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Distribution of interevent avalanche times in disordered and frustrated spin systems
Authors:
John Ferre,
Amin Barzegar,
Helmut G. Katzgraber,
Richard Scalettar
Abstract:
Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality, manifest in power-law distributions of avalanche sizes. Considerably less work has been done on the statistics of the times between avalanches. This paper considers…
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Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality, manifest in power-law distributions of avalanche sizes. Considerably less work has been done on the statistics of the times between avalanches. This paper considers this issue, generalizing the work of Nampoothiri et al. [Phys. Rev. E 96, 032107 (2017)] in one space dimension to higher space dimensions. In addition to the interevent statistics of all avalanches, we also consider what happens when events are restricted to those exceeding a certain threshold size. Doing so raises the possibility of altering the definition of time to count the number of small events between the large ones, which provides for an analog to the concept of natural time introduced by the geophysics community with the goal of predicting patterns in seismic events. We analyze the distribution of time and natural time intervals both in the case of models that include only nearest-neighbor interactions, as well as models with (sparse) long-range couplings.
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Submitted 10 January, 2019; v1 submitted 30 August, 2018;
originally announced August 2018.
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Pinning dependent field driven domain wall dynamics and thermal scaling in an ultrathin Pt/Co/Pt magnetic film
Authors:
J. Gorchon,
S. Bustingorry,
J. Ferré,
V. Jeudy,
A. B. Kolton,
T. Giamarchi
Abstract:
Magnetic field-driven domain wall motion in an ultrathin Pt/Co(0.45nm)/Pt ferromagnetic film with perpendicular anisotropy is studied over a wide temperature range. Three different pinning dependent dynamical regimes are clearly identified: the creep, the thermally assisted flux flow and the depinning, as well as their corresponding crossovers. The wall elastic energy and microscopic parameters ch…
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Magnetic field-driven domain wall motion in an ultrathin Pt/Co(0.45nm)/Pt ferromagnetic film with perpendicular anisotropy is studied over a wide temperature range. Three different pinning dependent dynamical regimes are clearly identified: the creep, the thermally assisted flux flow and the depinning, as well as their corresponding crossovers. The wall elastic energy and microscopic parameters characterizing the pinning are determined. Both the extracted thermal rounding exponent at the depinning transition, $ψ=$0.15, and the Larkin length crossover exponent, $φ=$0.24, fit well with the numerical predictions.
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Submitted 29 July, 2014;
originally announced July 2014.
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Spatially periodic domain wall pinning potentials: Asymmetric pinning and dipolar biasing
Authors:
P. J. Metaxas,
P. -J. Zermatten,
R. L. Novak,
S. Rohart,
J. -P. Jamet,
R. Weil,
J. Ferré,
A. Mougin,
R. L. Stamps,
G. Gaudin,
V. Baltz,
B. Rodmacq
Abstract:
Domain wall propagation has been measured in continuous, weakly disordered, quasi-two-dimensional, Ising-like magnetic layers that are subject to spatially periodic domain wall pinning potentials. The potentials are generated non-destructively using the stray magnetic field of ordered arrays of magnetically hard [Co/Pt]$_m$ nanoplatelets which are patterned above and are physically separated from…
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Domain wall propagation has been measured in continuous, weakly disordered, quasi-two-dimensional, Ising-like magnetic layers that are subject to spatially periodic domain wall pinning potentials. The potentials are generated non-destructively using the stray magnetic field of ordered arrays of magnetically hard [Co/Pt]$_m$ nanoplatelets which are patterned above and are physically separated from the continuous magnetic layer. The effect of the periodic pinning potentials on thermally activated domain wall creep dynamics is shown to be equivalent, at first approximation, to that of a uniform, effective retardation field, $H_{ret}$, which acts against the applied field, $H$. We show that $H_{ret}$ depends not only on the array geometry but also on the relative orientation of $H$ and the magnetization of the nanoplatelets. A result of the latter dependence is that wall-mediated hysteresis loops obtained for a set nanoplatelet magnetization exhibit many properties that are normally associated with ferromagnet/antiferromagnet exchange bias systems. These include a switchable bias, coercivity enhancement and domain wall roughness that is dependent on the applied field polarity.
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Submitted 28 April, 2013;
originally announced April 2013.
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Modified current induced domain wall motion in GaMnAs nanowire
Authors:
Nicolas Vernier,
Jean-Paul Adam,
Andre Thiaville,
Vincent Jeudy,
Aristide Lemaitre,
Jacques Ferré,
Giancarlo Faini
Abstract:
We report on current induced domain wall propagation in a patterned GaMnAs microwire with perpendicular magnetization. An unexpected slowing down of the propagation velocity has been found when the moving domain wall extends over only half of the width of the wire. This slowing down is related to the elongation of a longitudinal wall along the axis of the wire. By using an energy balance argument,…
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We report on current induced domain wall propagation in a patterned GaMnAs microwire with perpendicular magnetization. An unexpected slowing down of the propagation velocity has been found when the moving domain wall extends over only half of the width of the wire. This slowing down is related to the elongation of a longitudinal wall along the axis of the wire. By using an energy balance argument, the expected theoretical dependence of the velocity change has been calculated and compared with the experimental results. According to this, the energy associated to the longitudinal domain wall should change when a current passes through the wire. These results provide possible evidence of transverse spin diffusion along a longitudinal domain wall.
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Submitted 25 March, 2013;
originally announced March 2013.
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Model of bound interface dynamics for coupled magnetic domain walls
Authors:
P. Politi,
P. J. Metaxas,
J. -P. Jamet,
R. L. Stamps,
J. Ferré
Abstract:
A domain wall in a ferromagnetic system will move under the action of an external magnetic field. Ultrathin Co layers sandwiched between Pt have been shown to be a suitable experimental realization of a weakly disordered 2D medium in which to study the dynamics of 1D interfaces (magnetic domain walls). The behavior of these systems is encapsulated in the velocity-field response v(H) of the domain…
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A domain wall in a ferromagnetic system will move under the action of an external magnetic field. Ultrathin Co layers sandwiched between Pt have been shown to be a suitable experimental realization of a weakly disordered 2D medium in which to study the dynamics of 1D interfaces (magnetic domain walls). The behavior of these systems is encapsulated in the velocity-field response v(H) of the domain walls. In a recent paper [P.J. Metaxas et al., Phys. Rev. Lett. 104, 237206 (2010)] we studied the effect of ferromagnetic coupling between two such ultrathin layers, each exhibiting different v(H) characteristics. The main result was the existence of bound states over finite-width field ranges, wherein walls in the two layers moved together at the same speed. Here, we discuss in detail the theory of domain wall dynamics in coupled systems. In particular, we show that a bound creep state is expected for vanishing H and we give the analytical, parameter free expression for its velocity which agrees well with experimental results.
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Submitted 24 May, 2011;
originally announced May 2011.
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Dynamic binding of driven interfaces in coupled ultrathin ferromagnetic layers
Authors:
P. J. Metaxas,
R. L. Stamps,
J. P. Jamet,
J. Ferré,
V. Baltz,
B. Rodmacq,
P. Politi
Abstract:
We demonstrate experimentally dynamic interface binding in a system consisting of two coupled ferromagnetic layers. While domain walls in each layer have different velocity-field responses, for two broad ranges of the driving field, H, walls in the two layers are bound and move at a common velocity. The bound states have their own velocity-field response and arise when the isolated wall velocitie…
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We demonstrate experimentally dynamic interface binding in a system consisting of two coupled ferromagnetic layers. While domain walls in each layer have different velocity-field responses, for two broad ranges of the driving field, H, walls in the two layers are bound and move at a common velocity. The bound states have their own velocity-field response and arise when the isolated wall velocities in each layer are close, a condition which always occurs as H->0. Several features of the bound states are reproduced using a one dimensional model, illustrating their general nature.
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Submitted 12 May, 2010;
originally announced May 2010.
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Magnetic patterning of (Ga,Mn)As by hydrogen passivation
Authors:
Laura Thevenard,
Audrey Miard,
Laurent Vila,
Giancarlo Faini,
Aristide Lemaître,
Nicolas Vernier,
Jacques Ferré,
Stéphane Fusil
Abstract:
We present an original method to magnetically pattern thin layers of (Ga,Mn)As. It relies on local hydrogen passivation to significantly lower the hole density, and thereby locally suppress the carrier-mediated ferromagnetic phase. The sample surface is thus maintained continuous, and the minimal structure size is of about 200 nm. In micron-sized ferromagnetic dots fabricated by hydrogen passiva…
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We present an original method to magnetically pattern thin layers of (Ga,Mn)As. It relies on local hydrogen passivation to significantly lower the hole density, and thereby locally suppress the carrier-mediated ferromagnetic phase. The sample surface is thus maintained continuous, and the minimal structure size is of about 200 nm. In micron-sized ferromagnetic dots fabricated by hydrogen passivation on perpendicularly magnetized layers, the switching fields can be maintained closer to the continuous film coercivity, compared to dots made by usual dry etch techniques.
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Submitted 14 June, 2007;
originally announced June 2007.
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Creep and flow regimes of magnetic domain wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy
Authors:
P. J. Metaxas,
J. P. Jamet,
A. Mougin,
M. Cormier,
J. Ferre,
V. Baltz,
B. Rodmacq,
B. Dieny,
R. L. Stamps
Abstract:
We report on magnetic domain wall velocity measurements in ultrathin Pt/Co(0.5-0.8 nm)/Pt films with perpendicular anisotropy over a large range of applied magnetic fields. The complete velocity-field characteristics are obtained, enabling an examination of the transition between thermally activated creep and viscous flow: motion regimes predicted from general theories for driven elastic interfa…
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We report on magnetic domain wall velocity measurements in ultrathin Pt/Co(0.5-0.8 nm)/Pt films with perpendicular anisotropy over a large range of applied magnetic fields. The complete velocity-field characteristics are obtained, enabling an examination of the transition between thermally activated creep and viscous flow: motion regimes predicted from general theories for driven elastic interfaces in weakly disordered media. The dissipation limited flow regime is found to be consistent with precessional domain wall motion, analysis of which yields values for the damping parameter, $α$.
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Submitted 13 December, 2007; v1 submitted 27 February, 2007;
originally announced February 2007.
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Domain wall mobility, stability and Walker breakdown in magnetic nanowires
Authors:
A. Mougin,
M. Cormier,
J. P. Adam,
P. J. Metaxas,
J. Ferre
Abstract:
We present an analytical calculation of the velocity of a single 180 degree domain wall in a magnetic structure with reduced thickness and/or lateral dimension under the combined action of an external applied magnetic field and an electrical current. As for the case of field-induced domain wall propagation in thick films, two motion regimes with different mobilities are obtained, below and far a…
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We present an analytical calculation of the velocity of a single 180 degree domain wall in a magnetic structure with reduced thickness and/or lateral dimension under the combined action of an external applied magnetic field and an electrical current. As for the case of field-induced domain wall propagation in thick films, two motion regimes with different mobilities are obtained, below and far above the so-called Walker field. Additionally, for the case of current induced motion, a Walker-like current density threshold can be defined. When the dimensions of the system become comparable to the domain wall width, the threshold field and current density, stating the wall's internal structure stability, are reduced by the same geometrical demagnetising factor which accounts for the confinement. This points out the fact that the velocity dependence over an extended field/current range and the knowledge of the Walker breakdown are mandatory to draw conclusions about the phenomenological Gilbert damping parameter tuning the magnetisation dynamics.
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Submitted 21 February, 2007;
originally announced February 2007.
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Magnetic properties and domain structure of (Ga,Mn)As films with perpendicular anisotropy
Authors:
Laura Thevenard,
Ludovic Largeau,
Olivia Mauguin,
Gilles Patriarche,
Aristide Lemaître,
Nicolas Vernier,
Jacques Ferré
Abstract:
The ferromagnetism of a thin GaMnAs layer with a perpendicular easy anisotropy axis is investigated by means of several techniques, that yield a consistent set of data on the magnetic properties and the domain structure of this diluted ferromagnetic semiconductor. The magnetic layer was grown under tensile strain on a relaxed GaInAs buffer layer using a procedure that limits the density of threa…
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The ferromagnetism of a thin GaMnAs layer with a perpendicular easy anisotropy axis is investigated by means of several techniques, that yield a consistent set of data on the magnetic properties and the domain structure of this diluted ferromagnetic semiconductor. The magnetic layer was grown under tensile strain on a relaxed GaInAs buffer layer using a procedure that limits the density of threading dislocations. Magnetometry, magneto-transport and polar magneto-optical Kerr effect (PMOKE) measurements reveal the high quality of this layer, in particular through its high Curie temperature (130 K) and well-defined magnetic anisotropy. We show that magnetization reversal is initiated from a limited number of nucleation centers and develops by easy domain wall propagation. Furthermore, MOKE microscopy allowed us to characterize in detail the magnetic domain structure. In particular we show that domain shape and wall motion are very sensitive to some defects, which prevents a periodic arrangement of the domains. We ascribed these defects to threading dislocations emerging in the magnetic layer, inherent to the growth mode on a relaxed buffer.
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Submitted 17 February, 2006; v1 submitted 16 February, 2006;
originally announced February 2006.
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Magnetic domain structure and dynamics in interacting ferromagnetic stacks with perpendicular anisotropy
Authors:
S. Wiebel,
J. P. Jamet,
N. Vernier,
A. Mougin,
J. Ferre,
V. Baltz,
B. Rodmacq,
B. Dieny
Abstract:
The time and field dependence of the magnetic domain structure at magnetization reversal were investigated by Kerr microscopy in interacting ferromagnetic Co/Pt multilayers with perpendicular anisotropy. Large local inhomogeneous magnetostatic fields favor mirroring domain structures and domain decoration by rings of opposite magnetization. The long range nature of these magnetostatic interactio…
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The time and field dependence of the magnetic domain structure at magnetization reversal were investigated by Kerr microscopy in interacting ferromagnetic Co/Pt multilayers with perpendicular anisotropy. Large local inhomogeneous magnetostatic fields favor mirroring domain structures and domain decoration by rings of opposite magnetization. The long range nature of these magnetostatic interactions gives rise to ultra-slow dynamics even in zero applied field, i.e. it affects the long time domain stability. Due to this additionnal interaction field, the magnetization reversal under short magnetic field pulses differs markedly from the well-known slow dynamic behavior. Namely, in high field, the magnetization of the coupled harder layer has been observed to reverse more rapidly by domain wall motion than the softer layer alone.
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Submitted 18 January, 2006;
originally announced January 2006.
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Universality of thermally assisted magnetic domain wall motion under spin torque
Authors:
Gen Tatara,
Nicolas Vernier,
Jacques Ferre
Abstract:
Thermally assisted motion of magnetic domain wall under spin torque is studied theoretically. It is shown that the wall velocity $v$ depends exponentially on the spin current,
$\Is$, below the threshold value, in the same way as in a thermally activated motion driven by a force. A novel property of the spin torque driven case at low temperature is that the linear term in spin current is univers…
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Thermally assisted motion of magnetic domain wall under spin torque is studied theoretically. It is shown that the wall velocity $v$ depends exponentially on the spin current,
$\Is$, below the threshold value, in the same way as in a thermally activated motion driven by a force. A novel property of the spin torque driven case at low temperature is that the linear term in spin current is universal, i.e., $\ln v \sim \frac{π\hbar}{2e}(\Is/\kB T)$. This behavior, which is independent of pinning and material constants, could be used to confirm experimentally the spin torque as the driving mechanism.
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Submitted 10 November, 2004;
originally announced November 2004.
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Probing the interface magnetism in the FeMn/NiFe exchange bias system using magnetic second harmonic generation
Authors:
L. Sampaio,
A. Mougin,
J. Ferre,
P. Georges,
A. Brun,
H. Bernas,
S. Poppe,
T. Mewes,
J. Fassbender,
B. Hillebrands
Abstract:
Second harmonic generation magneto-optic Kerr effect (SHMOKE) experiments, sensitive to buried interfaces, were performed on a polycrystalline NiFe/FeMn bilayer in which areas with different exchange bias fields were prepared using 5 KeV He ion irradiation. Both reversible and irreversible uncompensated spins are found in the antiferromagnetic layer close to the interface with the ferromagnetic…
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Second harmonic generation magneto-optic Kerr effect (SHMOKE) experiments, sensitive to buried interfaces, were performed on a polycrystalline NiFe/FeMn bilayer in which areas with different exchange bias fields were prepared using 5 KeV He ion irradiation. Both reversible and irreversible uncompensated spins are found in the antiferromagnetic layer close to the interface with the ferromagnetic layer. The SHMOKE hysteresis loop shows the same exchange bias field as obtained from standard magnetometry. We demonstrate that the exchange bias effect is controlled by pinned uncompensated spins in the antiferromagnetic layer.
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Submitted 26 November, 2002;
originally announced November 2002.