Canted Field Research Articles

Magnetisation configuration in arrays of permalloy rectangles and its impact on magnetisation reversal

The remanent domain structures of composite element magnetic barcodes have been imaged using photo-emission electron microscopy with contrast from x-ray magnetic circular dichroism (XMCD-PEEM) and analysed with reference to the results of micromagnetic simulations. The magnetisation configuration at the end of wide strips is found to be perpendicular to the majority magnetisation direction. This transitions to an incomplete rotation for nominal strip widths below 300 nm and is found to affect the mechanics of magnetisation reversal for nominal strip widths below 200 nm, owing to a difference in magnetisation orientation when an external magnetic field is applied that is just smaller than the magnetic coercivity of the structures and a corresponding change in reversal dynamics. This change in domain structure as strip width decreases is consistent with both the influence of shape anisotropy and with measurements of magnetic hysteresis. The magnetisation reversal characteristics of composite element structures are found to be dependent on the relative magnetisation configurations of neighbouring strips, which in turn are found to vary stochastically upon the application and removal of a magnetic field along the easy axis of the structure. It is found that the application of a canted field is necessary to ensure sharp, consistent magnetisation reversal of bits when writing a binary code. These results confirm that either improved lithography of narrower strips or non-rectangular elements would be necessary to further increase the number of individually programmable bits in a barcode.

Controlling the phase diagram of finite spin- 12 chains by tuning the boundary interactions

Searching for simple models that possess non-trivial controlling properties is one of the central tasks in the field of quantum technologies. In this work, we construct a quantum spin-$1/2$ chain of finite size, termed as controllable spin wire (CSW), in which we have $\hat{S}^{z} \hat{S}^{z}$ (Ising) interactions with a transverse field in the bulk, and $\hat{S}^{x} \hat{S}^{z}$ and $\hat{S}^{z} \hat{S}^{z}$ couplings with a canted field on the boundaries. The Hamiltonians on the boundaries, dubbed as tuning Hamiltonians (TH's), bear the same form as the effective Hamiltonians emerging in the so-called `quantum entanglement simulator' that is originally proposed for mimicking infinite models. We show that tuning the TH's (parametrized by $\alpha$) can trigger non-trivial controlling of the bulk properties, including the degeneracy of energy/entanglement spectra, and the response to the magnetic field $h_{bulk}$ in the bulk. A universal point dubbed as $\alpha^s$ emerges. For $\alpha > \alpha^s$, the ground-state diagram versus $h_{bulk}$ consists of three `phases', which are Ne\'eL and polarized phases, and an emergent pseudo-magnet phase, distinguished by entanglement and magnetization. For $\alpha < \alpha^s$, the phase diagram changes completely, with no step-like behaviors to distinguish phases. Due to its controlling properties and simplicity, the CSW could potentially serve in future the experiments for developing quantum devices.

Effect of magnetic field orientation and disorder on Majorana polarization in wires with topological superconductivity

Majorana polarization, previously introduced by Sticlet et al. [Phys. Rev. Lett. 108, 096802 (2012)], is studied for wires in a topological superconductive state with varying orientation of the magnetic field. Numerical calculations show that in the case of a canted field, this polarization can differ in sign, as well as absolute magnitude, at the opposite ends of a wire. Since the Majorana polarization changes sign at one end when the orientation of the magnetic field is changed from perpendicular to longitudinal, there is always a range of angles for which this quantity is significantly suppressed or equals zero. Thus, the Majorana polarization does not always appear as a local order parameter for an arbitrary angle of the magnetic field in the plane perpendicular to the effective Rashba spin-orbital interaction field. It is shown that the introduction of disorder does not lead to qualitatively new effects. At the same time, additional regions with weak Majorana polarization do show up in high magnetic ...

Symmetry breaking in spin spirals and skyrmions by in-plane and canted magnetic fields

The influence of in-plane and canted magnetic fields on spin spirals and skyrmions in atomic bilayer islands of palladium and iron on an Ir(111) substrate is investigated by scanning tunneling microscopy at low temperatures. It is shown that the spin spiral propagation direction is determined by the island’s border which can be explained by equilibrium state calculations on a triangular lattice. We find a different response of spin spirals to in-plane magnetic fields for a propagation direction parallel to the applied field as compared to perpendicular, which originates from their cycloidal nature. As a result, the spin spiral propagation direction may be reorientated by in-plane fields. Furthermore, it is demonstrated that also skyrmions are distorted in canted fields which allows to determine the sense of magnetization rotation as enforced by the interfacial Dzyaloshinskii–Moriya interaction.

Field-induced phase transitions in the helimagnet Ba2CuGe2O7

We present a theoretical study of the two-dimensional spiral antiferromagnet Ba2CuGe2O7 in the presence of an external magnetic field. We employ a suitable nonlinear sigma model to calculate the T=0 phase diagram and the associated low-energy spin dynamics for arbitrary canted fields, in general agreement with experiment. In particular, when the field is applied parallel to the c axis, a previously anticipated Dzyaloshinskii-type incommensurate-to-commensurate phase transition is actually mediated by an intermediate phase, in agreement with our earlier theoretical prediction confirmed by the recent observation of the so-called double-k structure. The sudden pi/2 rotations of the magnetic structures observed in experiment are accounted for by a weakly broken U(1) symmetry of our model. Finally, our analysis suggests a nonzero weak-ferromagnetic component in the underlying Dzyaloshinskii-Moriya anisotropy, which is important for quantitative agreement with experiment.

Monitoring magnetization reversal and perpendicular anisotropy by the extraordinary Hall effect and anisotropic magnetoresistance.

Simultaneous magnetotransport measurements of the extraordinary Hall effect and anisotropic magnetoresistance were used to monitor the normal and in-plane projections of magnetization in thin Co/Pd multilayers with perpendicular anisotropy. By reconstructing the magnitude and orientation of the magnetization vector we were able to track the reversal of magnetization and distinguish among the processes of coherent rotation and domain nucleation. The Stoner–Wohlfarth model was used to extract anisotropy constants from data collected during the coherent rotation. We show that magnetization reversal occurs coherently over a major part of the cycle under a canted magnetic field when the field's inclination exceeds a certain sample-dependent angle. The applicability range of the Stoner–Wohlfarth model and thus reliability of the calculated anisotropy constants is significantly improved when measurements are performed under canted fields.

Growth and shape directionality of domains in exchange-coupled ferromagnet/antiferromagnet bilayers

Real time domain wall (DW) propagation processes were observed using the magneto-optic indicator film technique (MOIF) in both single crystal and polycrystalline epitaxial exchange-coupled ferromagnet/antiferromagnet (FM/AFM) bilayers. In both cases a new phenomenon of preferable directions of a DW's expansion under a canted magnetic field was found. Upon application of a magnetic field oriented slightly (4°÷10°) off the unidirectional anisotropy axis clockwise or counterclockwise, unlike along this axis, during remagnetization from the ground state the domain growth occurred in that same direction at an angle of (14°÷45°). During remagnetization to the ground state upon field reduction, but no inversion, the preferred domain growth direction was at the angle with reversed sign, however in case the field reduction to zero or inversion, the preferred DW growth direction disappeared or was at the original angle, respectively. It was revealed the angle of the domain wall orientation in canted field does not depend on the value of field angle.

Low temperature spin reorientation in dysprosium iron garnet

The spin reorientation (SR) phase transition in dysprosium iron garnet (Dy3Fe5O12 or DyIG) have been studied by specific heat Cp(T) and high field magnetisation measurements MT(H) and MH(T) on single crystals at low temperature. A first order SR is observed with a sharp jump at TSR = 14.5±0.5 K in the Cp(T) curve which corresponds to a spontaneous change from the high temperature (HT) easy direction ⟨111⟩ to an ⟨uuw⟩ angular low temperature (LT) phases. Above TSR, the magnetic structure is described by the irreducible representation (IR) A2g of the rhombohedral space group R 3 c. Below TSR, the magnetic structure changes in the monoclinic the space group C2/c with the IR Ag. When the field H is kept aligned along the hard symmetry directions ⟨100⟩ and ⟨110⟩, we obtain respectively the variation of the angular positions θ(T) and θ'(T) from the total spontaneous magnetisation down to 1.5 K (θ = 39.23° and θ' = 30.14°) and the results are in good agreement with the previous observations in low fields. When the sample is allowed to rotate freely on itself, the critical field Hc(T) between the HT⟨111⟩ and the LT⟨uuw⟩ angular phases permits us to precise the transition line up to 15 T and 40 K between the so called canted field induced (FI) and the associated collinear magnetic phases. The experimental magnetic phase diagram (MPD) is precisely determined in the (Hc-T) plane and the domains of the existence and the stability of the two magnetic phases are specified.

Collective excitations in a 2D electron system: Canted field geometry

We investigate the charge and spin collective modes induced in a 2D electron gas by a weak electromagnetic perturbation in the presence of a dc magnetic field which makes an angle θ with the electron layer. The excitation frequencies are determined within the framework of the Landau–Silin theory of Fermi liquids by solving a semi-classical equation for transport in the self-consistent electromagnetic field associated with particle density fluctuations. The quasiparticle interaction is spin dependent and varies parametrically with the degree of spin polarization. In the long wavelength limit, we obtain analytic results for the frequencies of the collective modes as functions of θ.