In this paper, the magnetic and transport properties were systematically studied for EuAg$_4$As$_2$ single crystals, crystallizing in a centrosymmetric trigonal CaCu$_4$P$_2$ type structure. It was confirmed that two magnetic transitions occur at $te
xtit{T}$$_{N1}$ = 10 K and $textit{T}$$_{N2}$ = 15 K, respectively. With the increasing field, the two transitions are noticeably driven to lower temperature. At low temperatures, applying a magnetic field in the $textit{ab}$ plane induces two successive metamagnetic transitions. For both $textit{H}$ $parallel$ $textit{ab}$ and $textit{H}$ $parallel$ $textit{c}$, EuAg$_4$As$_2$ shows a positive, unexpected large magnetoresistance (up to 202%) at low fields below 10 K, and a large negative magnetoresistance (up to -78%) at high fields/intermediate temperatures. Such anomalous field dependence of magnetoresistance may have potential application in the future magnetic sensors. Finally, the magnetic phase diagrams of EuAg$_{4}$As$_{2}$ were constructed for both $textit{H}$ $parallel$ $textit{ab}$ and $textit{H}$ $parallel$ $textit{c}$.
We develop a theory of the magnetic field-induced formation of Skyrmion crystal state in chiral magnets in two spatial dimensions, motivated by the recent discovery of the Skyrmionic phase of magnetization in thin film of Fe$_{0.5}$Co$_{0.5}$Si and i
n the A-phase of MnSi. Ginzburg-Landau functional of the chiral magnet re-written in the CP$^1$ representation is shown to be a convenient framework for the analysis of the Skyrmion states. Phase diagram of the model at zero temperature gives a sequence of ground states, helical spin $rightarrow$ Skyrme crystal $rightarrow$ ferromagnet, as the external field $B$ increases, in good accord with the thin-film experiment. In close analogy with Abrikosovs derivation of the vortex lattice solution in type-II superconductor, the CP$^1$ mean-field equation is solved and shown to reproduce the Skyrmion crystal state.
