Micromagnetic simulation for the effects of Fe nanowires distribution on the magnetic properties of the Nd<sub>2</sub>Fe<sub>14</sub>B/á-Fe nanocomposite magnets (2018)

At present, the development of the exchange coupled nanocomposite magnets faces several challenges. High magnetization is usually accompanied by low coercivity, which is a major barrier for achieving high-energy products in this type of magnets. Fe nanowires are reported to have high coercivity due to its strong shape anisotropy,. Hence, it may be an good approach to enhance the coercivity of Nd <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> Fe $_{14}\mathrm {B}/ \alpha -$Fe nanocomposite magnets by introducing Fe nanowires as the soft phase. In the present work, the effects of Fe nanowire arrays on the magnetic properties of nanocomposite magnets are investigated by micromagnetic simulation. The simulation model is shown in Fig. 1. The nanowires arranged along the Z direction and the demagnetization curves of the Fe nanowires indicate the strong shape anisotropy. The nanowires have a length of 105 nm and a square cross section with the side length of S. The hard magnetic Nd <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> Fe <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</inf> B phase matrix is set as spherical without shape anisotropy. Fig. 1 The simulation model and the demagnetization curve of the Fe nanowires. The effects of different angles $(\theta = 0 ^{circ}$, 30°, 45°, 60°, and $90 ^{circ})$ between the long axis (Z axis) of nanowires and the easy axis of the hard phase on the magnetic properties are investigated firstly. The size of the nanowires are set as $150 \times 9 \times 9$ nm. The simulated demagnetization curves are shown in Fig. 2. The coercivity increases with the increasing $ \theta $ from 0° to 90°. When the nanowires are parallel to the easy axis of hard phase $\left({ \theta = 0 ^{circ}}\right)$, the hysteresis loop is a standard square and the moments reverse uniformly in one stage. The demagnetization curve for $ \theta = 90 ^{circ}$ show a long slope. The moments reverse in two steps, parts of the moments rotate slowly followed by all the moments reversing uniformly in one stage. The distribution of magnetization in the first step shows that the moments of the soft phase rotate to the direction of the nanowire due to the shape anisotropy, as shown in Fig. 2 inset, where red color means outward, blue means inward. Since the size of nanowire is smaller than the exchange length, the moments in the soft phase are strongly exchange coupled by hard phase. Since the fully reserved direction (-Z direction) of Fe nanowires is the hard magnetization direction and the moments are blocked, that's why the coercivity of $ \theta = 90 ^{circ}$ is much larger than that of $ \theta = 0 ^{circ}$. Fig. 2 The demagnetization curves of the models with different $ \theta $ and the magnetization distribution for $ \theta = 90 ^{circ}$ inset. In addition, the size effects of nanowires with $\mathrm {S}=9$ nm, 18 nm, 27 nm, and 54 nm were also studied in the model of $ \theta = 0 ^{circ}$ and 90°. The simulation results show that the nucleation occurs at a low applied field and the coercivities decrease as increasing the nanowires diameters. For $ \theta = 90 ^{circ}$, the coercivity is relatively stable with the increasing diameters of nanowires. The reason could be attributed to the fact that when the sizes is larger than the exchange length, the exchange coupling effect becomes insignificant and the dipolar coupling is dominant for $ \theta = 90 ^{circ}$. As a conclusion, the coercivity of the nanocomposite Nd <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> Fe $_{14}\mathrm {B}/ \alpha -$Fe can be increased by introducing the soft magnetic nanowire arrays with the long axis along the direction other than the easy axis of hard phase and the diameter smaller than the exchange length.