Raffi Budakian Joonho Jang Investigating Magnetic Order in ...

Investigating Magnetic Order in MesoscopicSuperconductors Using Cantilever Torque MagnetometryRaffi BudakianJoonho Jang1 µm

Outline Introduction to superconductivity in Sr 2RuO 4 Describe torque magnetometry measurements to detect momentsfrom edge currents in mesoscopic SRO samples Measurements in NbSe 2(Model system that is layered and s-wave)SRO Measurements Preliminary evidence of moment due to edge currents Nonlinear diamagnetic susceptibility Concluding Remarks

Superconductivity in Sr 2 RuO 4 Layered perovskite structure similar to high T ccuprates Normal state is metallic T c= 1.5 K

Evidence for Unconventional SuperconductivitySuppression of T cfromnon-magnetic impurities(NMR)Oxygen Knight shiftSpin-polarizedneutron scatteringMackenzie et al. (1998)Ishida et al. (1998)Duffy et al. (2000)Spin component of wavefunction is even parity

Evidence for Time Reversal Symmetry BreakingµSRKerr RotationComplex order parameterLuke et al. (1998)Xia et al. (2006) Domains with orbital order have a net magnetic moment. Magnetic fields from domains are screened by the collective motion of CP.

Screening Currents Around Chiral Domains

Experimental Evidence for TRS BreakingExperiment Status Domain SizeµSR -----Josephson tunneling < 1 µmKerr Rotation ~ 50 – 100 µmSQUID Imaging < 2 µmHall probe Imaging < 1 µm

Vortex Matter in Chiral Superconductors 2 Vectors are needed to describe the SC order(1) d-vector - direction normal to the spin polarization(2) L-vector - the angular momentumMackenzie (2003)Integer quantum vortex:Orbital phase winds by 2πd-vector is stationaryHalf-integer quantum vortex:Orbital phase winds by πd-vector winds by ± π

Cantilever Torque Magnetometry Measurementsfiber optic interferometerfor displacement detectionsuperconductingparticleSuperconductordisplacement signalLens90 deg.phase shiftpiezocantileverCantileverzOptical fiberyamplitude controlxPLLfrequency demodulation

300 mK Force Microscope

Micron-Size Superconducting NbSe 2 Particles0.0! fc (Hz)-0.2-0.4-0.6-0.8-1.04.7 K5.5 K6.0 K6.5 K7.0 K7.2 K7.5 K7.8 K2H-NbSe 2 Partilce2 _m-100 -50 0 50 100H x(Oe)8!" (X 10 -13 emu Oe -1 )642T c = 7.3 K00 2 4 6 7.3 8Temperature (K)

Vortex State in Mesoscopic NbSe 2 SamplesFrequency (Hz)5300.55300.05299.55299.0-100 0 100H x(Oe)Moment (X10 -12 emu)6040200-20-40-60-150 -100 -50 0 50 100 150H x(Oe)Moment (X10 -12 emu)26.020.815.610.45.20.0-150 -140 -130 -120 -110 -100 -90 -80 80 90 100 110 120 130 140 150H x(Oe)

Diamagnetic Susceptibility of NbSe 260404392.820Hz (Oe)0-204392.64392.44392.2Frequency (Hz)-40-604392.0-60 -40 -20 0 20 40 60H x (Oe)

Response to ab-Plane Field4394Frequency (Hz)4393H z (Oe)02040608010012014016043924391-140 -120 -100 -80 -60 -40 -20 0H x(Oe)

Switching Noise in Vortex Dynamics4394.2Frequency (Hz)4394.04393.84393.64393.44393.2H z = -140 Oe4393.804393.754393.704393.654393.60-55.0 -54.5 -54.0 -53.5-80 -60 -40 -20 0 20H x(Oe)T = 4.7 K4393.854393.754393.70 4393.75 4393.80 4393.904393.704393.704393.70 4393.75 4393.80 4393.854393.904393.854393.654393.654393.65 4393.704393.75 4393.804393.854393.804393.604393.604393.60 4393.65 4393.704393.754393.804393.754393.554393.55 4393.60 4393.65 4393.704393.754393.7001020304050Time (s)

Torque Magnetometry of Micron-Size Sr 2 RuO 4 Particles1 µmT c= 1.2 Kc-axis1 µm Samples are cleaved from bulkcrystals and glued to the cantileverwith the c-axis normal to the cantileverface.Samples grown by Y. Maeno

Zero-Field Magnetization Measruements3.0a2 (mHz)2.021.51.0Negative field coolZero field coolPositive field cool0.500 20 40 60 80 100(!H) 2 (Oe) 2Magnetic Moment (X10 -13 emu)0.60.40.20.0-0.2-0.40.00.40.81.2Negative field cool (1-2 G)Positive field cool (1-2) GZero field cool108a1 (mHz)64200 2 4 6 8 10Temperature (K)!H (Oe)

M. Matsumoto & M. SigristJ. Phys. Soc. Jpn. 994 (1999)Assume the particle is a single chiral domainperimeter:thickness:

Diamagnetic Susceptibility Measurements in Sr 2 RuO 4Sr 2 RuO 4 4488.34Frequency (Hz)4488.324488.30T = 0.45 KH z = 0 Oe2 µm4488.28Particle dimensions: 3 µm × 4 µm × 0.5 µmMagnetic moment (X10 -12 emu)1050-5-104488.26-2 -1 0 1 2H x (Oe)-20 -10 0 10 20H x (Oe)

404488.94488.8H z (Oe)2004488.74488.6Frequency (Hz)4488.5-204488.4-40-10 -5 0 5 10H x (Oe)

Remarks Torque magnetometry measurements of mesoscopic samples is apromising technique for detection of edge currents Mesoscopic anular geometry might be useful in stabilizing fractional vorticesQuestions Why do we not observe training effects in the zero-field magnetization ? What is the origin of the nonlinear diamagnetic susceptibility ?