Compound Torsional Oscillator: Frequency Dependence and Hysteresis of Supersolid 4 He (and Search for Superfluid Sound Mode) Harry Kojima Rutgers University in collaboration with Yuki Aoki and Joe Graves

outline Compound Torsional Oscillator  motivation  oscillator  results on NCRI(T,  ), dissipation(T,  ), dependence of NCRI on drive displacement, velocity and acceleration  relaxation effects of dissipation  vortex analogies with HTSC Search for superfluid sound mode  motivation  generator and detector – heater/bolometer  ballistic phonon propagation  search for propagation with low velocity

Compound Torsional Oscillator motivation probing NCRI of identical solid 4 He as function of frequency  glassy solid 4 He (Nussinov, et al, cond-mat/ )  critical displacement, velocity or acceleration?  vortex liquid (Anderson, Nature Physics 3, 160(2007)) “Clearly the crucial experiment for our hypothesis is to change the torsional vibration frequency, holding all other variables constant. This has not been done. It would seem to be urgent to do so, because no other hypothesis yet proposed is consistent with any appreciable fraction of the data.”

driver detector1 detector2 dilution refrigerator Compound Torsion Oscillator Cell volume=0.6 cm 3 Inner Diameter=10 mm Inner Height= 8 mm S/V=7 cm -1 sample cell (stycast 1266) BeCu rods in-phase mode: 496 Hz, Q~1.3  10 6 out-phase mode: 1.2 kHz, Q~ 0.76  10 6

“raw” data, 496 Hz mode

“raw” data, 1.2 kHz mode

NCRI fraction: rim velocity < 20  m/s

Change in Dissipation due to Solid 4 He rim velocity ~ 20  m/s

dissipation vs. frequency shift

Critical Velocity and Hysteresis T = 19 mK

velocity =  m/s T = 63 mK Note: no hysteresis! reversible!

hysteresis at 30 mK Start here.

supersolid – type II HTSC vortex – flux lines analogy rotation --- magnetic field ac oscillation --- ac magnetic field angular momentum --- magnetization picture (T): increasing superfluid fraction (or NCRIf)  decreasing number of vortices

analogies to vortices in sc T 45 mK: reversible  “vortex liquid state”  s /  [%] Velocity [  m/sec] T [mK] 62 mK 19 mK Hz T < 45 mK: vortices can go out, as V is decreased. T < 45 mK: vortices cannot enter as, V is increased. T > 45 mK: vortices can go in and out reversibly. zero field cooled field cooled

relaxation effects T = 30 mK

relaxation at T = 10 mK drive level time

“relaxation time” vs. T ring down time ~ 120 s

long time behavior after decreasing drive

vortex-matter phase diagram V T vortex liquid vortex glass supersolid

Summary Small ρ s /ρ : ~ 0.1% No frequency dependence in  s /  below 20 mK, v=20  m/sec. Possible frequency dependence at higher temperature and at high velocity. Comparison with glassy solid 4 He theory on-going. Hysteresis and reversible regimes in NCRIf and oscillator response. Analogy with vortex phase diagram of HTSC.

2.8 mm Heater Pulse Method with 0.5~10  sec width heat pulse. M.C. Fill line Pressure gauge 4.3 mm Magnet Heat Pulse Experiment (Experimental Setup) Ti bolometer 3 mm 0.5 mm bolometer

signal (t, T)

time derivative of signal(t,T)

pulse propagation velocity vs. T “expected” velocity shift = C – C 0 ~ (1/2)(  s /  )C 0 37 bar 56 bar 37 bar P=53. 6bar (  s /  Penn State) P=30bar (  s /  from Penn State) P=30 bar (Rutgers)

Search for fourth sound 3D plot expected T dependence of fourth sound

conclusions Transverse ballistic phonon propagation Temperature dependence of the transverse ballistic phonon velocity below 200 mK did not change within ±0.15 % which is expected to increase 0.5 % from the theory at low temperature if the  s is 1 % (Pulse energy = 3 nJ/pulse). Search of the Fourth sound like propagation mode. Heat pulse response of solid 4 He was measured up to 10 msec(=0.4 m/sec), using the high sensitivity Ti bolometer at 38 bar. Signature of new mode has not been observed within  T=5  K.

conclusions compound torsional oscillator with cylinder –frequency dependence of NCRIf and dissipation –critical velocity (not amplitude or acceleration) –hysteresis – possible analogy with HTSC fourth sound –not yet observed, but crucial –search is continuing by increasing sensitivity, etc

comparison with vortex liquid theory Vortex Liquid Anderson ( Nature Physics 3, 160(2007) )

comparison with glassy behaviour Nussinov et. al. (cond-mat/ ) Fitting parameters; A=2.0x10 -3 sec -1 s 0 =6.7  sec  /k B =219 mK Fitting parameter; B=0.3 sec -2 Using; s 0,  Using; A, s 0,  Using; B, s 0,  f 0 =495.8 Hz f 0 = Hz