Spin Flop Research Articles

Surface monolayers in a magnetic field

We study theoretically the magnetic properties of the surface monolayers with the antiferromagnetic (AF) and ferromagnetic (FM) exchange interactions where the Dzyaloshinskii-Moriya interaction (DMI) is a result of the mirror symmetry breaking. To study the DMI helices in magnetic field a method is proposed. In zero field the DMI gives rise a cycloid in both AF and FM cases. The cycloid orientation is determined by the DMI induced in-plane anisotropy with the symmetry of the layer lattice. As a result we have one, two and three chiral domains in the rectangular, square and triangular lattices respectively. The magnetic structure of the $M n/W(1 1 0)$ monolayer is explained. The out-of-plane anisotropy may restore a collinear magnetic order. The chiral domains are rotated by the in-plane field. In some field directions the spin flops are predicted. In the out-of-plane field the chirality follows the field direction. The length of the cycloid wave-vector decreases. In the perpendicular field there is the spin flop to the corresponding collinear state. A possibility of the layer electric polarization is discussed.

Collinear magnetic structure and multiferroicity in the polar magnet Co2Mo3O8

Among numerous multiferroic phenomena observed in spin frustrated lattice, giant magnetoelectricity in honeycomb lattice ${(\mathrm{Fe},\phantom{\rule{0.28em}{0ex}}\mathrm{Mn})}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ has stimulated great interest and substantial effort in searching for novel members in this 238 family. In this work, we synthesize successfully compound ${\mathrm{Co}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, a structural analogue of ${\mathrm{Fe}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$, and present a series of characterizations on its structural, magnetic, and electric properties. An antiferromagnetic transition takes place at the Neel temperature ${T}_{N}=39\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ with appearance of electric polarization and dielectric anomaly, which provides clear evidence of simultaneous magnetic and ferroelectric transitions. The neutron powder diffraction (NPD) and magnetic susceptibility data confirm the $c$-axis collinear antiferromagnetic orders and emergent ferroelectric polarization. In particular, such antiferromagnetic order is relatively robust against magnetic field up to 9 T, different from ${\mathrm{Fe}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ with ferrimagnetic transition or ${\mathrm{Mn}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ with spin flop in the low-field region. Our data on single crystals demonstrate the second-order magnetoelectric effect in terms of magnetic field dependence of ferroelectric polarization response, while no linear magnetoelectric response is allowed. It is suggested that ${\mathrm{Co}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ provides a unique platform on which rich multiferroic physics in the presence of collinear magnetic order can be explored.

Antiferromagnetic domain wall control via surface spin flop in fully tunable synthetic antiferromagnets with perpendicular magnetic anisotropy

Antiferromagnetic (AF) domain walls have recently attracted revived attention, not only in the emerging field of AF spintronics, but also more specifically for offering fast domain wall velocities and dynamic excitations up to the terahertz frequency regime. Here we introduce an approach to nucleate and stabilize an AF domain wall in a synthetic antiferromagnet (SAF). We present experimental and micromagnetic studies of the magnetization reversal in [(Co/Pt)$_{X-1}$/Co/Ir]$_{N-1}$(Co/Pt)$_X$ SAFs, where interface induced perpendicular magnetic anisotropy (PMA) and AF interlayer exchange coupling (IEC) are completely controlled via the individual layer thicknesses within the multilayer stack. By combining strong PMA with even stronger AF IEC, the SAF reveals a collective response to an external magnetic field applied normal to the surface, and we stabilize the characteristic surface spin flop (SSF) state for an even number N of AF-coupled (Co/Pt)$_{X-1}$/Co multilayer blocks. In the SSF state our system provides a well-controlled and fully tunable vertical AF domain wall, easy to integrate as no single crystal substrates are required and with uniform 2D-magnetization in the film plane for further functionalization options, such as for example lateral patterning via lithography.

Magnetic field-temperature phase diagram of multiferroic (NH4)2FeCl5\xb7H2O

Owing to their overall low energy scales, flexible molecular architectures, and ease of chemical substitution, molecule-based multiferroics are extraordinarily responsive to external stimuli and exhibit remarkably rich phase diagrams. Even so, the stability and microscopic properties of various magnetic states in close proximity to quantum critical points are highly under-explored in these materials. Inspired by these opportunities, we combined pulsed-field magnetization, first-principles calculations, and numerical simulations to reveal the magnetic field–temperature (B–T) phase diagram of multiferroic (NH4)2FeCl5⋅H2O. In this system, a network of intermolecular hydrogen and halogen bonds creates a competing set of exchange interactions that generates additional structure in the phase diagram—both in the vicinity of the spin flop and near the 30 T transition to the fully saturated state. Consequently, the phase diagrams of (NH4)2FeCl5⋅H2O and its deuterated analog are much more complex than those of other molecule-based multiferroics. The entire series of coupled electric and magnetic transitions can be accessed with a powered magnet, opening the door to exploration and control of properties in this and related materials.

V51 -NMR study on the S=12 square lattice antiferromagnet K2V3O8

Static and dynamic properties of the quasi-two-dimensional antiferromagnet K$_2$V$_3$O$_8$ have been investigated by $^{51}$V-NMR experiments on nonmagnetic V$^{5+}$ sites. Above the structural transition temperature $T_{\rm{S}}$ = 115 K, NMR spectra are fully compatible with the $P4bm$ space group symmetry. The formation of superstructure below $T_{\rm{S}}$ causes splitting of the NMR lines, which get broadened at lower temperatures so that individual peaks are not well resolved. Evolution of NMR spectra with magnetic field along $c$-axis below the magnetic transition temperature $T_{\rm{N}} \sim 4$ K is qualitatively consistent with a simple N\'{e}el order and a spin flop transition. However, broad feature of the spectra does not rule out possible incommensurate spin structure. The spin-lattice relaxation rate $1/T_1$ below $T_{\rm{N}}$ shows huge enhancement for a certain range of magnetic field, which is independent of temperature and attributed to cross relaxation due to anomalously large nuclear spin-spin coupling between V$^{5+}$ and magnetic V$^{4+}$ sites. The results indicate strong gapless spin fluctuations, which could arise from incommesurate orders or complex spin textures.

Magnetic anisotropy and topological Hall effect in the trigonal chromium tellurides Cr5Te8

Nontrivial spin configurations tend to bring about novel transport properties in magnetic materials. We report the magnetic anisotropy and topological Hall effect in trigonal ${\mathrm{Cr}}_{5}{\mathrm{Te}}_{8}$ single crystals. Below the magnetic transition temperature, the spins are canted ferromagnetic aligned along $c$ axis with antiferromagnetic components in $ab$ plane. This peculiar magnetic structure gives rise to the anisotropic anomalous Hall effect (AHE) in ${\mathrm{Cr}}_{5}{\mathrm{Te}}_{8}$. When the current flows along the $ab$ plane, ${\mathrm{Cr}}_{5}{\mathrm{Te}}_{8}$ exhibits a conventional AHE depicted by skew scattering mechanism. On the other hand, the topological Hall effect appears with current along $c$ axis, which stems from the noncoplanar spin configuration with scalar spin chirality during the spin flop process.

Magnetic properties of the low-dimensional BaM2Si2O7 system (M=Cu, Co, Mn)

We investigated the magnetic properties of the low-dimensional $\mathrm{Ba}{M}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$ ($M$ = Cu, Co, and Mn) system using both experimental measurements and theoretical calculations. Magnetization, specific heat, and single crystal neutron diffraction measurements have been performed on single crystal ${\mathrm{BaMn}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$. The spin structure was determined and a magnetic phase diagram with applied field along the $b$ axis was constructed, which contains a spin flop transition around 6 T. Magnetization and specific heat measurements confirmed the presence of weak ferromagnetism in ${\mathrm{BaCo}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$. Furthermore, we performed local-spin density approximation with on-site Coulomb energy ($\mathrm{LSDA}+U$) calculations for the $\mathrm{Ba}{M}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}$ ($M$ = Cu, Co, and Mn) system. Based on the first-principles calculations, the origin of the magnetic differences of the three materials is discussed.

Magnetic structure and magnetization of z -axis helical Heisenberg antiferromagnets with XY anisotropy in high magnetic fields transverse to the helix axis at zero temperature

A helix has a wavevector along the z axis with the magnetic moments ferromagnetically-aligned within xy planes with a turn angle kd between the moments in adjacent planes in transverse field Hx = 0. The magnetic structure and x-axis average magnetization per spin of this system in a classical XY anisotropy field HA is studied versus kd, HA, and large Hx at zero temperature. For values of HA below a kd-dependent maximum value, the xy helix phase transitions with increasing Hx into a spin-flop (SF) phase where the ordered moments have x, y, and z components. The moments in the SF phase are taken to be distributed on either one or two xyz spherical ellipses. The minor axes of the ellipses are oriented along the z axis and the major axes along the y axis where the ellipses are flattened along the z axis due to the presence of the XY anisotropy. From energy minimization of the SF spherical ellipse parameters for given values of kd, HA and Hx, four kd-dependent SF phases are found: either one or two xyz spherical ellipses and either one or two xy fans, in addition to the xy helix phase and the paramagnetic (PM) phase with all moments aligned along Hx. The PM phase occurs via second-order transitions from the xy fan and SF phases with increasing Hx. Phase diagrams in the Hx-HA plane are constructed by energy minimization with respect to the SF phases, the xy helix phase, and the xy fan phase for four kd values. One of these four phase diagrams is compared with the magnetic properties found experimentally for the model helical Heisenberg antiferromagnet EuCo2P2 and semiquantitative agreement is found.

Antiferromagnetism and the emergence of frustration in the sawtooth lattice chalcogenide olivines Mn2SiS4−xSex ( x=0–4 )

The magnetism in the sawtooth lattice of Mn in the olivine chalcogenides, ${\mathrm{Mn}}_{2}{\mathrm{SiS}}_{4\ensuremath{-}x}{\mathrm{Se}}_{x}$ ($x=1--4$), is studied in detail by analyzing their magnetization, specific heat, and thermal conductivity properties and complemented with density functional theory calculations. The air-stable chalcogenides are antiferromagnets and show a linear trend in the transition temperature ${T}_{N}$ as a function of Se content ($x$), which shows a decrease from ${T}_{N}\ensuremath{\approx}86\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for ${\mathrm{Mn}}_{2}{\mathrm{SiS}}_{4}$ to 66 K for ${\mathrm{Mn}}_{2}{\mathrm{SiSe}}_{4}$. Additional magnetic anomalies are revealed at low temperatures for all the compositions. Magnetization irreversibilities are observed as a function of $x$. The specific heat and the magnetic entropy indicate the presence of short-range spin fluctuations in ${\mathrm{Mn}}_{2}{\mathrm{SiS}}_{4\ensuremath{-}x}{\mathrm{Se}}_{x}$. A spin-flop antiferromagnetic phase transition in the presence of applied magnetic field is present in ${\mathrm{Mn}}_{2}{\mathrm{SiS}}_{4\ensuremath{-}x}{\mathrm{Se}}_{x}$, where the critical field for the spin flop increases from $x=0$ towards 4 in a nonlinear fashion. Density functional theory calculations show that an overall antiferromagnetic structure with ferromagnetic coupling of the spins in the $ab$ plane minimizes the total energy. The band structures calculated for ${\mathrm{Mn}}_{2}{\mathrm{SiS}}_{4}$ and ${\mathrm{Mn}}_{2}{\mathrm{SiSe}}_{4}$ reveal features near the band edges similar to those reported for Fe-based olivines suggested as thermoelectrics; however the experimentally determined thermal transport data do not support superior thermoelectric features. The transition from long-range magnetic order in ${\mathrm{Mn}}_{2}{\mathrm{SiS}}_{4}$ to short-range order and spin fluctuations in ${\mathrm{Mn}}_{2}{\mathrm{SiSe}}_{4}$ is explained using the variation of the Mn-Mn distances in the triangle units that constitutes the sawtooth lattice upon progressive replacement of sulfur with selenium. Overall, the results presented here point towards the role played by magnetic anisotropy and geometric frustration in the antiferromagnetic state of the sawtooth olivines.

Gd2Te3: an antiferromagnetic semimetal

We report high-precision magnetization (), magnetic susceptibility (), specific heat (Cp (T, H)) and ‘zero-field’ electrical resistivity, , data taken on Gd2Te3 single crystal over wide ranges of temperature and magnetic field (H), with either -axis or -plane. and unambiguously establish that the b-axis is the easy direction of magnetization whereas any direction in the ac-plane is a hard direction. The -type anomaly in ‘zero-field’ specific heat, Cp (T, H = 0), and an abrupt drop in (characteristic of the paramagnetic (PM) — antiferromagnetic (AFM) phase transition) are observed at the Néel temperature, K. and Cp (T,H) clearly demonstrate that shifts to lower temperatures with increasing H irrespective of whether H points in the easy or hard direction. When , the isotherms at temperatures in the range 2.5 K K reveal the existence of a field-induced spin-flop (SF) transition at fields 4.0 T 4.5 T. The first principles electronic band structure and density of states calculations, based on the density functional theory, correctly predict an AFM ground state (stabilized primarily by the 4f Gd3+ – 5p Te2−– 4f Gd3+ superexchange interactions) and the observed semi-metallic behavior for the Gd2Te3 compound. Moreover, these calculations yield the values for the ordered magnetic moment per Gd atom at T = 0, mJ mol−1 K−2 for the Sommerfeld coefficient for the electronic specific heat contribution and K for the Curie–Weiss temperature, respectively. These theoretical estimates conform well with the corresponding experimental values , mJ mol−1 K−2 and K.

Strong decoupling between magnetic subsystems in the low-dimensional spin- 12 antiferromagnet SeCuO3

We report on the magnetocrystalline anisotropy energy (MAE) and spin reorientation in antiferromagnetic state of spin $S=1/2$ tetramer system SeCuO$_3$ observed in torque magnetometry measurements in magnetic fields $H<5$~T and simulated using density functional calculations. We employ simple phenomenological model of spin reorientation in finite magnetic field to describe our experimental torque data. Our results strongly support collinear model for magnetic structure in zero field with possibility of only very weak canting. Torque measurements also indicate that, contrary to what is expected for uniaxial antiferromagnet, in SeCuO$_3$ only part of the spins exhibit spin flop instead all of them, allowing us to conclude that AFM state of SeCuO$_3$ is unconventional and comprised of two decoupled subsystems. Taking into account previously proposed site-selective correlations and dimer singlet state formation in this system, our results offer further proof that AFM state in SeCuO$_3$ is composed of a subsystem of AFM dimers forming singlets immersed in antiferromagnetically long-range ordered spins, where both states coexist on atomic scale. Furthermore, we show, using an ab-initio approach, that both subsystems contribute differently to the MAE, corroborating the existence of decoupled subnetworks in SeCuO$_3$. Combination of torque magnetometry, phenomenological approach and DFT simulations to magnetic anisotropy presented here represents a unique and original way to study site-specific reorientation phenomena in quantum magnets.

Exchange bias of [Pt/Co]/IrMn with two-directional isotropy

The anisotropy of [Pt/Co]/IrMn multilayer samples is studied by analyzing the remanence state. Then the sample with two-directional isotropy is measured after perpendicular and in-plane field cooling, we observe an absence of spin flop coupling after field cooling and that the perpendicular exchange bias is larger than the in-plane exchange bias. The comparison of exchange bias along the two directions is modeled based on the frozen net spins of uncompensated units in the growth plane.

Magnetic and magnetotransport properties of single-crystalline R2PdGe6 (R = Pr, Gd and Tb)

Single crystals of R2PdGe6 (R = Pr, Gd and Tb) compounds were grown by the Bi-flux method. Pr2PdGe6 is an antiferromagnetic compound with Néel temperature TN = 15 K, in which a field-induced magnetic transition (spin flip) occurs when a magnetic field is applied along either a or b axis; a small magnetization and hysteresis loop were observed when a field is applied along c axis. Gd2PdGe6 is a collinear antiferromagnetic compound with TN = 37 K along b axis. Tb2PdGe6 is an antiferromagnetic compound with TN = 48 K and its hard magnetization direction is along b axis. The temperature dependences of the resistance of the entire three compounds present inflection points at the respective TN. A large resistance (as well as magnetoresistance) change can be found at the spin flip transition of Pr2PdGe6, but the change is not obvious at the spin flop transition of Gd2PdGe6.

Electrically controlled nuclear polarization of individual atoms.

Nuclear spins serve as sensitive probes in chemistry1 and materials science2 and are promising candidates for quantum information processing3-6. NMR, the resonant control of nuclear spins, is a powerful tool for probing local magnetic environments in condensed matter systems, which range from magnetic ordering in high-temperature superconductors7,8 and spin liquids9 to quantum magnetism in nanomagnets10,11. Increasing the sensitivity of NMR to the single-atom scale is challenging as it requires a strong polarization of nuclear spins, well in excess of the low polarizations obtained at thermal equilibrium, as well as driving and detecting them individually4,5,12. Strong nuclear spin polarization, known as hyperpolarization, can be achieved through hyperfine coupling with electron spins2. The fundamental mechanism is the conservation of angular momentum: an electron spin flips and a nuclear spin flops. The nuclear hyperpolarization enables applications such as in vivo magnetic resonance imaging using nanoparticles13, and is harnessed for spin-based quantum information processing in quantum dots14 and doped silicon15-17. Here we polarize the nuclear spins of individual copper atoms on a surface using a spin-polarized current in a scanning tunnelling microscope. By employing the electron-nuclear flip-flop hyperfine interaction, the spin angular momentum is transferred from tunnelling electrons to the nucleus of individual Cu atoms. The direction and magnitude of the nuclear polarization is controlled by the direction and amplitude of the current. The nuclear polarization permits the detection of the NMR of individual Cu atoms, which is used to sense the local magnetic environment of the Cu electron spin.

Cation order imaging and magnetic properties in the Ca2Fe2-xGaxO5 brownmillerite (0 ≤ x ≤ 1)

Polycrystalline Ca2Fe2-xGaxO5 brownmillerite samples of nominal x = 0.5, 0.7, 0.9 and 1 compositions have been synthesized by solid state reaction under normal pressure conditions. Whatever x is, room temperature structural analyses by Rietveld refinements and electron microscopy techniques highlight a centrosymmetric Pnma space group. Furthermore, STEM-HAADF observations point towards a preferential Ga occupation at the tetrahedral sites of the structure in agreement with the Rietveld analyses. This structure remains unchanged up to 1000 K as shown by thermo-diffraction analysis. As the Ga content x increases, the room temperature unit cell volume decreases gradually consistently with the fourfold coordination of the smallest Ga3+ ionic radius than that of high spin Fe3+ in the same tetrahedral coordination. This magnetic dilution by a diamagnetic cation is responsible for the TN decrease revealed by magnetization measurements and allows a spin flop transition to be observed. Despite their similarities with the Ca2Fe2-xAlxO5 samples, no electric polarization could be evidenced for the homologous Ca2Fe2-xGaxO5 series.

Magnetocaloric Effect in Layered Organic Conductor λ-(BETS)2FeCl4

Magnetocaloric effect (MCE) and magnetic torque measurements have been carried out in the π–d system λ-(BETS)2FeCl4 [BETS = bis(ethylenedithio)tetraselenafulvalene], which shows an antiferromagnetic insulating (AFI) phase below ∼8.5 K. In the magnetic torque curve, a sharp structure at ∼1.2 T and a step at ∼10 T are observed at low temperatures, which are caused by the spin-flop (SF) transition and the transition from the AFI to paramagnetic metallic (PM) phase, respectively. The MCE, directly related to the magnetic entropy, shows a small sharp peak at the SF transition and a sharp dip at the AFI–PM transition. The overall feature above 3 K is qualitatively interpreted by a simple picture: antiferromagnetic (AF) π spins and paramagnetic 3d spins at the Fe sites. However, a broad dip in the MCE is additionally found at ∼5 T below ∼3 K, which is not explained by the above picture. The results are compared with those of κ-(BETS)2FeBr4, which shows an AF order of the 3d spins at the Fe sites.

Fe4Nb2O9 : A magnetoelectric antiferromagnet

The structural, magnetic, and electrical properties of a ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ polycrystalline sample have been characterized. It is found that this compound crystallizes in the $P\overline{3}c1$ space group of the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{A}{\mathrm{l}}_{2}{\mathrm{O}}_{3}$ structure and is thus isostructural to ${\mathrm{Co}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ and ${\mathrm{Mn}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$, two linear magnetoelectric oxides. But in marked contrast, its ${\ensuremath{\varepsilon}}^{\ensuremath{'}}(T)$ curve reveals two broad transitions at ${T}_{N1}\phantom{\rule{0.16em}{0ex}}\ensuremath{\cong}90\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{N2}\phantom{\rule{0.16em}{0ex}}\ensuremath{\cong}77\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the former corresponding to the antiferromagnetic ordering temperature. Below ${T}_{N1}$, the M$(H)$ magnetization curves reveal the existence of spin flop at about 6 T. In this temperature region, a H-induced electric polarization for ${\ensuremath{\mu}}_{0}Hg6$ T is evidenced by both sets of ${I}_{p}{(T)}_{H}$ and $P{(H)}_{T}$ curves. All these results point towards ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ being a magnetoelectric member of the ${A}_{4}{B}_{2}{\mathrm{O}}_{9}$ family ($A=\mathrm{Mn}$, Fe, Co and $B=\mathrm{Nb}$, Ta).

Influence of classical anisotropy fields on the properties of Heisenberg antiferromagnets within unified molecular field theory

A comprehensive study of the influence of classical anisotropy fields on the magnetic properties of Heisenberg antiferromagnets within unified molecular field theory versus temperature T, magnetic field H, and anisotropy field parameter hA1 is presented for systems comprised of identical crystallographically-equivalent local moments. The anisotropy field for collinear z-axis antiferromagnetic (AFM) ordering is constructed so that it is aligned in the direction of each ordered and/or field-induced thermal-average moment with a magnitude proportional to the moment, whereas that for XY anisotropy is defined to be in the direction of the projection of the moment onto the xy plane, again with a magnitude proportional to the moment. Properties studied include the zero-field Neel temperature TN, ordered moment, heat capacity and anisotropic magnetic susceptibility of the AFM phase versus T with moments aligned either along the z axis or in the xy plane. Also determined are the high-field magnetization perpendicular to the axis or plane of collinear or planar noncollinear AFM ordering, the high-field magnetization along the z axis of a collinear z-axis AFM, spin-flop (SF), and paramagnetic (PM) phases, and the free energies of these phases versus T, H, and hA1. Phase diagrams at T = 0 in the Hz-hA1 plane and at T > 0 in the Hz-T plane are constructed for spins S = 1/2. For hA1 = 0 the SF phase is stable at low field and the PM phase at high field with no AFM phase present. As hA1 increases, the phase diagram contains the AFM, SF and PM phases. Further increases in hA1 lead to the disappearance of the SF phase and the appearance of a tricritical point on the AFM-PM transition curve. Applications of the theory to extract hA1 from experimental low-field magnetic susceptibility data and high-field magnetization versus field isotherms for single crystals of AFMs are discussed.

Nonlinear magnetoelectric effect in paraelectric state of Co4Nb2O9 single crystal

We report the structural, magnetoelectric (ME), magnetic and electric control of magnetic properties in Co4Nb2O9 (CNO) single crystal. A detailed ME measurement reveals a nonlinear ME effect instead of a linear ME effect in CNO single crystal. By fitting the magnetization-electric field (M-E) curve, it can be found that the linear ({alpha }_{e}) and quadratic (γ) coefficients equal to ~8.27 ps/m and ~−6.46 ps/MV for upper branch, as well as ~8.38 ps/m and ~6.75 ps/MV for the lower branch. More importantly, a pronounced response was observed under a small cooling magnetic field, which cannot even cause the spin flop. This suggests a magnetoelectric effect can occur at paraelectric state for CNO single crystal. Furthermore, we also found that the magnetization of every axis responds to electric field applied along a-axis, but fails to do so when the electric field is applied c-axis. Such findings supply a direct evidence to the magnetic structure and ME coupling mechanism indirectly reflected by our neutron experiment.

Modelling compensated antiferromagnetic interfaces with MuMax3

We show how compensated antiferromagnetic interfaces can be implemented in the micromagnetic simulation program MuMax3. We demonstrate that we can model spin flop coupling as a uniaxial anisotropy for small canting angles and how we can take into account the exact energy terms for strong coupling between a ferromagnet and a compensated antiferromagnet. We also investigate athermal training in biaxial antiferromagnets and reproduce the training effect in a polycrystalline IrMn/CoFe bilayer.