2. EXPERIMENTAL TECHNIQUES
useful association of the two images. Lift Mode AFM operates by first scanning a line on the sample surface in Tapping Mode to obtain the topographical information. Then, the tip is lifted to a distance above the sample set by the operator and the same line retraced in a non-contact mode to obtain (for example) near surface magnetic field information. The process is repeated until the scan is complete and both images are saved. To perform MFM, a ferromagnetic tip and a ferromagnetic or paramagnetic sample are required. In the standard MFM experiment, the phase shift ( ), of the cantilever oscillation is related to the force (F) experienced by the tip due to the magnetic stray field (H) generated by the sample according to the expression:
= Q
K
@Fz
@z = Q
K
@2Hz
@z2 (2.3)
where Q is the quality factor of the oscillation, K is the force constant of the cantilever and z the distance between the tip and the sample. Bright and dark regions in the MFM images correspond to the opposite out-of-plane components of the magnetization vector.
Lift Mode AFM can also be used to record topography and electric fields or phase imaging data.
In this work sample surface morphology has been investigated by a Dimension 3100 Atomic Force Microscope (AFM) equipped with a Nanoscope IVa controller (Veeco Instruments) and to obtain magnetic information MFM mode has been used. The AFM technology provides scientists with a powerful tool to characterize a variety of sample surfaces. Minimal sample preparation, use in ambient conditions, and the ability to image nonconducting specimens at the atomic scale (in some cases) makes AFM an extremely versatile and useful form of microscopy.
2.4 Magnetic analysis
2.4.1 Alternating Gradient Force Magnetometry
An AGFM is a highly sensitive measurement system, capable of measuring hysteresis properties on a wide range of sample types and strengths, in particular allows good sensitive (10 8 emu) magnetic measurements on thin film samples. The principle is based on the detection of the oscillation amplitude of a sample fixed on a quartz probe which vibrates in a small alternative gradient field. In an AGFM an alternating gradient field is utilized to exert a periodic force on a sample placed in an AC field. The force is proportional to the magnitude of the gradient field and the magnetic moment of the sample. The force deflects the sample and this deflection is measured by a piezoelectric sensing element mounted on the probe arm. The output signal from the piezoelectric element is synchronously detected at the operating frequency of the gradient field.
Operating near the mechanical resonant frequency of the assembly enhances the signal from the piezoelectric element. This device allowing magnetic measurements up to 20 kOe good sensitivity and can measure samples with a total magnetization as small as 10 6 emu. Due to the high resonance frequency (typically some hundred Hz) the acquisition time is short (some minutes). The measurements can be done with a field parallel or perpendicular to the film plane.
2.4.2 SQuID
A SQuID (Superconducting Quantum Interference Device) is the most sensitive avail-able device for measuring magnetic fields, these magnetometers are used to characterize materials when the highest detection sensitivity over a broad temperature range and using applied magnetic fields up to several Tesla is needed. Nowadays, this instrument is widely used worldwide in research laboratories. The system is designed to measure the magnetic moment of a sample, from which the magnetization and magnetic suscep-tibility can be obtained. Therefore, SQUID magnetometers are versatile instruments that perform both, DC and AC magnetic moment measurement. The core of instru-ment consists of two superconductors separated by thin insulating layers to form two parallel Josephson junctions (Fig. 2.8). The device may be configured as a magne-tometer to detect small magnetic fields. The great sensitivity of the SQUID devices is associated with measuring changes in magnetic field associated with one flux quantum.
One of the discoveries associated with Josephson junctions was that flux is quantized
2. EXPERIMENTAL TECHNIQUES
in units
Figure 2.8: - Schematic representation of a SQuID circuit working
0 = h
2e = 2.07· 10 15T m2 (2.4)
If a constant biasing current is maintained in the SQUID device, the measured volt-age oscillates with the changes in phase at the two junctions, which depends upon the change in the magnetic flux. Counting the oscillations allows you to evaluate the flux change which has occurred. The main components of a SQUID magnetometer are: (a) superconducting magnet; (b) superconducting detection coil which is coupled induc-tively to the sample; (c) a SQUID connected to the detection coil.
2.4.2.1 Anomalous Hall E↵ect (AHE).
The stronger e↵ect that Hall discovered in ferromagnetic conductors came to be known as the anomalous Hall e↵ect (AHE). Considering a magnetic film, when a magnetic field is applied perpendicularly to the film plane and a current is injected in the x direction, in addition to the transversal voltage proportional to the applied magnetic field that corresponds to the ordinary Hall e↵ect (OHE), appears a term derived from the spontaneous magnetization of the material. This additional contribution is the
2.4 Magnetic analysis
AHE. Hall voltage for the configuration illustrated in figure 2.9 is given by:
VH = R0I
t Bcos↵ +µ0RSI
t M cos✓ +KI
t M2sin2✓sin2 (2.5) where M cos✓ is the perpendicular component (normal to the film-plane) of the mag-netization (Mz), M sin✓ is the in-plane component (Mxy), I is the applied current, and t is the film thickness. Bcos↵ is the component of the applied magnetic flux density in the direction perpendicular to the current (i.e., along the film normal). When the applied magnetic field is perpendicular to the film plane, the Hall resistivity can be written as a sum of the OHE contribution, proportional to the applied magnetic field, and the AHE contribution proportional to the magnetization of the material, which is in general larger than the first term in ferromagnets:
⇢H = ⇢xy = µ0(R0Hz+ RaMz) (2.6) where only component along the perpendicular z-axis are considered.
Based on the large collections of experimental results and indications from some theo-retical calculations, it is now becoming accepted that there are at least three di↵erent regimes for the behavior of AHE. The origin of the AHE has been explained by the
KUMAR AND LAUGHLIN: INVESTIGATING THE MAGNETIZATION PROCESS OF THE STORAGE LAYER 1201
relation. This suggests that the proposed methodology may be utilized to extract and evaluate the magnetic properties of the RL even when it is not possible to use the MOKE system, as will be the case in ultra-thin RL films wherein the incident laser penetrates into the SUL as well.
II. EXPERIMENTALPROCEDURE
HITPERM nanocrystalline alloy was used as the SUL in this study. The preparation and properties of SUL films of this alloy is described in our earlier work [5], [6]. The SUL films of 100 nm (nominal) thickness were sputtered under radio-frequency conditions on 7059 Corning glass substrates at 4.5 W/cm sputter power density. Fe–Pt (52–54 at % Fe) thin films of 30 nm (nominal) thickness were sputtered from a composite target and constituted the RL. Cr–Pt ( 5 at % Pt) films ( 80 nm thick) were used as seed layers to promote the (002) perpendicular texture formation in the Fe–Pt RL. Previ-ously, we have reported on the preparation of (002) textured phase Fe–Pt using Cr as seed layer [7]. A thin Pt film ( 3 nm) was used as buffer layer between the Fe–Pt RL and the Cr–Pt seed layer. While the HITPERM SUL was prepared at room temperature (RT), the Cr–Pt, Pt, and Fe–Pt films were deposited in situ at 250 C–280 C. Single-layered films of Fe–Pt were also prepared for purposes of comparison. In this case, 50-nm-thick films were sputter-deposited in situ at 250 C–280 C. Measurements of the Hall voltage were made on square samples using the Van der Pauw method with an applied current of 25 mA. A VSM and a custom-built MOKE system (at Seagate Research, Pittsburgh) were both employed to evaluate and compare the magnetic properties with that obtained using the Hall technique. Structural analysis was performed using X-ray diffractometry (XRD) with Cu radiation.
III. EVALUATIONMETHODOLOGY
The Hall voltage in a magnetic thin film is given by the following expression [8], for the configuration illustrated in Fig. 1:
(1) where is the perpendicular component (normal to the film-plane) of the magnetization , is the in-plane component , is the applied current, and is the film thick-ness. is the component of the applied magnetic flux den-sity in the direction perpendicular to the current (i.e., along the film normal). Although is defined in Fig. 1 to be the angle between the directions of and in the plane, in this work, we shall mention only the nominal value of , which is defined to be the angle between the current and the projection of the applied field onto the plane.
Fig. 1. Schematic of the configuration for measurement of the Hall voltage in a thin film structure.
scattering of conduction electrons from the magnetic moments in the sample. can be much larger than in magnetic metals, due to the high density of carriers at RT conditions.
The third term is from the planar Hall effect, which is a pseudo Hall effect because it actually has its origin in anisotropic magnetoresistance (AMR). The constant is related to the difference in resistivity between the directions parallel to and perpendicular to the magnetization. The technique to distin-guish and extract the AHE and the PHE components is based on the fact that the two have different symmetries with regard to the applied field . The components with “odd” and “even”
symmetries in the characteristics of a ferromagnetic thin film correspond to the perpendicular component (AHE term) and the square of the in-plane component (PHE term) of magnetization, respectively. Assuming that the NHE is negli-gible, this suggests that the component with even symmetry can be eliminated by subtracting the output signals of for the applied field from those of the corresponding points for . The “odd” component of the Hall voltage is then obtained as
(2)
In a similar manner, the component with odd symmetry can also be eliminated by adding the corresponding portions of for and , to get the “even” component of the Hall voltage.
Now, the “odd” component of the Hall voltage that corre-sponds to the AHE output is due to the perpendicular compo-nent of magnetization in both the RL and the SUL. In such a scenario, we propose a simple model in which it is assumed that that an effective perpendicular magnetization averaged over the total thickness is the source of the AHE. In other words, we assume that the entire film-stack behaves as a single layer of magnetic thin film, at least as far as the AHE is concerned. Fur-thermore, in this model, we shall assume that the perpendicular magnetization behavior of the SUL does not depend on the ex-istence of the RL. With these two assumptions, we shall derive an expression for the perpendicular (i.e., along the film-normal)
Figure 2.9: - Schematic of the configuration for the measurement of Hall voltage (VHall) in a thin film. After [94].
most recent theory by S. Onoda et al. [95], which distinguished these three regimes as a function of the longitudinal conductivity ( xx). A regime with extremely high conductivity ( xx > 106⌦ 1cm 1 in which AHxy ⇠ xx, skew scattering dominates over
AH, and the anomalous Hall angle H/ xx is constant; an intrinsic or scattering-independent regime, in which xyAH is roughly independent of xx. At lower conductivi-ties (104⌦ 1cm 1 < xx< 106⌦ 1cm 1) and bad-metal regime in which xyAH decreases
71
2. EXPERIMENTAL TECHNIQUES
with decreasing xxat a rate faster than linear ( xx < 104⌦ 1cm 1). In this last regime a scaling H / xxn with 1.6 < n <1.8 has been reported experimentally. For metallic thin films exhibiting this approximate scaling, it is natural that H is suppressed by the strong disorder (excluding weak localization corrections).
An AHE measurement facility has been implemented in the SQuID magnetometer at the IMEM institute. Since VHall /MZ, hysteresis loops with applied magnetic field perpendicular to the film plane are measured after capping the samples with Au thin film, in order to allow electrical conduction. The Hall voltage is measured on square (3 mm⇥ 3 mm) samples at right angles to the applied current in the film plane, fol-lowing van der Pauw method. The applied current is 1 mA and the perpendicular magnetic field up to 5.5 T. Measurements are repeated exchanging the contacts, thus the resulting measurement is a mean on four di↵erent contacts configurations.