## 4 Application
### Cardiac Magnetic Field and MCG  
The MCG is traditionally measured using SQUIDs, which offer high sensitivity and mature clinical applications. However, the use of these devices requires liquid helium cooling, significantly increasing maintenance costs. Using atomic magnetometers is a method that substantially reduces costs, and the sensitivity of newly developed magnetometers is now approaching SQUIDs [66; 67]. Magnetoresistive sensors represent another relatively inexpensive method for MCG measurements, although they currently exhibit lower sensitivity  
Figure 7: Temperature response of MP-SAWS. (**a**) Graphical representation of the temperature-dependent characteristic frequency shift within the physiological temperature range; (**b**) comparative study of the admittance curve within the physiological temperature range. and signal-to-noise ratios [68]. SAWSs based on the delta-E effect also demonstrate high sensitivity in magnetic field sensing [38; 39; 40]. In this study, the MP-SAWS was compact and capable of 2D dynamic measurements. Although its sensitivity needs further improvement, it shows potential for application in the human magnetic field measurements. By detecting the cardiac magnetic field, an MCG can be generated. The transducer model is illustrated in Figure 8a. The length ratio of the two materials in the direction of the magnetic field is maintained at 1:1, ensuring the preservation of the stress-sensing relationship. The arrangement of the materials is LiNbO\({}_{3}\)-Terfenol-D-LiNbO\({}_{3}\). The length ratio is set at 1:2:1, which satisfies the overall length ratio of 1:1. The established model has the capability to detect the magnetic field in a specific direction. Magnetic field scanning is conducted within simulation software, and the correspondence between the external magnetic field and the lateral stress is presented in Figure 8b. In the simulation model we established, the three materials were closely bonded. The boundary conditions for the left surface of the left LiNbO\({}_{3}\) and the right surface of the right LiNbO\({}_{3}\) were fixed. The boundary conditions between LiNbO\({}_{3}\) and Terfenol-D were set as free. After applying the magnetic field, the stress caused by the magnetostriction of Terfenol-D could be applied to the LiNbO\({}_{3}\) on both sides. During the stress simulation process, a relationship curve (Figure 6a) between the stress and MP-SAWS characteristic frequency was obtained. According to the results of the anti-interference testing process, the magnetic field itself has minimal impact on the operation of the SAW device. The magnetostrictive stress induced by the magnetic field serves as the link connecting the magnetic field and the SAW device. By combining the two corresponding relationship sets, the correspondence between the magnetic field and the MP-SAWS resonant frequency can be computed using computer calculations, as shown in Figure 8c. Based on the relationship curve derived from magnetic field sensing, a non-linear inverse correlation between the magnetic field and the characteristic frequency is shown. MP-SAWS demonstrates higher sensitivity when measuring strong magnetic fields. Figure 8: Magnetic field measurement using MP-SAWS. (**a**) Magnetic field sensing model based on magnetostriction; (**b**) the curve between magnetic flux density and stress; and (**c**) the curve between magnetic flux density and the resonant frequency of MP-SAWS. The cardiac magnetic field is generated by bioelectric currents originating from the heart. Both MCG and electrocardiograms (ECGs) are used to diagnose heart diseases. MCG provides superior advantages over ECG for diagnosing myocardial ischemia and coronary heart disease [69]. The intensity of the cardiac magnetic field ranges from 50 pT to 100 pT, indicating its weakness and susceptibility to interference from external magnetic fields. Currently, there is limited research on cardiac magnetic field measurements, and the application of MCG has not been widely adopted.