Charge Ordering and Magnetic Exchange in the Ladder-Type Compound NH$_4$V$_2$O$_5$

The low-temperature electronic and magnetic properties of NH$_4$V$_2$O$_5$, an isoelectronic analog of the spin-ladder compound $\alpha'$-NaV$_2$O$_5$, are investigated using DFT+$U$ calculations. Two charge-ordering patterns - zigzag and linear chains of V$^{4+}$/V$^{5+}$ ions - are considered. The zigzag configuration is found to be energetically preferred and exhibits insulating behavior with a band gap of 1.7 eV. In this state, magnetic V$^{4+}$ (d$^1$) ions form antiferromagnetically coupled spin chains. Calculated exchange interactions reveal strong diagonal (intrarung) and interladder couplings, indicating a complex spin-ladder network. These results suggest that NH$_4$V$_2$O$_5$ retains essential spin-ladder characteristics while displaying new structural and magnetic features arising from the larger size and non-spherical geometry of the NH$_4^+$ ion compared to Na$^+$.