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Propagation of a magnetic disturbance in superfluid 3HeB
Volume 54A, number 3
PHYSICS LETTERS
8 September 1975
PROPAGATION OF A MAGNETIC DISTURBANCE IN SUPERFLUID 3 He-B ~ R.A. WEBB, R.E. SAGER and J.C. WHEATLEY Department of Physics, University of California, San Diego, La Jolla, CA 92037, USA
Received 9 July 1975 A strong disturbance evoked magnetically has been observed to propagate in 3He-B at 20.7 bar over a distance of about one centimeter. We report observations in superfluid 3He-B of the propagation over a substantial distance in space of a disturbance of complex characteristics which is evoked by a magnetic as opposed to a thermal or mechanical means. The theory of spin currents and waves has been reviewed by Leggett [ 1 ]. Although the existence of spin currents has been used to explain various experimental phenomena [ 2 - 4 ] the propagation of a magnetic disturbance has not yet been reported. That a mode propagating over a distance of order 1 cm may be difficult to observe can be understood in terms of the coherent dipolar coupling between the interpenetrating superfluids [ 1,4, 5 ] which inhibits independent flow of the individual superfiuids by allowing "tunneling" between them. The resultant propagation can be highly dispersive and attempts to observe it might have to be confined to small distances [1,5]. In our parallel ringing experiments [2] we observed in 3He-B for zero field a relatively long-lived ringing mode with a frequency roughly proportional to AH, the field turned off. Owing to its interpretation [6, 7], it is called the wall-pinned mode (WPM). Relaxation of the WPM evolves primarily by a decrease of frequency rather than amplitude with time. The above properties of the WPM, as opposed to other modes o f dynamic magnetism we have observed, suggested that a propagating magnetic disturbance possibly related to it might be observable, although with probably quite complicated properties. The 3He is confined to a rectangular cavity I m m × 10 mm in section, and its magnetization is sensed by the 3.4 mm long "magnetization sensing" coils located as shown in the inset to fig. 1 and connected to the input of an RF-biased SQUID. The long solenoid pro* Supported by the U.S. ERDA under contract number AT(04-3)-34, P.A. 143.
rides a "measuring" field (when the current in this solenoid is turned off a WPM can be observed) while the "remote" coil provides an additional field in space which is controlled separately from the "measuring" '
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Fig. 1. Temperature dependence of the reciprocal of the time delay in 3He-B at 20.7 bar observed for a propagating magnetic disturbance from "remote" to "sensing" coils for HR/H M = 7 gauss/5 gauss. The dashed lines correspond to a (1 -T[Tc) 1/2 variation of (td)-l. The inset shows schematically the geometry for the measurements. Dimensions are in millimeters. Different symbols correspond to different runs. 243
Volume 54A, number 3
PHYSICS LETTERS
field and which is used to generate a magnetic disturbance in the 3He. Coil sets are wound 1o reduce the net mutual inductance between the sensing coils and both the remote and measuring coil systems. No magnetic effect of the 3He-B is observed at the sensing coils when only the remote field is turned off. This in itself is not necessarily surprising since, if the propagating disturbance relates to the WPM, it is quite probable that there is little phase coherence over the volume sensed. To detect any propagating disturbance we therefore applied both a remote field H R and a measuring field H M. At zero time we turned offHR : then after a delay t d we turned o f f H M and observed the resultant WPM via the sensing coil. The WMP produced by turning o f f H m is thus used as a detector. We found that the amplitude of the detecting WPM was a function of t d : about the same size for large and small values of t d but with a single or double minimum at values of t d which depend on the temperature T and on both H M and H R . In the vicinity of minima the detecting WPM amplitude was usually completely obscured. The detection method is made more sensitive by observing the amplitude of the detecting WPM somewhat after the time at which H M is turned off (0.7 msec for these measurements). Experimental values of the reciprocals of observed time delays t d are plotted logarithmically versus (1 - T/Tc) in fig. 1 for 3He-B at a pressure of 20.7 bar and for fixed values o f H R ~ 7 gauss at the remote coil center and H M = 5 gauss. The two branches shown reflect the double minimum feature observed in some of the measurements. Owing to the qualitative nature of the detector, location of two minima was not always obvious; no doubt part of the scatter may be attributed to this. The geometry is sufficiently complicated that two wave crests could have been produced. Since the center-to-center distance between remote and sensing coils is 1 cm, the vertical scale on fig. 1 thus estimates the propagation velocity of the disturbance in cm/sec, but we of course have no precise knowledge of the appropriate distance to use. Near T c the propagation velocity may be proportional to (1 -- T/Tc)I/2, but as (1 - T/Tc) increases in the vicinity of 0.1 the velocity increases rather rapidly. The observed t d depends strongly on the size of the measuring field. For the value o f H R used for the data in fig. 1 there is at least a three-fold decrease of t d expected as H M -+ 0 near
244
8 September 1975
7"~. and probably a greater corresponding decrease al lower temperatures. The delay tcl also decreases for fixed H M as H R increases. It is possible that the propagating disturbance is some kind of propagating WPM originally produced by turning o f f H R. ha that case we know [8] from other measurements on a uniform system that the frequency at a given time t after turnoff is greater both for larger HR/H M and larger H R at fixed H M. This may be related to the increased effective propagation velocity cited above in reference to such changes. Formulae for the velocities of undispersed spin waves may be found in Leggett [1 ] although they are no doubt not directly applicable to this work. Maki [9] suggests that for wall pinning a longitudinal spin wave has zero wave vector. This may be the closest nondispersive wave to the present case. For such a mode, Leggett (eq. (12.29) of ref. [1 ]) finds near To) that C2/C2 = (2/5)(1 +¼Z0)/(1 + F 0 ) , where C4 is the velocity of fourth sound and Z 0 and F 0 are Landau parameters. Using known experimental values [4] at 20.7 bar, we find from theory that C = 1.2 × 103 (l T/Tc)I/2 cm/sec. This is almost an order of magnitude larger than we can infer from fig. 1, although the very substantial velocity increases observed as H M -+ 0 and H R increases and as (I - T/Tc) increases tend to make the difference of observed from such a calculated velocity much smaller. We are much indebted to Prof. A.J. Leggett, Prof. K. Maki and Dr. It. Ebisawa for discussions of this work
References
[1] A.J. Leggett, Rev. Mod. Phys. 47 (1975) 331. [2] R.A. Webb, R.L. Kleinberg and J.C. Wheatley, Phys. Rev. Lett. 33 (1974) 145. [3] L.R. Curruccini and D.D. Osheroff, Phys. Rev. Lett. 34 (1975) 564. [4] J.C. Wheatley, Rev. Mod. Phys. 47 (1975) 415. [5] K. Maki and T. Tsuneto, Phys. Rev. B11 (1975) 2539. [6] K. Maki and C.-R. Hu, J. Low Temp. Phys. 18 (1974) 377: 19 (1975) 259. {7] W.F. Brinkman, Phys. Lett. 49A (1974) 411. [8] R.A. Webb, R.E. Sager and J.C. Wheatley, submitted for publication. [9] K. Maki, Phys. Rev. B11 (1975) 4264.
PHYSICS LETTERS
8 September 1975
PROPAGATION OF A MAGNETIC DISTURBANCE IN SUPERFLUID 3 He-B ~ R.A. WEBB, R.E. SAGER and J.C. WHEATLEY Department of Physics, University of California, San Diego, La Jolla, CA 92037, USA
Received 9 July 1975 A strong disturbance evoked magnetically has been observed to propagate in 3He-B at 20.7 bar over a distance of about one centimeter. We report observations in superfluid 3He-B of the propagation over a substantial distance in space of a disturbance of complex characteristics which is evoked by a magnetic as opposed to a thermal or mechanical means. The theory of spin currents and waves has been reviewed by Leggett [ 1 ]. Although the existence of spin currents has been used to explain various experimental phenomena [ 2 - 4 ] the propagation of a magnetic disturbance has not yet been reported. That a mode propagating over a distance of order 1 cm may be difficult to observe can be understood in terms of the coherent dipolar coupling between the interpenetrating superfluids [ 1,4, 5 ] which inhibits independent flow of the individual superfiuids by allowing "tunneling" between them. The resultant propagation can be highly dispersive and attempts to observe it might have to be confined to small distances [1,5]. In our parallel ringing experiments [2] we observed in 3He-B for zero field a relatively long-lived ringing mode with a frequency roughly proportional to AH, the field turned off. Owing to its interpretation [6, 7], it is called the wall-pinned mode (WPM). Relaxation of the WPM evolves primarily by a decrease of frequency rather than amplitude with time. The above properties of the WPM, as opposed to other modes o f dynamic magnetism we have observed, suggested that a propagating magnetic disturbance possibly related to it might be observable, although with probably quite complicated properties. The 3He is confined to a rectangular cavity I m m × 10 mm in section, and its magnetization is sensed by the 3.4 mm long "magnetization sensing" coils located as shown in the inset to fig. 1 and connected to the input of an RF-biased SQUID. The long solenoid pro* Supported by the U.S. ERDA under contract number AT(04-3)-34, P.A. 143.
rides a "measuring" field (when the current in this solenoid is turned off a WPM can be observed) while the "remote" coil provides an additional field in space which is controlled separately from the "measuring" '
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L.10 I
.15
Fig. 1. Temperature dependence of the reciprocal of the time delay in 3He-B at 20.7 bar observed for a propagating magnetic disturbance from "remote" to "sensing" coils for HR/H M = 7 gauss/5 gauss. The dashed lines correspond to a (1 -T[Tc) 1/2 variation of (td)-l. The inset shows schematically the geometry for the measurements. Dimensions are in millimeters. Different symbols correspond to different runs. 243
Volume 54A, number 3
PHYSICS LETTERS
field and which is used to generate a magnetic disturbance in the 3He. Coil sets are wound 1o reduce the net mutual inductance between the sensing coils and both the remote and measuring coil systems. No magnetic effect of the 3He-B is observed at the sensing coils when only the remote field is turned off. This in itself is not necessarily surprising since, if the propagating disturbance relates to the WPM, it is quite probable that there is little phase coherence over the volume sensed. To detect any propagating disturbance we therefore applied both a remote field H R and a measuring field H M. At zero time we turned offHR : then after a delay t d we turned o f f H M and observed the resultant WPM via the sensing coil. The WMP produced by turning o f f H m is thus used as a detector. We found that the amplitude of the detecting WPM was a function of t d : about the same size for large and small values of t d but with a single or double minimum at values of t d which depend on the temperature T and on both H M and H R . In the vicinity of minima the detecting WPM amplitude was usually completely obscured. The detection method is made more sensitive by observing the amplitude of the detecting WPM somewhat after the time at which H M is turned off (0.7 msec for these measurements). Experimental values of the reciprocals of observed time delays t d are plotted logarithmically versus (1 - T/Tc) in fig. 1 for 3He-B at a pressure of 20.7 bar and for fixed values o f H R ~ 7 gauss at the remote coil center and H M = 5 gauss. The two branches shown reflect the double minimum feature observed in some of the measurements. Owing to the qualitative nature of the detector, location of two minima was not always obvious; no doubt part of the scatter may be attributed to this. The geometry is sufficiently complicated that two wave crests could have been produced. Since the center-to-center distance between remote and sensing coils is 1 cm, the vertical scale on fig. 1 thus estimates the propagation velocity of the disturbance in cm/sec, but we of course have no precise knowledge of the appropriate distance to use. Near T c the propagation velocity may be proportional to (1 -- T/Tc)I/2, but as (1 - T/Tc) increases in the vicinity of 0.1 the velocity increases rather rapidly. The observed t d depends strongly on the size of the measuring field. For the value o f H R used for the data in fig. 1 there is at least a three-fold decrease of t d expected as H M -+ 0 near
244
8 September 1975
7"~. and probably a greater corresponding decrease al lower temperatures. The delay tcl also decreases for fixed H M as H R increases. It is possible that the propagating disturbance is some kind of propagating WPM originally produced by turning o f f H R. ha that case we know [8] from other measurements on a uniform system that the frequency at a given time t after turnoff is greater both for larger HR/H M and larger H R at fixed H M. This may be related to the increased effective propagation velocity cited above in reference to such changes. Formulae for the velocities of undispersed spin waves may be found in Leggett [1 ] although they are no doubt not directly applicable to this work. Maki [9] suggests that for wall pinning a longitudinal spin wave has zero wave vector. This may be the closest nondispersive wave to the present case. For such a mode, Leggett (eq. (12.29) of ref. [1 ]) finds near To) that C2/C2 = (2/5)(1 +¼Z0)/(1 + F 0 ) , where C4 is the velocity of fourth sound and Z 0 and F 0 are Landau parameters. Using known experimental values [4] at 20.7 bar, we find from theory that C = 1.2 × 103 (l T/Tc)I/2 cm/sec. This is almost an order of magnitude larger than we can infer from fig. 1, although the very substantial velocity increases observed as H M -+ 0 and H R increases and as (I - T/Tc) increases tend to make the difference of observed from such a calculated velocity much smaller. We are much indebted to Prof. A.J. Leggett, Prof. K. Maki and Dr. It. Ebisawa for discussions of this work
References
[1] A.J. Leggett, Rev. Mod. Phys. 47 (1975) 331. [2] R.A. Webb, R.L. Kleinberg and J.C. Wheatley, Phys. Rev. Lett. 33 (1974) 145. [3] L.R. Curruccini and D.D. Osheroff, Phys. Rev. Lett. 34 (1975) 564. [4] J.C. Wheatley, Rev. Mod. Phys. 47 (1975) 415. [5] K. Maki and T. Tsuneto, Phys. Rev. B11 (1975) 2539. [6] K. Maki and C.-R. Hu, J. Low Temp. Phys. 18 (1974) 377: 19 (1975) 259. {7] W.F. Brinkman, Phys. Lett. 49A (1974) 411. [8] R.A. Webb, R.E. Sager and J.C. Wheatley, submitted for publication. [9] K. Maki, Phys. Rev. B11 (1975) 4264.