Tuning magnetoelectricity in a mixed-anisotropy antiferromagnet

Abstract

Control of magnetization and electric polarization is attractive in relation to tailoring materials for data storage and devices such as sensors or antennae. In magnetoelectric materials, these degrees of freedom are closely coupled, allowing polarization to be controlled by a magnetic field, and magnetization by an electric field, but the magnitude of the effect remains a challenge in the case of single-phase magnetoelectrics for applications. We demonstrate that the magnetoelectric properties of the mixed-anisotropy antiferromagnet LiNi_1-xFe_xPO₄ are profoundly affected by partial substitution of Ni²⁺ ions with Fe²⁺ on the transition metal site. This introduces random site-dependent single-ion anisotropy energies and causes a lowering of the magnetic symmetry of the system. In turn, magnetoelectric couplings that are symmetry-forbidden in the parent compounds, LiNiPO₄ and LiFePO₄, are unlocked and the dominant coupling is enhanced by almost two orders of magnitude. Our results demonstrate the potential of mixed-anisotropy magnets for tuning magnetoelectric properties.

Fig. 1. Unit cell, (x, T) phase diagram and magnetic susceptibility of LiNi_1−xFe_xPO₄.

a Crystallographic unit cell of LiMPO₄ with four magnetic ions (red numbered spheres) and the two most important exchange paths, J_bc and J_ab, shown. The MO₆ octahedra and PO₄ tetrahedra are illustrated with red and blue shading, respectively. b (x, T) phase diagram constructed from experimental data and simulation. The open circles correspond to phase transitions observed in the simulated specific heat. Filled stars represent phase transitions detected in magnetic susceptibility and neutron diffraction experiments for samples with x = 0, 0.06, 0.20 and 1. Both simulations and experiments reveal three phases: Commensurate phases with S∣∣c (grey shading) and S∣∣b (blue shading) are seen at small and large x, respectively, while an oblique phase is present in the range 0.1 < x < 0.6 (red shading). For each phase, the observed form of the magnetoelectric tensor at low temperature is indicated. The gradient of the blue shading illustrates that the ordered moment along b, 〈S∣∣b〉, decreases when decreasing x while 〈S∣∣a〉 ≈ 〈S∣∣c〉 = 0. For small x there exists an incommensurate (IC) phase in a narrow temperature interval above the commensurately ordered phase (cyan shading)^,. c Magnetic susceptibility of LiNi_0.8Fe_0.2PO₄ measured with 0.5 T applied along the three crystallographic axes; a (red curve), b (blue curve) and c (grey curve). Fits to the Curie-Weiss law are shown with black lines. The solid parts of the lines indicate the fitted interval (50−300 K) and the dash-dotted parts are extrapolations to lower temperatures. The vertical dashed lines mark transitions at 21 and 25 K. d, e Corresponding susceptibilities for LiNiPO₄ and LiFePO₄, measured with 0.5 and 0.1 T respectively. Reprinted with permission from refs. and . Copyright (2023) by the American Physical Society. Error bars in all panels are smaller than symbol sizes.

Fig. 2. Neutron diffraction.

a Temperature profiles of neutron diffraction intensities for three magnetic Bragg peaks for LiNi_0.8Fe_0.2PO₄. Circle, diamond and square symbols denote (0, 0, −1), (0, 1, 0) and (3, 0−1) respectively. Intensities are scaled as indicated in the legend. The solid lines show the fits described in the main text. Peak intensities obtained with polarized neutrons in the NSF (b and d) and SF (c and e) channels after correcting for non-perfect beam polarization. Circle, diamond and square symbols are for neutron polarizations along x, y and z respectively. The symbols are coloured black for nuclear or total magnetic scattering, red for S∣∣a, blue for S∣∣b and purple for S∣∣c. The crystal was oriented with the a axis vertical such that NSF intensities for P∣∣z reflect a axis spin components for both (0,1,0) and (0,0,1). Grey curves in d, e show optical second harmonic generation measurements reprinted with permission from ref. . Copyright (2023) by the American Physical Society. f Moment rotation angle, φ, as a function of temperature with insets showing projections in the (0, 0, 1) plane of the magnetic structures for T ≤ T₁ and T₁ ≤ T ≤ T₂. The red and blue shadings illustrate the extends of the two respective phases. The two transitions at T₁ and T₂ are marked by vertical dashed lines in all panels. Error bars of the neutron counts, N, follow Poisson statistics as $\sqrt{N}$ and the errors in f are propagated from the neutron counts. Error bars are smaller than symbol sizes in all panels.

Fig. 3. Pyrocurrent and magnetoelectric effect.

Panels a-c show the pyrocurrent for LiNi_0.8Fe_0.2PO₄ as a function of temperature for magnetic fields applied along a (red and orange curves), b (dark and light blue curves) and c (grey and black curves), respectively. The insets indicate which elements of the ME tensor, α, were probed. The error on the measured current is of the order of 5 fA. The colour codes given in a–c are followed in the remaining panels of this figure. d Electric polarization as a function the reduced temperature with transition temperatures 21, 25 and 50 K at zero field for LiNiPO₄, LiNi_0.8Fe_0.2PO₄ and LiFePO₄, respectively. Note the two y-axes: the left one for the data for the mixed system (solid lines) and the right one for the parent compounds (dashed lines). The curve shown for LiNiPO₄ is from ref. and that for LiFePO₄ is reprinted with permission from ref. . Copyright (2023) by the American Physical Society. e Temperature dependency of the electric polarization originating from tensor elements not present in the parent compounds. For T < T₁ and T₁ < T < T₂, all observed non-zero ME tensor elements in LiNi_0.8Fe_0.2PO₄ are indicated. The measurements shown in a-e were carried out with an applied magnetic field strength of 2 T where the ME effect is still linear. The errors on the polarization are of the order of 1 μCm⁻². f Field dependency of the average of the induced electric polarization for T < 5 K for non-zero couplings. The error bars are estimated from the variations observed in the temperature profiles of the polarization (see Supplementary Fig. 4). Note that strong and weak ME components are plotted on two different y-axes as illustrated with encircled symbols and arrows. The dashed lines are linear fits, $P_i^{\mathrm{E}}={\alpha }_{ij}{H}_j$, to the data with the obtained ME coefficients, α_ij, listed in the legend. The inset shows the corresponding data for LiFePO₄ with H∣∣b, E∣∣a.

Fig. 4. Monte Carlo simulations.

a Magnetic susceptibility (left axis) for fields along a (red curve), b (blue curve) and c (grey curve) and specific heat (right axis, black curve) for LiNi_1−xFe_xPO₄ with x = 0.20. b–d The absolute value of the C-type order parameter plotted as a function of temperature for spin components along the three crystallographic axes and for different values of x. The colours of the curves illustrate the Fe concentration from red (x = 0) over blue to grey (x = 1). Note that in d the curves for x ≥ 0.20 coincide. The maximum error bar sizes for each of the variables are indicated at the lowest temperatures in a and b.