ the magnetization at 30 mK (fig. 1) displays a small jump: the magnetization is close to the free spin value. The temperature dependence of the inverse magnetization of the second layer is shown in fig. 5. This plot indicates an antiferromagnetic behavior with a Curie-Weiss temperature of -5 mK. Heat capacity measurements show a complex behavior in this coverage region, with a series of structural phase transitions, from the liquid state to a very low-density solid, commensurable with the first layer, and then to an incommensurate solid, with associated coexistence regions. Third layer promotion begins in the same coverage region. Neutron scattering results show that substantial changes occur in the first layer in this coverage range, involving a possible phase transition and a clear density change. The interplay between commensurability of the first layer with the graphite and between the first and second layers seems to be quite subtle, and these features evolve with the total coverage. Results presented at this conference on ‘He films adsorbed on “He-preplated Grafoil [5] also indicate antiferromagnetic behavior in this coverage range. All the experiments confirm the exist-
2 0 5 .N 5 C 9 E 3 c .-$ &
0.30
3 E
0.00
0.25 0.20 0.15 0.10 0.05
I.. ,,,,,,,,,,, 0
IO
.,,,
I..
20 Temperature
_i
.,,.,,
L
30
,,,,.
3 40
(mK)
Fig. 5. Inverse of the second-layer magnetization as a function of temperature. for a coverage within the antiferromagnetic region (note the large Weiss temperature).
H. Godfrin et al. I Magnetic behavior of ‘He films
ence of a large antiferromagnetic interaction before a substantial number of atoms has been promoted to the third layer, and this interaction is clearly confined to the second layer, which is believed to be triangular and commensurate with the first layer.
6. From
antiferromagnetism
to ferromagnetism
Between the coverage corresponding to an antiferromagnetic second layer and that of the ferromagnetic peak a complicated experimental situation is found. In the Grenoble data the inverse magnetization is a complicated function of the temperature, that cannot be described by a Curie-Weiss law. Heat capacity data also display an unusual behavior [2]. Although the trend of the Curie-Weiss temperature is a gradual change from negative to positive values as the coverage is increased [4,5], the Grenoble data show that at the lowest temperatures the inverse magnetization, in the antiferromagnetic region, extrapolates to a finite temperature close to that obtained at the ferromagnetic peak coverage. This could be the signature of mixed phases or that of competing interactions.
7. Solid at sub-monolayer
coverages
Exchange at sub-monolayer coverages has been investigated for many years by measuring T, and T2 at temperatures on the order of 1 K. Recent results [9] provide values of the exchange constant in the incommensurable solid range, assuming a Heisenberg coupling. Values as high as J = 1 mK were found. Measurements of the Curie-Weiss temperature performed at Grenoble [4] show that an upper limit on the order of 50 p.K can be placed on the magnitude of the exchange constant in the same coverage range. Recent heat capacity data give values intermediate between the previous ones. This is the hierarchy expected from multiple spin exchange, since all processes contribute to T2, combinations including squared terms appear in the heat capacity expression, and large cancellation of terms reduce the Curie-Weiss temperature.
181
At the commensurable density the system has some mobility [9], but the exchange constant is very small; around this coverage a small ferromagnetic deviation from the Curie law has been detected [4] in the commensurate and in the domain wall phases. Preliminary heat capacity data [2] show a complex structure in the coverage dependence of the exchange, similar to that found in the second layer.
8. Theory The first problem is certainly to determine whether a single mechanism must explain both the ferro and the antiferromagnetic exchange, or if different processes must be taken into account. Several theories are available: the multiple spin exchange (MSE) model developed by Roger [lo], the indirect exchange [ll] calculations by Tasaki (IE), and the Kagome lattice model of Elser [ 121, for example. Multiple spin exchange, given its success in the case of bulk solid “He is a natural candidate to explain the properties of the two-dimensional solid. The antiferromagnetism of the low-density second-layer solid could arise from competing interactions as found in the bulk solid. At higher coverages, triangular exchange is expected to be dominant, explaining the ferromagnetic interactions observed experimentally. A convincing fit of the magnetization and heat capacity data has been presented by Roger [lo]. Indirect exchange is also expected to be non-negligible when fluid layers are present; its effect is, however, incorporated in first approximation in the Heisenberg term of MSE. The IE model includes RKKY exchange and a vacancy-mediated exchange due to Heritier. The semi-quantitative theory due to Jichu and Kuroda [13] and Tasaki [l l] also provides a physically appealing explanation of the high coverage results obtained at Grenoble. It would be extremely interesting to develop this theory using heat capacity data. Elser’s model involves an unusual registered phase in the second layer. This topological model applies in principle at a single coverage; it is therefore difficult to test experimentally its
182
H. Godfrin et al.
/ Magnetic behavior of .‘He films
validity. It explains successfully the missing entropy detected by Greywall in the antiferromagnetic coverage region. This effect, however, can also be explained by MSE. Clearly, more experimental and theoretical work is needed, but present results are encouraging.
9. Conclusions The phase diagram of adsorbed “He is richer than that of bulk ‘He. In addition to substrate induced phases, solid and fluid phases in two dimensions can be obtained with a large range of interatomic distances. Two-dimensional ferro and antiferromagnetic interactions have been investigated. Fundamental models of localized or itinerant fermions can be tested under controlled conditions. Although the quality of present substrates is still a limitation, the improvement in their characterization allows a selective elimination of spurious effects. It is therefore not surprising to see the rapidly increasing interest on this subject.
References [1] M. Bretz, J.G. Dash, D.C. Hickernell, E.O. McLean and O.E. Vilches, Phys. Rev. A 8 (1973) 1589; ibid., A 9 (1974) 2814.
D.S. Greywall, Phys. Rev. B 41 (1990) 1842, and references therein. V.L.P. Frank and H.P. Schild[31 H.J. Lamer, H. Godfrin, berg, in: Proc. of the 19th Int. Conf. on Low Temperature Physics, part I, D.S. Betts, ed.. Physica B 16.5 & 166 (North-Holland. Amsterdam, 1990) p. 597. and references therein. R.E. Rapp and D.D. Osheroff, Physica A [41 H. Godfrin. 163 (1990) 101, and references therein. C.P. Lusher and B.P. Cowan, in: Proc. of [51 .I. Saunders, the 19th Int. Conf. on Low Temperature Physics, part 1, D.S. Betts, ed., Physica B 165 & 166 (North-Holland, Amsterdam, 19YO) p. 693; C.P. Lusher, J. Saunders and B.P. Cowan, in: Proc. of the 19th Int. Conf. on Low Temperature Physics, part I, D.S. Betts, ed., Physica B 165 & 166 (North-Holland, Amsterdam, 1990) p. 691. 161 R. Higley, D. Sprague and R. Hallock, Phys. Rev. Lett. 63 (1989) 2570. Phys. Rev. B 171 R.A. Guyer. K. McCall and D. Sprague, 40 (1989) 7417. PI L.J. Friedman, A.L. Thompson, C.M. Gould and H.M. Bozler, Phys. Rev. Lett. 62 (1989) 1635. PI B. Cowan, L. Abou El-Nasr. M. Fardis and A. Hussain, Phys. Rev. Lett. 58 (1987) 2308. [lOI M. Roger, Phys. Rev. Lett. 64 (1990) 297: ibid., in: Proc. of the 19th Int. Conf. on Low Temperature Physics, part I. D.S. Betts, ed.. Physica B 165 & 166 (North-Holland, Amsterdam. 1990) p. 697. [Ill S. Tasaki, Prog. Theor. Phys. 70 (1988) 1311. 1121V. Elser, Phys. Rev. Lett. 62 (1989) 2405. Prog. Theor. Phys. 67 (lY82) [131 H. Jichu and Y. Kuroda, 715: ibid.. 69 (1983) 1358.
PI
177-182
Magnetic H.
Godfrin”3b,
behavior R.E.
of “He films
Rappb’”
and
H.J.
Lauter”
“Insritut Laue-Langevin, 156X 38042 Grenoble Cedex. France hCNRS-CRTBT, 166X 38042 Grenoble Cedex, France ‘I.F.- UFRJ. Cid. Univ.. CP 68528 Rio de Janeiro 21944, Brazil The invited
talk was given
by H. Godfrin.
Recent studies of the magnetic properties of ‘He films have revealed a very rich behavior, directly connected to the theories of two-dimensional Fermi liquids and solids. The experimental database and the associated theories are reviewed in this article.
I. Introduction There is considerable current interest in the behavior of thin films of 3He adsorbed on solid substrates. This review article will concentrate on the nuclear magnetic properties of a few two-dimensional “He magnetic systems, the structure of which is known; we shall refer to the original publications in the case of more complex or insufficiently characterized systems.
2. Adsorbed
3He
The introduction of exfoliated graphite substrates by the Nancy group and the measurements performed on helium films by the Seattle group opened a new field of research in surface physics. Presently, the experimental database covers most of the phase diagram of 3He films adsorbed on graphite. Solid, liquid, commensurate phases and coexistence regions have different signatures in NMR, neutron scattering, heat capacity or adsorption isotherm measurements. As shown in fig. 1, there is a good general agreement between these results. Solids are Contact address: H. Godfrin, Grenoble Cedex, France, GODFRINGFRILL.
CNRS-CRTBT 166X 38042 tel. 7688 1156, BITNET:
by neutron-diffraction peaks, characterized Curie-like nuclear magnetization, low heat display low magcapacity; liquids, conversely, netization, high heat capacity, and do not give rise to detectable diffraction signals. At very low magnetic exchange interactions temperatures, yield large effects in the magnetization and in the heat capacity, which are also well correlated with the structural phase transformations. Basically, the phase diagram (fig. 2) has been determined by high-temperature heat capacity data [l], identification of structural phases has been improved by recent heat capacity work [2] and neutron scattering [3], the nuclear magnetic properties have been determined by NMR magnetization data [4], which provide also the sign of the interactions (ferro or antiferromagnetism), and by heat capacity, which is more sensitive to the magnitude of the exchange parameters. However, despite the good agreement suggested by fig. 1 the discrepancy between coverage scales used in different laboratories is presently on the order of 5%.
3. Two-dimensional
Fermi fluids
Two-dimensional Fermi sub-monolayer coverages,
fluids are found at low at partially filled sec-
178
H. Godfrin
et al.
I Magnetic
behavior
of .‘He films
M
3mK
A A
&&+1D
CP
1st layer
0
0
+
o+-=+xx
++
+
o 0
0.08
0.06
A
2.5 mK
4.6
32
1.6
0.0
C’
”
”
”
I”’
/
“‘A
11.2
6.4
5.6
2.6
0.0
0.00
0.10
0.20 Coverage
0.30
0.40
(atoms/AZ)
Fig. 1. From top to bottom: isotherms of magnetization times temperature (41 at 3, 5 and 30 mK (+: all temperatures 30 mK), layer density measured [3] by neutron scattering (note the splitting around 0.18 A-‘). and heat capacity isotherms 5, 50 and 200 mK [2] are shown as a function of coverage.
below at 2.5,
H. Godfrin et al. I Magnetic behavior of 3He films
179
but here the coexistence region between the liquid and the commensurate phase is the dominant feature. Novel results on the susceptibility of multilayers of 3He have been obtained on Nucleopore [6] and more recently on Grafoil [5] substrates preplated with 4He. Well-defined steps are observed on the low-temperature magnetization of the liquid. This effect is similar to that expected for free Fermions in a box [7] of finite thickness. Similar steps are also observed in the heat capacity of thick 3He films adsorbed on Grafoil
0.10
P’ 0.04
PI. 4. Nuclear temperature
(K)
Fig. 2. Phase diagram [l, 21 of 3He on graphite. for the first and the second layer. F: fluid; R: registered; S: incommensurate solid.
ond layer coverages, and in the third layer. The first layer fluid coexists with a spurious phase (about 2% of a monolayer), and the corrugation of the graphite potential gives rise to single particle band effects. The second layer fluid seems in principle to be more suitable for a quantitative investigation. The experimental results follow the trend expected for a Fermi liquid: the magnetization is Curie-like above 1 K, and reaches a plateau at low temperatures; the heat capacity is constant at high temperatures, and decreases linearly in the low-temperature regime. Heat capacity [l, 21 has been used to determine the effective mass, which displays a much larger variation than in the three-dimensional liquid. An interesting feature has been observed in both the first and the second layer: the heat capacity extrapolates to a finite value at zero temperature, and an anomaly appears at about 3 mK [2]. Magnetization measurements covering the low-temperature regime have been performed on the second layer with pure 3He films at Grenoble [4], and with a 4He first layer at London [5]; typical degeneracy effects are observed. This is also the case for sub-monolayer 3He films [5],
ferromagnetism
As shown in fig. 1, the dominant feature in the low-temperature (3 mK) magnetization isotherm is the large excess magnetization for coverages around 0.23 atoms/A’ (“ferromagnetic peak”). The magnetization exceeds the free spin value expected for all the 3He atoms contained in the experimental cell. This demonstrates that strong ferromagnetic interactions occur among the 3He atoms located in the vicinity of the substrate. Measurements at a coverage of 0.233 A-’ performed down to sub-mK temperatures [4] showed a dramatic increase of the magnetization (note the logarithmic scale in fig. 3) well described for T > J by the exact high-temperature series expansion of the Heisenberg Hamiltonian; this allowed to deduce a value of J = 2.1 mK at this coverage. For T < J an exponential divergence of the magnetization was found, confirming theoretical predictions based on the Heisenberg model. Heat capacity data [2] are shown in fig. 4. The discrepancy between these data and the high-temperature series expansion is due in part to an incomplete solidification of the second layer and to the possible existence of an ordered phase at low magnetic fields, similar to that observed [8] in confined geometries for the very low field magnetization. Finally, results presented at this conference on 3He films adsorbed on 4He-preplated Grafoil [5] display a very similar magnetic behavior. The Heisenberg description of the nuclear fer-
H. Godfrin et al. I Magnetic behavior of ‘He films
180
aware of the existence of any better “model system” for the 2D ferromagnetic Heisenberg Hamiltonian. l-
B, =14.21mT
$1 Z
5. Nuclear
10-30-
“0
4
Temperature
(mK)
Fig. 3. Magnetization of the second layer of ‘He adsorbed on graphite. at the ferromagnetic peak coverage (0.23 A-‘) and very low temperatures [4]. Solid line: high-temperature series expansion of the 2D Heisenberg ferromagnet. 200
160
N t.c:: 80 u
o0
5
10
15
20
T (mK) Fig. 4. Heat capacity measured (21 around the ferromagnetic peak. Lines correspond to the series expansions of 2D Heisenberg ferromagnet.
romagnetic interactions around the “ferromagnetic peak” represents very well the temperature variation of the magnetization at moderate fields, and also provides a reasonably good model for the heat capacity at temperatures above a possible low field transition. We are not
antiferromagnetism
At coverages around 0.18 A ’ the magnetization at 30 mK (fig. 1) displays a small jump: the magnetization is close to the free spin value. The temperature dependence of the inverse magnetization of the second layer is shown in fig. 5. This plot indicates an antiferromagnetic behavior with a Curie-Weiss temperature of -5 mK. Heat capacity measurements show a complex behavior in this coverage region, with a series of structural phase transitions, from the liquid state to a very low-density solid, commensurable with the first layer, and then to an incommensurate solid, with associated coexistence regions. Third layer promotion begins in the same coverage region. Neutron scattering results show that substantial changes occur in the first layer in this coverage range, involving a possible phase transition and a clear density change. The interplay between commensurability of the first layer with the graphite and between the first and second layers seems to be quite subtle, and these features evolve with the total coverage. Results presented at this conference on ‘He films adsorbed on “He-preplated Grafoil [5] also indicate antiferromagnetic behavior in this coverage range. All the experiments confirm the exist-
2 0 5 .N 5 C 9 E 3 c .-$ &
0.30
3 E
0.00
0.25 0.20 0.15 0.10 0.05
I.. ,,,,,,,,,,, 0
IO
.,,,
I..
20 Temperature
_i
.,,.,,
L
30
,,,,.
3 40
(mK)
Fig. 5. Inverse of the second-layer magnetization as a function of temperature. for a coverage within the antiferromagnetic region (note the large Weiss temperature).
H. Godfrin et al. I Magnetic behavior of ‘He films
ence of a large antiferromagnetic interaction before a substantial number of atoms has been promoted to the third layer, and this interaction is clearly confined to the second layer, which is believed to be triangular and commensurate with the first layer.
6. From
antiferromagnetism
to ferromagnetism
Between the coverage corresponding to an antiferromagnetic second layer and that of the ferromagnetic peak a complicated experimental situation is found. In the Grenoble data the inverse magnetization is a complicated function of the temperature, that cannot be described by a Curie-Weiss law. Heat capacity data also display an unusual behavior [2]. Although the trend of the Curie-Weiss temperature is a gradual change from negative to positive values as the coverage is increased [4,5], the Grenoble data show that at the lowest temperatures the inverse magnetization, in the antiferromagnetic region, extrapolates to a finite temperature close to that obtained at the ferromagnetic peak coverage. This could be the signature of mixed phases or that of competing interactions.
7. Solid at sub-monolayer
coverages
Exchange at sub-monolayer coverages has been investigated for many years by measuring T, and T2 at temperatures on the order of 1 K. Recent results [9] provide values of the exchange constant in the incommensurable solid range, assuming a Heisenberg coupling. Values as high as J = 1 mK were found. Measurements of the Curie-Weiss temperature performed at Grenoble [4] show that an upper limit on the order of 50 p.K can be placed on the magnitude of the exchange constant in the same coverage range. Recent heat capacity data give values intermediate between the previous ones. This is the hierarchy expected from multiple spin exchange, since all processes contribute to T2, combinations including squared terms appear in the heat capacity expression, and large cancellation of terms reduce the Curie-Weiss temperature.
181
At the commensurable density the system has some mobility [9], but the exchange constant is very small; around this coverage a small ferromagnetic deviation from the Curie law has been detected [4] in the commensurate and in the domain wall phases. Preliminary heat capacity data [2] show a complex structure in the coverage dependence of the exchange, similar to that found in the second layer.
8. Theory The first problem is certainly to determine whether a single mechanism must explain both the ferro and the antiferromagnetic exchange, or if different processes must be taken into account. Several theories are available: the multiple spin exchange (MSE) model developed by Roger [lo], the indirect exchange [ll] calculations by Tasaki (IE), and the Kagome lattice model of Elser [ 121, for example. Multiple spin exchange, given its success in the case of bulk solid “He is a natural candidate to explain the properties of the two-dimensional solid. The antiferromagnetism of the low-density second-layer solid could arise from competing interactions as found in the bulk solid. At higher coverages, triangular exchange is expected to be dominant, explaining the ferromagnetic interactions observed experimentally. A convincing fit of the magnetization and heat capacity data has been presented by Roger [lo]. Indirect exchange is also expected to be non-negligible when fluid layers are present; its effect is, however, incorporated in first approximation in the Heisenberg term of MSE. The IE model includes RKKY exchange and a vacancy-mediated exchange due to Heritier. The semi-quantitative theory due to Jichu and Kuroda [13] and Tasaki [l l] also provides a physically appealing explanation of the high coverage results obtained at Grenoble. It would be extremely interesting to develop this theory using heat capacity data. Elser’s model involves an unusual registered phase in the second layer. This topological model applies in principle at a single coverage; it is therefore difficult to test experimentally its
182
H. Godfrin et al.
/ Magnetic behavior of .‘He films
validity. It explains successfully the missing entropy detected by Greywall in the antiferromagnetic coverage region. This effect, however, can also be explained by MSE. Clearly, more experimental and theoretical work is needed, but present results are encouraging.
9. Conclusions The phase diagram of adsorbed “He is richer than that of bulk ‘He. In addition to substrate induced phases, solid and fluid phases in two dimensions can be obtained with a large range of interatomic distances. Two-dimensional ferro and antiferromagnetic interactions have been investigated. Fundamental models of localized or itinerant fermions can be tested under controlled conditions. Although the quality of present substrates is still a limitation, the improvement in their characterization allows a selective elimination of spurious effects. It is therefore not surprising to see the rapidly increasing interest on this subject.
References [1] M. Bretz, J.G. Dash, D.C. Hickernell, E.O. McLean and O.E. Vilches, Phys. Rev. A 8 (1973) 1589; ibid., A 9 (1974) 2814.
D.S. Greywall, Phys. Rev. B 41 (1990) 1842, and references therein. V.L.P. Frank and H.P. Schild[31 H.J. Lamer, H. Godfrin, berg, in: Proc. of the 19th Int. Conf. on Low Temperature Physics, part I, D.S. Betts, ed.. Physica B 16.5 & 166 (North-Holland. Amsterdam, 1990) p. 597. and references therein. R.E. Rapp and D.D. Osheroff, Physica A [41 H. Godfrin. 163 (1990) 101, and references therein. C.P. Lusher and B.P. Cowan, in: Proc. of [51 .I. Saunders, the 19th Int. Conf. on Low Temperature Physics, part 1, D.S. Betts, ed., Physica B 165 & 166 (North-Holland, Amsterdam, 19YO) p. 693; C.P. Lusher, J. Saunders and B.P. Cowan, in: Proc. of the 19th Int. Conf. on Low Temperature Physics, part I, D.S. Betts, ed., Physica B 165 & 166 (North-Holland, Amsterdam, 1990) p. 691. 161 R. Higley, D. Sprague and R. Hallock, Phys. Rev. Lett. 63 (1989) 2570. Phys. Rev. B 171 R.A. Guyer. K. McCall and D. Sprague, 40 (1989) 7417. PI L.J. Friedman, A.L. Thompson, C.M. Gould and H.M. Bozler, Phys. Rev. Lett. 62 (1989) 1635. PI B. Cowan, L. Abou El-Nasr. M. Fardis and A. Hussain, Phys. Rev. Lett. 58 (1987) 2308. [lOI M. Roger, Phys. Rev. Lett. 64 (1990) 297: ibid., in: Proc. of the 19th Int. Conf. on Low Temperature Physics, part I. D.S. Betts, ed.. Physica B 165 & 166 (North-Holland, Amsterdam. 1990) p. 697. [Ill S. Tasaki, Prog. Theor. Phys. 70 (1988) 1311. 1121V. Elser, Phys. Rev. Lett. 62 (1989) 2405. Prog. Theor. Phys. 67 (lY82) [131 H. Jichu and Y. Kuroda, 715: ibid.. 69 (1983) 1358.
PI