Barrier For Magnetization Reversal Research Articles

The effect of uniaxial pressure on the magnetic anisotropy of the Mn12-Ac single-molecule magnet

We study the effect of uniaxial pressure on the magnetic hysteresis loops of the single-molecule magnet Mn12-Ac. We find that the application of pressure along the easy axis increases the fields at which quantum tunneling of magnetization occurs. The observations are attributed to an increase in the molecule's magnetic anisotropy constant D of 0.142(1)%/kbar. The increase in D produces a small, but measurable increase in the effective energy barrier for magnetization reversal. Density-functional theory calculations also predict an increase in the barrier with applied pressure.

Magnetization Reversal of Individual Co Nanoislands

We investigate the magnetization reversal of individual Co islands on Cu(111) in the size range of N=700 to 18,000 atoms by spin-polarized scanning tunneling microscopy at 8 K. The switching field H(sw) changes with island size in a nonmonotonic manner: it increases with island size and reaches a maximum value of 2.4 T at N=5500 atoms, and it decreases for larger islands. We extract the energy barrier for magnetization reversal as a function of island size. The maximum H(sw) corresponds to an energy barrier of 1 eV. Our results elucidate a crossover of the magnetization reversal from an exchange-spring behavior to domain wall formation with increasing size at around 7500 atoms.

Joule Heating and Spin-Transfer Torque Investigated on the Atomic Scale Using a Spin-Polarized Scanning Tunneling Microscope

The influence of a high spin-polarized tunnel current onto the switching behavior of a superparamagnetic nanoisland on a nonmagnetic substrate is investigated by means of spin-polarized scanning tunneling microscopy. A detailed lifetime analysis allows for a quantification of the effective temperature rise of the nanoisland and the modification of the activation energy barrier for magnetization reversal, thereby using the nanoisland as a local thermometer and spin-transfer torque analyzer. Both the Joule heating and spin-transfer torque are found to scale linearly with the tunnel current. The results are compared to experiments performed on lithographically fabricated magneto-tunnel junctions, revealing a very high spin-transfer torque switching efficiency in our experiments.

Strong spin–orbit effects in small Pt clusters: Geometric structure,magnetic isomers and anisotropy

Ab initio density functional calculations including spin-orbit coupling (SOC) have been performed for Pt(n), n = 2-6 clusters. The strong SOC tends to stabilize planar structures for n = 2-5, whereas for clusters consisting of six atoms, three-dimensional structures remain preferred. SOC leads to the formation of large orbital magnetic moments and to a mixing of different spin states. Due to the spin-mixing the total magnetic moment may be larger or smaller than the spin moment in the absence of SOC. Both spin and orbital moments are found to be anisotropic. Because of the strong SOC the energy differences between coexisting magnetic isomers can be comparable to or even smaller than their magnetic anisotropy energies. In this case the lowest barrier for magnetization reversal can be determined by a magnetic isomer which is different from the ground state configuration.

Variation of the ground spin state in homo- and hetero-octanuclear copper(ii) and nickel(ii) double-star complexes with a meso-helicate-type metallacryptand core

Homo- and heterometallic octanuclear complexes of formula Na₂{[Cu₂(mpba)₃][Cu(Me₅dien)]₆}-(ClO₄)₆·12H₂O (1), Na₂{[Cu₂(Mempba)₃][Cu(Me₅dien)]₆}(ClO₄)₆·12H₂O (2), Na₂{[Ni₂(mpba)₃]-[Cu(Me₅dien)]₆}(ClO₄)₆·12H₂O (3), Na₂{[Ni₂(Mempba)₃][Cu(Me₅dien)]₆}(ClO₄)₆·9H₂O (4), {[Ni₂(mpba)₃][Ni(dipn)(H₂O)]₆}(ClO₄)₄·12.5H₂O (5), and {[Ni₂(Mempba)₃][Ni(dipn)-(H₂O)]₆}(ClO₄)₄·12H₂O (6) [mpba = 1,3-phenylenebis(oxamate), Mempba = 4-methyl-1,3-phenylenebis(oxamate), Me₅dien = N,N,N',N'',N''-pentamethyldiethylenetriamine, and dipn = dipropylenetriamine] have been synthesized through the "complex-as-ligand/complex-as-metal" strategy. Single-crystal X-ray diffraction analyses of 1, 3, and 5 show cationic M(II)₂M'(II)₆ entities (M, M' = Cu and Ni) with an overall double-star architecture, which is made up of two oxamato-bridged M(II)M'(II)₃ star units connected through three meta-phenylenediamidate bridges between the two central metal atoms leading to a binuclear metallacryptand core of the meso-helicate-type. Dc magnetic susceptibility data for 1-6 in the temperature range 2-300 K have been analyzed through a "dimer-of-tetramers" model [H = - J(S(1A)·S(3A) + S(1A)·S(4A) + S(1A)·S(5A) + S(2B)·S(6B) + S(2B)·S(7B) + S(2B)·S(8B)) - J'S(1A)·S(2B), with S(1A) = S(2B) = S(M) and S(3A) = S(4A) = S(5A) = S(6B) = S(7B) = S(8B) = S(M')]. The moderate to strong antiferromagnetic coupling between the M(II) and M'(II) ions through the oxamate bridge in 1-6 (-J(Cu-Cu) = 52.0-57.0 cm⁻¹, -J(Ni-Cu) = 39.1-44.7 cm⁻¹, and -J(Ni-Ni) = 26.3-26.6 cm⁻¹) leads to a non-compensation of the ground spin state for the tetranuclear M(II)M'(II)₃ star units [S(A) = S(B) = 3S(M') - S(M) = 1 (1 and 2), 1/2 (3 and 4), and 2 (5 and 6)]. Within the binuclear M(II)₂ meso-helicate cores of 1-4, a moderate to weak antiferromagnetic coupling between the M(II) ions (-J'(Cu-Cu) = 28.0-48.0 cm⁻¹ and -J'(Ni-Ni) = 0.16-0.97 cm⁻¹) is mediated by the triple m-phenylenediamidate bridge to give a ground spin singlet (S = S(A) - S(B) = 0) state for the octanuclear M(II)₂Cu(II)₆ molecule. Instead, a weak ferromagnetic coupling between the Ni(II) ions (J'(Ni-Ni) = 2.07-3.06 cm⁻¹) operates in the binuclear Ni(II)₂ meso-helicate core of 5 and 6 leading thus to a ground spin nonet (S = S(A) + S(B) = 4) state for the octanuclear Ni(II)₈ molecule. Dc magnetization data for 5 reveal a small but non-negligible axial magnetic anisotropy (D = -0.23 cm⁻¹) of the S = 4 Ni(II)₈ ground state with an estimated value of the energy barrier for magnetization reversal of 3.7 cm⁻¹ (U = -DS²). Ac magnetic susceptibility data for 5 show an unusual slow magnetic relaxation behaviour at low temperatures which is typical of "cluster glasses". The temperature dependence of the relaxation time for 5 has been interpreted on the basis of the Vogel-Fulcher law for weakly interacting clusters, with values of 2.5 K, 1.4 × 10⁻⁶ s, and 4.0 cm⁻¹ for the intermolecular interaction parameter (T₀), the pre-exponential factor (τ₀), and the effective energy barrier (U(eff)), respectively.

Magnetic Anisotropy in the [CuIILTbIII(hfac)2]2Single Molecule Magnet: Experimental Study and Theoretical Modeling

In the present article, we proffer an explanation for the origin of single molecule magnetism in [CuIILTbIII(hfac)2]2, a member of the novel class of mixed transition−lanthanide metal clusters. The theoretical model takes into account the crystal field acting on the TbIII ion as well as the exchange interaction between the TbIII and CuII ions and provides a good account of the low-lying energy levels, rigorously measured by inelastic neutron scattering and magnetic data. We demonstate that the single molecule magnet (SMM) behavior is not a sole consequence of the low-lying levels of the lanthanide metal ion but a property of the tetranuclear cluster itself. The energy levels are shown to increase with the decrease of the mean value of the Z-projection of the total angular momentum of the cluster, thus forming a barrier for magnetization reversal that is wholly consistent with the observed SMM behavior. On the basis of this study, recommendations are formulated on how the SMM properties for nd−4f clusters ...

A Model of Single Molecule Magnet Behaviour of 3<I>d</I>-4<I>f</I> Clusters

We report a model for the explanation of the single molecule magnet behavior of the [Cu II LTb III (hfac) 2 ] 2 cluster. The model takes into account the crystal field acting on the Tb III ion and the exchange interaction between Tb III and Cu II ions. The energies of the low-lying levels are shown to increase with the decrease of the mean value of the Z-projection of the total angular momentum of the cluster, thus forming a barrier for magnetization reversal that is in accordance with the experimental evidence.

Covalently Linked Dimers of Clusters: Loop‐ and Dumbbell‐Shaped Mn24 and Mn26 Single‐Molecule Magnets

Double impact: The use of both azide and di-2-pyridylketone-derived ligands has provided new Mn24 (left) and Mn26 complexes (right) with loop and dumbbell structures that are made up of two covalently linked Mn12 and Mn13 units, respectively. Both complexes are single-molecule magnets, and the Mn26 complex displays the largest barrier for magnetization reversal in a MnII/III complex known to date. MnII yellow, MnIII blue, O red, N green, C gray.

A Model of Single Molecule Magnet Behavior of the [Cu<sup>II</sup>LTb<sup>III</sup>(hfac)<sub>2</sub>]<sub>2</sub> Cluster

We report a model for the explanation of the single molecule magnet behavior of the [CuIILTbIII(hfac)2]2 cluster. The model takes into account the crystal field acting on the TbIII –ion and the exchange interaction between the TbIII and CuII ions. The energies of the low-lying levels are shown to increase with the decrease of the mean value of the z-projection of the total angular momentum of the cluster, thus forming a barrier for magnetization reversal that is in accordance with the experimental evidence.

Determination of the micromagnetic parameters in (Ga,Mn)As using domain theory

The magnetic domain structure and magnetic properties of a ferromagnetic (Ga,Mn)As epilayer with perpendicular magnetic easy axis are investigated. We show that despite strong hysteresis domain theory at thermodynamical equilibrium can be used to determine the micromagnetic parameters. Combining magneto-optical Kerr microscopy, magnetometry, and ferromagnetic resonance measurements, we obtain the characteristic parameter for magnetic domains ${\ensuremath{\lambda}}_{c}$, the domain wall width and specific energy, and the spin stiffness constant as a function of temperature. The nucleation barrier for magnetization reversal and the Walker breakdown velocity for field-driven domain wall propagation are also estimated.

Magnetic anisotropy in the octanuclear [formula omitted] cluster exhibiting Single-Molecule Magnet behavior: Quantum-spin and classical-spin approaches

A theoretical model is developed for the explanation of the magnetic properties of the [MnCl] 4[Re(triphos)(CN) 3] 4 single molecule magnet, which represents a 3d–5d molecular cube compressed along one of the C 3 axes. In the model, the strong local trigonal crystal field on each Re(II) ion is assumed to split the ground cubic 2 T 2( t 2 5 ) term into the states 2 A 1 and 2 E in such a way that 2 E term proves to be the ground one. The ground Kramers doublet that appears under the spin–orbit splitting of the 2 E term is shown to be fully anisotropic ( g ⊥ = 0) and the magnetic superexchange (mediated by cyanide bridge) between Re and Mn ions is approximated by the Ising-like Hamiltonian. In this case, the magnetic anisotropy of the trigonally distorted cube represents a first order effect that is totally incorporated in the effective Ising-like Hamiltonian, including the pseudo-spin-1/2 operator for the Re(II) ion and the operator of the true spin-5/2 for the Mn(II) ion. The developed pseudo-spin-1/2 formalism is applied to the explanation of the DC magnetic susceptibility and magnetization data, and the set of the best fit parameters is found. The temperature dependence of the DC magnetic susceptibility and the field dependence of the magnetization calculated with this set of parameters are in accord with the experimental data being at the same time compatible with the existence of the barrier for magnetization reversal. Finally, the applicability of the quantum–classical spin approach for the calculation of the magnetic properties of large 3d–5d clusters is discussed.

Effects of vibronic interaction in cyano-bridged clusters containing Mn(III) and Mn(II) ions

The effects of vibronic interaction in the formation of the barrier for magnetization reversal in the cyanide-based binuclear Mn(III)–CN–Mn(II) clusters containing octahedrally coordinated Mn(III) and Mn(II) ions were examined. Along with the orbitally dependent superexchange between the Mn(II) and Mn(III) ions the model includes an axial component of the crystal field, spin–orbit coupling and vibronic interaction operating within the ground 3 T 1 ( t 2 4 ) term of the low-spin Mn(III) ion. The vibronic coupling parameters for the Mn(III) ion in the octahedral surrounding of six carbon ions have been evaluated in the framework of the exchange charge model of the crystal field accounting for the exchange and covalence effects. The dominating role of the tetragonal vibrations for the 3T 1 term of a single Mn(III) ion was demonstrated. The ability of the investigated complex to act as a Single-Molecule Magnet was analyzed as a function of both the temperature and the strength of vibronic coupling with the tetragonal vibrations. Very strong vibronic interaction strongly facilitates tunneling through the barrier, i.e., suppresses the barrier for magnetization reversal and prevents from long life time of magnetization.

Ising limit for a pair of transition metal ions with unquenched orbital angular momenta and its relevance to single molecule magnets

We discuss the magnetic anisotropy of exchange-coupled pair of transition metal ions with unquenched orbital angular momenta in axially distorted octahedral surroundings. The case of ground orbital doublets of the metal ions is shown to give rise to a strong magnetic anisotropy and Ising type effective exchange Hamiltonian. Providing ferromagnetic exchange such Ising interaction is shown to create a magnetization reversal barrier.

Low-field EPR studies of levels near the top of the barrier in Mn 12-acetate reveal a new magnetization relaxation pathway

We show that X-band electron paramagnetic resonance (EPR) measurements using a dual-mode resonance cavity can directly probe the levels near the top of the magnetization reversal barrier in the single-molecule magnet (SMM) Mn 12-acetate. The observed transitions are much sharper than those reported in high-field EPR studies. The observed temperature dependence of the line positions points to the presence of a spin-diffusional mode. The correlation time for such fluctuations is of the order of 6×10 −8 s at 10 K, and follows an Arrhenius activation energy of 35–40 K. These results open a new avenue for understanding the mechanism of tunneling and spin–lattice relaxations in these SMMs.

Field dependence of the barrier to magnetization reversal of a Stoner-Wohlfarth particle

It is well known that the energy barrier for magnetization reversal, EB, varies quadratically with the magnetic field for the Stoner-Wohlfarth model. However, the enthalpy H (switching energy) required to reverse the magnetization is the sum of EB and the work Wf done by the Néel fluctuation field. The sum of these two terms gives an enthalpy of reversal. If the fluctuation field is uniaxial and parallel to the holding field, then the enthalpy barrier for switching is linear in the holding field. The linearity is consistent with certain experimental results. If the fluctuation field is anisotropic, then for the same size field, the probability of the particle’s switching will depend upon the direction of that field. The paper discusses the holding field variation of the energy barrier for different fluctuation field directions.

Control of the Barrier in Cyanide Based Single Molecule Magnets Mn(III)2Mn(II)3: Theoretical Analysis.

The aim of this communication is to probe the possibility of increasing the barrier for reversal of magnetization in the family of new cyano-bridged pentanuclear Mn(III)2Mn(II)3 clusters in which single molecule magnet behavior has been recently discovered. In this context, we analyze the global magnetic anisotropy arising from the unquenched orbital angular momenta of ground terms (3)T1(t2(4)) of the two apical Mn(III) ions. The model takes into account the trigonal component of the crystal field, spin-orbit interaction in (3)T1(t2(4)), and an isotropic exchange interaction between Mn(III) and Mn(II) ions. The height of the barrier is shown to be sensitive to the change of the trigonal field stabilizing orbital doublet (3)E, which carries the first-order orbital magnetic contribution and enhances with an increase of the trigonal field. This result is expected to be useful for the more rational design of new cyano-bridged SMMs with high blocking temperatures.

Current-induced effective magnetic fields inCo∕Cu∕Conanopillars

We present a method to measure the effective field contribution to spin-transfer-induced interactions between the magnetic layers in a trilayer nanostructure, which enables spin-current effects to be distinguished from the usual charge-current-induced magnetic fields. This technique is demonstrated on submicron Co/Cu/Co nanopillars. The hysteresis loop of one of the magnetic layers in the trilayer is measured as a function of current while the direction of magnetization of the other layer is kept fixed, first in one direction and then in the opposite direction. These measurements show a current-dependent shift of the hysteresis loop which, based on the symmetry of the magnetic response, we associate with spin-transfer. The observed loop-shift with applied current at room temperature is reduced in measurements at 4.2 K. We interprete these results both in terms of a spin-current dependent effective activation barrier for magnetization reversal and a spin-current dependent effective magnetic field. From data at 4.2 K we estimate the magnitude of the spin-transfer induced effective field to be $\sim 1.5 \times 10^{-7} $ Oe cm$^2$/A, about a factor of 5 less than the spin-transfer torque.

Molecular Cube of ReII and MnII That Exhibits Single-Molecule Magnetism

A pseudocubic, paramagnetic cluster of ReII and MnII, [{MnCl}4{Re(triphos)(CN)3}4], has been prepared, and its magnetic properties have been investigated. Antiferromagnetic coupling is observed between the "S = 1/2" ReII and S = 5/2 MnII centers resulting in an effective S = 8 ground state. AC susceptibility studies reveal that the molecule is a single-molecule magnet with an effective barrier for magnetization reversal of Ueff = 8.8 cm-1.

Thermally and field driven magnetization processes in nanometer-scale particle arrays

Nanometer-scale iron particles were fabricated by Scanning Tunneling Microscopy assisted chemical vapor deposition. With this, the particles can precisely be placed at a predetermined position and their dimensions can easily be controlled. The latter enabled us to perform a systematic study of the dependence of thermal activation on the particles' diameter (9-20 nm for the different arrays). Magnetic measurements included Hall magnetometry and variable field MFM. From the temperature dependence of the switching fields of our elongated particles we inferred a thermally activated nucleation-propagation type of magnetization reversal even for the smallest (9 nm) particles. The energy barrier for magnetization reversal in elongated particles is derived, from which dynamic coercivities can be calculated. The impact of thermal activation was found to scale with the particles' cross-section, in agreement with magnetic viscosity measurements.

Incoherent Magnetization Model for Perpendicular Recording Media

To study the influence of thermal fluctuation in perpendicular recording media, we investigated a new incoherent magnetization model and combined it with the Langevin equation method. In our model, the energy barrier for magnetization reversal is reduced by using an incoherent reversal process. We simulated the M-H curve and the torque curve for perpendicular media with small Hc/Hk values, and calculated the time decay of Mr due to thermal fluctuation in the perpendicular media. The results roughly agreed with the experimental values of the time decay.