Uniaxial Single-ion Anisotropy Research Articles

Macroscopic quantum tunneling in small antiferromagnetic particles: Effects of a strong magnetic field

We consider an effect of a strong magnetic field on the ground state and macroscopic coherent tunneling in small antiferromagnetic particles with uniaxial and biaxial single-ion anisotropy. We find several tunneling regimes that depend on the direction of the magnetic field with respect to the anisotropy axes. For the case of a purely uniaxial symmetry and the field directed along the easy axis, an exact instanton solution with two different scales in imaginary time is constructed. For a rhombic anisotropy the effect of the field strongly depends on its orientation: with the field increasing, the tunneling rate increases or decreases for the field parallel to the easy or medium axis, respectively. The analytical results are complemented by numerical simulations.

Field-induced magnetic ordering inNiCl2⋅4SC(NH2)2

We have investigated the low-temperature T field-induced ordering in ${\mathrm{NiCl}}_{2}\ensuremath{\cdot}4\mathrm{SC}({\mathrm{NH}}_{2}{)}_{2},$ from magnetization measurements. This is an $S=1$ system with a large single-ion uniaxial anisotropy leaving a singlet ground state. An external magnetic field $(\mathbf{B})$ parallel to the symmetry axis induces an antiferromagnetically ordered phase for ${B}_{c1}<B<{B}_{c2}.$ The establishment of this long-range order can be regarded as a Bose-Einstein condensation of magnons. The phase boundaries are predicted to obey power laws $[{B}_{c}(T)\ensuremath{-}{B}_{c}(0)]\ensuremath{\propto}{T}^{\ensuremath{\alpha}}.$ The determined phase boundaries could be fitted to power laws yielding ${\ensuremath{\alpha}}_{1}=2.63\ifmmode\pm\else\textpm\fi{}0.10$ for ${B}_{c1}(T)$ and ${\ensuremath{\alpha}}_{2}=2.55\ifmmode\pm\else\textpm\fi{}0.10$ for ${B}_{c2}(T).$

Many-body Green's function theory for thin ferromagnetic films: exact treatment of the single-ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many-body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second- and fourth-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. The single-ion anisotropy terms can be treated exactlyby introducing higher-order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest-order Green's functions. RPA-like approximations are used to decouple the exchange interaction terms in both the low-order and higher-order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.

Surface magnetization in semi-infinite ferromagnetic semiconductors with single-ion uniaxial anisotropy

A Green's function technique combined with the transfer-matrix method is used to calculate the surface localized-spin and the conduction-electron magnetization in semi-infinite ferromagnetic semiconductors (FMSs) in the ferromagnetic phase taking into account a single-ion uniaxial anisotropy. The theoretical results were applied to narrow-band as well as to wide-band FMSs.

Green's function calculation of the Curie temperature of FCC films: sensitivity to surface orientation

The Curie temperature T C of a Heisenberg ferromagnetic ultrathin film with uniaxial single-ion anisotropy and face-centered cubic (FCC) structure was calculated in the framework of a Green's function approach using the random phase approximation (RPA). The effect of surface orientation on T C( N), where T C is the Curie temperature and N the film thickness, was carefully investigated. The results follow a finite-size scaling relation with shift exponent λ≃1.5.

Heat capacity calorimetry of two Mn 4 large-spin clusters: [Mn 4(hmp) 6R 2](ClO 4) 2 [Hhmp=2-hydroxymethylpyridine, R=OAc − or Cl −

Heat capacities of two large-spin (ground spin state S=9) manganese clusters, [Mn 4(hmp) 6(O 2CCH 3) 2](ClO 4) 2 and [Mn 4(hmp) 6Cl 2](ClO 4) 2, Hhmp=2-hydroxymethylpyridine (Mn 4OAc and Mn 4Cl for short, respectively) were studied under 0–9 T magnetic fields in the 1.8–30 K temperature range. Broad humps were observed in Mn 4OAc and Mn 4Cl around 7.6 and 5 K, respectively, under zero magnetic field, which were shifted to lower temperatures with increasing magnetic field. However, the calorimetric studies could not detect any long-range ordering phenomena in these materials within the working range of temperature, which complies with the earlier reported magnetic measurements. Heat capacity of Mn 4OAc increased with increasing magnetic field at low temperatures up to 3 T, followed by a decrease, indicating a field-induced transition. In the case of Mn 4Cl, no field dependence of heat capacity was observed below 3 K when the magnetic field is lower than 0.5 T. The zero-field magnetic entropy amounted to 22.7 and 20.1 J K −1 mol −1 for Mn 4OAc and Mn 4Cl, respectively, which are close to R ln (2 S+1)=24.5 J K −1 mol −1 expected for an S=9 spin system. The uniaxial single-ion anisotropy parameter D′/ k B for Mn 4OAc and Mn 4Cl was determined to be −0.45 and −0.28 K, respectively (where k B is Boltzmann's constant). Comparison between the experimental and calculated magnetic heat capacities strongly suggests that both Mn 4OAc and Mn 4Cl possess the nature of S=9 one-dimensional antiferromagnetic chains.

Evidence for the singlet-dimer ground state in an S = 1 antiferromagnetic bond alternating chain.

Susceptibility, ESR, and magnetization measurements have been performed on single crystals of an S = 1 bond alternating chain compound: [Ni(333-tet) (mu-NO2)] (ClO4) (333-tet = N,N'-bis(3-aminopropyl)propane-1,3-diamine) and the compound doped with a small amount of Zn. We observed an anomalous angular dependence in the Zn-doped sample. These results are well explained by the model based on the valence-bond solid picture for the singlet-dimer phase. The picture implies that the free spins of S = 1 with a positive uniaxial single-ion anisotropy are induced at the edges of the chains without forming the singlet dimer.

Position-spacerenormalization-group investigation of the spin-3/2Blume-Emery-Griffiths model with repulsive biquadratic coupling

Phase transitions of a four-component lattice gas orspin-3/2 Blume-Emery-Griffiths model, with a single-ion uniaxialanisotropy and nearest-neighbour pair interactions, both bilinear andbiquadratic, are investigated for two-dimensional lattices usingan approximate renormalization-group approach of the Migdal-Kadanofftype. The set of fixed points and flows provide the characteristicphase diagrams, in the case of repulsive biquadratic interaction, featuring four ordered phases including high-entropy ferrimagneticand staggered quadrupolar phases. Successive phase transitionsand multicritical points are also found.

Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin $S\geq 1$ and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences.

Effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation

Basing on the two-spin-per-site Heisenberg model, the effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation has been investigated by use of the mean field theory. It was found that single-ion uniaxial anisotropy has important effect on the phase digrams. In the ferromagnetic case ( J 3>0) the positive single-ion uniaxial anisotropies ( D) suppress the internal spin fluctuation and raise the phase trasition temperature, and negative single-ion uniaxial anisotropies ( D) increase the internal spin fluctuation and reduce the phase trasition temperature. In the antiferromagnetic case ( J 3<0), there exist two critical values J c1 and J c2 (| J c2|<| J c1|) in the positive D values. In the | J 3|<| J c2| range intra-spin exchange coupling prevails inter-spin exchange coupling, the positive D values suppress the internal spin fluctuation and raise the phase transition temperature. In the | J 3|>| J c1| range the two sub-spins behave as a rigid spin and the positive D values make the reduction of the phase transition temperature. We also observe that the larger D values make the range of internal spin fluctuation to move towards the larger | J 3| range.

Critical properties of mixed anisotropic heisenberg spin system

We combined the two-site cluster approximation with the discretized path integral representation (DPIR) to deal with the mixed anisotropic Heisenberg spin system with a single-ion uniaxial anisotropy. The magnetization and phase diagrams show that anisotropic parameters play an important part in critical properties of the system.

Effects of anisotropy on the thermodynamic properties of an S=1 Heisenberg chain

Effects of the exchange anisotropy ( J z ≠ J x, y ) and the uniaxial single-ion anisotropy (∑ i D( S z i ) 2) on the thermodynamic properties of one-dimensional (1D) spin S=1 antiferromagnetic Heisenberg chain with periodic boundary are investigated by a method of approach, in which the discretized path-integral representation (DPIR) is used to transform the one-dimensional quantum spin Heisenberg chain into the two-dimensional classical Ising spin system, then the double-chain approximation (DCA) is used to calculate the thermodynamic properties, such as the magnetization in the presence of the external field, the zero-field magnetic susceptibility and the magnetic specific heat.

Thermodynamic Properties of the Antiferromagnetic Heisenberg Chain with Anisotropy (Uniaxial and Non-Uniaxial)

We use a method which combines the discretized path-integral representation (DPIR) with the double-chain approximation (DCA) to study the thermodynamic properties of an S = 1 antiferromagnetic Heisenberg chain (AFHC) with both uniaxial and non-uniaxial single-ion anisotropy. The magnetization in the presence of an external magnetic field, the zero-field magnetic susceptibility and the magnetic specific heat of the system are obtained. The effects of the anisotropy on the thermodynamic properties of the AFHC are examined and discussed in details.

Bilinear-biquadratic quantum exchange model with single-ion uniaxial anisotropy

Anisotropic XXZ Heisenberg ferromagnets with biquadratic exchange and single-ion anisotropy are studied by an improved two-site cluster effective field theory. In particular, the cross-over from anisotropic Ising to isotropic Heisenberg behaviour in the variation of T c with biquadratic exchange strength is studied and compared with the results of other methods.

Study of Blume–Emery–Griffiths model by a modified Bethe-Peierls method

We present here a study of the Blume–Emery–Griffiths (BEG) model for general spins using a modified Bethe–Peierls (BP) method calling it the Bethe–Peierls–Lines (BPL) method, incorporating the well known Lines approximation. We compare our results of BPL as well as BP methods for the ferro-to para-magnetic transition temperatures Tc with those available from other theories such as the Correlated-Effective-Field Theory (CEFT), Cluster Variation Method (CVM) and the Monte-Carlo (MC) method. We find that our BPL method gives results for variation of Tc with the single-ion uniaxial anisotropy (D) and biquadratic interaction (J') coefficients close to those obtained by CVM method for spin S = 1 on a honeycomb lattice. We also find that the BPL results are in good agreement for the cubic lattice for S = 3/2 and J' = 0 with those of the MC results, and for S = 1 and J' = −0.5J with those of the CVM results. For these three dimensional lattices our BPL method gives the correct reentrant behaviour for negative values of J'. We also compare our BP and BPL results for magnetic susceptibility with those of the CEFT for S = 3/2 and 3 nearest neighbours and find fairly good agreement for D > 0.

Quantum Heisenberg spin-glass model with mixed-anisotropy interactions in applied magnetic fields

In the static replica symmetric approximation, a quantum Heisenberg S=1 spin-glass model with single-ion uniaxial anisotropy and infinite-range random Dzyaloshinskii-Moriya (DM) interaction in applied magnetic fields is investigated. The local susceptibility and the corresponding order parameters are calculated numerically, and are found to be in good agreement with those of thermofield dynamics. The dependences of entropy and specific heat on temperature are studied numerically at various magnetic fields. It is shown that the entropy is always positive and the quantum fluctuation has a very strong effect on the specific heat. Especially, the typical crossover behaviour of the specific heat of a spin glass at various magnetic fields for mixed-anisotropy interactions is found.

Critical behavior of quantum spin systems with uniaxial single-ion anisotropy

We use a method combining the two-spin cluster expansion with the discretized path-integral representation (DPIR) to study the quantum transverse Ising model with spin-1 and mixed spins in the presence of a single-ion uniaxial anisotropy field. The free energy and the critical transverse field of the systems are obtained. The anisotropy field dependence of the critical transverse field are treated by a numerical analysis.

Surface Spin Waves in Anisotropic Heisenberg Magnet with a Single-Ion Uniaxial Anisotropy11The project supported by National Natural Science Foundation of China.

The technique of Green's function is used to investigate the surface spin waves in semi-infinite anisotropic Heisenberg magnet with a single-ion uniaxial anisotropy. The dispersion relations of surface excitations are obtained for the ferromagnetic, antiferromagnetic and ferrimagnetic systems, respectively. Results in some particular cases are discussed.

Surface magnons for a Heisenberg model with biquadratic exchange and single-ion uniaxial anisotropy

A semi-infinite Heisenberg system (ferromagnetism, antiferromagnetism or ferrimagnetism) with biquadratic exchange and single-ion uniaxial anisotropy is considered. The Green function method is employed to calculate the effect of the biquadratic exchange on the surface magnon spectrum. We show that the consistent progressive modes of surface magnons can be excited in the antiferromagnetic and ferrimagnetic systems.

Surface spin waves in a semi-infinite magnetic superlattice with a single-ion uniaxial anisotropy

Surface spin waves in a semi-infinite magnetic superlattice with a single-ion uniaxial anisotropy are investigated by use of the transfer-matrix method. The dispersion equations for surface spin waves are obtained. The authors find that not all of the structures of the superlattice can excite the surface spin waves and that the anisotropy term need not favour the excitation of surface spin waves, but that it will certainly influence the value of the energy of the excited surface spin waves.