PART II
THE NANOSTUCTURES
CHAPTER IV Magnetic nanostructures
This chapter is dedicated to the study of FePt and Co nanostructures synthesized trough colloidal crystal masks.
The morphology (SEM/AFM) of the dots is first discussed, followed by a crystallographic analysis (XRD) of the samples.
Finally, the magnetic properties are studied, both from a qualitative (MFM) and quantitative (SQUID/MOKE) points of view.
CHAPTER IV -‐ Magnetic nanostructures -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 95 1. Introduction -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 97 1.1 Bulk material or isolated magnetic particles… A difference? -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 97 1.2. Studied Materials -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 103 1.2.1 FePt -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 103
Crystallographic structures and phase diagram of Fe-‐Pt alloys -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 103
Synthesis of FePt nanoparticles -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 105 1.2.2 Co -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 106 2. Experimental part -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 107 2.1 Colloïdal mask preparation -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 107 2.2 Deposition of nanodots & characterization -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 108 3. Results and discussion -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 110 3.1 Morphological study of the nanodots -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 110 3.1.1 FePt -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 111 3.1.2 Co -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 117 3.1.3 Defects -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 119 3.2 Crystallographic study (DRX) -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 119 3.2.1 FePt -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 119 3.2.1 Co -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 124 3.3 Magnetic study -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 124 3.3.1 FePt -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 125
Quantitative study (SQUID) -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 125
Qualitative study (MFM) -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 131 3.3.2 Co -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 136
Quantitative study (SQUID) -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 136
Qualitative study (MFM) -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 139 4. Conclusions -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 142 5. References -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ 143
1. Introduction
In recent years, patterned magnetic structures have attracted a huge interest due to their potential applications in many technological fields, such as magnetic information storage or non-‐volatile magnetic random access memory (MRAM). Indeed, the never-‐
ending race towards miniaturization logically requires the storage of data in an ever-‐
decreasing space, increasing therefore the recording density.
Although the components of a magnetic hard disk are multiple (read head, write head, etc.), this chapter focuses on the implementation and study of nanostructures fabricated by NSL, which could be used as magnetic recording media. In a first step, let us consider some issues and consequences of the shaping of ferromagnetic compounds at the nanoscale.
1.1 Bulk material or isolated magnetic particles… A
difference?Ferromagnetic materials exhibit a long-‐range ordering phenomenon at the atomic level, which causes the atomic magnetic moments to line up parallel with each other in a restricted region called a domain. Within the domain, the magnetization is intense, but in a bulk sample the material will usually be demagnetized because many domains will be randomly oriented with respect to each other.
When a magnetic field is applied (Figure IV -‐ 1), the magnetization of the material increases until saturation (Ms). This process takes place in two different ways: (1) the growth of domains which are already aligned with field by shifting their walls, and (2) the coherent rotation of the domains to a direction parallel with the magnetic field.
When the magnetic field is removed, a remnant magnetization (Mr) is maintained.
The magnetization will only relax back to zero under the application of a reverse magnetic field, called coercive field* (Hc) and will reach saturation in the opposite direction (-‐Ms) by further increasing the field.
The full cycle of magnetization is obtained by changing the direction of the applied magnetic field and is complete when reaching again saturation.
The lack of retraceability in the magnetization curve is the property called hysteresis and is related to the existence of magnetic domains in the material. Once the magnetic domains are oriented, it takes some energy to turn them back again. A ferromagnetic material can possess a well-‐defined axis (the easy-‐axis) along which its magnetic moments will preferably align.
* The coercive field, also called coercivity, of a ferromagnetic material is the intensity of the applied magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has been driven to saturation. Coercivity is usually measured in oersted (Oe) or ampere/meter (A/m) units. However, due to a misuse of language, it is sometimes expressed in tesla (T), which is the unit of the magnetic induction B.
Several books[1] may inform the reader seeking additional information on the basics of magnetism.
Figure IV -‐ 1
Magnetization versus field (M-‐H loop) for a ferromagnetic material[2]
To begin, let us consider an unmagnetized sample (point 0).
(a) As the magnetic field strength is increased in the positive direction, the magnetization follows a non-‐linear magnetization curve (initial magnetization curve) and reaches the saturation level (Ms), when all the magnetic domains are aligned with the direction of the field;
(b) If the magnetic field is relaxed to zero, the ferromagnetic material retains a degree of magnetization (Mr);
(c) In order to drive the magnetization back to zero, the applied magnetic field must be reversed (-‐Hc);
(d) If the reversed magnetic field is further increased, the saturation level in the opposite direction is reached;
(e) Reducing H to zero brings the sample to a level of residual magnetism equal to that achieved in point (b) but in the opposite direction (-‐Mr);
(f) A magnetic field equal to the coercive field (HC) is needed to remove the magnetization.
The parameters described above (Hc, Ms & Mr) play a major role in the selection of materials to be used in magnetic information storage. When the easy-‐axis is well defined (large remnant magnetization along the easy-‐axis in the absence of applied field) and if the field necessary to reverse the magnetic moment is large enough, the material will be called a permanent magnet and can be used to store information. Indeed, data is stored in the media based on the two stable magnetic configurations corresponding to Mr and -‐
Mr.
The stability of the media can be evaluated on the basis of the magnetic anisotropy of the used material. The anisotropy energy describes the amount of energy required to reverse the magnetization from one stable state to the other. This depends on several factors, most importantly the effective anisotropy constant (K). The magnetic anisotropy is positively correlated with the coercivity, which is often used to provide a qualitative estimate of anisotropy of the material. The magnetic hardness parameter (κ) is often used to classify materials by measuring the relative importance of anisotropy compared with magnetostatic effects.
Magnetic Hysteresis
3Figure 1:The magnetization ’M’ vs magnetic field strength ’H’ for a ferromag- netic:
(a) starting at zero the material follows at first a non-linear magneti- zation curve and reaches the saturation level , when all the magnetic domains are aligned with the direction of a field; when afterwards driv- ing magnetic field drops to zero, the ferromagnetic material retains a considerable degree of magnetization or ”remember” the previous state of magnetization;
(b) at this point, when H = 0 a ferromagnet is not fully demagnetized and only the partial domain reorientation happened;
(c) saturation level in the opposite direction of applied field;
(d) in order to demagnetize a ferromagnetic material the strong mag- netic field of the opposite direction (called “coercive field, ‘Hc’) has to be applied.
back again. This property of ferromagnetic materials is useful as a mag- netic ”memory”. Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as ”permanent mag- nets”. The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.
Basic relations of magnetic hysteresis theory
In vacuum the generated magnetic flux density or magnetic induction is proportional to applied fieldB:
B=µ0H, (1)
whereµ0= 4π·10−7V s/Am= 1,26·10−6V s/Am. The units of the magnetic field areA/mand for the magnetic flux densityBwe haveV s/m2= 1 Tesla.
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Magnetic Hysteresis
3Figure 1:The magnetization ’M’ vs magnetic field strength ’H’ for a ferromag- netic:
(a) starting at zero the material follows at first a non-linear magneti- zation curve and reaches the saturation level , when all the magnetic domains are aligned with the direction of a field; when afterwards driv- ing magnetic field drops to zero, the ferromagnetic material retains a considerable degree of magnetization or ”remember” the previous state of magnetization;
(b) at this point, when H = 0 a ferromagnet is not fully demagnetized and only the partial domain reorientation happened;
(c) saturation level in the opposite direction of applied field;
(d) in order to demagnetize a ferromagnetic material the strong mag- netic field of the opposite direction (called “coercive field, ‘Hc’) has to be applied.
back again. This property of ferromagnetic materials is useful as a mag- netic ”memory”. Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as ”permanent mag- nets”. The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.
Basic relations of magnetic hysteresis theory
In vacuum the generated magnetic flux density or magnetic induction is proportional to applied fieldB:
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Two main cases are apparent: magnetically soft samples, with a hardness parameter κ ≪ 1, and magnetically hard samples, with larger values of κ.
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Parallel to the research on materials is the intense development of new-‐shaped structures such as magnetic nanoparticles as candidates for the media of future magnetic data storage systems. As illustrated in Figure IV -‐ 1, bulk magnets are composed of many domains that form in an effort to minimize the magnetostatic energy of the material. The magnetostatic energy can further be reduced through the formation of closure domains, where the magnetization has a direction approximately parallel to the surface of the sample. A scheme of a simplified domain configuration is shown in Figure IV -‐ 2.
Figure IV -‐ 2
Simplified scheme of magnetic domain configuration in (a) Multi-‐domain and (b) single-‐domain particles.[3]
By reducing the particle size to the nanoscale, the transition from multi-‐domain to single-‐domain is reached, as the energy required to make a domain wall is larger than the decrease in magnetostatic energy resulting from dividing the grain into two domains.
Like bulk ferromagnets, an array of single-‐domain magnetic nanoparticles can exhibit hysteresis in the M-‐H loop. However, the main difference between a bulk magnetic material and an array of magnetic nanoparticles lies in the mechanism by which the magnetization is cycled through the hysteresis loop. In a single-‐domain nanoparticle, domain wall movement is not possible and only coherent magnetization rotation can be used to overcome the effective anisotropy (K) of the particle. The behavior of uniformly magnetized, non-‐interacting single-‐domain particles was identified by Stoner &
Wohlfarth.[4]
In the case of soft magnetic particles, a vortex arrangement of magnetic moments is favored in between the single-‐ and multi-‐domain regimes. This type of magnetic domain will be further detailed with the study of Co nanostructures in section 3.3.2.
For particles of hard material, the vortex-‐domain state isn’t favored for any range of diameters. These magnetic domains are illustrated in Figure IV -‐ 3.
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Figure 1. Schematic of magnetic domain configuration for a) multi-domain and b) single domain ferromagnets.
The transition from multi-domain to single domain becomes very apparent when one considers the coercivity as a function of particle size as shown in Fig. 2 below.
Particle diameter (Arbitrary units)
n M U)
'z I 0 0 3
Figure 2. Coercivity as a function of particle size.
I"'.,'- -Ir'"I'. .'I..'.I
: single-domain multi-domain 1
For large sizes the particles are multi-domain becoming more bulk-like with increasing size. The mechanism of magnetization reversal is domain wall nucleation and motion for the multi-domain case [I]. As the particle size is reduced the increase of energy due to domain wall formation dominates over the decrease in energy attributed to the formation of domains. Thus, below a critical particle size domain walls will no longer
* -
0 50 100 150 200 250 300
M. .IBonder et al.
Figure 1. Schematic of magnetic domain configuration for a) multi-domain and b) single domain ferromagnets.
The transition from multi-domain to single domain becomes very apparent when one considers the coercivity as a function of particle size as shown in Fig. 2 below.
Particle diameter (Arbitrary units)
n M U)
'z 3 I 0 0
Figure 2. Coercivity as a function of particle size.
I"'.,'- -Ir'"I'. .'I..'.I
: single-domain multi-domain 1
For large sizes the particles are multi-domain becoming more bulk-like with increasing size. The mechanism of magnetization reversal is domain wall nucleation and motion for the multi-domain case [I]. As the particle size is reduced the increase of energy due to domain wall formation dominates over the decrease in energy attributed to the formation of domains. Thus, below a critical particle size domain walls will no longer
* -
0 50 100 150 200 250 300
!%#$
The importance of particle size to its magnetic behavior becomes very apparent when one considers the coercivity as a function of particle size as shown in Figure IV -‐ 4.
Generally, a single-‐domain state is associated with a higher coercivity than the multi-‐
domain state.
Figure IV -‐ 3
Possible magnetic domains in a spherical magnetic particle
(a) Single-‐domain particle; (b) Multi-‐domain particle; (c) Vortex-‐domain particle.[3]
Figure IV -‐ 4
Schematic evolution of magnetic coercivity with size of particle, highlighting four regimes: (a) superparamagnetic (SPM) regime with 0<Diameter<DSPM ; (b) ferromagnetic single-‐domain particle with DSPM<Diameter<D0, (c) vortex-‐domain state for D0<Diameter< D1 (only for soft magnetic materials) and (d) multi-‐domain state for Diameter>D1.[3]
Taking into account only two possible spin arrangements, single-‐domain and two domains separated by a domain wall, the single-‐domain critical diameter (!!"!") between these two regimes for a spherical particle is given by the following expression.
!!"!" = !" ! !"
!!!! (Equation IV -‐ 2)
62 3 Magnetism of Small Particles
Coercivity
Diameter
Dcr D0
0
a b c d
D1 SPM
Fig. 3.5.Curve of coercivity vs. size of magnetic particle, showing four regimes: (a) super- paramagnetic 0<D<Dspmcr , (b) ferromagnetic single-domain, forDspmcr <D<D0, (c) vortex state, forD0<D<D1(for soft magnetic samples) and (d) multidomain, forD>D1=Dcr
10 100
Diameter Hc(Oe)
1000 10000
10 nm 100 nm 1µ 10µ 100µ
CoO Fe O2 3
Co (76 K)0 Fe (76 K)0
Fe O3 4 BaO 6 Fe O2 3
Fig. 3.6. Dependence of the magnetic coercivity with size of different magnetic small parti- cles. (Reprinted (re-drawn) with permission from [37]. Copyright (1961), American Institute of Physics)
!"#$%&'()*+"#, -.%/"',
()*+"#,
!/+0%&,
!.1&2' 1+2+*+$#&/"3,
4)&23"5"/6,
7"+*&/&2,,
8)2/&9', ()*+"#,
DcrSPM D0 D1
64 3 Magnetism of Small Particles
a b c
Fig. 3.7. Three possible spin configurations for the lowest energy state of a spherical magnetic particle: (a) single-domain, (b) two-domain structure and (c) vortex
is the magnetostatic energy. The magnetostatic energy for a single-domain sphere is given, using (2.102), p.49:
Ea=−1
2µ0Hd·MV=1 6µ0Ms2 4
3πR3. (3.1)
A dimensionless quantity can be obtained fromEa, dividing byµ0Ms2V, whereV is the volume of the particle: the result,ga=1/6, does not depend on the radius of the particle.
For the configuration with two domains, on the other hand, the magnetic field at a distance from the particle will be reduced, since it will represent a field due to two opposing dipoles. One can therefore, to a first approximation, ignore the mag- netostatic term. In the domain wall, the region separating the two domains, there will be contributions from exchange and anisotropy. Inside the two domains, these terms are again zero, since the magnetic moments are aligned along the anisotropy axis. Assuming that the magnetic moments in the wall turn outside the plane, two components ofm(which is a vector of unitary length) vary of the order of 1 in a distance of the order of∆/2, where∆is the domain wall width parameter. There- fore,(∇m)2≈(∆m/∆x)2∼2(2/∆)2. Considering that the domain wall occupies a fraction of the order of∆/Rof the volume of the sphere, the exchange energy, from ((2.54), p.35), isEex≈(8A/∆2)(∆/R). The anisotropy energy of the moments inside the volumeVdof the domain wall,K1sin2θ·Vd=K1(1/2)(∆/R)V, where we have used the average sin2θ=1/2.
Therefore, the energy corresponding to the arrangement with two domains is Eb≈1
R
!8A
∆ +K1∆ 2
"
V. (3.2)
The variable ∆ can be eliminated by minimizing the energy, i.e., solving dE/d∆=0. The solution is
∆s=4
#A
K1 =4∆, (3.3)
(a) (b) (c)
-‐ 101 -‐
In this expression, A is the exchange stiffness constant†, K is the anisotropy constant, Ms is the saturation magnetization and μ0 is the vacuum magnetic permeability.
For most magnetic materials, this diameter is in the range of 10-‐100 nm. However, the limit can reach several hundred nanometers for high-‐anisotropy materials.[5]
However, if nothing is mentioned about the hardness of the material, the vortex state has to be considered. Brown has developed expressions for the critical diameters between the different regimes. The following equations report for the calculations of D0 and D1 mentioned in Figure IV -‐ 4. D0 represents the upper-‐limit of the single-‐domain configuration, while the critical diameter for a transition from vortex to multi-‐domain for a soft-‐magnetic material is given by D1.
D! = 7.211 !"
!!!!! (Equation IV -‐ 3)
!! =
!.!"#$ !!
!!!!!
!!!.!"#$ !!
!!!!!
(Equation IV -‐ 4)
One should note that the values of the parameters that appear in the literature present a wide dispersion, reflecting the experimental uncertainty of some magnetic quantities, for example, in the estimate of the exchange stiffness constant A. Moreover, those models are based on spherical particles, which can explain the difference in case of particles with other shapes. However, it is obvious that the critical single-‐domain diameter increases with anisotropy (Figure IV -‐ 5).
Figure IV -‐ 5
Critical single-‐domain diameters versus modulus of the anisotropy constant for several magnetic materials, showing the correlation between these two parameters.[5]
† The exchange constant (A) describes the strength of the exchange interaction inside a ferromagnetic system. In solids, the electronic orbitals of neighboring atoms overlap, which leads to the correlation of electrons. This results in the interatomic exchange interaction that makes the total energy of the crystal depend on the relative orientation of spins localized on neighboring atoms. The exchange interaction is the largest magnetic interaction in solids (≈1eV) and is responsible for the existence of parallel, i.e. ferromagnetic, and antiparallel, i.e.
antiferromagnetic, spin alignment.
50 2 Magnetic Domains
Fig. 2.11.Critical single-domain diameters versus modulus of the anisotropy constant for several magnetic materials, showing the correlation between these two quantities. It is evident that the critical diameters increase with increasing|K| [13]. (Reproduced from [13] with permission from Wiley)
Therefore, as expected, if the domain wall energy increases, the critical single- domain diameter will also increase. In other words, if the price paid for the creation of a domain wall increases, the single-domain configuration will remain energetically more favorable up to larger diameters.
A more accurate value for the parameterα, which gives an estimate for the re- duction in magnetostatic energy in the case of a spherical particle isα=0.472 [8].
Values of critical single-domain diameters computed using this value ofαare given in Table2.9. These critical diameters depend, from (2.105), on the value (the abso- lute value) of the anisotropy constantK1, and this dependence is shown, for several materials, in Fig.2.11.
2.4.2 Domain Wall Motion
A magnetic field applied to a multidomain sample will, in principle, induce a dis- placement of the magnetic domain walls. Consider, for example, the 180◦domain wall between two magnetic domains shown in Fig.2.9. A magnetic field applied in thezdirection will create a torque on the magnetic moments inside the wall; this will generate a magnetization component perpendicular to the plane of the wall (theyz plane). This component, in its turn, creates a demagnetizing field also perpendicular
!!!""#$%&'()%
*+,-,./0%1,2304'56&/,2%5,/&4-4+""2&)%
As the particle diameter further decreases, loss of data due to thermal instability (superparamagnetic effect) may arise. Superparamagnetism refers to the influence of thermal energy on a ferromagnetic nanoparticle. In the superparamagnetic size regime the moments of the nanoparticle fluctuate due to thermal energy. This fluctuation tends to randomize the moments of the nanoparticle unless a magnetic field is applied.
Considering an uniaxial single-‐domain magnetic particle, the two states of magnetization are separated from each other by an energy barrier, KV, where K and V stand respectively for the anisotropy constant of the material and the particle volume. If the thermal energy, kBT, becomes comparable to the barrier height, the magnetization is no longer stable and the particle is said to be superparamagnetic. This thermally activated switching follows the Arrhenius-‐Neel equation (Equation IV -‐ 5) where f is the frequency of switching between magnetization states, τ is the relaxation time and fo is the proportionality constant equal to 10-‐9s-‐1.
!= !! =!! !!!!"!! (Equation IV -‐ 5)
By fixing τ to 100 s (which is roughly the time to measure the remanence of a sample), the superparamagnetic critical volume can be obtained (!!"!"# = (25!!!) !) and used to calculate the superparamagnetic critical diameter (Equation IV -‐ 6).
!!"!"# = !
! !!"!"# !! (Equation IV -‐ 6)
Table IV -‐ 1 gives some values of the single-‐domain critical diameter (!!"!") and the superparamagnetic critical diameter for different spherical particles.
Moreover, the size and shape of a patterned thin film may also strongly influence its magnetic behavior.
Many methods can be used to synthesize magnetic structures from sub-‐micron scale to nanometer dimensions. Both top-‐down and bottom-‐up strategies have been reported in
Table IV -‐ 1
Critical single-‐domain diameter (DSD) and critical superparamagnetic diameter (DSPM) for spherical particles composed of different materials.[ 5]
Material !!"!" (nm) !!"!"# (nm)
Fe3O4 12 4
Fe 19 16
Ni 54 35
Co 96 8
Nd2Fe14B 21 4
FePt 340 3
SmCo5 1170 2
the literature, forming either periodic structure (such as arrays of various shaped elements) or isolated single nanodots.
Due to the small size of the nanostructures, their magnetic characterization is not easy to perform and do require sensitive methods.
Among those materials, Co and FePt will be further studied through this thesis.
1.2. Studied Materials
1.2.1 FePt
Crystallographic structures and phase diagram of Fe-‐Pt alloys
Recent reviews[6, 7], focused on the present reality and evolution of magnetic data storage, clearly highlighted that one of the most promising candidates for high-‐density magnetic recording was the face-‐centered tetragonal (fct) L10 phase of FePt. For most applications, a permanent magnet should have not only optimised magnetic properties, but also appropriate nonmagnetic properties (electrical, mechanical, corrosion behavior etc.).
Modern permanent magnet materials are based on intermetallic compounds of rare earths and 3d transition metals with very high magnetocrystalline anisotropy, such as Nd2Fe14B and SmCo5.[8, 9] Distinct advantages of Fe-‐Pt alloys are, as opposed to the rare-‐
earth-‐transition-‐metal-‐based compounds, that they are very ductile and chemically inert.[10] Since the mid-‐1930s,[11] Fe-‐Pt alloys are known to exhibit high coercivities due to high magnetocrystalline anisotropy of the L10 FePt phase, but the high price prevented widespread applications of these alloys.
Depending on the Fe to Pt elemental ratio, iron-‐platinum alloys can display chemically disordered‡ face centered cubic (fcc) phase (A1, Fm3m) or chemically ordered phases, such as (L12, Pm3m) for Fe3Pt, face centered tetragonal (fct) phase (L10, P4/mmm) for FePt and (L12, Pm3m) for Pt3Fe. The L12 structure is a cubic phase that can form around a 1:3 stoichiometry. In Fe3Pt (FePt3), the Pt (Fe) atoms occupy the cube corners and the Fe (Pt) atoms occupy the face-‐centre positions.
The structure variations (Figure IV -‐ 6) have dramatic effects on the magnetic properties of the alloys. For example, the Fe3Pt material is paramagnetic, the FePt3 is antiferromagnetic, the FePt (A1) phase presents a very small magnetic anisotropy and displays soft magnetic properties while the FePt (L10) phase, which is made of an alternate stacking of Fe and Pt planes, has a large uniaxial magnetocrystalline anisotropy[12] (K ≅ 7.106 J/m3) and shows strong ferromagnetic properties.
‡ Chemically disordered (versus chemically ordered) indicates that any atomic site in the unit cell has an equal chance of being occupied either by iron or platinum atom.
