Which one of the following species responds to an external magnetic field?

To determine which species responds to an external magnetic field, we identify the complex containing unpaired electrons.

Complexes with unpaired electrons are:

$$\mathrm{Paramagnetic}$$

while complexes with all electrons paired are:

$$\mathrm{Diamagnetic}$$

(A)

$$\mathrm{[Fe(H_2O)_6]^{3+}}$$

Oxidation state of iron:

$$\mathrm{Fe^{3+}}$$

Electronic configuration:

$$\mathrm{3d^5}$$

$$\mathrm{H_2O}$$ is a weak field ligand and does not cause electron pairing.

Thus, the complex contains:

$$\mathrm{5\ unpaired\ electrons}$$

Hence:

$$\mathrm{[Fe(H_2O)_6]^{3+}}$$

is strongly paramagnetic.

(B)

$$\mathrm{[Ni(CN)_4]^{2-}}$$

Oxidation state of nickel:

$$\mathrm{Ni^{2+}}$$

Electronic configuration:

$$\mathrm{3d^8}$$

$$\mathrm{CN^-}$$ is a strong field ligand and causes complete pairing of electrons.

Thus:

$$\mathrm{0\ unpaired\ electrons}$$

Hence, the complex is diamagnetic.

(C)

$$\mathrm{[Co(CN)_6]^{3-}}$$

Oxidation state of cobalt:

$$\mathrm{Co^{3+}}$$

Electronic configuration:

$$\mathrm{3d^6}$$

$$\mathrm{CN^-}$$ is a strong field ligand.

All electrons pair in the lower-energy orbitals.

Thus:

$$\mathrm{0\ unpaired\ electrons}$$

Hence, the complex is diamagnetic.

(D)

$$\mathrm{[Ni(CO)_4]}$$

Oxidation state of nickel:

$$\mathrm{Ni^0}$$

Electronic configuration:

$$\mathrm{3d^{10}}$$

$$\mathrm{CO}$$ is a very strong field ligand and causes complete pairing.

Thus:

$$\mathrm{0\ unpaired\ electrons}$$

Hence, the complex is diamagnetic.

Therefore, the only paramagnetic complex is:

$$\boxed{\mathrm{[Fe(H_2O)_6]^{3+}}}$$

Correct option:

$$\boxed{\mathrm{A}}$$