Magnetic properties of the low-dimensional spin-$\frac{1}{2}$ magnet $\alpha$-Cu${}_2$As${}_2$O${}_7$

In this work, we study the interplay between the crystal structure and magnetism of the pyroarsenate $\alpha$-Cu${}_2$As${}_2$O${}_7$ by means of magnetization, heat capacity, electron spin resonance, and nuclear magnetic resonance measurements as well as density functional theory (DFT) calculations and quantum Monte Carlo (QMC) simulations. The data reveal that the magnetic Cu-O chains in the crystal structure represent a realization of a quasi-one-dimensional (1D) coupled alternating spin-1/2 Heisenberg chain model with relevant pathways through nonmagnetic AsO${}_4$ tetrahedra. Owing to residual 3D interactions, antiferromagnetic long range ordering at $T_{\mathrm{N}}\simeq 10$ K takes place. Application of the external magnetic field $B$ along the magnetically easy axis induces the transition to a spin-flop phase at $B_{\mathrm{SF}}\sim 1.7$ T (2 K). The experimental data suggest that substantial quantum spin fluctuations take place at low magnetic fields in the ordered state. DFT calculations confirm the quasi-one-dimensional nature of the spin lattice, with the leading coupling $J_1$ within the structural dimers. QMC fits to the magnetic susceptibility evaluate $J_1=164$ K, the weaker intrachain coupling $J_1^{\prime }/J_1=0.55$, and the effective interchain coupling $J_{\mathrm{ic}1}/J_1=0.20$.

Figure 1

The crystal structure of $\alpha$-Cu${}_2$As${}_2$O${}_7$. (a) Edge-sharing Cu${}_2$O${}_6$ plaquettes form structural dimer units along the $b$ axis. The dimers are linked by AsO${}_4$ anion groups forming a plane of coupled dimer chains; (b) Side view of the chain planes linked with interjacent As${}_2$O${}_7$ anions.

Figure 2

Magnetic susceptibility $\chi =M/B$ of a $\alpha$-Cu${}_2$As${}_2$O${}_7$ single crystal measured at $B=1$ T applied along the crystallographic $b$- and $c$-axis, respectively.

Figure 3

Temperature dependence of the magnetic susceptibility $\chi \left(T\right)$. Inset: The pronounced anomaly in the Fisher's heat capacity $\partial$($\chi T$)/$\partial T$ at $B=1$ T along the $b$-axis implies long-range magnetic order below $T_{\mathrm{N}}\simeq 10$ K.

Figure 4

Magnetic field $B$ dependence of the magnetization $M$ for $B\parallel b$ axis at different temperatures slightly above and below $T_{\mathrm{N}}$. CP and SF denote the presumably collinear phase in the low-field regime and the spin-flop phase at high magnetic fields. The spin-flop transition at $B_{\mathrm{SF}}\simeq 1.7$ T ($T=2$ K) is associated with the magnetic anisotropy in the system.

Figure 5

Upper panel: Temperature dependence of the specific heat capacity $c_{\mathrm{p}}$ at $B=0$ and 9 T; lower panel: Experimental data in different magnetic fields $B\parallel b$-axis after subtraction of an arbitrary polynomial background function $f$($T$) = a$T$ + b$T^3$. $T_{\mathrm{N}}^{\chi }$ indicates the temperature of the anomaly in $\partial$($\chi T$)/$\partial T$ at small fields (cf. Fig. 3).

Figure 6

Magnetic phase diagram for $\alpha$-Cu${}_2$As${}_2$O${}_7$ single crystals according to magnetization and specific heat measurements when applying field along the magnetically easy $b$-axis.

Figure 7

Temperature dependence of the ESR parameters with $B\parallel b$ at 340 GHz. Main panel: effective $g$-factor and linewidth, upper and lower curve respectively. Inset: The shift of the ESR resonance line at low temperature reflects the increasing internal magnetic field in the vicinity of the ordered state.

Figure 8

Frequency versus resonance field diagram of the ESR signal in the ordered and paramagnetic states for $B\parallel b$. At 4 K a single resonance mode is observed above $\sim$5 T (solid circles). Solid thin line corresponds to the paramagnetic resonance branch $\nu =g{\mu }_{\mathrm{B}}{B}_{\mathrm{res}}/h$. Solid thick lines show the expected AFM resonance branches for uniaxial anisotropy with $B\parallel$ easy b-axis.[16]

Figure 9

${}^{75}$As NMR spectra (dots) measured at 30 K and 4 K for the magnetic field direction parallel to the $b$-axis. Solid lines represent simulated spectra (see the text).

Figure 10

Temperature dependence of the ${}^{75}$As spin lattice relaxation rate ${\left(T_1^{-1}T\right)}^{-1}$ in comparison with the static susceptibility. Thin solid line is the guide for the eye.

Figure 11

LDA total and atomic-resolved density of states of $\alpha$-Cu${}_2$As${}_2$O${}_7$. The main contribution to the valence band is due to Cu and O states (full orange and dashed red line, respectively). The Fermi level is at zero energy.

Figure 12

Microscopic spin model for $\alpha$-Cu${}_2$As${}_2$O${}_7$. Magnetic layers are formed by alternating $J_1-J_1^{\prime }$ chains running along $b$ that are coupled by two inequivalent couplings $J_{\mathrm{ic}1}$ and $J_{\mathrm{ic}3}$. The leading coupling $J_1$ corresponds to the magnetic exchange within the structural Cu${}_2$O${}_6$ dimers.

Figure 13

QMC fits to the experimental (exp.) magnetic susceptibility. The $J_1:J_1^{\prime }:J_{\mathrm{ic}1}$ ratios are given in the legend. The difference plots (inset) indicate the relative goodness of fit ${\left(\Delta \chi /\chi \right)}^2$ for the two parameter sets of $J_1:J_1^{\prime }:J_{\mathrm{ic}1}$.

Figure 14

Left panel: diagonal spin correlations $\langle S_0^z{S}_{\text{R}}^z\rangle$(R) in the magnetic ground state of Cu${}_2$As${}_2$O${}_7$. The correlations along $J_1$-$J_1^{\prime }$ bonds (thick solid line, empty squares) closely resemble those of an alternating Heisenberg chain with $J_1^{\prime }$:$J_1=0.55$ (dotted line). In contrast, the correlations between the $J_1$-$J_1^{\prime }$ chains are substantially smaller (dashed and thin solid lines). Right panel: 0-$R$ pathes in the spin lattice of Cu${}_2$As${}_2$O${}_7$ used for the $\langle S_0^z{S}_{\text{R}}^z\rangle$(R) plot in the left panel.