Superfluid Onset and Prewetting of 4He on Rubidium

J. A. Phillips, D. Ross, P. Taborek and J. E. Rutledge 
Department of Physics and Astronomy 
University of California, Irvine 92697 

(1998)
 
 
Abstract 

Introduction 

Experimental Methods 

Data 

Discussion 

Conlcusions  

References 
 
 
 
 

Projects Page 
 
 
 
 

Discussion

figure 13The most striking feature of the phase diagram in Figure 4 is the hysteresis in the prewetting thick/thin transition. Prewetting steps on Cs prepared in a similar way as the Rb surfaces described here are essentially identical in the forward and reverse directions [8]. On rough or porous surfaces, however, capillary condensation can give rise to hysteretic behavior on Cs [29]. We have ruled out this possibility on our substrates by carefully measuring isotherms using 3He (for which neither wetting nor superfluidity is an issue) on substrate 2; there was no observable hysteresis and no excessive adsorption at saturation (Figure 13), suggesting that the hysteresis we observe with 4He is an intrinsic property of the 4He surface phases, and not an artifact due to the substrate. Qualitatively similar hysteresis was observed on our surface 1. Demolder et al. [11] used a heat flow technique to map the superfluid onset of 4He on Rb at temperatures between 1.0 K and 1.7 K. They also found that its position in the m - T plane was hysteretic. Our measurements of the Dm at onset for forward isotherms agree with their forward isotherms in the region where our data overlap. The width of the hysteresis in Dm which they observe is considerably narrower than ours, possibly because their helium films are carrying a finite heat current. 
Another significant difference between Rb and Cs is the width of the prewetting steps which are approximately 3 times wider on Rb than Cs. Below the prewetting critical temperature, Tcpw, prewetting is a first order transition which ideally occurs at constant chemical potential, but even for T>Tcpw, maxima in the compressibility of the supercritical film give rise to broader step-like structures in isotherms. Monitoring the temperature dependence of the width of the transition is a standard method of locating the prewetting critical point [8]. In contrast to the Cs case, the width of the prewetting transitions on Rb is a smooth, almost linear function of temperature, with no obvious break in slope. These observations suggest that our Rb surfaces are  more disordered than our Cs surfaces. The source of the substrate inhomogeneity is presumably variations in the wetting properties of substrate patches with different crystallographic orientation [30]. If this is the case, then the observed hysteresis is associated with prewetting broadened by the effects of substrate inhomogeneity. In this interpretation, the reverse branch is due to a spinodal line (stability limit) of the thick film superfluid phase. Our belief that the forward branch represents the equilibrium transition while the reverse branch is metastable is based on the fact that the Rb substrate is surrounded by strong binding surfaces (quartz and gold) which are covered with a thick superfluid film whenever the helium film on the Rb undergoes a thick/thin transition on either the forward or reverse isotherm. The thin->thick transition on the forward isotherm is nucleated at the edge of the Rb, while the thick->thin transition on the reverse isotherm requires a fluctuation and can therefor be supercooled. The reduction of hysteresis in the region near 1.95 K marks the remnant of the broadened prewetting critical point. Above 1.95K, there is some remaining hysteresis in the prewetting transitions, but not in the position of the KT line. Prewetting is in the 2D Ising universality class, and the phase transitions in this type of system are well known to be strongly affected by disorder [31-34], while the KT transition, which is in the XY universality class, is relatively insensitive to disorder [35]. 
The junction in the m-T plane of the first order prewetting line and the higher order KT line shown in Figure 4 has an unusual topology. Model calculations [36,37] show that the junction between a first order and higher order transition at a tricritical point usually occurs with no change in slope. Although the connection between the reverse transition (spinodal) and the KT line does appear to be smooth, the KT line meets the forward transition in a sharp, cusp-like angle. Cusp-like junctions in which the two transition lines meet tangentially are also allowed  [38, 39]. 
Previous investigators have reached differing conclusions on the behavior of the superfluid onset transition at low temperatures. Demolder et al. [11] analyzed their results using an extrapolation scheme that properly accounted for the temperature dependences of the leading thermodynamic terms and concluded that the superfluid onset line does not intersect bulk liquid - vapor coexistence at a finite temperature. Wyatt et al. [13] studied mass transport across a Rb surface for 0.1K<T<0.35K in a region very close to coexistence (Dm<0.006K). They interpret a jump in the critical superflow velocity to indicate a wetting temperature just above 0.3 K where a prewetting line joins the bulk liquid - vapor coexistence line. In terms of the surface energy balance, the difference between a 0.3 K wetting temperature and T = 0 K prewetting is minuscule and might easily be due to very small differences in the surface chemistry [40]. Wyatt et al. also suggest that both the thin and thick films along the prewetting lines are superfluid. In contrast, all of the Rb surfaces we investigated were wet at coexistence. Furthermore, the dissipation peak which is the hallmark of the KT transition was observed only in the thick phase. The behavior in the thin phase undergoes a subtle continuous change near T=0.3K, which does not resemble the standard signature of either a superfluid onset transition or a first order transition with a discontinuity in the film thickness. 
figure 14It is useful to compare the superfluid transition observed on Rb with superfluid onset on conventional substrates and Cs, as shown in the schematic d-T phase diagrams shown in Figure 14. Figure 14a shows the phase diagram for 4He adsorbed on a conventional substrate such as mylar or gold. The helium film exists in only two states, superfluid (S) and normal (N), which are separated by the dashed KT line. The d>0 intercept at T=0 corresponds to the dead layer. The linear dependence of d on T at low temperature is very similar to that given by Eq. 2, while the divergence at Tl is due to finite size effects, with . Figure 14b shows the combined prewetting /superfluid onset phase diagram for 4He on Cs. Cs substrates thicker than approximately 3 layers have a wetting temperature Tw>0. For 0<T<Tw, a thin phase can coexist with bulk liquid. For Tw<T<Tcpw, there is a range of film thickness which is unstable. The KT line is almost exactly the same as in Fig 14a, except that it terminates at a critical endpoint when it collides with the range of unallowed d. For temperatures below the critical endpoint, the signatures of the KT transitions are not observed [9], because the film never attains the critical onset thickness. A candidate phase diagram which summarizes our observations of superfluid onset on Rb is shown in Figure 14c, which should be compared to the data in Figure 15. In this case, there is no wetting temperature, but there is a prewetting transition, which corresponds to a range of unstable thickness. The hysteresis we observe is due to metastable states between the phase boundary and the spinodal line. On the forward isotherms, the transition takes place at the upper phase boundary, while on the reverse isotherms, the transition takes place on the lower spinodal line. Where the spinodal line and the phase boundary meet marks the end of hysteresis at a critical point. In this case, however, the KT line intersects the prewetting phase boundary very close to the prewetting critical point. Since both the thickness and the superfluid order parameter are singular there, it is presumably a multicritical point. The resulting phase diagram resembles the well known bulk 3He-4He mixture phase diagram (with d playing the role of  4He concentration) which also has a multicritical point where the lambda line hits the phase separation curve. 
The fact that the standard signatures of a KT transition (superfluid jump and dissipation peak) are observed all along the prewetting line implies that the KT line does not stop at the multicritical point, but rather continues along the upper phase boundary and along the spinodal. This is surprising because the physics which determines the prewetting behavior and the superfluid transition is ordinarily quite distinct, and it is not obvious why the two transitions should not be completely independent. Apparently, on Rb the combination of the multicritical point and the substrate disorder merge the two phenomena into a single strongly coupled transition. 
figure 15

Although the positions of the features which mark the surface phase transitions are quite reproducible from one Rb sample to another, the size and shape of the features vary considerably, and as noted above, cannot be simply explained by the standard KT model. The discrepancies in the superfluid jump are particularly puzzling since the predicted value, which is universal, has been experimentally verified on a number of substrates. It should be noted that in any oscillator experiment, particularly at low temperature, a potential source of error in measurements of df is the superfluid coupling factor k of Eq 1. In systems in which k approaches 1 such exfoliated graphite studied in [21], the observed values of df are very small because the oscillator couples to almost all of the fluid even when it is superfluid. The data can be corrected for this effect by multiplying the observed values of df by 1/(1-k). The values of the superfluid jumps corrected using this procedure agree with the KT prediction even for exfoiliated graphite, where the correction can be as large as a factor of 50 [21]. We have not applied such a correction to our Rb data, (equivalent to choosing k=0 on Rb) so the values of df shown in Figures 3 and 7 are lower bounds. It is interesting to note that even this lower bound for df is often considerably larger than the KT prediction. 
The KT predictions for the dissipation are not universal, although the dissipation is expected to be proportional to the temperature [3]. This trend has been observed in systems with thick helium films at relatively high temperature [4, 18], but experiments at lower temperature [25, 21] show anomalies in both the height and the width of the peaks which can not be explained by the standard theory [3]. Dissipation measurements using an oscillating substrate are subject to the same corrections for the superfluid coupling factor as discussed above, so our values of DR again represent a lower bound.