## Introduction

Over the last years we have been investigating one-dimensional magnets containing CuX_{2} ribbon chains because of their unusual intrachain nearest- and next-nearest neighbor spin exchange relations between the *S*=1/2 magnetic entities. These CuX_{2} ribbon chains are formed by linking CuX_{4} basal-square-planes of axially elongated CuX_{6 }(X=O, Cl, Br,...) octahedra together via their trans-edges.

In such ribbon chain compounds it is frequently found that the spin exchange interactions are such that the next-nearest-neighbor (NNN) exchange is antiferromagnetic (AFM), the nearest-neighbor (NN) exchange is ferromagnetic (FM), and the NNN spin exchange is often considerably stronger than the NN spin exchange. Due to the inherent competition of the NN and NNN spin exchange interactions, such CuX_{2} ribbon chain systems have been observed to develop unusual AFM incommensurate spiral spin structures [1] and sometimes concomitantly multiferroic behavior[2].

**Fig. 1:** Crystal structure of CuAs_{2}O_{4}. The oxygen atoms are represented by small (red) spheres, and the arsenic atoms by (dark grey) medium spheres. The Cu^{2+} cations are located in the center of considerably axially elongated oxygen octahedra. The As atoms form AsO_{3} pyramids, which link the oxygen atoms in the basal planes with the apical oxygen atoms of neighboring chains such that the basal planes of neighboring chains are perpendicular to each other.

Over the last decade, much interest has been devoted to ribbon chain systems with spin exchange parameters lying within the so-called frustrated regime, i.e. between the Majumdar-Ghosh point, a=*J*_{NN}/J_{NNN}=2, and the "FM point", a=-4. a=-4 constitutes a quantum critical point (QCP) in the vicinity of which small perturbations, such as interchain exchange and anisotropic exchange couplings may induce a pronounced response of the system.

Here we describe the magnetic properties of Trippkeite (CuAs_{2}O_{4}), featuring edge-sharing CuO_{2} ribbon chains. CuAs_{2}O_{4} is exceptional because it shows a FM ground state below ≈7.4K [3]. Trippkeite is a natural mineral which is isostructural to the family of compounds with the general composition MT_{2}O_{4} (M^{2+}=Mg, Mn, Fe, Co, Ni, Zn; T^{3+}=As, Sb, Bi), with schafarzikite, FeSb_{2}O_{4}, being the most popular member. **Figure 1** illustrates the crystal structure of CuAs_{2}O_{4}.

Magnetic properties of CuAs_{2}O_{4}

**Fig. 2:** Inverse magnetic susceptibility (corrected by χ_{0} for diamagnetic and van Vleck paramagnetic contributions from closed electronic shells) of a polycrystalline sample of CuAs_{2}O_{4 }(main panel). The solid red line is a result of a TMRG calculation of the magnetic for the ratio *J*_{NN}/*J*_{NNN}=-4.25, assuming FM NN spin exchange interaction and AFM NNN spin-exchange interaction of -38K. (upper inset) Low-temperature heat capacity of CuAs_{2}O_{4}. (lower panel)The anisotropy of the Cu magnetic moment determined on a small single crystal of 8mg at 1.85K.

**Figure 2** summarizes the magnetic properties of CuAs_{2}O_{4}. CuAs_{2}O_{4} shows long-range FM order below a Curie temperature of ≈7.4K indicated by a rapid increase of the magnetization and a l-type anomaly in the heat capacity. At 1.85K the magnetization of a small single crystal (≈8mg) exhibits saturation with a saturated moment of 1.2m_{Bohr}, in good agreement with the expect saturation moment of a Cu^{2+} spin *S*=1/2 system. The high-temperature magnetic susceptibility follows a Curie law with a Curie-Weiss temperature of 39K, indicating predominant FM spin exchange interactions. Below ≈150K the inverse susceptibility noticeably bends upwards away from the high-temperature Curie-Weiss law, similar to what has also been observed in the integrated signal intensity gained from the EPR spectroscopy experiment (not shown here). The temperature dependence of the susceptibility over the whole temperature range, including the upward deviation from the high-temperature Curie-Weiss law, can be well modeled by the magnetic susceptibility of a Heisenberg chain with NN and NNN spin exchange interactions calculated employing the Transfer Matrix Renormalization Group (TMRG) method. Figure 2 (main frame) displays our experimental data in comparison with the TMRG susceptibility results calculated for the ratio *J*_{NN}/*J*_{NNN}=-4.25 and *J*_{NNN}≈-38K and a g-factor of g=2.16, the latter being very close to the g-factor obtained from the Curie-Weiss fit of the high-temperature susceptibility data.

## Density Functional Theory (DFT) calculation of the spin exchange parameters

The NN and NNN intrachain spin exchange interactions, *J*_{NN} and *J*_{NNN}, of CuAs_{2}O_{4} were evaluated by performing energy-mapping analyses based on first-principles DFT calculation. We calculated the electronic energies of three magnetically ordered (one FM; two different AFM configurations) by employing the projected augmented-wave method encoded in the Vienna *ab initio* simulation package and the generalized gradient approximation for the exchange and correlation functional. The energies states were written in terms of the standard Heisenberg spin Hamiltonian invoking NN and NNN intrachain spin exchange interactions. In order to probe the effect of electron correlations associated with the Cu 3*d* orbitals, we performed DFT plus on-site repulsion (DFT+*U*) calculations with *U*_{eff}=0, 4, 6 and 8eV for Cu. The results of the mapping analysis are summarized in **Tab. 1**.

U_{eff }(eV) |
J_{NN} (K) |
J_{NNN} (K) |

0 | 42.3 | -25.9 |

4 | 38.8 | -13.5 |

6 | 34.0 | -10. |

8 | 27.5 | -7.1 |

**Tab. 1:** Values of the NN and NNN spin exchange constants, *J*_{NN} and *J*_{NNN}, respectively, obtained from the DFT+*U *calculations.

The strong FM-NN interaction in CuAs_{2}O_{4} is traced to the fact that the bond angle of the Cu-O-Cu superexchange path is close to 90° (≈91.5°) and the magnetic orbitals of the NN Cu^{2+} ions lead to a large overlap density around the bridging oxygen atoms. The weaker AFM–NNN interaction is a consequence of the twisting of the CuO_{2} ribbon chains which reduces the hopping integral between the NNN Cu^{2+} ions. The *U*_{eff} values of 6 and 8eV, most appropriate for Cu^{2+}, indicate -3.9<*J*_{NN}/*J*_{NNN}<-3.4 close to the FM–QCP at α=-4 and the experimental finding.

## Pressure dependence of the FM Curie temperature

**Fig. 3:** Low-field magnetic susceptibility of a polycrystalline sample of CuAs_{2}O_{4} measured with different hydrostatic pressures applied. The inset shows the pressure dependence of the Curie temperature.

Several CuO_{2} ribbon chain systems with α≈-4 and FM alignment of the moments within a single ribbon chain have been investigated before, however none of which showed long-range FM ordering at low temperatures. Due to weak interchain spin exchange interactions, some systems which do contain FM ribbon chains actually exhibit long-range AFM ordering with an antiparallel alignment of the neighboring chains. Other systems with α≈-4 have been found to undergo an AFM incommensurate spin-spiral structure along the ribbon chains at low temperature. In order to investigate the stability of the FM groundstate of CuAs_{2}O_{4} we have carried out magnetization measurements under hydrostatic pressure. We found that hydrostatic pressure stabilizes the FM groundstate and a moderate magnitude hydrostatic pressure leads to a linear increase of the Curie temperature with pressure (**Fig. 3**).