Theory of domain structure in ferromagnetic phase of diluted magnetic semiconductors near the phase transition temperature

TL;DR

This paper presents a theoretical analysis of how disorder affects domain structures in p-type diluted magnetic semiconductors near the phase transition, revealing a critical ratio of charge carriers to magnetic ions that influences domain formation.

Contribution

It introduces a critical ratio of charge carriers to magnetic ions that determines the domain structure and critical thickness in DMS, highlighting differences from conventional magnets.

Findings

Existence of a critical ratio r of charge carriers to magnetic ions.

Sample critical thickness diverges as pproaches r.

Control of domain structure period via variation of r.

Abstract

We discuss the influence of disorder on domain structure formation in ferromagnetic phase of diluted magnetic semiconductors (DMS) of p-type. Using analytical arguments we show the existence of critical ratio $\nu_{\rm {cr}}$ of concentration of charge carriers and magnetic ions such that sample critical thickness $L_{\rm{cr}}$ (such that at $L<L_{\rm{cr}}$ a sample is monodomain) diverges as $\nu \to \nu_{\rm {cr}}$. At $\nu > \nu_{\rm {cr}}$ the sample is monodomain. This feature makes DMS different from conventional ordered magnets as it gives a possibility to control the sample critical thickness and emerging domain structure period by variation of $\nu $. As concentration of magnetic impurities grows, $\nu_{\rm {cr}}\to \infty$ restoring conventional behavior of ordered magnets. Above facts have been revealed by examination of the temperature of transition to inhomogeneous magnetic state (stripe domain structure) in a slab of finite thickness $L$ of p-type DMS. Our analysis is carried out on the base of homogeneous exchange part of magnetic free energy of DMS calculated by us earlier [\prb, {\bf 67}, 195203 (2003)].