Geometrical Dependence of Domain-Wall Propagation and Nucleation Fields in Magnetic-Domain-Wall Sensors

We study the key domain-wall properties in segmented nanowire loop-based structures used in domain-wall-based sensors. The two reasons for device failure, namely, distribution of the domain-wall propagation field (depinning) and the nucleation field are determined with magneto-optical Kerr effect and giant-magnetoresistance (GMR) measurements for thousands of elements to obtain significant statistics. Single layers of ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$, a complete GMR stack with ${\mathrm{Co}}_{90}{\mathrm{Fe}}_{10}/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ as a free layer, and a single layer of ${\mathrm{Co}}_{90}{\mathrm{Fe}}_{10}$ are deposited and industrially patterned to determine the influence of the shape anisotropy, the magnetocrystalline anisotropy, and the fabrication processes. We show that the propagation field is influenced only slightly by the geometry but significantly by material parameters. Simulations for a realistic wire shape yield a curling-mode type of magnetization configuration close to the nucleation field. Nonetheless, we find that the domain-wall nucleation fields can be described by a typical Stoner-Wohlfarth model related to the measured geometrical parameters of the wires and fitted by considering the process parameters. The GMR effect is subsequently measured in a substantial number of devices (3000) in order to accurately gauge the variation between devices. This measurement scheme reveals a corrected upper limit to the nucleation fields of the sensors that can be exploited for fast characterization of the working elements.

Figure 1

(a) Schematic of the structure, with three loops represented. (b) Atomic-force-microscopy image of a ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ wire of 300-nm nominal width. (c) Scanning-electron-microscopy image of a ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ wire of 300-nm nominal width.

Figure 2

Schematic representation of the field sequences for the measurement of the propagation and nucleation fields for a simplified device based on two turns. (a)–(d) Propagation field. (a) The sensor is in the initial state with a pair of domain walls in it. The propagation-field measurement can be carried out for any state of the sensor (filled with DWs or empty). (b) The field is rotated clockwise and is increased to inject domain walls from the nucleation pad at each 180° turn. (c) The nucleated domain wall should continue to propagate around the corners and farther into the device as the field rotation continues. As long as the wall continues to propagate, the field is kept constant; however, if pinning is detected, the field is increased to sustain the propagation. (d) The device is entirely filled up with domain walls at all alternate corners in the structure. (e)–(g) Nucleation-field measurement. (e) An empty state for the initial configuration is obtained by rotating the field counterclockwise with a field higher than the propagation-field value. (f) The field is increased and rotated counterclockwise until a nucleation event occurs. (g) The final state with a filled sensor.

Figure 3

Propagation and nucleation fields for the investigated samples. The boxes associated with the data points in the plot represent 25% (first quartile) to 75% (third quartile) of the distribution. The whiskers or dashed lines represent 5%–25% and 75%–95%. In this manner, the plot represents the key features of the entire distribution. The round points represent the average value of the propagation, while the diamonds represent the nucleation field. (a) Plot of the nucleation- and propagation-field values as a function of the width of the wire for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (28 nm) and ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (32 nm). The black line is the pure Stoner-Wohlfarth behavior for ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (32 nm). The blue and green lines represent the adapted model fitted with a scaling constant $C=0.7$. (b) Similar plot as (a) for ${\mathrm{Co}}_{90}{\mathrm{Fe}}_{10}$ (17 nm).

Figure 4

Simulation results of the nucleation field as a function of the minimum width of the wire. The green and blue full line represent the Stoner-Wohlfarth (SW) model for the ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (28 nm) and ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (32 nm), respectively. The dashed lines are the SW model with a scaling factor $C=0.9$. A simulation snapshot of the magnetization is taken at a field just 1 mT below the nucleation field value of a 200-nm-wide wire of ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ (32 nm).

Figure 5

Nucleation field of the device as a function of the resistance. The different nominal widths are represented by different colors: 350 (blue), 300 (red), 250 (green), and 200 nm (purple).