Remagnetization of finite-length ferromagnetic cobalt atomic chains

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Abstract

The remagnetization mechanisms of finite-length ferromagnetic cobalt atomic chains at the Pt(664) surface have been investigated. It has been found that the remagnetization of short chains occurs due to the simultaneous flipping of all magnetic moments. At longer chain lengths, remagnetization occurs through the formation of a Neel-type anti-clockwise domain wall. The remagnetization of long chains can be achieved through both the formation of anti-clockwise and clockwise domain walls. The energy barriers for remagnetization of atomic chains with lengths ranging from 5 to 100 atoms have been calculated using the geodesic nudged elastic band method. In the framework of the harmonic approximation of the transition state theory, frequency prefactors have been calculated. A non-monotonic and sufficiently strong dependence of the frequency prefactors on both the chain length and an external magnetic field has been identified. The magnetization curves of Co atomic chains have been constructed, and the residual magnetization values and coercive force of the chains have been determined. The dependences of the coercive force on the chain length, temperature, and remagnetization rate of the magnetic field have been analyzed.

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About the authors

S. V. Kolesnikov

Lomonosov Moscow State University

Author for correspondence.
Email: kolesnikov@physics.msu.ru
Russian Federation, Moscow, 119899

E. S. Sapronova

Lomonosov Moscow State University

Email: kolesnikov@physics.msu.ru
Russian Federation, Moscow, 119899

A. M. Saletsky

Lomonosov Moscow State University

Email: kolesnikov@physics.msu.ru
Russian Federation, Moscow, 119899

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2. Fig. 1. Schematic representation of an atomic chain and coordinate axes. Vector D lies in the yz plane. Vector B is directed along the easy magnetization axis y (a). Schematic representations of the simultaneous reversal of magnetic moments during magnetization reversal of a short chain (b) and the formation of Neel domain walls during magnetization reversal of a long chain (c, d).

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3. Fig. 2. Dependence of the average modulus of the magnetization projection onto the easy magnetization axis |My| and the derivative −d |My| dT on temperature T.

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4. Fig. 3. Successive images of the magnetic state of a chain of 50 Co atoms during its magnetization reversal in an external magnetic field of By = 1 T by forming an antidomain wall. The initial state, saddle point, and final state are designated as min 1, SP 1, and min 2, respectively. The intermediate images (A, B, C, D, E, F) are shown for clarity. The designations correspond to the energy diagram in Fig. 4a.

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5. Fig. 4. (a) Energy diagram for two methods of magnetization reversal of a chain of 50 Co atoms in an external field By = 1 T. EI (EII) is the energy of the chain in the process of magnetization reversal through the formation of an antidomain (domain) wall. (b) Magnetic configuration of an atomic chain of 50 Co atoms at the saddle point SP 2 (domain wall).

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6. Fig. 5. Dependences of energy barriers ΔE and frequency prefactors ν0 for magnetization reversal of a chain of Co atoms on the chain length N. External magnetic field By = 1 T.

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7. Fig. 6. (a) Magnetization curves of chains of 15 and 100 Co atoms at a temperature of 5 K. (b) Dependence of the value of (1 – Mr) on the length N of the chain at temperatures of 5, 6, and 7 K, where Mr is the residual magnetization of the chain. (c) Dependence of the coercive force Bc on the length N of the chain at the same temperatures. (d) Dependence of the coercive force Bc of a chain of 100 Co atoms on temperature. In all cases, the rate of change of the magnetic field is 130 T/s.

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