## 4 State of Art
### Magnetic Force Sensors
#### 4.3.2 Terfenol-D
The sensor was capable of measuring AC current at temperatures from 18 \({}^{\circ}\)C to 90 \({}^{\circ}\)C. The nonlinear effects originated by the magnetostrictive alloy were identified and methods for compensating these effects were proposed. A hysteresis compensation technique for a magnetic field sensor, containing a magnetostrictive alloy device, was presented by [PERSON] _et al_. [70]. The sensing head integrated a rod of Terfenol-D and a FBG. Due to the nonlinear effects taking place in such materials the magneto elastic material was accurately modeled in order to compensate for hysteresis. The algorithm allowed the improvement in the sensor performance. In 2009 and for the first time, a fiber optic magnetic field sensor with a thin film of Terfenol-D instead of the bulk magnetostrictive materials was reported by [PERSON] _et al_. [71] as shown in Figure 15.  
By magnetron sputtering deposition process, Terfenol-D thin films were deposited on etched FBGs. Two methods to improve the sensitivity were demonstrated. In one, the magnetostrictive alloy was deposited over different diameters of cladding-etched FBGs. The maximum sensitivity response to magnetic field was 0.95 pm/mT for an 85  diameter sensor. The other method was coating FBGs with a layer of magnetostrictive alloys (FeNi and Terfenol-D) and a multilayer with both materials. The multilayer has the highest sensitivity of 1.08 pm/mT. In this experiment, the authors not only reduced the dimensions of the sensor, but also improved the sensitivity to magnetic field. The dependence of shape anisotropy on the strain response of magnetic field sensors based on magnetostrictive alloys and FBGs was studied by [PERSON] _et al._[72]. The maximum sensor sensitivity was 18 /mT when a biased uniform field was applied for a 20 mm long Terfenol-D cuboid shape. For gradient magnetic fields, they were able to detect a significant change in the magnetostrictive response at different positions, attaching FBGs along the cuboid containing the magnetic field direction. [PERSON] _et al._[73] presented a sensor for DC and AC magnetic field measurements. The grating was coated with a layer of a composite mixed with particles of Terfenol-D. Different compositions were tested and the best magnetostrictive response was using a 30% volume fraction of Terfenol-D mixed in a matrix of epoxy resin as blinder. The effect of a compressive pre-stress in the sensor was also investigated. They achieved a resolution of 0.4 mT without and 0.3 mT with pre-stress. The sensitivity obtained for the magnetic field was 2.2 \(\times\) 10\({}^{-6}\) mT\({}^{-1}\), using an FBG interrogation system. Recently, [PERSON] _et al._[74] presented a novel sensor for detect static magnetic fields using a inscribed FBG and a micromachined slot sputtered with Terfenol-D. The grating and the slot were created with a femtosecond laser inscribing. The sensitivity to magnetic field in transmission was 0.3 pm/mT. They also measured in reflection with different polarization states achieving sensitivities between 0.2 pm/mT and 0.1 pm/mT. The use of a femtosecond laser to inscribing a FBG and create a micromachined slot simplifies greatly the fabrication process. The first fiber optic sensor for measurement of magnetic field by integrating a highly birefringent photonic crystal fiber (HiBi PCF) combined with a Terfenol-D epoxy resin composite material was reported by [PERSON] _et al._[51]. An in fiber modal interferometer was assembled by evenly exciting both eigenmodes of the HiBi PCF. Changes in the cavity length as well as the effective refractive  
Figure 15: Configuration of optical fiber magnetic sensor used by [PERSON] _et al._[71]. index were induced by exposing the sensing head to magnetic fields. The sensitivity obtained was 0.006 nm/mT to a range of 300 mT. Also a FBG coated with the same composite material was fabricated. For this sensor, the sensitivity achieved was 0.003 nm/mT.