Wide range linear magnetometer based on a sub-microsized K vapor cell

³⁹K atoms have the smallest ground state (²S_1/2) hyperfine splitting of all the most naturally abundant alkali isotopes and, consequently, the smallest characteristic magnetic field value B₀=A/μ_B≈170G, where A is the ground state's magnetic dipole interaction constant. In the hyperfine Paschen-Back regime (B≫B₀, where B is the magnitude of the external magnetic field applied on the atoms), only eight Zeeman transitions are visible in the absorption spectrum of the D₁ line of ³⁹K, while the probabilities of the remaining 16 Zeeman transitions tend to zero. In the case of ³⁹K, this behavior is reached already at relatively low magnetic field B>B₀. For each circular polarization (σ^-,σ⁺), four spectrally resolved atomic transitions having sub-Doppler widths are recorded using a sub-microsized vapor cell of thickness L=120-390nm. We present a method that allows to measure the magnetic field in the range of 0.1-10kG with micrometer spatial resolution, which is relevant in particular for the determination of magnetic fields with large gradients (up to 3 G/µm). The theoretical model describes well the experimental results.