  Recent breakthroughs in quantum technology pave the way for extensive
utilization of higher-dimensional quantum systems, which outperform their qubit
counterparts in terms of capabilities and versatility. We present a framework
for accurately predicting weak external magnetic fields using a
higher-dimensional many-body quantum probe. We demonstrate that dimension
serves as a valuable resource for quantum sensing when a transverse spin-s
Ising chain interacts locally with a magnetic field whose strength has to be
determined. We observe the distinct performance of sensors for spin chains with
half-integer and integer spins. Furthermore, we highlight that the time
duration appropriate for quantum-enhanced sensing increases with the increase
of dimension. Additionally, we observe that, in addition to nearest-neighbor
interactions, incorporating interactions between the next nearest-neighbor
sites increases sensing precision, particularly for spin chains with integer
spins. We also prove the dimensional-dependence of the bound on quantum Fisher
information which provides the limit on the precision in estimating parameters.
