Magnetic heat conductance between CMN single crystals and liquid3He

Measurements of the magnetic Kapitza resistance between single crystals of CMN and lanthanum-diluted CMN in contact with ultrapure liquid³He are presented. The investigations were performed in the temperature range 2–100 mK and in magnetic fields up to 600 Oe. For the first time, a magnetic thermal coupling between bulk crystals with dimensions of up to 3 mm and liquid³He was observed. In the case of pure CMN and liquid³He below 7 mK, the relationR T ⁿ withn=4±1 is seen. A strong dependence ofR with magnetic field and Ce³⁺ content is found.     

The Origin of the Magnetic Channel of the Thermal Boundary Resistance Between Liquid 3He and Ag Sinters at Very Low Temperatures

At temperatures below about 10mK, the temperature dependence of the thermal boundary resistance between liquid ³ He and metal sinters deviates significantly from the behaviour expected from the acoustic mismatch theory (R _K T ^–3). This behaviour is explained in terms of the existence of a magnetic channel for the coupling between the ³ He quasiparticles and the sinter; the origin of this coupling, however, is unknown so far. In our studies of the magnetic properties of Ag sinters made of powders of submicron grain size we have detected and identified a magnetically ordering subsystem which, although it contributes only a few ppms to the total mass, dominates the magnetic properties of the sinters. We present the results of our investigation of the magnetic properties of these Ag sinters which strongly deviate from the behaviour of bulk silver, and discuss a possible mechanism how a magnetically ordered subsystem may open up the magnetic channel of the thermal boundary resistance to liquid ³ He at very low temperatures. The main conclusion of our study is that our results should allow the tuning of the thermal boundary resistance between liquid ³ He and sintered metal heat exchangers at very low temperatures.     

Thermal resistance between a paramagnetic salt (CMN) and liquid helium at millikelvin temperatures

We report new measurements of the thermal resistance between cerium magnesium nitrate (CMN) and liquid helium. AtT=100 mK, the thermal resistanceR for powdered CMN in contact with liquid³He-⁴He or liquid³He is about 2000 times the Kapitza boundary resistance. From the field and temperature dependences ofR we conclude that it is dominated by the phonon-bottlenecked spin-lattice resistance. However, if high-purity liquid³He is in contact with CMN, we observe, below 20 mK, a magnetic boundary resistance in parallel to the spin-lattice resistance. This resistance is two orders of magnitude smaller than the spin-lattice resistance atT=10 mK, and is described byR T ^1.4. The absolute values of the magnetic boundary resistance, as well as the spatially limited phonon-bottlenecked resistance, are extremely sensitive to the surface treatment of the CMN crystals.     

Thermal resistance between liquid3He and copper potassium tutton salt

The thermal resistance between liquid³He and copper potassium tutton salt (CPS) has been measured through its magnetic ordering temperature (T _c=29.6 mK). The thermal resistanceR for pure³He has a broad minimum near 60 mK and increases continuously throughT _cwith decreasing temperature, except for a dip atT _c. BelowT _c,R is proportional toT ^–1.5. Effects of⁴He coating have been studied by stepwise addition of⁴He into liquid³He. The thermal resistance increased drastically for the liquid containing 150 ppm⁴He and more for 95%⁴He. By sudden depressurization of the liquid³He containing 480 ppm⁴He, a considerable decrease ofR was observed. SinceR for pure³He was much smaller than the calculated Kapitza resistance, the present experimental results indicate the existence of surface magnetic coupling between liquid³He and CPS.     

Thermal resistance between powdered cerium magnesium nitrate and liquid helium at very low temperatures

Experiments have been performed from magnetic temperatures of 2–20 mK on the effect of minute⁴He impurities and a magnetic field on the thermal resistance between powdered cerium magnesium nitrate (CMN) and liquid³He. The thermal resistance decreases with decreasingT and increasing small field but is increased dramatically at a givenT by the addition of roughly a monolayer of⁴He. The resistance is interpreted as resulting from a surface magnetic coupling between CMN and liquid³He.This work has been supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A. 143, and by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant No. AF-AFOSR-631-67A.     

Thermal contact between cerium magnesium nitrate and liquid3He at very low temperatures

A new experimental arrangement has been used to measure the times for equilibrium between cerium magnesium nitrate (CMN) and liquid³He. Measurements have been made on a single crystal of CMN from temperatures of 5.5–15 mK and on a powdered specimen from temperatures of 2.5–35 mK. The thermal resistance deduced from the single-crystal data is proportional toT ^–2. The thermal resistance obtained from the powder data may be separated into three contributions: a resistance which is proportional toT ^–2in series with a parallel combination of a phonon resistance (with resistivity _P =3×10 ^–4 T ^–3sec·cm²·K ⁴ ·erg ^–1 ) and a magnetic resistance (with resistivity _M =9×10 ² T sec·cm ² ·erg ^–1 in zero applied magnetic field). A reduction in the magnetic resistance was observed when the powdered CMN was placed in a magnetic field, the magnitude of this reduction being comparable to that expected from a Redfield-like theory. TheT ^–2resistance is discussed in terms of two-dimensional energy transport within the CMN. The 17-Hz susceptibility of the powdered CMN was measured in magnetic fields of 0, 18.9, 30.2, and 37.8 G. The magnetic temperatureT* (H=37.8 G) was found to differ by +0.5 mK from the magnetic temperature in zero field whenT* (H=0)=3 mK.Work supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A.143.Supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under AFOSR Contract No. AFOSR/F-44620-72-C-0017.     

Thermal boundary resistance at interfaces between sapphire and indium

The Kapitza thermal boundary resistanceR _K has been measured above 1 K on several sapphire-indium boundaries prepared with different methods. By vapor-deposition of indium on sapphire and subsequent cold-welding with bulk indium, reproducible results were obtained. With the indium superconducting, we foundR _KT ^–3 within a certain temperature range, andR _K(1K)=42–44 and 30–36 cm² K/W for polished and rough sapphire surfaces, respectively. The calculation according to the acoustic mismatch theory yieldsR _K(1K)20 cm² K/W. Samples prepared by ultrasonic soldering also follow the relationR _KT ^–3 approximately, and giveR _K(1K)=14–17 cm² K/W. However, it is doubtful whether the calculation presuming a smooth boundary can be applied to the latter samples. Furthermore, we found that the method of vapor deposition and subsequent pouring on molten indium does not give good contacts. Moreover, the electronic contribution to the heat transfer across the boundary has been proved by ruling out other effects.     

Kapitza resistance and thermal conductivity of Kapton in superfluid helium

We have determined simultaneously the Kapitza resistance, R_K, and the thermal conductivity, κ, of Kapton HN sheets at superfluid helium temperature in the range of 1.4–2.0 K. Five sheets of Kapton with varying thickness from 14 to 130 μm, have been tested. Steady-state measurement of the temperature difference across each sheet as a function of heat flux is achieved. For small temperature difference (10–30 mK) and heat flux density smaller than 30 W m⁻², the total thermal resistance of the sheet is determined as a function of sheet thickness and bath temperature. Our method determines with good accuracy the Kapitza resistance, R_K=(10540±444)T⁻³×10⁻⁶ K m² W⁻¹, and the thermal conductivity, κ=[(2.28±0.54)+(2.40±0.32)×T]×10⁻³ W m⁻¹ K⁻¹. Result obtained for the thermal conductivity is in good agreement with data found in literature and the Kapitza resistance’s evolution with temperature follows the theoretical cubic law.     

On the anomalous CMN-He3 3 thermal boundary resistance

It is proposed that the mechanism of the anomalously high thermal transfer rates observed between CAIN and liquid He³ is simply the electromagnetic dipole coupling between electrons and He³ nuclei. A crude theory based on this assumption explains the observed linear dependence of the Kapitza resistanceR _K onT, the order of magnitude of the coefficient, and the absence to date of the effect in dilute He³-He⁴ solutions. We predict that (1)R _K (T) should go through a minimum at about 1 mdeg, (2)R _K should be decreased by applying a magnetic field, (3) a similar linearT dependence (though with much larger coefficient) should be seen in dilute solutions below 5 mdeg, and (4) a similar, though probably less striking effect, should be observed for ferromagnetic metals in contact with He 3 at sufficiently low temperatures.Supported by Nordita.An up-to-date account of the experimental and theoretical situation regarding this effect can be found in Ref. 1:     

The Kapitza resistance between copper and3He

The Kapitza resistanceR _K between copper and³He has been measured at low pressure in a guarded cell in the temperature range 0.05–0.5 K. An extreme sensitivity to surface damage was observed. For an annealed, electropolished surfaceR _K agreed within a factor of two with the acoustic mismatch theory below 0.1 K. It was also noted thatR _K between copper and liquid³He was identical toR _K between copper and an adsorbed³He film. The data are compared with several mechanisms proposed theoretically to account forR _K .This work was supported in part by the Advanced Research Projects Agency under Contract HC 15-67-C-0221.     

A simple theory for the dependence of the electrical resistance of the magnetic superconductors TmRh4B4 and ErRh4B4 on temperature and field

The warmup rate of the¹⁶⁵Ho-enhanced nuclear spins in a HoVO₄ single crystal in contact with dilute³He is shown to be dominated by the Kapitza resistanceR _K at low bath temperature (T _b <100 mK). This result is obtained from an analysis of the NMR signal during the warmup, following a demagnetization which cools the sample to a temperature of about 5 mK. The temperature variation ofR _K (T _b< ^/–3 ) is consistent with the acoustic mismatch model, but the magnitude is 40 times smaller than the theoretical predictions for a solid-liquid interface. The spin-lattice relaxation is also estimated, and found to be in agreement with the results of other authors.     

Review paper: Heat transfer between liquid helium and solids below 100 mK

The many experimental determinations of heat transfer between liquid helium and solids are reviewed and compared with the existing theories. Generally heat transfer is a complex process at low temperatures, involving parallel heat paths with several resistances in series in each path. The standard theories for the individual resistances are reviewed and as far as possible a definite value of the expected resistance obtained. The experiments have been considered in five groups: cerium magnesium nitrate in liquid³He, cerium magnesium nitrate in dilute³He in liquid⁴He, metals in liquid³He, metals in dilute³He in liquid⁴He, and miscellaneous experiments. Where appropriate, the experimental results have been reevaluated in terms of standard models for heat transfer and presented as resistance versus temperature on diagrams showing the theoretical predictions. Between 20 and 100 mK many measurements show good agreement with acoustic mismatch theory for thermal boundary resistance. Below 20 mK most experiments have been made with finely divided solids (sintered metals or powdered paramagnetic salts); invariably the resistance has been anomalously low, with the metal/³He systems showingR T ^–1 and the metal/dilute³He in⁴He systems showingR T ^–3. The cerium magnesium nitrate/helium experiments have shown a temperature—independent resistance and sometimes anR T ^~1 dependence. These resistances have been attributed to the spin-lattice resistance in cerium magnesium nitrate. Evidence for heat transfer by magnetic coupling has been reviewed and it is concluded that the positive evidence has other explanations, while the lack of dependence upon helium pressure,³He phase, and large magnetic fields is strong negative evidence. If the disagreement of experimental results with standard theory is not to be attributed to magnetic coupling, then several theoretical questions remain to be answered; these questions are posed. Basically, at low temperatures the excitations in solids and liquid helium have wavelengths and mean free paths much larger than the size of the finely divided particles or pores between the particles. Thus theories for bulk solids and bulk liquid helium are not appropriate for describing excitations and their interactions at these low temperatures.     

Adsorption of3He and4He on copper and on argon-coated copper below 20 K

Measurements have been made of adsorption isotherms of ³ He and of ⁴ He on copper and on a monolayer of argon deposited on copper in the temperature range 6.18–18.55 K and in the pressure range 0.25 to 75 Torr. From these many isotherms, calculations have been made of the isosteric heat of adsorptionQ _st/R. In the limit of zero coverage on the argon monolayerQ _st/R=76±2 K for ³ He and 76±2 K for ⁴ He. For adsorption on the bare copper,Q _st/R is difficult to extrapolate to zero coverage, but it probably lies (for both ³ He and ⁴ He) between 135 and 165 K. At theoretical monolayer helium coverage,Q _st/R=44±2 K for ³ He on the argon monolayer and 47±2 K for ⁴ He. At theoretical monolayer helium coverage on the bare copper,Q _st/R=61±4 K for ³ He and 77±5 K for ⁴ He. The results are compared with theoretical evaluations for helium adsorbed on an argon monolayer and with some previous experimental data, and the agreement is found to be fair. All the data are summarized in tables. Finally, a review is given of evaluations, including those from this work, of the monolayer capacity of ³ He and ⁴ He on the substrates studied.Work supported by a contract with the Department of Defense (Themis Program) and with the Office of Naval Research and by a Grant from the National Science Foundation.     

Thermal boundary resistance between liquid helium and silver sinter at low temperatures

We present measurements of the thermal coupling between Ag sinter (nominal grain size 700 Å) and superfluid³He-B atp = 0.3, 10, and 20 bar as well as a phase-separated³He⁴-He mixture atp = 0.5 bar in the submillikelvin regime. In order to analyze the data of the pure³He-B sample with respect to different contributions to the thermal resistance, a one-dimensional model for the heat flow in the sinter is presented. As a result it is shown that the thermal conductivity of the liquid in the sinter has to be taken into account to extract the temperature and pressure dependence of the boundary resistance in the confining geometry of the sinter. Depending on the value of this thermal conductivity, a boundary resistance proportional toT ^–2 orT ^–3 is found. Moreover, it is shown that a pressure dependence of the boundary resistance might be explained by a pressure dependence of the thermal conductivity of the liquid in the sinter. The data on the phase-separated mixture are equally well described by aT ^–2- and aT ^–3-dependence of the boundary resistance. We point out that a common problem in most measurements of the Kapitza resistance performed so far is the small temperature interval investigated, which usually does not allow a definite conclusion concerning the temperature dependence.     

Thermal boundary conductance between the U2D2 solid and B superfluid phases of3He

We present the first measurement of the thermal boundary conductance, 1/R _B , between the U2D2 spin ordered solid and theB superfluid phases of³He. We find that 1/R _B is exceedingly high, roughly seven orders of magnitude greater than that between sintered silver powder and liquid³He. ForT<0.56 mK, 1/R _B appeared to be thermally activated, i.e. 1/R _B exp(–/k _B T), with =4.5(±0.5) mK, close to the superfluid gap energy. We also present a theory involving magnon-quasiparticle coupling as a model to explain the experimental observations.     

Electron-Phonon Coupling in Bolometers Used for Cryogenic Particle Detection

Superconducting transition-edge sensors have been used extensively in cryogenic particle detectors, either as thermometers for microcalorimetry or as bolometers for the detection of the prompt phonons resulting from a particle decay in a single crystal absorber. Bolometer action depends upon the energy coupling of the prompt phonons to the bolometer electrons. A study has been made of the electron-phonon coupling for a series of Au-Ti bolometers on a Si substrate and of the use of these bolometers for prompt phonon detection below 1 K. The electron-phonon coupling was found to be proportional to the normalized resistance (R/R _n) of the bolometer; R is the bolometer resistance and R _n is the normal resistance. When extrapolated to R/R _n = 1, this coupling was consistent with /VT ³ = 3 × 10⁹ Wm^–3K^–4 where is the thermal conductance from the bolometer electrons to the Si phonons and V and T are the volume and transition temperature of the bolometer. The response of the bolometers to heat pulses generated by a thin film heater on the opposite face of a Si single crystal were similar to that generally seen above 1 K, apart from a delay time constant that varied from 0.5 to 1.3 µs as the transition temperature decreased from 600 to 200 mK. This delay time constant is attributed to the thermal equilibrium time of normal regions of the bolometer.     

Magnetic thermal boundary resistance between enhanced nuclear spin sytems and liquid3He

The Kapitza resistance between TmVO₄ and liquid³He in the temperature range 1–40 mK was measured. The Kapitza resistance was proportional to T² below about3 mK. By adding a small amount of⁴He, the Kapitza resistance was enlarged. Applying magnetic fields up to about 70 Oe, the resistance also increased. The decreasing Kapitza resistivity with decreasing temperature was also observed between HoVO₄ and liquid³He. Its value, however, was two orders of magnitude smaller than that for TmVO₄. The experimental results can be explained by the magnetic coupling between enhanced nuclear spins of Tm or Ho and nuclear spins of adsorbed solid³He on the surface of the crystal. By using this model numerical calculation of the Kapitza resistivity was made.     

Effects of electric fields on the silver photodoping of As2Se3 films

The effects of different electric fields (4.2, 8.3, 12.5, 16.7 and 20.8 Vcm_–1) on the sheet resistance, R _s, and optical band gap, E _obg, of As₂Se₃ samples (1×10⁵nm) that were photodoped by Ag (5×10³nm) have been studied. The R _s and E _obg of samples subjected to an electric field of 12.5 Vcm_–1 decrease linearly to a distance of 5 mm from both electrodes, and then saturate at larger distances. This result suggests that there is a critical value of the electric field which affects photodoping. The dependence of R _s and E _obg on the distance from the electrodes shows similar profiles for these electrodes.     

Temperature dependence of the critical current in one-dimensional indium strips

The first reported measurements of the temperature dependence of the critical current in narrow, thin-film indium strips are presented. The results are compared with several models and excellent agreement with a (1 –t ²)^3/2 temperature dependence is found.This work was supported in part by the National Science Foundation.