When a heat flux Q is applied downward through a sample of liquid 4He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity induced gradient in Tlambda. All the helium in the sample is then at the same reduced temperature tSOC = ((T[sub SOC] - T[sub lambda])/T[sub lambda]) and the helium is said to be in the Self-Organized Critical (SOC) state. We have made preliminary measurements of the 4He SOC state specific heat, C[del]T(T(Q)). Despite having a cell height of 2.54 cm, our results show no difference between C[del]T and the zero-gravity 4He specific heat results of the Lambda Point Experiment (LPE) [J.A. Lipa et al., Phys. Rev. B, 68, 174518 (2003)] over the range 250 to 450 nK below the transition. There is no gravity rounding because the entire sample is at the same reduced temperature tSOC(Q). Closer to Tlambda the SOC specific heat falls slightly below LPE, reaching a maximum at approximately 50 nK below Tlambda, in agreement with theoretical predictions [R. Haussmann, Phys. Rev. B, 60, 12349 (1999)]

Chatto, A. R.

Day, P. K.

Duncan, R. V.

Goodstein, D. L.

Lee, R. A. M.

English

A. R. Chatto

R. A. M. Lee

R. V. Duncan

P. K. Day

D. L. Goodstein

Crossref

Measurement of the SOC State Specific Heat in 4He 
A. R. Chatto*, R. A. M. Lee*, R. V. Duncan1*, P. K. Day** and D. L. Goodstein* 
* Condensed Matter Physics, California Institute of Technology, Pasadena, CA 91125, USA 
^Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131-1156, USA 
** Jet Propulsion Laboratory, Pasadena, CA 91109, USA 
Abstract. When a heat flux Q is applied downward through a sample of liquid 4He near the lambda transition, the helium 
self organizes such that the gradient in temperature matches the gravity induced gradient in 7\. All the helium in the sample 
is then at the same reduced temperature ^soc and the helium is said to be in the Self-Organized Critical (SOC) 
state. We have made preliminary measurements of the 4He SOC state specific heat, CyT(T(Q)). Despite having a cell height 
of 2.54 cm, our results show no difference between CyT and the zero-gravity
 4He specific heat results of the Lambda Point 
Experiment (LPE) [J.A. Lipa et al., Phys. Rev. B, 68, 174518 (2003)] over the range 250 to 450 nK below the transition. 
There is no gravity rounding because the entire sample is at the same reduced temperature ^soc(2)- Closer to 7^, the SOC 
specific heat falls slightly below LPE, reaching a maximum at approximately 50 nK below 7\, in agreement with theoretical 
predictions [R. Haussmann, Phys. Rev. B, 60, 12349 (1999)]. 
Keywords: Self-Organized Criticality, Specific Heat, Helium, Superfluidity 
PACS: 65.20+w,67.40.Kh,05.65+b 
INTRODUCTION 
In 1987, the Self-Organized Critical (SOC) state was 
predicted for the normal phase of 4He in the pres-
ence of gravity [1]. Gravity creates a hydrostatic pres-
sure gradient in the helium which creates a gradient 
in 7^, the superfluid transition temperature, of V7\ = 
1.273 / iK/cm [2]. The thermal conductivity K(t), where 
Tx 
S diverges as t —• 0 [3]. When a heat flux Q 
is applied downward through a sample of helium, the 
resulting temperature gradient parallels the gradient in 
7^, and the helium self organizes to satisfy the condition 
Q/K = V7 \ . Therefore, while there is a gradient in tem-
perature, the temperature difference from 7\ is uniform 
throughout the entire sample, as shown in Fig. 1. 
The SOC state in 4He was first observed in 1997 
by Moeur et al. [4]. They saw not only the expected 
normal phase SOC state, but also self-organization at 
temperatures below 7\ at higher heat flux. In addition, 
they found that K diverged at 7DAS(2)> where 7 D A S ( 2 ) 
is the measured temperature at which perfect thermal 
conductivity of the superfluid state fails abruptly under 
a heat flux Q applied upwards through the helium [5]. 
This encouraged the interpretation that the heat flux was 
depressing the critical point 7\ to the lower T^(Q) = 
7DAS(2)> a n d that the SOC state was therefore always 
on the 'normal' side of 7 \ . In contrast, Weichman and 
Miller presented a theoretical model in one dimension 
that treated the high heat flux self organization as a 
superfluid with a series of phase slips in order to maintain 
the requisite temperature gradient [6]. 
In this paper, we report the first measurements of the 
specific heat of the SOC state [7]. 
EXPERIMENT 
Our cell is constructed with two 2.3 cm diameter gold 
plated copper endplates epoxied to a cylindrical insulat-
ing Vespel® sidewall in order to give a 2.54 cm sam-
ple height. We have three high resolution thermometers 
(HRTs); one on each of the top and bottom endplates 
and a third on a 165 pm thick copper foil that pene-
trates the sidewall. This foil is positioned 0.64 cm above 
the bottom endplate and is in direct contact with the he-
lium sample. We measured the size of our helium sample 
(0.389 moles) through a calibrated extraction and con-
firmed it with a traditional pulse heat capacity measure-
ment in the superfluid phase. 
Since the temperature of the SOC state is determined 
by the heat flux through the helium, one cannot put in 
a pulse of energy and measure the temperature change 
as in a conventional heat capacity measurement. Instead, 
the heat capacity is measured by establishing the SOC 
state throughout the sample at one heat flux, then switch-
ing to a new heat flux and measuring the amount of en-
ergy needed to re-establish the SOC state throughout the 
sample at its new temperature. This is shown schemat-
ically in Fig. 1. As heat is slowly added, the derivative 
of the top endplate thermometer is used to find the time 
when profiles 1 and 3 are reached, while the midplane 
thermometer measures the SOC temperature change. 
CP850, Low Temperature Physics: 24th International Conference on Low Temperature Physics; 
edited by Y. Takano, S. P. Hershfield, S. O. Hill, P. J. Hirschfeld, and A. M. Goldman 
© 2006 American Institute of Physics 0-7354-0347-3/06/$23.00 
137 
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
2 1 3 TV 110 
Temperature 
FIGURE 1. Profiles of helium temperature vs. sample height 
during the experimental procedure: (1) SOC state is fully es-
tablished at the first heat flux; (2) Heat flux is decreased which 
raises the SOC temperature; (3) Energy is added to fully es-
tablish SOC state for the second heat flux. (Note: for Q < 
100 nW/cm2, the helium instead self organizes above 7\.) 
In traditional helium heat capacity measurements, 
where the helium is isothermal, the gradient in 7\ causes 
the heat capacity to be gravity rounded, (i.e. averaged 
over a range of reduced temperatures.) In contrast, in the 
SOC state, the temperature gradient is equal to V7\ and 
the entire sample is equidistant from criticality. There-
fore, there is no gravity rounding in our data, despite 
a sample height of 2.54 cm. Our SOC specific heat re-
sults shown in Fig. 2 are compared directly to a fit of 
the Lambda Point Experiment (LPE) results [8]. Hauss-
mann's prediction for the SOC specific heat using Dy-
namic Renormalization Group (DRG) theory is also plot-
ted [9]. 
We also measured the SOC temperature versus heat 
flux. Our results for 0.5 to 4.5 / iW/cm 2 are well fit by 
'soc(fi) = - ( f i / f io ) 0 ' 8 1 3 with Q0 = 760 ± 10 W/cm
2 . 
Our Qo differs from Moeur et al. [4], but agrees well with 
a later experiment [10]. 
CONCLUSIONS 
The data in Fig. 2 show no measurable difference from 
the LPE results in the range 250 to 450 nK below 7\ -
i.e. the SOC state heat capacity is the same as that for 
the static superfluid. This may imply that the helium in 
this heat flux range of the SOC state is essentially in 
the superfluid phase. If so, this rebuts arguments that 
7DAS (Q) is a depressed critical point, despite the fact that 
the thermal conductivity K diverges at this temperature. 
Closer to 7 \ , we measure a slight depression in the 
specific heat, relative to LPE, which starts at approxi-
mately 250 nK below the transition. This differs from 
105h 
"o 
100r 
CD 
X 
£ 95h 
o 
CD 
Q. 
CO 
90h 
85 
• SOC specific heat 
Unrounded specific heat (LPE) 
DRG prediction 
• ^ ^ ^ ' \ 
-400 -300 -200 -100 
T - T ^ ( n K ) 
FIGURE 2. Specific heat of the SOC state 
the prediction of the DRG theory, where the depression 
starts at approximately 100 nK below 7\ [9]. However, 
both theory and experiment reach a maximum at approx-
imately 50 nK below 7 \ . 
ACKNOWLEDGMENTS 
We would like to thank Dmitri Sergatskov, Steve Boyd, 
Alex Babkin, Alexander Churilov, and Talso Chui for 
helpful discussions and assistance with cell construction 
and cryovalve assembly and operation. This work was 
supported in part by the Fundamental Physics Discipline 
of the Microgravity Science Office of NASA. 
REFERENCES 
l. 
2. 
3. 
4. 
7. 
9. 
10. 
A. Onuki, Jpns. J. Appl. Phys., 26-S3, 365 (1987). 
G. Ahlers, Phys. Rev. Lett., 171, 275 (1968). 
Note: this is true only in the small Q limit. 
W. A. Moeur, P. K. Day, F-C. Liu, S. T. P. Boyd, M. J. 
Adrianns, and R. V. Duncan, Phys. Rev. Lett., 78, 2421 
(1997). 
R. V. Duncan, G. Ahlers, and V. Steinberg, Phys. Rev. 
Lett., 60, 1522(1988). 
P. B. Weichman, and J. Miller, J. Low Temp. Phys., 119, 
155 (2000). 
Note: these measurements are very different from 
previous work [10] on the SOC/superfluid two-phase heat 
capacity. 
J. A. Lipa, J. A. Nissen, D. A. Strieker, D. R. Swanson, 
and T. C. P. Chui, Phys. Rev. B, 68, 174518 (2003). 
R. Haussmann, Phys. Rev. B, 60, 12349 (1999). 
R. A. M. Lee, A. R. Chatto, D. A. Sergatskov, A. V. 
Babkin, S. T. P. Boyd, A. M. Churilov, T. D. McCarson, 
T. C. P. Chui, P. K. Day, R. V. Duncan, and D. L. 
Goodstein, J. Low Temp. Phys., 134, 495 (2004). 
138 
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp


Measurement of the SOC State Specific Heat in 4He

Measurement of the SOC State Specific Heat in 4He A. R. Chatto*, R. A. M. Lee*, R. V. Duncan1*, P. K. Day** and D. L. Goodstein* * Condensed Matter Physics, California Institute of Technology, Pasadena, CA 91125, USA ^Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131-1156, USA ** Jet Propulsion Laboratory, Pasadena, CA 91109, USA Abstract. When a heat flux Q is applied downward through a sample of liquid 4He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity induced gradient in 7\. All the helium in the sample is then at the same reduced temperature ^soc and the helium is said to be in the Self-Organized Critical (SOC) state. We have made preliminary measurements of the 4He SOC state specific heat, CyT(T(Q)). Despite having a cell height of 2.54 cm, our results show no difference between CyT and the zero-gravity 4He specific heat results of the Lambda Point Experiment (LPE) [J.A. Lipa et al., Phys. Rev. B, 68, 174518 (2003)] over the range 250 to 450 nK below the transition. There is no gravity rounding because the entire sample is at the same reduced temperature ^soc(2)- Closer to 7^, the SOC specific heat falls slightly below LPE, reaching a maximum at approximately 50 nK below 7\, in agreement with theoretical predictions [R. Haussmann, Phys. Rev. B, 60, 12349 (1999)]. Keywords: Self-Organized Criticality, Specific Heat, Helium, Superfluidity PACS: 65.20+w,67.40.Kh,05.65+b INTRODUCTION In 1987, the Self-Organized Critical (SOC) state was predicted for the normal phase of 4He in the pres-ence of gravity [1]. Gravity creates a hydrostatic pres-sure gradient in the helium which creates a gradient in 7^, the superfluid transition temperature, of V7\ = 1.273 / iK/cm [2]. The thermal conductivity K(t), where Tx S diverges as t —• 0 [3]. When a heat flux Q is applied downward through a sample of helium, the resulting temperature gradient parallels the gradient in 7^, and the helium self organizes to satisfy the condition Q/K = V7 \ . Therefore, while there is a gradient in tem-perature, the temperature difference from 7\ is uniform throughout the entire sample, as shown in Fig. 1. The SOC state in 4He was first observed in 1997 by Moeur et al. [4]. They saw not only the expected normal phase SOC state, but also self-organization at temperatures below 7\ at higher heat flux. In addition, they found that K diverged at 7DAS(2)> where 7 D A S ( 2 ) is the measured temperature at which perfect thermal conductivity of the superfluid state fails abruptly under a heat flux Q applied upwards through the helium [5]. This encouraged the interpretation that the heat flux was depressing the critical point 7\ to the lower T^(Q) = 7DAS(2)> a n d that the SOC state was therefore always on the 'normal' side of 7 \ . In contrast, Weichman and Miller presented a theoretical model in one dimension that treated the high heat flux self organization as a superfluid with a series of phase slips in order to maintain the requisite temperature gradient [6]. In this paper, we report the first measurements of the specific heat of the SOC state [7]. EXPERIMENT Our cell is constructed with two 2.3 cm diameter gold plated copper endplates epoxied to a cylindrical insulat-ing Vespel® sidewall in order to give a 2.54 cm sam-ple height. We have three high resolution thermometers (HRTs); one on each of the top and bottom endplates and a third on a 165 pm thick copper foil that pene-trates the sidewall. This foil is positioned 0.64 cm above the bottom endplate and is in direct contact with the he-lium sample. We measured the size of our helium sample (0.389 moles) through a calibrated extraction and con-firmed it with a traditional pulse heat capacity measure-ment in the superfluid phase. Since the temperature of the SOC state is determined by the heat flux through the helium, one cannot put in a pulse of energy and measure the temperature change as in a conventional heat capacity measurement. Instead, the heat capacity is measured by establishing the SOC state throughout the sample at one heat flux, then switch-ing to a new heat flux and measuring the amount of en-ergy needed to re-establish the SOC state throughout the sample at its new temperature. This is shown schemat-ically in Fig. 1. As heat is slowly added, the derivative of the top endplate thermometer is used to find the time when profiles 1 and 3 are reached, while the midplane thermometer measures the SOC temperature change. CP850, Low Temperature Physics: 24th International Conference on Low Temperature Physics; edited by Y. Takano, S. P. Hershfield, S. O. Hill, P. J. Hirschfeld, and A. M. Goldman © 2006 American Institute of Physics 0-7354-0347-3/06/$23.00 137 Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp2 1 3 TV 110 Temperature FIGURE 1. Profiles of helium temperature vs. sample height during the experimental procedure: (1) SOC state is fully es-tablished at the first heat flux; (2) Heat flux is decreased which raises the SOC temperature; (3) Energy is added to fully es-tablish SOC state for the second heat flux. (Note: for Q < 100 nW/cm2, the helium instead self organizes above 7\.) In traditional helium heat capacity measurements, where the helium is isothermal, the gradient in 7\ causes the heat capacity to be gravity rounded, (i.e. averaged over a range of reduced temperatures.) In contrast, in the SOC state, the temperature gradient is equal to V7\ and the entire sample is equidistant from criticality. There-fore, there is no gravity rounding in our data, despite a sample height of 2.54 cm. Our SOC specific heat re-sults shown in Fig. 2 are compared directly to a fit of the Lambda Point Experiment (LPE) results [8]. Hauss-mann's prediction for the SOC specific heat using Dy-namic Renormalization Group (DRG) theory is also plot-ted [9]. We also measured the SOC temperature versus heat flux. Our results for 0.5 to 4.5 / iW/cm 2 are well fit by 'soc(fi) = - ( f i / f io ) 0 ' 8 1 3 with Q0 = 760 ± 10 W/cm2 . Our Qo differs from Moeur et al. [4], but agrees well with a later experiment [10]. CONCLUSIONS The data in Fig. 2 show no measurable difference from the LPE results in the range 250 to 450 nK below 7\ -i.e. the SOC state heat capacity is the same as that for the static superfluid. This may imply that the helium in this heat flux range of the SOC state is essentially in the superfluid phase. If so, this rebuts arguments that 7DAS (Q) is a depressed critical point, despite the fact that the thermal conductivity K diverges at this temperature. Closer to 7 \ , we measure a slight depression in the specific heat, relative to LPE, which starts at approxi-mately 250 nK below the transition. This differs from 105h "o 100r CD X £ 95h o CD Q. CO 90h 85 • SOC specific heat Unrounded specific heat (LPE) DRG prediction • ^ ^ ^ ' \ -400 -300 -200 -100 T - T ^ ( n K ) FIGURE 2. Specific heat of the SOC state the prediction of the DRG theory, where the depression starts at approximately 100 nK below 7\ [9]. However, both theory and experiment reach a maximum at approx-imately 50 nK below 7 \ . ACKNOWLEDGMENTS We would like to thank Dmitri Sergatskov, Steve Boyd, Alex Babkin, Alexander Churilov, and Talso Chui for helpful discussions and assistance with cell construction and cryovalve assembly and operation. This work was supported in part by the Fundamental Physics Discipline of the Microgravity Science Office of NASA. REFERENCES l. 2. 3. 4. 7. 9. 10. A. Onuki, Jpns. J. Appl. Phys., 26-S3, 365 (1987). G. Ahlers, Phys. Rev. Lett., 171, 275 (1968). Note: this is true only in the small Q limit. W. A. Moeur, P. K. Day, F-C. Liu, S. T. P. Boyd, M. J. Adrianns, and R. V. Duncan, Phys. Rev. Lett., 78, 2421 (1997). R. V. Duncan, G. Ahlers, and V. Steinberg, Phys. Rev. Lett., 60, 1522(1988). P. B. Weichman, and J. Miller, J. Low Temp. Phys., 119, 155 (2000). Note: these measurements are very different from previous work [10] on the SOC/superfluid two-phase heat capacity. J. A. Lipa, J. A. Nissen, D. A. Strieker, D. R. Swanson, and T. C. P. Chui, Phys. Rev. B, 68, 174518 (2003). R. Haussmann, Phys. Rev. B, 60, 12349 (1999). R. A. M. Lee, A. R. Chatto, D. A. Sergatskov, A. V. Babkin, S. T. P. Boyd, A. M. Churilov, T. D. McCarson, T. C. P. Chui, P. K. Day, R. V. Duncan, and D. L. Goodstein, J. Low Temp. Phys., 134, 495 (2004). 138 Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp

Caltech Authors - Main

Measurement of the SOC State Specific Heat in 4He 
A. R. Chatto*, R. A. M. Lee*, R. V. Duncan1*, P. K. Day** and D. L. Goodstein* 
* Condensed Matter Physics, California Institute of Technology, Pasadena, CA 91125, USA 
^Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM 87131-1156, USA 
** Jet Propulsion Laboratory, Pasadena, CA 91109, USA 
Abstract. When a heat flux Q is applied downward through a sample of liquid 4He near the lambda transition, the helium 
self organizes such that the gradient in temperature matches the gravity induced gradient in 7\. All the helium in the sample 
is then at the same reduced temperature ^soc and the helium is said to be in the Self-Organized Critical (SOC) 
state. We have made preliminary measurements of the 4He SOC state specific heat, CyT(T(Q)). Despite having a cell height 
of 2.54 cm, our results show no difference between CyT and the zero-gravity 4He specific heat results of the Lambda Point 
Experiment (LPE) [J.A. Lipa et al., Phys. Rev. B, 68, 174518 (2003)] over the range 250 to 450 nK below the transition. 
There is no gravity rounding because the entire sample is at the same reduced temperature ^soc(2)- Closer to 7^, the SOC 
specific heat falls slightly below LPE, reaching a maximum at approximately 50 nK below 7\, in agreement with theoretical 
predictions [R. Haussmann, Phys. Rev. B, 60, 12349 (1999)]. 
Keywords: Self-Organized Criticality, Specific Heat, Helium, Superfluidity 
PACS: 65.20+w,67.40.Kh,05.65+b 
INTRODUCTION 
In 1987, the Self-Organized Critical (SOC) state was 
predicted for the normal phase of 4He in the pres-
ence of gravity [1]. Gravity creates a hydrostatic pres-
sure gradient in the helium which creates a gradient 
in 7^, the superfluid transition temperature, of V7\ = 
1.273 / iK/cm [2]. The thermal conductivity K(t), where 
Tx S diverges as t —• 0 [3]. When a heat flux Q 
is applied downward through a sample of helium, the 
resulting temperature gradient parallels the gradient in 
7^, and the helium self organizes to satisfy the condition 
Q/K = V7 \ . Therefore, while there is a gradient in tem-
perature, the temperature difference from 7\ is uniform 
throughout the entire sample, as shown in Fig. 1. 
The SOC state in 4He was first observed in 1997 
by Moeur et al. [4]. They saw not only the expected 
normal phase SOC state, but also self-organization at 
temperatures below 7\ at higher heat flux. In addition, 
they found that K diverged at 7DAS(2)> where 7 D A S ( 2 ) 
is the measured temperature at which perfect thermal 
conductivity of the superfluid state fails abruptly under 
a heat flux Q applied upwards through the helium [5]. 
This encouraged the interpretation that the heat flux was 
depressing the critical point 7\ to the lower T^(Q) = 
7DAS(2)> a n d that the SOC state was therefore always 
on the 'normal' side of 7 \ . In contrast, Weichman and 
Miller presented a theoretical model in one dimension 
that treated the high heat flux self organization as a 
superfluid with a series of phase slips in order to maintain 
the requisite temperature gradient [6]. 
In this paper, we report the first measurements of the 
specific heat of the SOC state [7]. 
EXPERIMENT 
Our cell is constructed with two 2.3 cm diameter gold 
plated copper endplates epoxied to a cylindrical insulat-
ing Vespel® sidewall in order to give a 2.54 cm sam-
ple height. We have three high resolution thermometers 
(HRTs); one on each of the top and bottom endplates 
and a third on a 165 pm thick copper foil that pene-
trates the sidewall. This foil is positioned 0.64 cm above 
the bottom endplate and is in direct contact with the he-
lium sample. We measured the size of our helium sample 
(0.389 moles) through a calibrated extraction and con-
firmed it with a traditional pulse heat capacity measure-
ment in the superfluid phase. 
Since the temperature of the SOC state is determined 
by the heat flux through the helium, one cannot put in 
a pulse of energy and measure the temperature change 
as in a conventional heat capacity measurement. Instead, 
the heat capacity is measured by establishing the SOC 
state throughout the sample at one heat flux, then switch-
ing to a new heat flux and measuring the amount of en-
ergy needed to re-establish the SOC state throughout the 
sample at its new temperature. This is shown schemat-
ically in Fig. 1. As heat is slowly added, the derivative 
of the top endplate thermometer is used to find the time 
when profiles 1 and 3 are reached, while the midplane 
thermometer measures the SOC temperature change. 
CP850, Low Temperature Physics: 24th International Conference on Low Temperature Physics; 
edited by Y. Takano, S. P. Hershfield, S. O. Hill, P. J. Hirschfeld, and A. M. Goldman 
© 2006 American Institute of Physics 0-7354-0347-3/06/$23.00 
137 
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
2 1 3 TV 110 
Temperature 
FIGURE 1. Profiles of helium temperature vs. sample height 
during the experimental procedure: (1) SOC state is fully es-
tablished at the first heat flux; (2) Heat flux is decreased which 
raises the SOC temperature; (3) Energy is added to fully es-
tablish SOC state for the second heat flux. (Note: for Q < 
100 nW/cm2, the helium instead self organizes above 7\.) 
In traditional helium heat capacity measurements, 
where the helium is isothermal, the gradient in 7\ causes 
the heat capacity to be gravity rounded, (i.e. averaged 
over a range of reduced temperatures.) In contrast, in the 
SOC state, the temperature gradient is equal to V7\ and 
the entire sample is equidistant from criticality. There-
fore, there is no gravity rounding in our data, despite 
a sample height of 2.54 cm. Our SOC specific heat re-
sults shown in Fig. 2 are compared directly to a fit of 
the Lambda Point Experiment (LPE) results [8]. Hauss-
mann's prediction for the SOC specific heat using Dy-
namic Renormalization Group (DRG) theory is also plot-
ted [9]. 
We also measured the SOC temperature versus heat 
flux. Our results for 0.5 to 4.5 / iW/cm 2 are well fit by 
'soc(fi) = - ( f i / f io ) 0 ' 8 1 3 with Q0 = 760 ± 10 W/cm 2 . 
Our Qo differs from Moeur et al. [4], but agrees well with 
a later experiment [10]. 
CONCLUSIONS 
The data in Fig. 2 show no measurable difference from 
the LPE results in the range 250 to 450 nK below 7\ -
i.e. the SOC state heat capacity is the same as that for 
the static superfluid. This may imply that the helium in 
this heat flux range of the SOC state is essentially in 
the superfluid phase. If so, this rebuts arguments that 
7DAS (Q) is a depressed critical point, despite the fact that 
the thermal conductivity K diverges at this temperature. 
Closer to 7 \ , we measure a slight depression in the 
specific heat, relative to LPE, which starts at approxi-
mately 250 nK below the transition. This differs from 
105h 
"o 
100r 
CD 
X 
£ 95h 
o 
CD 
Q. 
CO 
90h 
85 
• SOC specific heat 
Unrounded specific heat (LPE) 
DRG prediction 
• ^ ^ ^ ' \ 
-400 -300 -200 -100 
T - T ^ ( n K ) 
FIGURE 2. Specific heat of the SOC state 
the prediction of the DRG theory, where the depression 
starts at approximately 100 nK below 7\ [9]. However, 
both theory and experiment reach a maximum at approx-
imately 50 nK below 7 \ . 
ACKNOWLEDGMENTS 
We would like to thank Dmitri Sergatskov, Steve Boyd, 
Alex Babkin, Alexander Churilov, and Talso Chui for 
helpful discussions and assistance with cell construction 
and cryovalve assembly and operation. This work was 
supported in part by the Fundamental Physics Discipline 
of the Microgravity Science Office of NASA. 
REFERENCES 
l. 
2. 
3. 
4. 
7. 
9. 
10. 
A. Onuki, Jpns. J. Appl. Phys., 26-S3, 365 (1987). 
G. Ahlers, Phys. Rev. Lett., 171, 275 (1968). 
Note: this is true only in the small Q limit. 
W. A. Moeur, P. K. Day, F-C. Liu, S. T. P. Boyd, M. J. 
Adrianns, and R. V. Duncan, Phys. Rev. Lett., 78, 2421 
(1997). 
R. V. Duncan, G. Ahlers, and V. Steinberg, Phys. Rev. 
Lett., 60, 1522(1988). 
P. B. Weichman, and J. Miller, J. Low Temp. Phys., 119, 
155 (2000). 
Note: these measurements are very different from 
previous work [10] on the SOC/superfluid two-phase heat 
capacity. 
J. A. Lipa, J. A. Nissen, D. A. Strieker, D. R. Swanson, 
and T. C. P. Chui, Phys. Rev. B, 68, 174518 (2003). 
R. Haussmann, Phys. Rev. B, 60, 12349 (1999). 
R. A. M. Lee, A. R. Chatto, D. A. Sergatskov, A. V. 
Babkin, S. T. P. Boyd, A. M. Churilov, T. D. McCarson, 
T. C. P. Chui, P. K. Day, R. V. Duncan, and D. L. 
Goodstein, J. Low Temp. Phys., 134, 495 (2004). 
138 
Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp


Measurement of the SOC State Specific Heat in ^4He

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Measurement of the SOC State Specific Heat in ^4He

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