Micromagnetic insight into a magnetoreceptor in birds: Existence of magnetic field amplifiers in the beak

The Earth’s magnetic field provides an important source of directional information for many living organisms, especially birds, but the sensory receptor responsible for magnetic field detection still has to be identified. Recently, magnetic iron oxide particles were detected in dendritic endings of the ophthalmic nerves in the skin of the upper beak of homing pigeons and were shown to fulfill the special prerequisites of a biological receptor. Here we study the proposed receptor theoretically and formulate the criteria for which it becomes operational and can be used for registering the weak magnetic fields as, e.g., the geomagnetic field, by a bird.

Figure 1

(Color online) A chain of maghemite platelets detected by the transmission electron microscopy imaging method in the beak of homing pigeons [23] is of central importance for the magnetoreceptor organ in birds. The functioning of the magnetoreceptor depends on the total magnetization of the chain and thus on the magnetic domain structure of the individual platelets. Two possible domain distributions (four domain and a single domain) are discussed.

Figure 2

(Color online) Cubic anisotropy energy density calculated from Eq. (13). Plot (a) shows the energy density distribution in which the coordinate axes are the easy axes $\left(K_0=0.3,K_1=3.0\right)$. Plot (b) shows the energy distribution in which the coordinate axes are the hard axes $\left(K_0=1,K_1=-1.0\right)$. The values of $K_0$ and $K_1$ are chosen in arbitrary units

Figure 3

(Color online) A schematic presentation of the maghemite platelet chain with $N$ platelets. The length of the chain is $L$, while the length, the width, and the thickness of an individual platelet is $\Delta x$, $\Delta y$, and $\Delta z$, respectively. The external magnetic field ${\vec{B}}_0$ is applied along the chain, which is chosen as the $x$ axis.

Figure 4

(Color online) Distribution of magnetic domains in chains of maghemite platelets with different number of platelets. The figure shows stable configurations obtained with the use of the relaxation procedure described in Sec. 2B. For each chain length the so-called 1D and 4D configurations are considered (see text). The number of platelets in the chain is given near the image of the corresponding structure. For the computation the system was subdivided into cubic elements of $10\times 10\times 10{\text{nm}}^3$ and the external magnetic field of 0.5 G is directed along the chain.

Figure 5

(Color online) Relative magnetization of the maghemite platelet chains shown in Fig. 4. Plot (a): components of the magnetization vector calculated for the 1D structures; plot (b): components of the magnetization vector calculated for the 4D structures. The values are normalized to the saturation magnetization of maghemite given in Table . The dashed curve in (b) was calculated using Eq. (21) and illustrates the magnetic field amplification mechanism in the system.

Figure 6

(Color online) Calculated distributions of magnetic domains in chains with eight, nine, and ten maghemite platelets. Prior to relaxation all platelets were assumed to have four equally sized circular magnetic domains. The external magnetic field of 0.5 G is applied along the chain. For the computation the system was subdivided into cubic elements of $20\times 20\times 20{\text{nm}}^3$.

Figure 7

(Color online) Relative magnetization calculated for the chains of maghemite platelets with $N\le 10$. The structures with eight, nine, and ten platelets are shown in Fig. 6. In the micromagnetic calculation the system is subdivided into cubic elements of $20\times 20\times 20{\text{nm}}^3$. The external magnetic field is directed along the chain being equal to 0.5 G.

Figure 8

(Color online) The total energy of the maghemite platelet chains calculated using Eq. (3) for structures with different distributions of magnetic domains as a function of the number of platelets in the system. The calculated energies correspond to the stable structures shown in Figs. 4, 6. Squares show the energies calculated for the 1D configurations, while dots and triangles show the results obtained for the 4D configurations. For the micromagnetic computation the chains were subdivided into cubic elements of $10\times 10\times 10{\text{nm}}^3$ (squares and dots) and $20\times 20\times 20{\text{nm}}^3$ (triangles). The open triangle for $N=10$ corresponds to the energy calculated for the structure shown in Fig. 6. The energy for this structure is shown by a different symbol because the structure with $N=10$ cannot be considered as a 4D configuration, since in an external magnetic field of 0.5 G the 4D configuration in a chain with ten platelets is not stable.