WO2023244174A1

WO2023244174A1 - Magnetometer and a method for measuring vector components of a magnetic field using the magnetometer

Info

Publication number: WO2023244174A1
Application number: PCT/SG2023/050417
Authority: WO
Inventors: Yihong Wu; Xin Chen; Hang Xie
Original assignee: National University Of Singapore
Priority date: 2022-06-15
Filing date: 2023-06-13
Publication date: 2023-12-21

Abstract

A magnetometer for measuring vector components of a magnetic field is described in an embodiment. The magnetometer comprising: a first section comprising a first magnetic layer; and a second section comprising a second magnetic layer, the second section being in-plane with and at an angle to the first section and is electrically connected to the first section. The first magnetic layer and the second magnetic layer each has a perpendicular magnetic anisotropy with near zero hysteresis, and are adapted to generate a first and second anomalous Hall voltage, respectively, in response to oscillatory spin-orbit torques generated in the respective magnetic layer and the magnetic field. The oscillatory spin-orbit torques are generated in response to an alternating current passing through the first magnetic layer and the second magnetic layer. The first anomalous Hall voltage includes a first second-harmonic Hall voltage associated with a first in-plane vector component of the magnetic field and the second anomalous Hall voltage includes a second second-harmonic Hall voltage associated with a second in-plane vector component of the magnetic field. The first in-plane vector component being in-plane with and at the angle to the second in-plane vector component. The first anomalous Hall voltage or the second anomalous Hall voltage includes a first-harmonic Hall voltage associated with an out-of-plane vector component of the magnetic field. A method for measuring vector components of a magnetic field using the magnetometer is also described.

Description

Magnetometer and a method for measuring vector components of a magnetic field using the magnetometer

Technical Field

The present disclosure relates to a magnetometer and a method for measuring vector components of a magnetic field using the magnetometer.

Background

Advancements in magnetic sensing have contributed immensely to a wide range of scientific and technological fields from fundamental physics, chemistry and biology to practical applications such as data storage and medical imaging. However, the ability to measure a vector magnetic field with high spatial resolution using a single magnetic sensor remains elusive. Compact and low-cost magnetic sensors such as Hall and magnetoresistance (MR) sensors are commercially available, but these sensors typically detect a magnetic field only in a specific direction. To detect magnetic field components in three orthogonal directions in space, a common method is to integrate three individual magnetic sensors whose detection axes are orthogonal to one another or to use a magnetic flux guide to change a direction of one of the field components.

An example of a triaxial Hall sensor consists of three sets of uniaxial Hall sensors being placed orthogonal to one another. However, assembling three elements into a triaxial magnetometer requires sophisticated engineering expertise and the resultant product is often bulky and costly. Another example is to place three Hall sensors on a planar surface and to incorporate magnetic flux concentrators (MFC) or guides to change the flux directions of specific magnetic field components so that they can be detected by the Hall sensors on the planar surface. However, the accuracy of these sensors depends strongly on the shape and/or dimension of the MFC or guide and its alignment with the Hall sensors. Further, the use of either multiple sensors or bulky magnetic flux concentrators results in high costs and low spatial resolution, high noise, and crosstalk among the measurement axes. Apart from Hall sensors and MR sensors, a triaxial magnetometer can also be realized using other types of magnetic sensors, such as a nitrogen-vacancy (NV) magnetometer. However, the NV-magnetometer requires sophisticated and expensive optics and microwave sources to operate, making it unsuitable for general and cost-sensitive applications. It is therefore desirable to provide a magnetometer and a method for measuring vector components of a magnetic field using the magnetometer which address the aforementioned problems and/or provides a useful alternative. Further, other desirable features and characteristics will become apparent from the subsequent detailed description and the appended claims, taken in conjunction with the accompanying drawings and this background of the disclosure.

Summary

Aspects of the present application relate to a magnetometer and a method for measuring vector components of a magnetic field using the magnetometer.

In accordance with a first aspect, there is provided a magnetometer for measuring vector components of a magnetic field, the magnetometer comprising: a first section comprising a first magnetic layer; and a second section comprising a second magnetic layer, the second section being in-plane with and at an angle to the first section and is electrically connected to the first section, the first magnetic layer and the second magnetic layer each having a perpendicular magnetic anisotropy with near zero hysteresis; wherein the first magnetic layer is adapted to generate a first anomalous Hall voltage in response to a first oscillatory spin-orbit torque and the magnetic field and the second magnetic layer is adapted to generate a second anomalous Hall voltage in response to a second oscillatory spin-orbit torque and the magnetic field, the first oscillatory spin-orbit torque and the second oscillatory spin-orbit torque being generated in the first magnetic layer and the second magnetic layer respectively in response to an alternating current passing through the first magnetic layer and the second magnetic layer, wherein the first anomalous Hall voltage includes a first second-harmonic Hall voltage associated with a first in-plane vector component of the magnetic field and the second anomalous Hall voltage includes a second second- harmonic Hall voltage associated with a second in-plane vector component of the magnetic field, the first in-plane vector component of the magnetic field being in-plane with and at the angle to the second in-plane vector component of the magnetic field, and wherein the first anomalous Hall voltage or the second anomalous Hall voltage further includes a first-harmonic Hall voltage associated with an out-of-plane vector component of the magnetic field, the out-of-plane vector component being orthogonal to the first in-plane vector component and the second in-plane vector component of the magnetic field.

By having a first section comprising a first magnetic layer and a second section comprising a second magnetic layer where the second section is in-plane with and at an angle to the first section and is electrically connected to the first section, and that the first magnetic layer and the second magnetic layer each has a perpendicular magnetic anisotropy with near zero hysteresis, the magnetometer is adapted to generate a first anomalous Hall voltage in the first section and a second anomalous Hall voltage in the second section in response to an alternating current and the magnetic field for measuring a first in-plane vector component, a second in-plane vector component and an out-of-plane vector component of the magnetic field. The aforementioned magnetometer is adapted to measure the out-of-plane (OP) component H_z, and in-plane (IP) components (H_x or H_y) of the magnetic field using a simple, single integrated device structure. The magnetometer in accordance with the present disclosure therefore require neither multiple sensors nor any magnetic flux guide or magnetic flux concentrator for redirecting flux directions of specific magnetic field components for magnetic field measurements. This circumvents potential problems in relation to conventional magnetometers, including overcoming difficulties in manufacturing, reducing manufacturing costs and improving spatial resolutions of the measured magnetic field, reducing measurement noises and crosstalk among the measurement axes of the magnetometers.

The magnetometer may be of a L-shape, and the first section and the second section may be orthogonal to each other to form two orthogonal arms of the L-shape magnetometer. The first section may comprise a first Hall cross structure for measuring the first anomalous Hall voltage and the second section may comprise a second Hall cross structure for measuring the second anomalous Hall voltage. Having the first section and the second section orthogonal or perpendicular to each other allow for simplified calculations, as compared to embodiments with the first section at an angle (other than 90°) to the second section, to obtain the measured magnetic field using the magnetometer.

The first magnetic layer may comprise a first ferromagnetic layer and a first metal layer, the first metal layer may be adapted to inject a spin current into the first ferromagnetic layer in response to the alternating current to create the first oscillatory spin-orbit torque. The first ferromagnetic layer may comprise cobalt (Co), iron (Fe), nickel (Ni), cobalt iron boron (CoFeB), or alloys of Co, Fe, Ni, Mn, Cr, Gd, Pt or Ir.

The first metal layer may comprise a heavy metal, an antiferromagnetic material, a topological insulator or a transition metal dichalcogenides (TMD). The heavy metal may comprise platinum (Pt), palladium (Pd), tantalum (Ta), tungsten (W), lead (Pb), niobium (Nb), CuPt, AuPt or NiPt. The antiferromagnetic material may include IrMn, PtMn, PtNiMn or Cr. The topological insulator may include Bi2Ses, Bi2Tes, or Sb2Tes. The transition metal dichalcogenides may include WTe2, MoTe2 or PtSe2.

A thickness of the first ferromagnetic layer may be adapted to allow the first ferromagnetic layer to be in a superparamagnetic regime.

The first magnetic layer may be the same as the second magnetic layer. By having the first magnetic layer structurally identical to the second magnetic layer, the first section and the second section of the magnetometer can be fabricated at the same time and requiring only a single calibration for both the first section and the second section. This provides ease of manufacturing and calibration of the magnetometer.

In accordance with a second aspect, there is provided a method for measuring vector components of a magnetic field using a magnetometer. The magnetometer comprises: (i) a first section comprising a first magnetic layer and (ii) a second section comprising a second magnetic layer, the second section being in-plane with and at an angle to the first section and is electrically connected to the first section, the first magnetic layer and the second magnetic layer each having a perpendicular magnetic anisotropy with near zero hysteresis. The method comprising: providing an alternating current to the magnetometer to generate a first oscillatory spin-orbit torque in the first magnetic layer and a second oscillatory spin-orbit torque in the second magnetic layer, the first oscillatory spin-orbit torque and the second oscillatory spin-orbit torque being generated in the first magnetic layer and the second magnetic layer respectively in response to the alternating current passing through the first magnetic layer and the second magnetic layer, wherein the first magnetic layer is adapted to generate a first anomalous Hall voltage in response to the first oscillatory spin-orbit torque and the magnetic field and the second magnetic layer is adapted to generate a second anomalous Hall voltage in response to the second oscillatory spin-orbit torque and the magnetic field; and measuring the first anomalous Hall voltage of the first section and the second anomalous Hall voltage of the second section, wherein the first anomalous Hall voltage includes a first second-harmonic Hall voltage associated with a first inplane vector component of the magnetic field and the second anomalous Hall voltage includes a second second-harmonic Hall voltage associated with a second in-plane vector component of the magnetic field, the first in-plane vector component of the magnetic field being in-plane with and at the angle to the second in-plane vector component of the magnetic field, and wherein the first anomalous Hall voltage or the second anomalous Hall voltage further includes a first-harmonic Hall voltage associated with an out-of-plane vector component of the magnetic field, the out-of- plane vector component being orthogonal to the first in-plane vector component and the second in-plane vector component of the magnetic field.

The first section may be integrated with the second section to form a single structure of the magnetometer.

The magnetometer may be of a L-shape and the first section and the second section may be orthogonal to each other to form two orthogonal arms of the L-shape magnetometer, and wherein the first section and the second section may be aligned with a x-axis and a y-axis in the Cartesian coordinates respectively, the first second- harmonic Hall voltage of the first section and the second second-harmonic Hall voltage of the second section are linear with respective to a x-component of the magnetic field (H_x) and a y-component of the magnetic field (H_y) respectively, and the first-harmonic Hall voltage is linear with respect to a z-component of the magnetic field (H_z).

The x-component of the magnetic field (H_x) may be determined by multiplying the first second-harmonic Hall voltage with a first pre-calibrated field coefficient, the y- component of the magnetic field (H_y) may be determined by multiplying the second second-harmonic Hall voltage with a second pre-calibrated field coefficient, and the z- component of the magnetic field (H_z) may be determined by multiplying the first- harmonic Hall voltage with a third pre-calibrated field coefficient.

Measuring the first anomalous Hall voltage of the first section and the second anomalous Hall voltage of the second section may include measuring the first second- harmonic Hall voltage, the second second-harmonic Hall voltage and the first-harmonic Hall voltage directly using lock-in techniques. It should be appreciated that features relating to one aspect may be applicable to the other aspects. Embodiments therefore provide a magnetometer and a method for measuring vector components of a magnetic field using the magnetometer. Particularly, by having a first section comprising a first magnetic layer and a second section comprising a second magnetic layer where the second section is in-plane with and at an angle to the first section and is electrically connected to the first section, and that the first magnetic layer and the second magnetic layer each has a perpendicular magnetic anisotropy with near zero hysteresis, the magnetometer is adapted to generate a first anomalous Hall voltage in the first section and a second anomalous Hall voltage in the second section in response to an alternating current and the magnetic field for measuring a first in-plane vector component, a second in-plane vector component and an out-of-plane vector component of the magnetic field. The aforementioned magnetometer and method for measuring vector components of a magnetic field using the magnetometer are therefore adapted to measure the out-of- plane (OP) H_z and the in-plane (IP) components (H_x or H_y) of the magnetic field using a simple, single integrated device structure. The magnetometer and the method for measuring vector components of a magnetic field using the magnetometer in accordance with the present disclosure therefore do not require multiple sensors nor any magnetic flux guide or concentrator for redirecting flux directions of specific magnetic field components for magnetic field measurements. This circumvents potential problems often experienced by these types of sensors, including difficulties in manufacturing, high manufacturing costs, low spatial magnetic field resolution, high noise and crosstalk among the measurement axes. Embodiments of the magnetometer in the present disclosure are able to measure all three independent magnetic field components (e.g. in the Cartesian coordinates) simultaneously without any crosstalk.

Brief of the

Embodiments will now be described, by way of example only, with reference to the following drawings, in which:

Figure 1 shows a schematic diagram of a magnetometer being placed in the presence of a magnetic field in accordance with an embodiment;

Figure 2 is a schematic diagram showing a L-shaped magnetometer formed on a silicon substrate in accordance with an embodiment; Figure 3 shows a schematic diagram of a cross-section of one of the sections or arms of the L-shaped magnetometer of Figure 2 in accordance with an embodiment;

Figure 4 is a schematic diagram showing an alternating current input to the L-shaped magnetometer of Figure 2 and outputs obtained from the L-shaped magnetometer for measuring vector components of a magnetic field in accordance with an embodiment;

Figure 5 is a flowchart showing steps of a method for measuring vector components of a magnetic field using a magnetometer in accordance with an embodiment;

Figure 6 is a diagram illustrating a sequence of measuring vector components of a magnetic field using the magnetometer of Figure 2 in accordance with an embodiment;

Figures 7 A, 7B and 7C show graphs of anomalous Hall resistance RH as a function of a perpendicular magnetic field in a z-direction for different ferromagnetic Cobalt-lron- Boron (CoFeB) layer thicknesses in accordance with an embodiment, where Figure 7A shows a graph of RH versus the perpendicular magnetic field for a CoFeB layer thickness of 1.1 nm, Figure 7B shows a graph of RH versus the perpendicular magnetic field for a CoFeB layer thickness of 1.3 nm and Figure 7C shows a graph of RH versus the perpendicular magnetic field for a CoFeB layer thickness of 1.5 nm;

Figures 8A, 8B and 8C show graphs of harmonic Hall resistances (including first- harmonic Hall resistance R and second-harmonic Hall resistance

as a function of magnetic field in accordance with an embodiment, where Figure 8A shows a graph of harmonic Hall resistances with a magnetic field in a z-direction, Figure 8B shows a graph of harmonic Hall resistances with a magnetic field in a x-direction and Figure 8C shows a graph of harmonic Hall resistances with a magnetic field in a y-direction;

Figures 9A, 9B and 9C show graphs of harmonic Hall resistances (including first- harmonic Hall resistance R^_x and second-harmonic Hall resistances Rf and R^y) as a function of magnetic field for a small magnetic field range of -100 Oe to 100 Oe in accordance with an embodiment, where Figure 9A shows a graph of the first-harmonic Hall resistance R _x as a function of the magnetic field H_z in a z-direction, Figure 9B shows a graph of the second-harmonic Hall resistance R^_x as a function of the magnetic field H_x in a x-direction and Figure 9C shows a graph of the second-harmonic Hall resistance R^y as a function of the magnetic field H_y in a y-direction; Figures 10A, 10B and 10C show schematic diagrams illustrating measurement geometries of the L-shaped magnetometer of Figure 2 for rotating magnetic fields in different planes in accordance with an embodiment, where Figure 10A shows a schematic diagram of the measurement geometry of the L-shaped magnetometer for a rotating magnetic field in a z-x plane, Figure 10B shows a schematic diagram of the measurement geometry of the L-shaped magnetometer for a rotating magnetic field in a y-z plane and Figure 10C shows a schematic diagram of the measurement geometry of the L-shaped magnetometer for a rotating magnetic field in a x-y plane;

Figures 11 A, 11 B and 11C show graphs of harmonic Hall resistances as a function of magnetic field for rotating magnetic fields in the different planes as shown in Figures 10A, 10B and 10C in accordance with an embodiment, where Figure 11A shows a graph of the first-harmonic Hall resistance R^₁ and the second-harmonic Hall resistance R^ of arm-X of the L-shape magnetometer with a magnetic field rotating in the z-x plane, Figure 11 B shows a graph of the first-harmonic Hall resistance R$₂ and the second-harmonic Hall resistance R^ of arm-Y of the L-shape magnetometer with a magnetic field rotating in the y-z plane and Figure 11C shows a graph of the second- harmonic Hall resistances R^ of arm-X and R^ of arm-Y with a magnetic field rotating in the x-y plane;

Figures 12A, 12B and 12C show graphs of measured field angle (0**., 6_yz and 0"_y) versus calculated field angle (0_zx, 6_yz and 0_xy) for rotating magnetic fields in the different planes as shown in relation to Figures 10A, 10B and 10C in accordance with an embodiment, where Figure 12A shows a graph of the measured field angle (6_ZX) versus the calculated field angle (0_ZX) for a rotating magnetic field in the z-x plane, Figure 12B shows a graph of the measured field angle (6_yz) versus the calculated field angle (0_yz) for a rotating magnetic field in the y-z plane and Figure 12C shows a graph of the measured field angle

versus the calculated field angle (0_xy) for a rotating magnetic field in the x-y plane;

Figure 13 show a photograph of an experimental setup for measuring vector components of a magnetic field generated by a permanent magnet in accordance with an embodiment; Figure 14 shows a schematic diagram illustrating a measurement configuration of the experimental setup of Figure 13 in accordance with an embodiment;

Figures 15A and 15B show three-dimensional (3D) plots of an amplitude (/-/) of a magnetic field measured using the L-shaped magnetometer of Figure 13 and simulated using the COMSOL Multiphysics® software, where Figure 15A shows a 3D plot of the amplitude (/-/) of the measured magnetic field obtained using the L-shaped magnetometer and Figure 15B shows a 3D plot of the amplitude (/-/) of the simulated magnetic field obtained using the COMSOL Multiphysics® software;

Figures 16A and 16B show three-dimensional (3D) plots of a polar angle (0_H) of a magnetic field measured using the L-shaped magnetometer of Figure 13 and simulated using the COMSOL Multiphysics® software, where Figure 16A shows a 3D plot of the polar angle ( e_H ) of the measured magnetic field obtained using the L-shaped magnetometer and Figure 16B shows a 3D plot of the polar angle (0_H) of the simulated magnetic field obtained using the COMSOL Multiphysics® software; and

Figures 17A and 17B show three-dimensional (3D) plots of an azimuthal angle (<p_H) of a magnetic field measured using the L-shaped magnetometer of Figure 13 and simulated using the COMSOL Multiphysics® software, where Figure 17A shows a 3D plot of the azimuthal angle (<p_H) of the measured magnetic field obtained using the L- shaped magnetometer and Figure 17B shows a 3D plot of the azimuthal angle (<p_H) of the simulated magnetic field obtained using the COMSOL Multiphysics® software.

Detailed description

Exemplary embodiments relate to a magnetometer and a method for measuring vector components of a magnetic field using the magnetometer.

As exemplified in the background section, the complexity of existing vector magnetometers originates from the fact that most magnetic sensors, for example Hall sensors and/or various types of MR sensors, can only detect the magnetic field in one direction. To address this, a magnetometer or magnetic sensor which can detect a magnetic field in all spatial directions simultaneously in a single-device configuration is developed in the present disclosure. Particularly, embodiments of the present magnetometer use the spin-orbit torque (SOT) effective field as a mechanism to convert a magnetic field component to another component that is perpendicular to itself. In the present embodiment, a heavy metal (HM)/ferromagnet (FM) heterostructure is used in the magnetometer to exploit this SOT effective field mechanism. Particularly, when an electric current passes through a HM/FM bilayer, non-equilibrium spins will be generated exerting a torque on the magnetization of the FM layer, namely the SOT. In general, there are two types of SOTs, termed as damping-like (DL) [T_DL <X m x (m x <?)] torque and field-like (FL) [T_FL <X (m x <?)] torque, respectively, where 8 is the spin polarization direction and m the unit vector in the magnetization direction of the FM. As will be made clear in subsequent sections, the SOT mechanism provides a means to detect all the three independent vector components of the magnetic field simultaneously using the magnetometer of the present disclosure.

Embodiments of the magnetometer exploit the field-dependence of SOT and the superparamagnetic (SP) behavior of FM in HM/FM heterostructures. The SP state allows the magnetometer to detect a vertical field component (W_z) (or out-of-plane component) of the magnetic field without any hysteresis, whereas the in-plane field dependence of the SOT enables the magnetometer to detect or measure in-plane field components, H_x and H_y, independently using the same device through the DL effective field of the SOT. As shown in subsequent description, H_z and H_x (H_y ) can be disentangled through the use of the harmonic Hall resistance measured using the magnetometer. Embodiments of the magnetometer can be implemented using simple Hall cross structures each being made of a magnetic layer (e.g. a FM/HM bilayer) with perpendicular magnetic anisotropy (PMA) and near zero hysteresis to exploit the fielddependence of SOT and the superparamagnetic (SP) behavior. In an embodiment, a magnetic layer with near zero hysteresis includes the magnetic layer having a coercivity of less than 0.01 Oe in its anomalous Hall effect (AHE) curve.

In the following description, the magnetometer was defined to be placed in the x-y plane and therefore the in-plane field components are defined as H_x and H_y, while the out-of-plane field component is defined as H_z in the z-direction. It will be appreciated by a skilled person that this, however, can change and be generalised (e.g. a plane of the magnetometer can be defined as x-z plane etc.). Further, in the present embodiments, a magnetic field, being a vector quantity, is resolved to its Cartesian components (i.e. H_x, H_y, H_z), but a skilled person would appreciate that these can be resolved in other coordinate systems. In the present disclosure, Figures 1 to 4 provide an overview of an apparatus and a magnetometer for detecting a magnetic field, with a L-shaped magnetometer being used as an exemplary embodiment, Figures 5 and 6 illustrate exemplary methods for measuring vector components of a magnetic field using the L-shaped magnetometer of Figure 2, and Figures 7A to 17B describe experiments performed in relation to an exemplary L-shaped magnetometer comprising a MgO/CoFeB/Ta/MgO/Ta heterostructure.

Figure 1 shows a schematic diagram 100 of a magnetometer 102 being placed in the presence of a magnetic field 104 in accordance with an embodiment. As shown in Figure 1 , the magnetic field 104 is a vector field having magnetic field vectors pointing at different directions within the magnetic field 104. The magnetometer 102 is adapted to measure vector components of the magnetic field 104 at specific positions or locations.

Figure 2 is a schematic diagram 200 showing a magnetometer 202 formed on a planar substrate 204 in accordance with an embodiment. The planar substrate 204 includes a silicon (Si) substrate as shown in the present example, but can include other materials or made of different materials. The planar substrate 204 provides structural support for the magnetometer 202.

The magnetometer 202 in the present embodiment is a L-shaped Hall device which includes two arms 206 and 208 aligned with the x-axis and the y-axis, respectively. The arm 206 (also referred to “arm-X” in subsequent description) is aligned with the x-axis (or in a x-direction) and the arm 208 (also referred to “arm-Y” in subsequent description) is aligned with the y-axis (or in a y-direction). Arm-X and arm-Y are therefore orthogonal arms which are in-plane and perpendicular to each other. Each of the arms 206, 208 comprises a magnetic layer which includes a Hall cross 210 and 212, respectively. In the present embodiment, the Hall crosses 210, 212 each includes a bilayer heterostructure comprising a ferromagnet (FM) layer 214 and a heavy metal (HM) layer 216.

The two in-plane field components H_x and H_y can be measured by the two Hallcrosses independently at the same time, whereas the vertical field component H_z along the z-direction can be measured from the same Hall signal of either the Hall-cross 210 or the Hall-cross 212. By doing so, all the three field components of the magnetic field can be measured or detected simultaneously. The detection and discrimination of the two in-plane field components H_x and H_y are based on the fact that the spin-orbit torque (SOT) effective field generated by an alternating current in the HM/FM bilayer is proportional to the in-plane field component along the driving current direction, which in this case is perpendicular to each other in the two arms 206, 208 of the L-shaped Hall device 202. On the other hand, the separation of contributions due to vertical and inplane field components of the Hall signal is made possible by using the harmonic technique, i.e., the in-plane and out-of-plane field components can be obtained from the first- and second-harmonic Hall signals, respectively. This is explained in more detail in the “Operation principle” section below.

Although not shown in Figure 2 for succinctness, a skilled person would understand that other material layers or material structures of the magnetometer 202 can be formed. For example, metal contact layers can be deposited on the HM/FM bilayer to form electrodes which can be connected to a current source and/or a voltmeter and/or a lock-in amplifier. Further, additional material layer(s) may also be deposited on the substrate prior to the formation of the HM/FM bilayer. For example, in an embodiment, a layer of dielectric (e.g. SiC>2) can be deposited on the silicon (Si) substrate 204 prior to the formation of the HM/FM bilayer.

Figure 3 shows a schematic diagram 300 of a cross-section of one of the sections or arms of the L-shaped magnetometer 202 of Figure 2 in accordance with an embodiment, to illustrate an interaction of the alternating current with the magnetisation in the FM layer for generating the spin-orbit torque (SOT). More particularly, a crosssection of arm-X is shown in Figure 3.

As described above, the arm-X 206 includes a magnetic layer 302 comprising a metal layer 304 and a ferromagnetic (FM) layer 306 formed on the silicon substrate 204. In the embodiments described below, the metal layer 304 includes a heavy metal (HM) layer. The HM layer includes tantalum (Ta) or platinum (Pt), and the FM layer 306 includes cobalt (Co) or cobalt-iron-boron (CoFeB). The FM layer 306 exhibits perpendicular magnetic anisotropy with a switchable magnetization direction pointing in the z direction as shown in Figure 3. In other words, the switchable magnetization direction of the FM layer 306 is in a direction out-of-plane or perpendicular to the longitudinal plane (i.e. the x-y plane of the magnetometer 202) of the magnetic layer 302. The switchable magnetization of the FM layer 306 can be in either an up-state 308 or the down-state 310 as shown in Figure 3, the up-state 308 being a state in which the switchable magnetization is in a direction perpendicular to the longitudinal plane of the magnetic layer 302 and the down-state 310 being a state in which the switchable magnetization is in an opposite direction to that of the up-state 308.

As shown in Figure 3, an alternating current 312 is provided to the magnetic layer 302, and more specifically to the metal layer 304 of the magnetic layer 302 in the present embodiment. Particularly, the metal layer 304 is adapted to inject a spin current into the ferromagnetic layer 306 in response to the alternating current to create an oscillatory spin-orbit torque to switch the switchable magnetic state of the FM layer 306 between two magnetic states in a magnetic field 314. An output voltage associated with arm-X of the magnetometer 202, which is generated in response to the oscillatory spin-orbit torque and the magnetic field, can then be measured. Particularly, the output voltage of the arm-X measured is a time-varying anomalous Hall voltage generated by the magnetic layer 302. The time-varying anomalous Hall voltage is a function of the alternating current and a Hall resistance of the magnetic layer 302. The Hall resistance can be used to deduce a magnitude and a direction associated with an in-plane component and an out-of-plane component of the magnetic field 314, which is described in more detail in the “Operation principle” section below.

Although Figure 3 has been described in relation to arm-X of the magnetometer 202, it should be appreciated that this can equally be applied to arm-Y of the magnetometer 202.

Figure 4 is a schematic diagram showing an alternating current input being provided to the L-shaped magnetometer 202 of Figure 2 to generate outputs using the L-shaped magnetometer 202 for measuring vector components of a magnetic field in accordance with an embodiment. An apparatus 400 comprising the L-shaped Hall device or magnetometer 202, a current source 402, and a number of measurement circuits 404, 406, 408 adapted to measure anomalous Hall voltages (e.g. V_Hx and V_Hy) or Hall resistances of the magnetometer 202 is shown in Figure 4.

In the present embodiment, the current source 402 is applied between two terminals, one at each end of arm-X and arm-Y of the L-shaped magnetometer 202, so that an alternating current is provided in the magnetic layer of each of arm-X and arm-Y. The alternating current provided creates an oscillatory spin-orbit torque in the magnetic layer of each of arm-X and arm-Y to switch the switchable magnetic state of the corresponding magnetic layer between two magnetic states in the magnetic field as described above. In the present embodiment, each of the measurement circuits 404, 406, 408 includes a voltmeter adapted to be electrically connected to the Hall cross structures of arm-X and arm-Y of the magnetometer 202. The measurement circuit 404 is adapted to measure an anomalous Hall voltage V_Hx comprising a second-harmonic Hall voltage

associated with arm-X, the measurement circuit 406 is adapted to measure an anomalous Hall voltage V_Hy comprising a second-harmonic Hall voltage Vy ^ associated with arm-Y, and the measurement circuit 408 may be connected to either arm-X or arm-Y to measure a first-harmonic Hall voltage (i.e. V or V °). The second-harmonic Hall voltage V_X ^OJ can be used to detect H_x and the second-harmonic Hall voltage

can be used to detect H_y, the two in-plane components of the magnet field. The first-harmonic Hall voltage (i.e. V“ or

can be used to detect the out-of- plane component H_z of the magnetic field. In some embodiments, suitable lock-in amplifiers can be used in each of the measurement circuits 404, 406, 408 to measure the various respective harmonic voltages directly.

Figure 5 is a flowchart showing steps of a method 500 for measuring vector components of a magnetic field using, for example, the L-shaped magnetometer 202.

In a step 502, an alternating current is provided to the magnetometer 202 to generate a first oscillatory spin-orbit torque in a first magnetic layer of a first section (e.g. arm-X) of the magnetometer 202, and a second oscillatory spin-orbit torque in a second magnetic layer of a second section (e.g. arm-Y) of the magnetometer 202. The first magnetic layer of the arm-X is adapted to generate a first anomalous Hall voltage in response to the first oscillatory spin-orbit torque and the magnetic field and the second magnetic layer of arm-Y is adapted to generate a second anomalous Hall voltage in response to the second oscillatory spin-orbit torque and the magnetic field.

In a step 504, the first anomalous Hall voltage of the first section (e.g. arm-X of the magnetometer 202) and the second anomalous Hall voltage of the second section (e.g. arm-Y of the magnetometer 202) are measured. The first anomalous Hall voltage and the second anomalous Hall voltage can be measured, for example, using the measurement circuits 404 and 406, respectively. As will be made clear in later description, the first anomalous Hall voltage includes a first second-harmonic Hall voltage associated with a first in-plane vector component of the magnetic field and the second anomalous Hall voltage includes a second second-harmonic Hall voltage associated with a second in-plane vector component of the magnetic field. In the present embodiment where arm-X and arm-Y are orthogonal to each other, the first inplane vector component of the magnetic field measured in relation to arm-X is also orthogonal to the second in-plane vector component of the magnetic field measured in relation to arm-Y. Further, as discussed in relation to Figure 4, the first anomalous Hall voltage or the second anomalous Hall voltage measured also includes a first-harmonic Hall voltage associated with an out-of-plane vector component (in the present embodiment, H_z) of the magnetic field. In this way, the three independent vector components of the magnetic field can be detected simultaneously.

Figure 6 is a diagram 600 illustrating a sequence for measuring vector components of a magnetic field using the magnetometer of Figure 2 in accordance with an embodiment. This is similar to the method 500 where an alternating current (AC) is first applied to the L-shaped Hall device 202 in a step 602, and various measurements 604, 606, 608 can be taken using arm-X and arm-Y of the magnetometer 202 to obtain the corresponding harmonic Hall voltages. As shown in Figure 6, the measurement 604 of the second- harmonic Hall voltage

associated with the arm-X can be used to detect the inplane field component H_x, the measurement 606 of the second-harmonic Hall voltage Vy ^ can be used to detect the in-plane field component

and the measurement 608 of the first-harmonic Hall voltage (i.e. V_x or

can be used to detect the out-of-plane component W_z of the magnetic field. Linear plots 610, 612, 614, 616 of the corresponding harmonic Hall voltages versus their corresponding magnetic field components are also shown in Figure 6. The linear plot 610 of V_X ^OJ against H_x corresponds to expected data obtained using the measurement 604, the linear plot 612 of Vy ^ against H_y corresponds to expected data obtained using the measurement 604, and the linear plot 614 of V against H_z and the linear plot 616

against H_z corresponds to expected data obtained using the measurement 608.

The detailed operation principle of the magnetometer as described in the present embodiments is discussed in the next section.

Operation principle All ferromagnetic materials exhibit anomalous Hall effect (AHE), which is proportional to a vertical component M_z of the magnetization (e.g. along the z-axis as shown in relation to Figure 2). As most ferromagnetic materials exhibit hysteresis, i.e., M_z is not a single-valued function of an external magnetic field, the AHE of a typical ferromagnet may not be suitable for use in the present application for sensing a magnetic field as this may cause difficulty in determining the out-of-plane field component H_z using its anomalous Hall effect (AHE) plot. However, hysteresis of a ferromagnetic layer can be reduced to be diminishingly small when the ferromagnet approaches the superparamagnetic limit.

In the present disclosure, magnetic layers comprising a ferromagnetic layer including Co or CoFeB and a heavy metal layer including Ta or Pt were used. In the present embodiments, a MgO layer is provided adjacent to the ferromagnetic layer as a capping layer. The thickness of the ferromagnetic layer can be optimized to reduce the hysteresis of the ferromagnetic layer to near zero by reducing an effective magnetic anisotropy of the ferromagnetic layer.

A magnetic hysteresis loop (i.e. a M-H loop) of a ferromagnetic layer may be modelled using the hyperbolic analytical approximation of the Everett integral based on the stochastic Preisach approach. According to this model, the ascending M_a and descending M_d branches of the M-H loop may be expressed as,

M_a = M_s tanh [a (H - H_c)] + F(H_m), (1a)

M_d = M_s tanh [a (H + H_c)] - F(H_m), (1b) where M_s is the saturation magnetization of the ferromagnetic layer, H_c is the coercivity of the ferromagnetic layer, H_m is the maximum excitation field, a is the differential permeability at H = H_c, and F(H_m) =

[tanh a(H_m + H_c) - tanh a(H_m - H_c)].

When the coercivity is negligible and the M-H loop is symmetrical at large magnetic fields, it can be approximated that H_c = 0 , F(H_m) = 0 , and M_a and M_d can be expressed as M_a = M_d = M_s tanh aH.

In the present embodiments where the magnetic layer comprises a heterostructure of MgO/(Co or CoFeB)/(Ta or Pt), although the coercivity is near zero, the magnetic layer still exhibits weak perpendicular magnetic anisotropy (PMA). Therefore, when a magnetic field is applied in an out-of-plane direction, the z-component of the magnetization will be given by M_z = M_s tanh aH_z. When the AHE is dominant over the ordinary Hall effect, the measured Hall resistance become:

RH = Ro + RAHE tanh aH_z, (2) where R_o is the offset resistance induced by misalignment of Hall voltage electrodes (e.g. the contacts for measuring V_Hx+ , V_Hx_ , V_Hy+ and V_Hy_) (if any), R_AHE is the anomalous Hall resistance, and a is a constant which, in general, depends on the sample structure.

However, when the ferromagnetic layer approaches the superparamagnetic limit, a is approximately given by M_sV/k_BT, where M_s is the saturation magnetization, V is the effective magnetic volume of sample, T is temperature, and k_B is the Boltzmann constant (it has been verified that the hyperbolic tangent function of Equation (2) above is more accurate than the Langevin function for fitting the experimental data in the present embodiments).

In the present embodiment where the magnetic layer comprises a HM/FM bilayer (thereby involving the SOT mechanism), the term H_z in Equation (2) above is replaced by the effective out-of-plane magnetic field component H_z ⁿ which includes both the external field and the SOT effective fields. Specifically, for the L-shaped magnetometer 202, H_z ⁿ = H_z + H$^L = H_Z + H^DLm_x for arm-X and H_z ^eff = H_z + H$^L = H_z + H^DLm_y for arm-Y. Here, H^DL is the magnitude of the DL SOT effective field, m_x is the normalized magnetization in the x-direction and m_y is the normalized magnetization in the y-direction. When an alternating current / = /_o sin&)t is provided to the L-shaped magnetometer 202, the Hall voltage of the arm-X may be written as:

V_Hx ⁼ IQRO sin rot + IQRAHE sin <*>t tanh

= I₀R₀ sin cot + I₀R_AHE sin oot tanh [BH_Z + AH_XI_O sin <ot], (3) where A = (V /k_BT)(h/2e)(0_SH/t_FMSH*^ff) and B = M_sV/k_BT.

When is small, using Taylor expansion, V_Hx may be approximately written as:

Using trigonometric identities, Equation (4) can be further reduced to:

Similar results can be obtained for arm-Y of the magnetometer 202, i.e.,

The above results demonstrate that H_x , H_y , and H_z (i.e. the three independent components of the magnetic field in Cartesian coordinates) can be simultaneously measured or obtained using the L-shaped magnetometer 202 through the harmonic Hall resistances or harmonic Hall voltages. Particularly, in an embodiment, the harmonic Hall resistances or voltages can be measured directly using lock-in techniques (e.g. using lock-in amplifiers or using a simple frequency-locking circuit). The values of H_z obtained from Equations (6) and (7) above are expected to be similar or the same when the arm-X and the arm-Y of the magnetometer 202 are physically close to each other. When the magnetic field for detection is small, the third-harmonic term (i.e.

and the fourth-harmonic term

^can be ignored in the above Equations (6) and (7). The constants A and B can be either calculated using the known parameters and constants, or pre-calibrated empirically using existing magnetometer at a low magnetic field. Therefore, the x-component of the magnetic field (H_x ), the y-component of the magnetic field (H_y) and the z-component of the magnetic field (W_z) may be determined by multiplying their respective harmonic Hall voltages or harmonic Hall resistances with a corresponding pre-calibrated field coefficient according to the Equations (6) and (7).

Experiments performed an exemplary embodiment

Figures 7 A to 17B are in relation to experiments perform in relation to a magnetometer comprising a MgO/CoFeB/Ta/MgO/Ta heterostructure in accordance with an embodiment. In line with the L-shaped magnetometer 202 as described in relation to Figure 2, a L-shaped magnetometer comprising a MgO/CoFeB/Ta/MgO/Ta heterostructure was fabricated with two mutually perpendicular arms (i.e. arm-X and arm-Y). In the present embodiment, arm-X and arm-Y use the same heterostructure (i.e. the magnetic layer of arm-X is the same as the magnetic layer of arm-Y).

In order to eliminate the hysteresis in the detected vertical component of the magnetic field, a thickness of the ferromagnetic layer CoFeB in the heterostructure is optimized such that it exhibits a perpendicular magnetic anisotropy (PMA) with negligible or nearzero hysteresis. In the present case, the thickness of the ferromagnetic layer was optimized by fabricating Hall bars and measuring their AHE loops.

Figures 7A, 7B and 7C show graphs of anomalous Hall resistance RH as a function of a perpendicular magnetic field in a z-direction for different ferromagnetic Cobalt-lron- Boron (CoFeB) layer thicknesses in accordance with an embodiment. In the present case, Hall bars comprising a stack of MgO(1.1)/CoFeB(d)/Ta(1.1)/MgO(2)/Ta(1.5) were used, where d denotes a thickness of the CoFeB layer which was varied at 1.1 nm, 1.3 nm and 1.5 nm. The other numbers inside the parentheses of the stack denote a thickness of the respective layer in nanometers (nm). The film stacks were deposited on a SiC>2/Si substrate using sputtering. The Hall bars were fabricated using photolithography and lift-off techniques. The completed devices were then annealed in vacuum for 1 hour at 250 °C.

Figure 7A shows a graph 700 of RH as a function of the perpendicular magnetic field for a CoFeB layer thickness of 1.1 nm, Figure 7B shows a graph 710 of RH as a function of the perpendicular magnetic field for a CoFeB layer thickness of 1.3 nm and Figure 7C shows a graph 720 of RH as a function of the perpendicular magnetic field for a CoFeB layer thickness of 1.5 nm. As can be observed in the graphs 700, 710 and 720, the Hall bars exhibit nearly zero hysteresis when d = 1.1 nm and 1.3 nm, though the Hall resistance decreases with decreasing d. The curves with zero hysteresis as shown in the graphs 700, 710 can be fitted well using the hyperbolic tangent function as discussed in relation to Equation (2) above. Further systematic studies, not discussed herein for succinctness, revealed that the optimum thickness for this heterostructure stack is between 1.3 - 1.4 nm, depending on the annealing temperature and duration.

After the thickness of the ferromagnetic layer of the heterostructure is optimized, a L- shaped magnetometer similar to that as shown in Figure 2 can be fabricated. In the present embodiments, the film stack comprises MgO(1.1)/(Co, Fe)B(1.4)/Ta(1.1)/MgO(2)/Ta(1.5) multilayers deposited on a SiC>2/Si substrate (similar to above, the number in parentheses denotes a thickness of a corresponding layer in nanometers), and the width and length of each arm of the fabricated magnetometer are 15 pm and 120 pm, respectively.

Figures 8A, 8B and 8C show graphs of harmonic Hall resistances (including first- harmonic Hall resistance R and second-harmonic Hall resistance R ) as a function of magnetic field where the magnetic field was swept in the z-direction, the x-direction and the y-direction, respectively. In the present experiments, the magnetometer was driven by an alternating current with an amplitude of 4 mA and frequency of 115 Hz.

Figure 8A shows a graph 800 of harmonic Hall resistances, R _x and R%%, of arm-X when the magnetic field was swept along the z- direction. As can be seen, the plot 802 (in circles) of R^_x is linear with respect to H_z at small magnetic fields and saturates at high magnetic fields, while the plot 804 (in squares) of Rf shows that the amplitude of is almost zero for the entire magnetic field range.

Figure 8B shows a graph 810 of harmonic Hall resistances, R^_x and

of arm-X when the magnetic field was swept along the x- direction. An opposite trend is obtained for this case as compared to that shown in relation to Figure 8A, where the plot 812 (in circles) of R^_x shows that the amplitude of R^_x is almost zero for the entire magnetic field range, while the plot 814 (in squares) of Rf is linear with respect to H_x at small magnetic fields and saturates at high magnetic fields. Figure 8C shows a graph 820 of harmonic Hall resistances with the magnetic field being swept in the y-direction. The results of the graph 820 were obtained using arm-Y of the magnetometer, and are similar to those obtained using arm-X as shown in Figure 8B, where the plot 822 (in circles) of Rfi_y shows that the amplitude of Rfi_y is almost zero for the entire magnetic field range, and the plot 824 (in squares) of R^y is linear with respect to H_y at small magnetic fields and saturates at large magnetic fields.

Figures 9A, 9B and 9C show graphs of harmonic Hall resistances (including first- harmonic Hall resistance R^_x and second-harmonic Hall resistances Rf and R^y) as a function of magnetic field for a small magnetic field range of -100 Oe to 100 Oe in accordance with an embodiment. Plots of linearity errors are given in the insets in each graph of Figures 9A, 9B and 9C. Lines passing through the data points (in circles) are linear fittings.

Figure 9A shows a graph 900 of the first-harmonic Hall resistance R^_x as a function of the magnetic field H_z in the z-direction. The graph 900 shows R^_x vs _zin a small magnetic field range from -50 Oe to +50 Oe. Within this range, the data points show a good linear fit 902 with the maximum linearity error provided by the plot 904 of linearity error being less than 3%. The graph 900 also shows negligible hysteresis, with a sensitivity of 149.44 mQ/Oe.

Figure 9B shows a graph 910 of the second-harmonic Hall resistance Rf as a function of the magnetic field H_x in the x-direction. As can be seen in Figure 9B, the graph 910 of R%% vs H_x exhibits a good linear fit 912 with the maximum linearity error being less than 3% as shown by the plot 914 in the inset. The graph 910 also shows negligible hysteresis, with a sensitivity of 3.36 mQ/Oe in a magnetic field range of -100 Oe to +100 Oe.

Figure 9C shows a graph 920 of the second-harmonic Hall resistance R^y as a function of the magnetic field H_y in the y-direction. Similar to that shown in relation to Figure 9B, the graph 920 of R^y vs H_y exhibits a good linear fit 922 with the maximum linearity error being less than 3% as shown by the plot 924 in the inset. The graph 920 also shows negligible hysteresis with a sensitivity of 3.30 mQ/Oe in a magnetic field range of -100 Oe to +100 Oe, similar to the results for arm-X. This indicates good uniformity in both the deposited film stacks and the patterned magnetometer. It should be noted that with the inclusion of the third-harmonics and the fourth harmonics as shown in relation to Equations (6) and (7), an expansion of the dynamic range of the magnetometer for measuring the vector field components H_x , H_y and H_z may be possible.

Figures 10A to 12C as described below illustrate the possibility of using the L-shape magnetometer of the present embodiment as a biaxial sensor. The L-shaped magnetometer was used to determine the direction of a magnetic field having a constant magnitude but with its direction rotating in three Cartesian-coordinate planes.

Figures 10A, 10B and 10C show schematic diagrams illustrating measurement geometries of the L-shaped magnetometer 202 of Figure 2 for rotating magnetic fields in three different planes.

Figure 10A shows a schematic diagram 1000 of the measurement geometry of the L- shaped magnetometer 202 for a rotating magnetic field in the z-x plane 1002. The angle 1004 between the direction of the magnetic field and the z-axis is defined as 6^_x. Figure 10B shows a schematic diagram 1010 of the measurement geometry of the L- shaped magnetometer 202 for a rotating magnetic field in the y-z plane 1012. The angle 1014 between the direction of the magnetic field and the y-axis is defined as 6_yz. Figure 10C shows a schematic diagram 1020 of the measurement geometry of the L- shaped magnetometer 202 for a rotating magnetic field in the x-y plane 1022. The angle 1024 between the direction of the magnetic field and the x-axis is defined as 6_xy.

As shown schematically in relation to Figures 10A, 10B and 10C, when the magnetic field rotates in the z-x plane 1002, the y-z plane 1012 and the x-y plane 1022, the first- harmonic Hall resistance and the second-harmonic Hall resistance are given by: i) rotation in the z-x plane 1002:

ii) rotation in the y-z plane 1012:

R ₂ = R_O + R_AHEHsm9_yz/H₀ and R = - (I_OR_AHEAHCOS0 _Z)/(2H_O) iii) rotation in the x-y plane 1022:

Here, H is the external magnetic field amplitude, e the angles

between the rotating field and z, y, x axes, respectively, on the corresponding z-x, y-z and x-y planes 1002. 1012, 1022. Each angle of 0_ZX, Gyz and 0xy is defined to be positive when the corresponding rotation direction and axis follows the right-handed rule.

Figures 11 A, 11 B and 11C show graphs of harmonic Hall resistances as a function of magnetic field for the rotating magnetic fields in the different planes 1002, 1012, 1022 as shown in the schematics of Figures 10A, 10B and 10C in accordance with an embodiment.

Figure 11A shows a graph 1100 of the first-harmonic Hall resistance and the

second-harmonic Hall resistance R^ of arm-X with a magnetic field rotating in the z-x plane 1002. A plot 1102 is shown for the first-harmonic Hall resistance and a plot 1104 is shown for the second-harmonic Hall resistance toget

her with their corresponding fitting curves. The plots 1102, 1104 and as a function of

0^_x from 0° to 360° when the L-shaped magnetometer 202 was driven by an alternating current with an amplitude of 4 mA and frequency of 115 Hz. The external field strength H used was 10 Oe. Both signals were acquired from the single-structure L-shaped magnetometer 202 simultaneously using a lock-in amplifier. The plot 1102 o

follows a cosine function while the plot 1104 of

ollows a sine function. They can be fitted well with respectively, where R$₁₀ and R^_o

are the amplitudes of the plot 1102 and the plot 1104, respectively.

Similar to the experiment performed in relation to Figure 11A, the L-shaped magnetometer 202 for Figure 11 B and 11 C was driven by an alternating current with an amplitude of 4 mA and frequency of 115 Hz. The external field strength H used was also 10 Oe.

Figure 11 B shows a graph 1110 of the first-harmonic Hall resistance ^ and the

second-harmonic Hall resistance R^' of arm-Y with a magnetic field rotating in the y-z plane 1012. A plot 1112 is shown for the first-harmonic Hall resistance /?$₂ and a plot 1114 is shown for the second-harmonic Hall resistance Rfy? together with their corresponding fitting curves. Figure 11C shows a graph 1120 of the second-harmonic Hall resistances R^ of arm-X and R^ of arm-Y with a magnetic field rotating in the x-y plane 1022. A plot 1122 is shown for the second-harmonic Hall resistance R^ of arm- X and a plot 1124 is shown for the second-harmonic Hall resistance R^ of arm-Y together with their corresponding fitting curves.

Similar to Figure 11 A, the plots 1112, 1114 of Figure 11B and the plots 1122, 1124 of Figure 11C are fitted with their corresponding cosine and sine functions. For example, referring to Figure 11 B, the plot 1112 of R^₂ - 6y_Z follows a sine function while the plot 1114 of RH2 - 0y_Z follows a cosine function. The plots 1122, 1124 can be fitted well with R

respectively, where ^are the

amplitudes of the plot 1112 and the plot 1114, respectively. The same can be applied to the plots 1122, 1124 of Figure 11C.

With the sine and cosine dependence of the harmonic Hall resistances obtained using the Figures 11A, 11 B and 11C, magnetic field angles 1104, 1114, 1124 can be calculated as:

Figures 12A, 12B and 12C show graphs of measured field angle (fi_zx, 6y_Z and 6_xy) versus calculated field angle (0_zx, 6_yx and 0_xy) for rotating magnetic fields in the different planes 1002, 1012, 1022 as shown in relation to Figures 10A, 10B and 10C. Figures 12A, 12B and 12C show the relationship between the calculated field angle as detected using the L-shaped magnetometer and the measured field angle in relation to the three coordinate planes z-x, y-z and x-y.

Figure 12A shows a graph 1200 of the measured field angle ) versus the calculated

field angle (0_ZX) for a rotating magnetic field in the z-x plane 1004. The inset 1202 shows the difference between

and 9_ZX (or “error”) for each data point across an angle range of 0° to 360°. Figure 12B shows a graph 1210 of the measured field angle (0y_Z) versus the calculated field angle (0_yz) for a rotating magnetic field in the y-z plane 1014 with an inset 1212 showing the difference between 0_yz and 0_yz for each data point across an angle range of 0° to 360°, and Figure 12C shows a graph 1220 of the measured field angle (0^) versus the calculated field angle (0_xy) for a rotating magnetic field in the x-y plane 1024 with an inset 1222 showing the difference between 0 _y and 0_xy for each data point across an angle range of 0° to 360°.

As shown in relation to Figures 12A, 12B and 12C, the calculated field angles as detected using the L-shaped magnetometer are almost the same as the measured field angle in relation to the three coordinate planes z-x, y-z and x-y, respectively. The insets 1202, 1212 and 1222 also show a maximum difference or error between the angles to be about 3°, with an average error from 0° to 360° being less than 1°.

The results as shown in relation to Figures 10A to 12C therefore show that the L- shaped magnetometer 202 can function as both a single-axial and a bi-axial magnetic field sensor. To further demonstrate its capability as a vector magnetometer, the same L-shaped magnetometer was used to map a magnetic field generated by a permanent magnet. The results for this are shown in relation to Figures 13 to 17B below.

Figure 13 show a photograph of an experimental setup 1300 for measuring vector components of a magnetic field generated by a permanent magnet in accordance with an embodiment.

The experimental setup 1300 includes a cylindrical N35 permanent magnet 1302 (B_s = 1.27 T) with a diameter of 10 mm and thickness of 5 mm being attached to a nonmagnetic fixture 1304 with its N-pole pointing down. The L-shaped Hall sensor or magnetometer 1306 was placed on a motorised X-Y stage 1308 below the permanent magnet 1302 at a distance of 33 mm from a bottom surface of the permanent magnet 1302, with its center being aligned with that of the permanent magnet 1302. The X- and Y-arms of the L-shaped magnetometer 1306 were aligned in parallel with the two rails 1310, 1312 of the motorised X-Y stage 1308, and are indicated as x-axis and y-axis, respectively.

Figure 14 shows a schematic diagram illustrating a measurement configuration 1400 of the experimental setup 1300 of Figure 13. By scanning the L-shaped magnetometer 1306 over an area of 50 mm * 12 mm at a distance 33 mm below the permanent magnet 1302, a vector magnetic field distribution 1402 on a plane located at 33 mm below the permanent magnet 1302 can be obtained, as shown in Figure 14. The vector magnetic field distribution 1402, including magnitudes and directions of the magnetic field vectors at different positions in the plane, was directly plotted using the magnetic field components, H_x, H_y, H_z which were measured simultaneously using the L-shaped magnetometer 1306 based on the detected harmonic Hall resistances R$ft, R^ft and R^. The amplitude 1404 (H), the polar angle 1406 (0_H) and the azimuthal angle 1408 (<p_H) of an exemplary magnetic field vector with respect to the defined Cartesian coordinates are shown in Figure 14.

To check the accuracy of the mapping results, the amplitudes (W), polar angles (0_H) and azimuthal angles (<p_H) of the vector magnetic field were extracted from the measured vector magnetic field components obtained using the L-shaped magnetometer 1306, i.e., H = (H² + H_y + H²)^1/2 , d_H = cos^-1(H_z/H) , and <p_H =

and compared with simulation results. The simulation results were obtained by performing simulation using the COMSOL Multiphysics® software.

Figure 15A shows a 3D plot 1500 of the amplitude (/-/) of the measured magnetic field obtained using the L-shaped magnetometer 1306 and Figure 15B shows a 3D plot 1510 of the amplitude (/-/) of the simulated magnetic field obtained using the COMSOL Multiphysics® software, Figure 16A shows a 3D plot 1600 of the polar angle (0_H) of the measured magnetic field obtained using the L-shaped magnetometer 1306 and Figure 16B shows a 3D plot 1610 of the polar angle (0_H) of the simulated magnetic field obtained using the COMSOL Multiphysics® software, and Figure 17A shows a 3D plot 1700 of the azimuthal angle (<p_H) of the measured magnetic field obtained using the L- shaped magnetometer 1306 and Figure 17B shows a 3D plot 1710 of the azimuthal angle (<p_H) of the simulated magnetic field obtained using the COMSOL Multiphysics® software.

As shown in relation to Figures 15A to 17B, the measured magnetic field amplitudes (/7 ), polar angles (0_H) and azimuthal angles (<p_H) obtained using the L-shaped magnetometer 1306 were in good agreement with the simulation results. The results as shown in relation to Figures 10A to 17B demonstrate that the L-shaped magnetometer of the present embodiment functions well as a vector magnetometer.

It should be noted that for commercial Hall vector magnetometers, a spatial distance between any two sensors for multi-axial magnetic field detection is typically larger than 150 pm. In contrast, the distance between the two Hall crosses at arm-X and arm-Y of the vector magnetometer described in the present disclosure is 70 pm. This distance between the two Hall cross structures can be further reduced to less than 30 pm or smaller (not shown here) if required. The significant enhancement of spatial resolution in the vector magnetometer of the present disclosure helps to extend the application of vector magnetometer in different fields. For example, the single-structure (or one-piece structure) magnetometer in accordance with the present disclosure can be used in a wide range of applications such as air/land/sea transport, virtual reality and augmented reality, factory automation, oil and mineral exploration, non-destructive testing, biomedical sensing, etc.

Although in the above embodiments, MgO(1.1)/(Co, Fe)B(1.4)/Ta(1.1)/MgO(2)/Ta(1.5) was used as the heterostructure stack of the L-shaped magnetometer, it should be appreciated that any material stacks which exhibit perpendicular magnetic anisotropy (PMA) with zero or near-zero hysteresis can be used to implement the vector magnetometer in accordance with the present disclosure. Thicknesses of each material layer (e.g. the FM and/or HM layers) can also be varied to achieve an optimum performance.

Further, although embodiments of the L-shaped magnetometer as described above show that the two sections (or two arms) of the magnetometer are orthogonal or perpendicular to each other, in an embodiment, the two magnetic sections of the magnetometer are not perpendicular to each other. This is possible because the magnetic field to be detected or measured is not necessarily decomposed into two orthogonal vectors, e.g. /7_X and /7_y. Therefore, as long as the two magnetic sections of the magnetometer are not parallel (i.e. at an angle to each other), the magnetometer can still be used to map a magnetic field. In this case, however, the equations for calculating the amplitude and the angle of the magnetic field becomes more complicated. For example, where H is the actual field to be detected, /7i and H2 are the two in-plane field components detected by the two magnetic sections, Q is the angle between the two magnetic sections and e_H is a magnetic field angle with respect to Hi.

The magnetic field amplitude is then given by:

and the field angle 9_H is given by:

H₂ sin ©

GH = arctan

H, +H₂ cos 9

As shown above, the equations for the magnetic field amplitude H and the magnetic field angle 0_H become more complicated than an embodiment having the L-shaped magnetometer with two magnetic sections being orthogonal to each other (i.e. when Q = 90°).

In an embodiment, a magnetic layer of a first section and/or a second section of the magnetometer includes a single ferromagnetic (FM) layer, in contrast to the bilayer FM/HM structure as described above. Example of such single FM layer includes (Ga, Mn)(As, P), GaMnAs and FePt, MnsSn. Particularly, SOT-induced switching has been observed in these FM single-layers with perpendicular magnetic anisotropy (PMA). Therefore, it is possible to replace the FM/HM bilayer structure as exemplified in the present embodiment with one of these FM single-layer for use in the magnetometer. To do this, structure optimization of the FM single-layer may be needed to eliminate the hysteresis of the AHE curve in the FM single-layer, so that the out-of-plane magnetic field component can be detected.

In an embodiment, different materials and/or structures can be used for the two magnetic sections of the magnetometer. To do this, separate calibration for each of these magnetic sections may be required. In addition, additional material deposition and/or processing steps may be required so that the two magnetic sections comprising different materials and/or structures can be formed. In contrast, if the two magnetic sections of the magnetometer are structurally identical and comprising the same material layers, they can be fabricated at the same time and require only a single calibration for both magnetic sections.

In some embodiments, an interlayer can be introduced between the FM layer and the HM layer in the heterostructure. An example of the interlayer is Ti. Although Figure 3 shows that the FM layer 306 is formed or deposited on the substrate 204, followed by the formation of the HM layer 304 on the FM layer 306, it should be appreciated that in another embodiment, the HM layer 304 can be formed on the substrate 204, followed by the formation of the FM layer 306 on the HM layer 304.

Other alternative embodiments of the invention include: (i) the ferromagnetic layer of the FM/HM bilayer structure comprises cobalt (Co), iron (Fe), nickel (Ni), cobalt iron boron (CoFeB), gadolinium (Gd), yttrium iron garnet (YIG), ferrites, or alloys of Co, Fe, Ni, Mn, Cr, V, CoFeB, Gd, Te, Pt or Ir, or any other ferromagnetic materials with a PMA; (ii) the metal layer comprises a heavy metal (HM), an antiferromagnetic (AFM) material, a topological insulator (Tl) or a transition metal dichalcogenides (TMD) or any material with a large spin-orbit interaction (SOI); (iii) the heavy metal includes platinum (Pt), palladium (Pd), tantalum (Ta), tungsten (W), lead (Pb), niobium (Nb), CuPt, AuPt or NiPt; (iv) the antiferromagnetic (AFM) material includes IrMn, PtMn or PtNiMn; (v) the TMD includes Bi2Ses, Bi2Tes, Sb2Tes, WTe2, MoTe2 or PtSe2; (vi) a magnetometer being formed on other substrate (e.g. Ge, GaAs etc.) and not limited to a silicon substrate as used in the present embodiments; and (vii) use of other structures for measuring the magnetic field components, such as a Hall bar, in place of the Hall crosses.

Although only certain embodiments of the present invention have been described in detail, many variations are possible in accordance with the appended claims. For example, features described in relation to one embodiment may be incorporated into one or more other embodiments and vice versa.

Claims

1. A magnetometer for measuring vector components of a magnetic field, the magnetometer comprising: a first section comprising a first magnetic layer; and a second section comprising a second magnetic layer, the second section being in-plane with and at an angle to the first section and is electrically connected to the first section, the first magnetic layer and the second magnetic layer each having a perpendicular magnetic anisotropy with near zero hysteresis; wherein the first magnetic layer is adapted to generate a first anomalous Hall voltage in response to a first oscillatory spin-orbit torque and the magnetic field and the second magnetic layer is adapted to generate a second anomalous Hall voltage in response to a second oscillatory spin-orbit torque and the magnetic field, the first oscillatory spin-orbit torque and the second oscillatory spin-orbit torque being generated in the first magnetic layer and the second magnetic layer respectively in response to an alternating current passing through the first magnetic layer and the second magnetic layer, wherein the first anomalous Hall voltage includes a first second-harmonic Hall voltage associated with a first in-plane vector component of the magnetic field and the second anomalous Hall voltage includes a second second-harmonic Hall voltage associated with a second in-plane vector component of the magnetic field, the first inplane vector component of the magnetic field being in-plane with and at the angle to the second in-plane vector component of the magnetic field, and wherein the first anomalous Hall voltage or the second anomalous Hall voltage further includes a first-harmonic Hall voltage associated with an out-of-plane vector component of the magnetic field, the out-of-plane vector component being orthogonal to the first in-plane vector component and the second in-plane vector component of the magnetic field.

2. The magnetometer of claim 1 , wherein the first section is integrated with the second section to form a single structure of the magnetometer.

3. The magnetometer of claim 1 or claim 2, wherein the magnetometer is of a L-shape and the first section and the second section are orthogonal to each other to form two orthogonal arms of the L-shape magnetometer.

4. The magnetometer of any one of claims 1 to 3 and wherein the first section comprises a first Hall cross structure for measuring the first anomalous Hall voltage and the second section comprises a second Hall cross structure for measuring the second anomalous Hall voltage.

5. The magnetometer of any one of the preceding claims, wherein the first magnetic layer comprises a first ferromagnetic layer and a first metal layer, the first metal layer is adapted to inject a spin current into the first ferromagnetic layer in response to the alternating current to create the first oscillatory spin-orbit torque.

6. The magnetometer of claim 5, wherein the first ferromagnetic layer comprises cobalt (Co), iron (Fe), nickel (Ni), cobalt iron boron (CoFeB), or alloys of Co, Fe, Ni, Mn, Cr, Gd, Pt or Ir.

7. The magnetometer of claim 5 or claim 6, wherein the first metal layer comprises a heavy metal, an antiferromagnetic material, a topological insulator or a transition metal dichalcogenides (TMD).

8. The magnetometer of claim 7, wherein the heavy metal comprises platinum (Pt), palladium (Pd), tantalum (Ta), tungsten (W), lead (Pb), niobium (Nb), CuPt, AuPt, NiPt.

9. The magnetometer of claim 7, wherein the antiferromagnetic material includes IrMn, PtMn, PtNiMn or Cr.

10. The magnetometer of claim 7, wherein the topological insulator includes Bi2Ses, Bi2Tes, or Sb2Tes.

11. The magnetometer of claim 7, wherein the transition metal dichalcogenides includes WTe2, MoTe2 or PtSe2.

12. The magnetometer of any one of claims 5 to 11 , wherein a thickness of the first ferromagnetic layer is adapted to allow the first ferromagnetic layer to be in a superparamagnetic regime.

13. The magnetometer of any one of the preceding claims, wherein the first magnetic layer is the same as the second magnetic layer.

14. A method for measuring vector components of a magnetic field using a magnetometer, the magnetometer comprising: (i) a first section comprising a first magnetic layer and (ii) a second section comprising a second magnetic layer, the second section being in-plane with and at an angle to the first section and is electrically connected to the first section, the first magnetic layer and the second magnetic layer each having a perpendicular magnetic anisotropy with near zero hysteresis, the method comprising: providing an alternating current to the magnetometer to generate a first oscillatory spin-orbit torque in the first magnetic layer and a second oscillatory spinorbit torque in the second magnetic layer, the first oscillatory spin-orbit torque and the second oscillatory spin-orbit torque being generated in the first magnetic layer and the second magnetic layer respectively in response to the alternating current passing through the first magnetic layer and the second magnetic layer, wherein the first magnetic layer is adapted to generate a first anomalous Hall voltage in response to the first oscillatory spin-orbit torque and the magnetic field and the second magnetic layer is adapted to generate a second anomalous Hall voltage in response to the second oscillatory spin-orbit torque and the magnetic field; and measuring the first anomalous Hall voltage of the first section and the second anomalous Hall voltage of the second section, wherein the first anomalous Hall voltage includes a first second-harmonic Hall voltage associated with a first in-plane vector component of the magnetic field and the second anomalous Hall voltage includes a second second-harmonic Hall voltage associated with a second in-plane vector component of the magnetic field, the first in-plane vector component of the magnetic field being in-plane with and at the angle to the second in-plane vector component of the magnetic field, and wherein the first anomalous Hall voltage or the second anomalous Hall voltage further includes a first-harmonic Hall voltage associated with an out-of-plane vector component of the magnetic field, the out-of-plane vector component being orthogonal to the first in-plane vector component and the second inplane vector component of the magnetic field.

15. The method of claim 14, wherein the first section is integrated with the second section to form a single structure of the magnetometer.

16. The method of claim 14 or claim 15, wherein the magnetometer is of a L-shape and the first section and the second section are orthogonal to each other to form two orthogonal arms of the L-shape magnetometer, and wherein the first section and the second section are aligned with a x-axis and a y-axis in the Cartesian coordinates respectively, the first second-harmonic Hall voltage of the first section and the second second-harmonic Hall voltage of the second section are linear with respective to a x- component of the magnetic field (H_x) and a y-component of the magnetic field (H_y) respectively, and the first-harmonic Hall voltage is linear with respect to a z-component of the magnetic field (H_z).

17. The method of claim 16, wherein the x-component of the magnetic field (H_x) is determined by multiplying the first second-harmonic Hall voltage with a first precalibrated field coefficient, the y-component of the magnetic field (H_y) is determined by multiplying the second second-harmonic Hall voltage with a second pre-calibrated field coefficient respectively, and the z-component of the magnetic field (H_z) is determined by multiplying the first-harmonic Hall voltage with a third pre-calibrated field coefficient.

18. The method of any one of claims 14 to 17, wherein measuring the first anomalous Hall voltage of the first section and the second anomalous Hall voltage of the second section includes measuring the first second-harmonic Hall voltage, the second second- harmonic Hall voltage and the first-harmonic Hall voltage directly using lock-in techniques.