# Direct visualization of local interaction forces in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ vortex matter

## TL;DR

This study visualizes and quantifies local vortex-vortex interaction forces in irradiated Bi2212 superconductors, revealing how these forces and pinning vary with magnetic field and defect type, providing insights into vortex matter behavior.

## Contribution

It introduces a method to directly measure local interaction forces in vortex matter and compares effects of different defect types on these forces.

## Key findings

- Interaction force magnitude grows with magnetic field.
- Irradiated samples have 20-50% smaller pinning forces than defected samples.
- Vortex structures are in equilibrium at the measured temperature.

## Abstract

We study the local vortex-vortex interaction force $\textbf{f}_i$ of the structure frozen during a field-cooling process in an electron-irradiated Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ sample. We compute this magnitude from snapshots of the vortex structure obtained via magnetic decoration experiments at various fields H in the same sample. Since the observed structures correspond to the equilibrium ones frozen at T$\sim$T$_{irr}$(H), at this temperature the local modulus of $\textbf{f}_i$ roughly equals the local pinning force at the decorated surface of the sample. We estimate the most probable local pinning force from the mode value of the f$_i$(r) distribution, f $_{p}^{m}$. We found that f $_{p}^{m}$ grows algebraically with H and in electron-irradiated samples is 50-20% smaller than for samples with columnar defects.

---
Source: https://tomesphere.com/paper/1905.05324