Angle Of External Field Research Articles

Observation of mode splitting in artificial spin ice: A comparative ferromagnetic resonance and Brillouin light scattering study

We report the dependence of the magnetization dynamics in a square artificial spin-ice lattice on the in-plane magnetic field angle. Using two complementary measurement techniques—broadband ferromagnetic resonance and micro-focused Brillouin light scattering spectroscopy—we systematically study the evolution of the lattice dynamics, for both a coherent radio frequency excitation and an incoherent thermal excitation of spin dynamics. We observe a splitting of modes facilitated by inter-element interactions that can be controlled by the external field angle and magnitude. Detailed time-dependent micromagnetic simulations reveal that the split modes are localized in different regions of the square network. This observation suggests that it is possible to disentangle modes with different spatial profiles by tuning the external field configuration.

Auto-oscillating Spin-Wave Modes of Constriction-Based Spin Hall Nano-oscillators in Weak In-Plane Fields

We experimentally study the auto-oscillating spin-wave modes in NiFe/$\beta-$W constriction-based spin Hall nano-oscillators as a function of bias current, in-plane applied field strength, and azimuthal field angle, in the low-field range of 40-80 mT. We observe two different spin-wave modes: i) a linear-like mode confined to the minima of the internal field near the edges of the nanoconstriction, with weak frequency dependencies on the bias current and the applied field angle, and ii) a second, lower frequency mode that has significantly higher threshold current and stronger frequency dependencies on both bias current and the external field angle. Our micromagnetic modeling qualitatively reproduces the experimental data and reveals that the second mode is a spin-wave bullet and that the SHNO mode hops between the two modes, resulting in a substantial increase in linewidths. In contrast to the linear-like mode, the bullet is localized in the middle of the constriction and shrinks with increasing bias current. Utilizing intrinsic frequency doubling at zero field angle we can reach frequencies above 9 GHz in fields as low as 40 mT, which is important for the development of low-field spintronic oscillators with applications in microwave signal generation and neuromorphic computing.

State diagram of spin-torque oscillator with perpendicular reference layer and planar field generation layer

The state diagram of spin-torque oscillator (STO) with perpendicular reference layer (REF) and planar field generation layer (FGL) was studied by a macrospin model and a micro-magnetic model. The state diagrams are calculated versus the current density, external field and external field angle. It was found that the oscillation in FGL could be controlled by current density combined with external field so as to achieve a wide frequency range. An optimized current and applied field region was given for microwave assisted magnetic recording (MAMR), considering both frequency and output field oscillation amplitude. The results of the macro-spin model were compared with those of the micro-magnetic model. The macro-spin model was qualitatively different from micro-magnetics and experimental results when the current density was large and the FGL was non-uniform.

Microwave-Assisted Magnetization Reversal for Granular Media by a Resonant Cavity Method

Microwave-assisted magnetization reversal was verified by a cavity method with intention to apply homogenous microwave to a millimeter-size CoPtCr-SiO2 medium. By applying 34 GHz microwave with various power, magnetization reversal of the medium was assisted. The amount of the reversal magnetization was estimated using an internal magnetic field evaluated with ferromagnetic resonance (FMR) field. As a result, it is found that: 1) when the incident angle of external field is set at 90° (perpendicular), assisting effect depends on microwave power and magnetization of the media; 2) mode value of switching field distribution of the media was reduced 300 Oe by 160-mW microwave assisting; and 3) when the incident angle of external field is set at 45° during the microwave assisting, dispersion of the SFD decreased with increasing microwave power.

Decoherence and Mode Hopping in a Magnetic Tunnel Junction Based Spin Torque Oscillator

We discuss the coherence of magnetic oscillations in a magnetic tunnel junction based spin torque oscillator as a function of the external field angle. Time-frequency analysis shows mode hopping between distinct oscillator modes, which arises from linear and nonlinear couplings in the Landau-Lifshitz-Gilbert equation, analogous to mode hopping observed in semiconductor ring lasers. These couplings and, therefore, mode hopping are minimized near the current threshold for the antiparallel alignment of free-layer with reference layer magnetization. Away from the antiparallel alignment, mode hopping limits oscillator coherence.

Resistive switching behaviors in Bi2Sr2CaCu2O8+d (Bi-2212) stacks

A coupled stacked Josephson junctions (SJJs) with completely perforated holes of 0.2 μm × 0.4 μm in high-Tc superconducting Bi2Sr2CaCu2O8+d (Bi-2212) were fabricated using a 3D focused ion beam etching method. We investigated external field angle θi dependence of junction resistance Rj at various magnetic fields and temperatures. When a constant external magnetic fields He value of 1 T and a bias current Ib value of 1 μA were applied to the sample with changing external field angle θi, unspecified equidistant and periodic peak structures in the SJJs were induced. The periodic peaks of Rj shows the resistive switching transition from zero resistance state to resistance state.

Role of reversal incoherency in reducing switching field and switching field distribution of exchange coupled composite bit patterned media

Model exchange coupled composite media, namely [Co/Pd]5/Pd(t)/[Co/Ni]3/Co multilayers, deposited onto prepatterned substrates have been investigated for potential use in bit patterned recording. Optimizing the thickness of the Pd interlayer allows decreasing the switching field (HC) and switching field distribution (σSFD) while maintaining thermal stability. The dependence of the remanent coercivity on the external field angle indicates that the gain in HC and σSFD originates from the incoherent magnetization reversal introduced by slightly decoupling the hard and soft multilayer stacks. This tendency is confirmed by further reductions in HC and σSFD, when inserting another Pd interlayer within the hard [Co/Pd]5 stack.

Periodic Peak Modulations in Bi-2212 Stacks Coupled to a Submicrometer Hole

Coupled stacked Josephson junctions (SJJs) in high-T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> superconducting (HTS) Bi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Sr <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CaCu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8+d</sub> (Bi-2212) are fabricated with a refined coupling configuration of a hole. Two types of coupled SJJs with a completely perforated hole of 0.1 mum x 0.2 mum and 0.2 mum x 0.4 mum were fabricated by using a 3-D focused ion beam (FIB) etching method. Those SJJs exhibited clearly oscillated critical current I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> under external magnetic fields H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> . With applying H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> , the clear periodic modulation patterns of I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> are obtained and well fitted to the calculated value from the hole area of 0.02 mum <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , DeltaB(= Phi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /S) , where S is hole area. The width and uniform transport properties of SJJs are confirmed by flux flow resistance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ff</sub> -H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> measurement with a bias current I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> of 1 muA at 10 K. We also investigated external field angle thetas <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> dependence of junction resistance R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> at 1 T and 10 K. When a constant H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> of 1 T and a I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> of 1 muA are applied to the sample with changing thetas <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , unspecified equidistant and periodic peak structures in SJJs were induced. Those peaks dependence on thetas <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> under H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> were experimentally observed by measurement of the R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> . We assign the origin of the peaks to the interrelations between the periodic mechanical vibrations of sample stage and the quantized flux behaviors around a submicrometer hole. Those peak structures of I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> could be excited by H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> ,thetas <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ,I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> , and some external signals from the peculiar properties of SJJs coupled to a hole.

Magnetization reversal of single domain permalloy nanowires

Magnetization reversal process and magnetoresistance (MR) hysteresis of single domain permalloy nanowires are numerically investigated by using OOMMF. It is shown that the abrupt jumps in the magnetoresistance are due to the domain formation and domain wall propagation so that a magnetic domain suddenly switches from one state into another. A nonmonotonic angular dependence of the jump (switching) field is found. Coherent rotation mode is responsible for the smooth variation of MR curves. The nucleation pattern of newly born domains depends on the tilted angle of external field.

Numerical Evaluation of Anisotropy of Magnetization Losses in Superconducting Wires With Elliptic Cross Section

AC losses are numerically estimated in straight superconductors with an elliptic cross section exposed to a transverse magnetic field. It is assumed that the distribution of magnetic field in the superconductors is determined by Bean's critical state model, in which the critical current density is independent of the magnitude of local magnetic field. The penetration process of magnetic flux into the superconductors approximated as a group of fine rectangular bars is evaluated by means of the minimization of magnetic energy for the application of the external magnetic fields with arbitrary angles to their broadest face. By using the obtained penetration process, the AC losses are also calculated from the distribution of magnetic vector potential inside the superconductors. Furthermore, the compensation for the numerical results of AC losses enables us to obtain a universal loss property that is scarcely affected by the aspect ratio of cross section and the angle of external field.

AC loss properties of elliptic superconducting wires exposed to a transverse magnetic field with an arbitrary angle

Analytical expressions of alternating current (AC) losses are derived in a superconducting wire with an infinite length and elliptic cross-section for limiting cases in which the amplitude of an external transverse magnetic field is much smaller or larger than the full penetration field. Since it is assumed that the superconducting wire is subject to Bean’s critical state model, in which the critical current density is independent of the magnitude of the local magnetic field, the AC losses under consideration are completely hysteretic. The expressions obtained explicitly include the effects of the aspect ratio of the wire cross-section and the external-field angle with respect to the broadest face. An approximated curve of the AC loss, which becomes equal to the analytical results under the limiting conditions mentioned above, is also proposed for a wide range of external-field amplitudes. In order to validate the proposed curve, the AC losses in the elliptic wires are numerically calculated by means of the minimization of magnetic energy. It is concluded that the discrepancy between the approximated curves and the numerical results of the AC losses is less than 40%.

楕円断面超伝導線材の斜め磁界損失特性

Analytical expressions of alternating current (AC) losses are derived in a superconducting wire with an infinite length and elliptic cross-section for limiting cases in which the amplitude of an external transverse magnetic field is much smaller or larger than the full penetration field. Since it is assumed that the superconducting wire is subject to Bean's critical state model, in which the critical current density is independent of the magnitude of the local magnetic field, the AC losses under consideration are completely hysteretic. The expressions obtained explicitly include the effects of the aspect ratio of the wire cross-section and the external-field angle with respect to the broadest face. An approximated curve of the AC loss, which becomes equal to the analytical results under the limiting conditions mentioned above, is also proposed for a wide range of external-field amplitudes. In order to validate the proposed curve, the AC losses in the elliptic wires are numerically calculated by means of the minimization of magnetic energy. It is concluded that the discrepancy between the approximated curves and the numerical results of the AC losses is less than 40%.

Numerical study of hysteresis and morphology in elongated tape particles

A three-dimensional micromagnetic model with cubic discretization is used to examine switching field dependence on particle size, aspect ratio, external field angle, and shape morphology for typical tape particles. For rectangular particles, discretization along the particle axis gives accurate switching fields for all radii approximately less than an exchange length. Switching fields are independent of aspect ratio for 5:1 and greater rectangular particles except for sufficiently small radii where uniform switching occurs. Spherocylinders, cylinders, and rectangular parallelepipeds give virtually the same switching field at least for all radii less than two exchange lengths. For radii approximately equal to an exchange length, the corresponding switching field of an ellipsoid is nearly twice that of these other shapes. Numerical results for approximate ellipsoids agree with analytical predictions and previous fine element method calculations.

Ｂｉ‐２２２３高温超電導テープ材臨界電流密度の磁場方向依存性

Dependence of the critical current density of Bi-2223 superconducting tape on the angle of external magnetic field is investigated theoretically and experimentally. The model proposed here is based on an effective coherence tensor model which can deal with the anisotropy of the coherence length, and has been derived so as to be applicable for the arbitrary angle of the external field. The resulting mathematical expression of the angular dependence of the critical current density shows that the critical current density is dependent only on the normal component of the magnetic field to the tape surface (i.e., the component perpendicular to the ab plane). The measurements of critical current density were made based on the four-point DC method, and the results show the validity of the theoretical considerations.

Angle dependence of the ferromagnetic resonance linewidth in easy-axis and easy-plane single crystal hexagonal ferrite disks

Ferromagnetic resonance measurements were made as a function of the static external field angle for c-plane disks of single crystal flux grown manganese substituted barium M-type (Ba-M) and zinc Y-type (Zn-Y) hexagonal ferrites at 50 and 8.8 GHz, respectively. A shorted waveguide technique was used. Analysis of the FMR field versus angle results confirmed the operational assumption of a uniform mode response. For the easy-axis Ba-M disk, the linewidth was 69 Oe when the external field and magnetization vectors were perpendicular to the disk. The linewidth increased to a maximum measured value of 472 Oe when the magnetization was directed 45.4° from the sample normal. For the easy-plane Zn-Y disk, the linewidth had a minimum value of 18 Oe when the field and magnetization vectors were in-plane. The maximum linewidth was 391 Oe when the magnetization was directed 25.2° from the disk normal. The linewidths were larger than predicted for reasonable values of the Landau–Lifshitz damping and showed angle dependences which indicated nonintrinsic contributions to the loss. A modified two magnon scattering calculation based on the model of Sparks, Loudon, and Kittel was used to investigate these linewidth differences. The calculation included anisotropy modifications to the spin wave band for each material. The angle dependences of the excess linewidths show qualitative agreement with the two magnon predictions, with inhomogeneity sizes on the order of 1 and 0.25 μm and volume fractions of 0.01 and 0.005 for the Ba-M and Zn-Y disks, respectively.

Micromagnetics of long ferromagnetic particles

A 3D micromagnetic model is used to examine nucleation field dependence on exchange length, particle size and external field angle for long ferromagnetic particles. Reasonable agreement is shown between the model's predictions and recent experiments on Ni particles. Illustrations of the reversal mode are included which show reversal beginning at the ends and proceeding towards the center of the particle. The amount of discretization necessary for accurate modelling is investigated. For a tape particle with a radius equal to the exchange length, a discretization along the length of the particle is found to be adequate.

Scaling in thin magnetoresistive films

The magnetoresistive response of long strips of thin ferromagnetic films under external field in the plane of the film is examined using analytic as well as numerical methods. This is done for a range of easy axis directions and external field angles. It is found that the dimensional as well as magnetic parameters are subsumed into two parameters—a zero-field equilibrium angle η and a field scale HS. The magnetoresistive response of the film to an external field HA appears in terms of the scaled variable (HA/ HS). As a result, the response of a large number of films for a given external field angle, and fixed η, falls on the same curve when expressed in terms of the scaled variable (HA/ HS). This also leads to a reciprocal relation between the sensitivity and range of linearity of the transfer function of a magnetoresistive transducer.

Lower critical field of an anisotropic extreme type-II superconductor.

It is shown that the procedure of Klemm and Clem (abbreviated as I) for the transformation to isotropic form of the Ginzburg-Landau free energy for a superconductor with a general effectivemass anisotropy leads to a current which is not perpendicular to the magnetic induction $\mathbf{B}$, unless $\mathbf{B}$ is in a crystal-symmetry direction. In general, the mean-field free energy is thus a function of a new parameter $\ensuremath{\beta}$, which depends upon the direction cosines of $\mathbf{B}$, as well as a function of the renormalized $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\kappa}}$ parameter of I, except at the upper critical field ${H}_{c2}$. A perturbation solution in $\ensuremath{\gamma}=\frac{\ensuremath{\beta}}{(1+\ensuremath{\beta})}$ is found to order ${\ensuremath{\gamma}}^{2}$, and the angular dependence of the lower critical field ${H}_{c1}$ is determined. The parameter $\ensuremath{\beta}$ is found to cause $\mathbf{B}$ to nearly lock on to a crystal-symmetry direction, so that as the external field angle is varied, $\mathbf{B}$ switches from near to one symmetry direction to (near to) another, yielding a kink in the angular dependence of ${H}_{c1}$ that is more pronounced than in I.