[Paper Review] Magnetoresistance oscillations and the half-flux-quantum state in spin-triplet superconductor Sr2RuO4

Xing Cai, Yiqun Ying+4 more|arXiv (Cornell University)|Jul 1, 2015

Advanced Condensed Matter Physics3 citations

TL;DR

This study investigates magnetoresistance oscillations in micron-sized, doubly connected Sr2RuO4 cylinders to probe the half-flux-quantum state in a spin-triplet superconductor. Using in-plane magnetic fields and current-dependent measurements, it identifies enhanced resistance oscillations linked to vortex crossing and observes dip features at specific in-plane fields, suggesting the emergence of half-flux-quantum states—particularly in samples with structural constrictions that localize vortex dynamics and amplify detectable signals.

ABSTRACT

We report results of our low-temperature magneto electric transport measurements on micron-sized short cylinders of odd-parity, spin-triplet superconductor Sr$_2$RuO$_4$ with the cylinder axis along the $c$ axis. The in-plane magnetic field and measurement current dependent magnetoresistance oscillations were found to feature an amplitude much larger than that expected from the conventional Little-Parks effect, suggesting that the magnetoresistance oscillations originate from vortex crossing. The free-energy barrier that controls the vortex crossing was modulated by the magnetic flux enclosed in the cylinder, the in-plane field, measurement current, and structural factors. Distinct features on magnetoresistance peaks were found, which we argue to be related to the emergence of half-flux quantum states, but only in samples for which the vortex crossing is confined at specific parts of the sample.

Motivation & Objective

• To experimentally probe the half-flux-quantum state in the spin-triplet superconductor Sr2RuO4 using low-temperature magneto-electric transport measurements.
• To determine the conditions under which the half-flux-quantum state becomes detectable in micron-sized, doubly connected Sr2RuO4 cylinders.
• To understand how vortex crossing dynamics and free-energy barriers are modulated by in-plane magnetic fields, measurement current, and sample geometry.
• To compare magnetoresistance oscillation signatures with previous torque magnetometry results and assess the feasibility of detecting exotic vortex states via transport measurements.

Proposed method

• Fabricated micron-sized, doubly connected Sr2RuO4 cylinders via mechanical exfoliation and focused ion beam (FIB) patterning on Si/SiO2 substrates.
• Employed four- or six-point electrical contacts (200 nm Au with 10 nm Ti underlayer) to enable precise current and voltage measurements.
• Performed low-temperature (20 mK) dc magnetoresistance measurements in a dilution refrigerator using a superconducting Helmholtz coil system for in-plane field control.
• Varied in-plane magnetic field (H||ab) and measurement current to probe vortex crossing dynamics and free-energy barrier modulation.
• Analyzed resistance oscillations using the Ambegaokar-Halperin (AH) model of thermally activated vortex crossing over a flux-dependent barrier.
• Correlated observed resistance features with structural inhomogeneities, such as constrictions or weak links, to isolate vortex crossing at specific locations.

Experimental results

Research questions

• RQ1 Can magnetoresistance oscillations in Sr2RuO4 cylinders reveal signatures of the half-flux-quantum state under in-plane magnetic fields?
• RQ2 How does the presence of structural constrictions or weak links affect vortex crossing dynamics and detectability of exotic vortex states?
• RQ3 What is the role of in-plane magnetic field and measurement current in stabilizing or modulating the half-flux-quantum state?
• RQ4 Why is the half-flux-quantum state more readily observable in torque magnetometry than in magnetoresistance measurements despite theoretical expectations?
• RQ5 How do the kinetic energy and spin-orbit coupling contributions to the free energy influence the stability and observability of the half-flux-quantum state?

Key findings

• Magnetoresistance oscillations exhibited amplitudes significantly larger than expected from the conventional Little-Parks effect, indicating vortex crossing as the dominant mechanism.
• Dip features in resistance oscillations appeared at in-plane fields of 400 Oe and 600 Oe, suggesting the emergence of half-flux-quantum states in samples with localized vortex dynamics.
• In samples with constrictions, a resistance dip emerged at 1000 Oe, consistent with theoretical expectations for half-flux-quantum state stabilization.
• The oscillation period of ~23.7 Oe corresponded to an effective radius of 527 nm, smaller than the SEM-measured radius, indicating flux screening or edge effects.
• Critical current differences of ~10 µA between cylinder arms were observed, indicating asymmetric vortex penetration or weak links.
• The AH model fit yielded a zero-temperature penetration depth larger than bulk values, consistent with reduced magnetic moment in torque measurements and supporting the presence of exotic vortex states.