Rhombohedral Antiferromagnet Research Articles

Quasistatic remanence in Dzyaloshinskii-Moriya interaction driven weak ferromagnets and piezomagnets

We explore remanent magnetization ($\mu$) as a function of time and temperature, in a variety of rhombohedral antiferromagnets (AFM) which are also weak ferromagnets (WFM) and piezomagnets (PzM). These measurements, across samples with length scales ranging from nano to bulk, firmly establish the presence of a remanence that is quasi static in nature and exhibits a counter-intuitive magnetic field dependence. These observations unravel an ultra-slow magnetization relaxation phenomenon related to this quasi static remanence. This feature is also observed in a defect free single crystal of $\alpha$-Fe$_2$O$_3$, which is a canonical WFM and PzM. Notably, $\alpha$-Fe$_2$O$_3$ is not a typical geometrically frustrated AFM and in single crystal form, it is also devoid of any size or interface effects, which are the usual suspects for a slow magnetization relaxation phenomenon. The underlying pinning mechanism appears exclusive to those AFM which are either symmetry allowed WFM, driven by Dzyaloshinskii-Moriya Interaction (DMI) or can generate this trait by tuning of size and interface. The qualitative features of the quasi static remanence indicate that such WFM are potential piezomagnets, in which magnetization can be tuned by \textit{stress} alone.

Incommensurate magnetic structures in rhombohedral Heisenberg antiferromagnet

The phase diagram of the ground state has been calculated for a rhombohedral antiferromagnet of the R3m symmetry with frustrated exchange in the base plane and competition of exchanges between the nearest and next-nearest planes. The diagram contains phases of collinear antiferromagnetic ordering of various types separated by five incommensurate magnetic states of the helicoidal type, differing in the ordering type and in the direction of the modulation vector. The commensurate and incommensurate phases converge at multi-critical points lying on a line corresponding to an antiferromagnet with an undistorted simple cubic lattice.

Acoustic birefringence in antiferromagnets

A theory of magnetic linear birefringence of a transverse sound in a rhombohedral antiferromagnets with allowance for basal magnetic anisotropy of various origins and an inhomogeneous distribution of magnetization in the crystal was constructed. The results of experimental studies of magneto-acoustic effects on iron borate and hematite are interpreted on the basis of the theory.

Theory of birefringence of sound in easy-plane rhombohedral antiferromagnets with inclusion of hexagonal anisotropy and mechanical stresses

The constructed thermodynamic theory of magnetic birefringence of transverse sound in easyplane weak ferromagnets with an axial basal anisotropy induced by boundary conditions has been generalized to the case of additional inclusion of the hexagonal anisotropy enhanced by isotropic mechanical stresses. The magnetoelastic contribution ΔCa to the effective elastic modulus C44eff = C44 + ΔCa, which determines the phase velocity of the magnetic mode of the acoustic wave in a crystal, has been calculated. It has been shown that the induced anisotropy with the twofold and sixfold symmetry leads to the appearance of an additional anisotropic term of the fourfold symmetry in the contribution ΔCa. The developed theory has made it possible to satisfactorily describe the existing experiments.

Modulated magnetic structure of weak rhombohedral ferromagnets α-Fe2O3:Ga and FeBO3:Mg

The effect of diamagnetic impurities on the stability of the homogeneous magnetic state of rhombohedral antiferromagnets with weak ferromagnetism (α-Fe2O3:Ga and FeBO3:Mg) is studied experimentally. It is shown that the application of an external magnetic field in the basal plane in the crystals under study in a certain temperature range induces a magnetic superstructure along the hard magnetization axis, which can be presented in the form of a ripplon phase with the azimuth of the local ferromagnetism vector oscillating about the direction of the field. The preferred orientation of the discovered modulated structures relative to crystallographic directions in the basal plane of α-Fe2O3:Ga and FeBO3:Mg is studied, and the dependence of the spatial period of the superstructure on the applied magnetic field and temperature is analyzed. The magnetic-field-induced transition of the studied crystals from a homogeneous to an inhomogeneous magnetic state is described phenomenologically on the basis of the thermodynamic potential with gradient terms. In the discussion of physical reasons for magnetic order parameter modulation in weak ferromagnetic doped with diamagnetic ions, preference is given to the mechanism associated with the emergence of uniaxial magnetic centers with a random distribution of azimuths of easy axes in the basal plane of the crystal in the vicinity of impurities. A model describing the formation of a modulated magnetic state in α-Fe2O3:Ga and FeBO3:Mg is proposed, according to which the competition between magnetoanisotropic and Zeeman interactions in the inhomogeneous magnetic phase of these crystals leads to periodic deviations in the direction of the local ferromagnetism vector from the direction of magnetization.

μ +-SR studies of the weak ferromagnets CoCO 3 and NiCO 3

We present the results of zero-field μ +-SR measurements on CoCO 3 and NiCO 3. Both compounds are rhombohedral antiferromagnets which exhibit a spontaneous weak magnetisation below 22.2 and 17.2 K , respectively. This arises due to an anisotropic superexchange (Dzyaloshinsky–Moriya) interaction. We have studied the temperature dependence of the internal field in the ordered state and the magnetic fluctuations in the paramagnetic state. We describe the possible muon-site obtained from dipolar-field calculations.

Magnetoacoustic activity of rhombohedral antiferromagnets

A quantitative theory of magnetic acoustic birefringence in rhombohedral antiferromagnets is developed. It is shown that acoustic activity and the Faraday effect associated with it are determined by the joint action of piezomagnetism and magnetostriction. The effect is estimated quantitatively, and the method of experimental determination of the piezomagnetic constant is indicated. The conditions for the transformation of linear polarization into circular polarization and for the rotation of linear polarization through 90° are determined.

Elastic neutron scattering and rhombohedral antiferromagnets

Infinite isoenergetic helix spin configurations minimize the energy of the classical Heisenberg rhombohedral antiferromagnet with nearest neighbor interactions. We comment about elastic neutron scattering data on ACrO2 (A=Cu, Ag, Pd) compounds which seem to support the degenerate helix scenario modified by quantum fluctuations in agreement with the theoretical expectation. We investigate by a microscopic approach the existence of static short range order in β-oxygen as suggested on the basis of recent elastic neutron scattering experiment.

Magnetic structure of antiferromagnetic PdCrO 2 possible degenerate helices on a rhombohedral lattice

Neutron powder diffraction was measured on PdCrO 2 which has a rhombohedral lattice of Cr 3+ ions. The observed magnetic scattering forms a rather broad bump with peaks at ⅓⅓/ indicating the 120° magnetic structure in a triangular lattice c-plane. The magnetic moments of 2 μ B lie in the c-plane and T N was found to be 40 K. Magnetic diffuse scattering is appreciable even at 150 K. The magnetic peak has an asymmetric saw-tooth profile toward the high- Q side implying that the stacking of the 120° structure is distributed as expected in “degenerate helices” proposed for the rhombohedral antiferromagnet.

Neutron powder diffraction study of the two-dimensional triangular lattice antiferromagnet CuCrO2

An S=3/2 Heisenberg antiferromagnet on a triangular lattice CuCrO2, in which stacking of the triangular lattice of magnetic Cr atoms forms a layered rhombohedral antiferromagnet, is studied by neutron powder diffraction. In the paramagnetic phase the powder diffraction pattern shows asymmetry, which proves a two-dimensional character. In the ordered phase, magnetic Bragg scattering has large width, indicating that the scattering is distributed on a line (1/31/3 zeta ) with peaks where zeta takes integer values. Although the magnetic long-range order is established in the c plane, correlation in the c direction is finite or the modulation vector is distributed on the line. Intensity of magnetic reflections is consistent with the 120 degrees structure in the a-c plane with moment (3.1+or-0.2) mu B.

Saw-tooth peaks in elastic neutron scattering by rhombohedral Heisenberg antiferromagnets

The phenomenology of the Heisenberg rhombohedral antiferromagnet (RAF) in classical approximation is characterized by the frustration of the minimum energy configuration consisting of infinite inequivalent helices. In absence of anisotropy long range order (LRO) is lost but a weak single ion anisotropy is sufficient to restore LRO and to produce unusual elastic neutron scattering profiles as Bragg lines for monocrystalline samples and saw-tooth peaks for policrystalline samples. The effect of quantum and thermal fluctuations as well as of a magnetic field is also considered.

Zero point motion and magnetic field effects on the spin configuration in a Heisenberg rhombohedral antiferromagnet. Application to solid oxygen

The ground state of the Heisenberg rhombohedral antiferromagnet in classical approximation exhibits infinite degeneracy corresponding to infinite unequivalent helices. We call degenerate helix (DH) such a spin configuration. In absence of anisotropy long-range order (LRO) is lost even in 3D with a possible algebraic decay of the correlation function due to a low-energy catastrophe related to ‘‘soft lines’’ of the magnon energy which vanishes for all wave vectors falling on the ‘‘degeneration line’’ ℒQ, the locus of the Q wave vectors characterizing the infinite helixes of the ground state. We have studied the effect of the zero point motion which removes the infinite degeneracy of the ground state so that quantum disorder sets up LRO. We have also studied the effect of an external magnetic field. We find that in classical approximation a magnetic field parallel to the c axis does not remove the infinite degeneracy of the ground state but it affects the spin-wave energy spectrum what could be observed in an inelastic scattering experiment. On the contrary, dramatic changes are expected when a magnetic field is applied perpendicular to the c axis because competition arises with the zero point motion effect so that the magnetic field in this configuration should act as a device to tune the DH phase. Possible application to solid oxygen is briefly analyzed.

Collinear and helical phases of the monoclinic and rhombohedral antiferromagnet. Application to the α- and β-phases of solid oxygen

Classical spins localised on the sites of a rhombohedral lattice and coupled by nearest-neighbour Heisenberg exchange show infinite degeneracy of the ground state; there are infinite inequivalent isoenergetic helices which minimise the classical ground-state energy. This configuration is referred to as a 'degenerate helix' (DH). A genuine DH configuration provides unusual elastic neutron scattering peaks, owing to the infinite inequivalent helices of the ground state. A DH configuration provides the first example of an elastic neutron scattering peak width not determined by the limited instrumental resolution. The rhombohedral Heisenberg antiferromagnet (RAF) model is suitable for describing the beta -phase of solid oxygen which is stable at intermediate temperatures (24-44 K) while in the low-temperature alpha -phase the lattice is stretched and becomes monoclinic. Recent experimental data for elastic and inelastic neutron scattering by polycrystalline samples of solid oxygen in both the alpha - and the beta -phases are satisfactorily interpreted on the basis of the authors' theoretical results.

Competition between thermal and quantum fluctuations in a Heisenberg rhombohedral antiferromagnet

The Heisenberg rhombohedral antiferromagnet (RAF) in the classical approximation is characterised by infinite degeneracy of the ground state corresponding to infinite inequivalent helices whose wavevectors Q belong to lines in the reciprocal space called degeneration lines LQ. A rich unusual scenario that called a degenerate helix (DH) is set up: this entails the presence of 'soft lines' in the magnon energy spectrum, the absence of LRO in 3D at any finite temperature and possible algebraic decay of the correlation function. Zero-point-motion fluctuations destroy this phenomenology, picking out a certain helix of the manifold LQ. It may be conjectured that the classical DH scenario could reappear at intermediate temperature when thermal fluctuations overcome quantum fluctuations. Indeed, the authors have found that this is the case-and conclude that the DH is not a mere artefact of the classical approximation but a genuine possibility for helimagnetic systems.

Order produced by quantum disorder in the Heisenberg rhombohedral antiferromagnet

In the classical approximation the Heisenberg rhombohedral antiferromagnet shows infinite degeneracy of the ground-state energy corresponding to infinite inequivalent iso-energetic helices whose wave-vectors Q belong to lines in the reciprocal space, called 'degeneration lines'. In absence of anisotropy the spin wave energy spectrum shows 'soft lines' vanishing for all wave-vectors falling on the degeneration lines. These soft lines destroy long-range order (LRO) at any finite temperature. The authors show that the zero-point motion, which is generally expected to contrast with the onset of LRO, favours in this case a single wave-vector removing the infinite degeneracy of the ground state, so LRO is restored by quantum disorder.

Neutron scattering in the rhombohedral Heisenberg antiferromagnet: application to β-oxygen

The rhombohedral Heisenberg antiferromagnet has an unexpected degeneracy of the ground state in the mean-field approximation. An infinite number of isoenergetic nonequivalent helices exist and these define a degeneration line as the locus of the Q vectors of these helices. The authors study the elastic neutron scattering cross section of such a 'degenerate helix' state for single crystals and polycrystals: in a single crystal they find a line of Bragg peaks, a ridge, corresponding to scattering wave-vectors falling on the degeneration line. In the case of a polycrystal the scattering consists of a broad peak and its width is determined by the minimum and the maximum magnitude of Q. The 'degenerate helix' state is stable against spin wave excitations but these have a large number of low-energy states in the range 3-20K when they use the interaction parameters appropriate for beta -O2. They argue that the present experimental data on beta -O2 do not necessarily imply absence of long-range order, but they are compatible with a 'degenerate helix' state with long-range order. A careful investigation of the form of the elastic peak is suggested to test the asymmetry they predict.

The rhombohedral Heisenberg antiferromagnet: infinite degeneracy of the ground state and magnetic properties of solid oxygen

Infinite degeneracy of the ground state, a 'soft line' in the elementary excitation energy spectrum, and no long-range order in 3D at finite temperature are all found for suitable exchange competition in Heisenberg helimagnets. The authors show here that a similar scenario arises in a Heisenberg model on a rhombohedral lattice with antiferromagnetic in-plane nearest-neighbour (NN) exchange coupling J and any inter-plane NN coupling J' if mod J' mod <3 mod J mod . Moreover, for small J' the in-plane spin configuration is similar to a 120 degrees phase, but any phase relation between the planes is possible. In the absence of anisotropy there is no long-range order, with a possible algebraic decay of the correlation function. A similar unorthodox behaviour is expected at intermediate temperature if the anisotropy is small enough to leave a structure of the excitation spectrum reminiscent of the 'soft line'. The authors think that these somewhat surprising properties of a rhombohedral antiferromagnet can be useful for understanding the magnetic behaviour of the beta -oxygen.

Mandelstam-Brillouin scattering of light in antiferromagnets (invited)

The report reviews experimental investigations on Mandelstam-Brillouin light scattering (MBS) from thermal and excited low energy (1–3 cm−1) quasiparticles (magnons and phonons) in antiferromagnets. Now such investigations have been performed in two rhombohedral antiferromagnets with weak ferromagnetism, FeBO3 and CoCO3. The spin wave spectrum of these substances has a low frequency branch. The MBS experiments allowed to distinguish the contributions in magnon energy from exchange, magnetic, and magnetodipole interactions. Spin wave velocities along trigonal axis and in basal plane of crystals were determined. The second part of the report is devoted to the results of optical experiments on investigation of relaxation processes of magnons with k∼0, excited by antiferromagnetic resonance. The overheating of magnon’s and phonon’s systems in crystal, caused by the so-called ’’bottle neck’’ during relaxation, was discovered. The observation experiments on MBS on parametrically excited magnons and phonons are described in the last part of the report.

Renormalized Field Theory of Rhombohedral Antiferromagnets with Weak Spin Anisotropy

Recently quenched magnetic mixtures with competing orthogonal spin anisotropies are under theoretical 1)~5) and experimenta16)~Il) investigations. Especially differences of the experimental results on Fel-XCoxCb· 2H206)~B) and anhydrated Fel_XCoxCb ) have yielded new problems. [1] According to the measurements by neutron scattering or the measurements of magnetic susceptibility and specific heat, both Fel-XCoxCb· 2H206),7) and Fel_XCoxCb ) exhibit considerably sharp PA(para-antiferro) transitions at A, Band C [Fig. l(a) and (b)]. To the contrary, A-OAF(antiferro-oblique antiferro) transition points A' and B' remain as sharp as P A transitions for Fel-XCoxCb·2H20, but get smeared for Fel-XCoxCb. [2] In Fel-XCoxCb·2H20, AB' crosses with BN at C, indifferently to each other, which means that C is a decoupled tetracritical point. On the other hand, CD line is not a smooth extention of BC line in Fel-XCoxCb ll ),*) so that C is considered to