Compound Torsional Oscillator: Frequency Dependence and Hysteresis of

Supersolid 4He

(and Search for Superfluid Sound Mode)

Harry KojimaRutgers 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 Oscillatormotivation

probing NCRI of identical solid 4He as function of frequency

glassy solid 4He (Nussinov, et al, cond-mat/0610743) 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.”

driverdetector1

detector2

dilution refrigerator

Compound Torsion Oscillator

Cell volume=0.6 cm3

Inner Diameter=10 mmInner Height= 8 mmS/V=7 cm-1

sample cell (stycast 1266)

BeCu rods

in-phase mode: 496 Hz, Q~1.3106

out-phase mode: 1.2 kHz, Q~ 0.76 106

“raw” data, 496 Hz mode

“raw” data, 1.2 kHz mode

NCRI fraction: rim velocity < 20 m/s

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

dissipation vs. frequency shift

Critical Velocity and

Hysteresis

T = 19 mK

velocity =100- 200 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: hysteresis “vortex glass state” T > 45 mK: reversible “vortex liquid state”

s/ [%]

Velocity [m/sec]T [mK]

62 mK19 mK

1172.8 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 fie

ld 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

vortexglass

supersolid

Summary

• Small ρs/ρ : ~ 0.1%

• No frequency dependence ins/ below 20 mK, v=20 m/sec.

• Possible frequency dependence at higher temperature and at high velocity.

• Comparison with glassy solid 4He 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 linePressure

gauge

4.3 mm

Magnet

Heat Pulse Experiment (Experimental Setup)

Ti bolometer 3 mm

0.5 mmbolometer

signal (t, T)

time derivative of signal(t,T)

pulse propagation velocity vs. T“expected” velocity shift = C – C0 ~ (1/2)(s/)C0

37 bar56 bar

1 sTC

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 plotexpected T dependence of fourth sound

conclusionsTransverse ballistic phonon propagationTemperature 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 4He 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 theoryVortex LiquidAnderson (Nature Physics 3, 160(2007) )

comparison with glassy behaviour Nussinov et. al. (cond-mat/0610743)

Fitting parameters;

A=2.0x10-3 sec-1

s0=6.7 sec

/kB=219 mK

Fitting parameter; B=0.3 sec-2

Using; s0,

Using; A, s0, Using; B, s0,

f0=495.8 Hz

f0=1172.8 Hz

0 20 0

1

[1 (2 ) ]

fB

ff f s

12

0[1 (2 ) ]

AsQ

f s

0 exp( / )Bs s k T