## 2 Materials and Methods  
The operation of the rf atomic magnetometer relies on the optical detection of couplings between neighbouring Zeeman sublevels of an atomic ground state generated by an oscillating rf magnetic field. Measurement output, i.e., inductive signal, reflects changes in the amplitude and phase of the rf resonance produced in atoms mainly by the secondary rf magnetic field. The rf spectrum is created by monitoring of the magnetometer signal as the rf field frequency is scanned across the magnetic resonance. Details of the signal generation could be found elsewhere [10,21], here we recall the major parts of the experimental setup. The experiment instrumentation consists of three separate parts: the sensor (rf atomic magnetometer labelled as (3) in Figure 1), the object (2) on a 2D (XY) translation stage, and, the primary rf coil (1) that has a variable lift-off (Z). The rf atomic magnetometer consists of a paraffin-coated caesium atomic vapour cell, two laser beams to interact with the atoms and detection optics/electronics for signal readout, Figure 2a. The volume of the roughly cubic vapour cell is 1 cm\({}^{3}\) and defines the sensing volume. The cell is at ambient temperature (stabilised at 21 \({}^{\circ}\)C \(\pm\) 1 \({}^{\circ}\)C by the laboratory air conditioning) and in a static magnetic bias field created by tri-axial square Helmholtz coils (side lengths of 1 m, 0.94 m, and 0.86 m). These coils are used with a proportional-integral-derivative (PID) feedback control loop to stabilise the magnetic field (all three axis) that is measured at a fluxgate (three axes Bartington Mag690) close to the cell. PID settings are chosen to also remove  
Figure 1: Generic configuration of an inductive measurement arrangement. The primary rf field (green arrow) produced by the rf coil (1) causes the response of the object (2) in the form of a secondary field (yellow arrow). The signal is recorded by a sensor (3). Here, the radio-frequency atomic magnetometer monitors only the components of the secondary field orthogonal to the sensor axis (black arrow). Lift-off, distance between primary field source and object, is labelled by the red arrow. Concentric yellow circles represent eddy currents, that have mainly surface character. In general, there could be also a component produced by object magnetisation that exhibits volume character. 50 Hz electronic magnetic field noise. The magnitude of the bias magnetic field defines the rf (Larmor) resonance frequency of the caesium atoms. A circularly polarised laser beam directed along the bias field, called the pump beam, creates a population imbalance within the ground state of the atomic energy levels, polarising the atomic spin states along the bias magnetic field. The beam is locked to the 6 \({}^{2}\)S\({}_{1/2}\) F = 3\(\rightarrow\) 6 \({}^{2}\)P\({}_{3/2}\) F\({}^{\prime}\) = 2 resonance transition (\(D_{2}\) line, 852 nm) and pumps atoms into a stretched state of the F = 4 ground state level, Figure 2b. Transfer of the atoms is achieved by so-called indirect pumping, which combines strong resonant pumping within the F = 3 level through the 6 \({}^{2}\)S\({}_{1/2}\) F = 3\(\rightarrow\) 6 \({}^{2}\)P\({}_{3/2}\) F\({}^{\prime}\) = 2 closed transition, spin-exchange collisions that replicate the F = 3 population imbalance in the F = 4 level, and transfer of the population from the F = 3 to F = 4 level through the off-resonant 6 \({}^{2}\)S\({}_{1/2}\) F = 3\(\rightarrow\) 6 \({}^{2}\)P\({}_{3/2}\) F\({}^{\prime}\) = 4, 5 transitions. Indirect pumping simultaneously addresses two aspects relevant to the magnetometer performance: (1) it depletes the F = 3 level, so that more atoms can contribute to the signal, (2) it creates a high degree of orientation within the F = 4 level without direct optical coupling, which both reduces the width of the rf resonance and increases the signal-to-noise ratio.