Neutron diffraction, muon-spin rotation, and high magnetic field investigation of the multiferroic antiferromagnetic quantum spin-chain system ${\mathrm{CuCrO}}_4$

Multiferroic behavior in the linear-chain spin $S=1/2$ compound ${\mathrm{CuCrO}}_4$ was proposed to appear due to competing nearest- and next-nearest-neighbor exchange interactions along the chain. Here, we report on our study of the long-range magnetic ordering using powder neutron diffraction and muon-spin rotation measurements. Consistently, both methods find incommensurate long-range antiferromagnetic ordering below 8.5(3) K. We determined the magnetic structure from neutron powder diffraction patterns based on the propagation vector $\vec{\tau }=(0,0,0.546\left(1\right))$. At 1.9 K, the magnetic moment of ${\mathrm{Cu}}^{2+}$ was refined to 0.48(2) ${\mu }_{\mathrm{B}}$. The Cu moments form a helicoidal spiral with an easy plane coinciding with the equatorial planes of the Jahn-Teller elongated ${\mathrm{CuO}}_6$ octahedra. Low-temperature high magnetic field measurements of the magnetization and the dielectric polarization show the multiferroic phase to extend up to $\sim 25$ T, after which a new, yet unknown phase appears. Full saturation of the magnetic moment is expected to occur at fields much beyond 60 T.

Figure 1

Crystal structure of ${\mathrm{CuCrO}}_4$ at 2 K as derived from the profile refinement of the HRPT 2-K NPD pattern. The blue and black spheres represent Cu and Cr cations, respectively. The oxygen atoms O1 (apical) and O2 (equatorial) are shown as red spheres. The diameters of the spheres correspond to the isotropic displacement parameters listed in Table 1.

Figure 2

NPD patterns of ${\mathrm{CuCrO}}_4$ collected at the multidetector neutron diffractometer HRPT at 20 K (top) and 2 K (bottom) using neutrons of 1.8857 Å wavelength. Magnetic Bragg reflections are not resolved in the 2-K pattern. The red circles represent the measured data, and the black solid line is the result of the Rietveld profile refinement. The blue solid line at the bottom of the graph shows the difference between the observed and calculated patterns. The vertical blue ticks mark the angles of the Bragg reflections used to calculate the refined pattern.

Figure 3

(a) Solid black line: The measured magnetic susceptibility, at 2.7 K, vs external magnetic field. The dotted red line is a fit to the data; see text for details. Inset: Magnetization vs applied magnetic field; the solid black line represent the pulsed-field collected data, and the solid red line is for the same sample measured in a SQUID magnetometer. (b) The real part of the dielectric permittivity measured in pulsed field (solid lines, left axis), and relative dielectric permittivity measured in dc fields, from Ref. [31] (dotted line, right axis).

Figure 4

(a) Heat map of the difference between neutron powder diffraction patterns of ${\mathrm{CuCrO}}_4$ measured between 1.9 and 9 K. The powder diffraction pattern taken at 9 K was subtracted to suppress nuclear scattering. The patterns have been collected with neutrons of a wavelength of 2.426 Å on ILL's medium-resolution high-intensity powder diffractometer, D20. Here, diff. counts, difference counts. (b) Difference of two neutron powder diffraction patterns collected at 1.9 and 9 K.

Figure 5

Integrated intensity vs temperature of the $20.1^{\circ }$ ($D$ = 6.95 Å) magnetic Bragg reflection. The red dashed line represents a fit of a power law according to Eq. (2) to the data points indicating a Néel temperature of $T_{\mathrm{c}}$ = 8.42(9) K and a critical exponent $\beta$ of 0.32(2). Error bars are of the size of the symbols. The upper and the lower insets display the heat capacity and the magnetic susceptibility (7 T), respectively, taken from Ref. [31]. In the insets the dotted vertical bars mark the critical temperature $T_{\mathrm{c}}$.

Figure 6

Difference of the neutron powder diffraction patterns of ${\mathrm{CuCrO}}_4$ collected at 1.9 and 9 K using neutrons with a wavelength of 2.426 Å. The inset displays the pattern at 1.9 K with a profile refinement assuming nuclear contributions only. Scaling factors are identical in both Rietveld refinements. The red circles represent the measured data, and the black solid lines are the result of the profile refinement. The blue solid line at the bottom of the graph shows the difference between the observed and calculated patterns. The vertical green ticks mark the angles of the magnetic Bragg reflections used to calculate the refined pattern.

Figure 7

(a) Magnetic structure of ${\mathrm{CuCrO}}_4$ at 1.9 K. Two nuclear unit cells are outlined. The ordered moment per Cu atom amounts to 0.48(1) ${\mu }_{\mathrm{B}}$. (b) Projection along [010] of the helicoidal spiral propagating along the crystallographic $c$ axis with ${\vec{\tau }}_c=0.546\left(1\right)$.

Figure 8

Zero-field $\mu \mathrm{SR}$ spectra on a short time scale. Note the strongly damped oscillation at 2.5 K indicative of long-range magnetic order with a broad internal-field distribution at magnetically inequivalent muon deposition sites.

Figure 9

Zero-field $\mu \mathrm{SR}$ spectra on a long time scale. Note the unusual functional form at high temperatures showing the presence of at least two crystallographically inequivalent muon sites. The spectrum at 2.5 K proves the presence of magnetic dynamics at this temperature since the long-time polarization falls below 1/3 (dashed line); see text.

Figure 10

Time-integrated muon-spin polarization, showing the onset of electronic relaxation below $\sim 9$ K and the absence of a magnetic anomalies between 10 and 160 K. The inset displays an enlarged view of the low-temperature region.

Figure 11

$\mu \mathrm{SR}$ frequency measuring the magnetic order parameter as a function of temperature. The red dashed line represents a mean-field power law [according to Eq. (2) with $2\beta$ = 0.5] with a critical temperature $T_{\mathrm{c}}$ = 8.1(3) K and zero frequency ${\nu }_0$ = 8.2(2) MHz.

Figure 12

Dynamic relaxation rate as a function of temperature showing a first peak at the Néel temperature and a second peak below $T_{\mathrm{N}}$ at 5 K. The dashed lines are guides to the eye.