Fig. 1: magnetoresistance of a FePt nanowire. The “bow-tie” effect is the signature of the magnetization hysteresis.
Magnetic imaging techniques can be used to observe magnetic walls. We have shown that this can also be achieved by measuring electrical resistance. This is done based on the collective vibrations of the magnetic moments (magnons). We are able to position a domain wall in a lithographed nanowire with a precision of around one percent.
In a ferromagnetic metal, magnetic moments (i.e. spins) are not rigorously aligned if the external magnetic field is not very strong or if the temperature is high enough. Still, their directions and their motions are not random and follow a collective behavior described as “magnons” (see inset). In the same way as phonons, magnons interact with the conduction electrons and thus have an influence on the resistance. This magnetoresistance effect (see inset) is called MMR, magnon magnetoresistance. MMR has been known for a long time, in particular its linearity and symmetry as a function of magnetic field, if it is strong enough. We have studied what happens under weak applied magnetic field in “magnetically structured” materials such as nanowires that contain magnetic domains separated by a wall.
We study a nanowire made of FePt, a ferromagnetic material with perpendicular magnetization that has two stable magnetization states (high/low or positive/negative). Let us follow the green arrows on Fig. 1. With a strong positive field, the magnetization is positive and the spin lattice is “rigid” with respect to the thermal vibrations: the magnon population is weak and so is their contribution to the resistance. We diminish the field intensity, the magnon population increases, as does their contribution to the resistance. This stays true until the magnetization reverses for a certain negative value of the field. A jump in the resistance is then observed, followed by a continuous decrease as the field becomes more and more negative. The magnon population diminishes again due to the alignment of the magnetic moments with the field. By considering in more detail the portion of the curve described by the blue arrows, a resistance plateau is observed during the reversal. This intermediate state corresponds to the pinning of a magnetic domain in the wire. One part of the wire is magnetized in one direction and the other in the opposite direction. The fraction of the wire with a given magnetization can be measured as explained in Fig. 2.
We have also detected the magnetization reversal in permalloy nanowires by MMR curves similar to the one shown in Fig. 1. Permalloy is however a soft magnetic material, but shape anisotropy is sufficient to force a magnetization aligned along the nanowire main axis, in one direction or the other, thus defining two magnetization states.
Fig. 2: Determination of the location of the wall responsible for the plateau observed in figure 1.By stopping at this plateau and subsequently further decreasing the applied magnetic field, a diminution of the magnetoresistance is observed. The slope is directly related to the fraction of the wire length having a positive magnetization, so that the position of the wall in the wire can be determined: 24%. This position is confirmed by visualizing the wall by magnetic force microscopy.
When a ferromagnetic material at zero temperature is saturated, the magnetization points in the same direction in the entire material. At the microscopic level, the magnetic moment of each atom points in this direction. If the temperature increases or if the applied field decreases, the magnetic moments can deviate slightly from their equilibrium position and start to precess around it. Due to the strong coupling between neighboring moments (responsible for ferromagnetism) this precession is coherent. For an atom chain carrying a magnetic moment, the trajectory of the moments carried by the atoms can be described as a wave called spin wave. Based on the wave-particle duality principle, we can then associate a quasi-particle called magnon with this excitation. All the tools from quantum mechanics can then be used to describe the interaction between these magnons and the electrons of an electric current flowing through the ferromagnetic material.
Magnetoresistance (MR) is the variation of electrical resistance as a function of applied magnetic field. Depending on the orientation of the electric current, of the magnetic field and on the measured voltage, several MR values are defined. Let us take a thin film as an example. The longitudinal MR is the classical MR where the current and the field are aligned and the voltage drop is measured on the same line. When the magnetic field is applied perpendicularly to the current flow and in the thin film plane, the difference in resistance between this configuration and the longitudinal configuration is called the anisotropic magnetoresistance (AMR). Its amplitude is around one percent. If the field is now applied out of plane and the voltage measured perpendicularly to the current flow, one obtains the Hall magnetoresistance (or Hall effect). Let us now take a stack consisting of two different ferromagnetic layers separated by a non-magnetic metallic layer. Let us flow some current and measure the voltage through this stack. By applying a magnetic field that reverses the magnetization in the softest material without modifying the hardest one, two configurations – parallel and antiparallel – of the magnetization are obtained. The resistance of the first one is much lower than that of the second one. One speaks of giant magnetoresistance (GMR). This is the effect discovered by Albert Fert for which he received the Nobel prize. Its amplitude can reach around ten percent. If the non-magnetic layer is replaced by a tunnel barrier, one speaks of tunnel magnetoresistance (TMR). Its amplitude is even larger than in the case of GMR. This effect is currently used in the read heads of hard disks.
Further reading: Nguyen VD et al., Physical Review Letters 107 (2011) 136605
Maj : 17/02/2014 (921)