Controllable two- vs three-state magnetization switching in single-layer epitaxial Pd1-xFex films and epitaxial Pd0.92Fe0.08/Ag/Pd0.96Fe0.04 heterostructure

We have investigated the low-temperature magnetoresistive properties of a thin epitaxial Pd0.92Fe0.08 film at different directions of the current and the applied magnetic field. The obtained experimental results are well described within an assumption of a single-domain magnetic state of the film. In a wide range of the appled field directions, the magnetization reversal proceeds in two steps via the intermediate easy axis. An epitaxial heterostructure of two magnetically separated ferromagnetic layers, Pd0.92Fe0.08/Ag/Pd0.96Fe0.04, was synthesized and studied with the dc magnetometry. Its magnetic configuration diagram has been constructed and the conditions have been determined for a controllable switching between stable parallel, orthogonal, and antiparallel arrangements of magnetic moments of the layers.


Introduction
The generation of the long-range triplet component of the superconducting pairing at noncollinear orientations of magnetizations in ferromagnetic layered systems is extensively studied in the framework of magnetic Josephson junctions (MJJ) (see reviews [1][2][3] and references therein for early works, and very recent papers [4,5] and references therein), and superconductive spin valves (SSV) [6][7][8][9]. The key points of underlying physics are non-uniform magnetic configurations in the system which mix singlet and triplet superconducting pairing channels. As a result, at collinear magnetic configurations, short-range singlet and zero-spin-projection triplet pairings carry Josephson supercurrent in MJJ. At non-collinear magnetic configurations, on the contrary, long-range equal-spin pairings can conduct supercurrent in MJJs with much thicker or long narrow weak links. This gives additional degrees of freedom to control the critical current of MJJ [10] or SSV [6], or current-phase relations in MJJ [11,12]. In particular, the spin-valve structure embedded into an MJJ can serve as an actuator for switching the MJJ between critical current modes or flipping its current-phase relation thus extending its functionality.
Palladium-iron alloy Pd1-xFex with x < 0.10 is of a strong practical interest for such MJJ and SSV structures [13][14][15][16][17] as a material for weak ferromagnetic links with tunable magnetic properties [18]. Epitaxial films of Pd1-xFex alloy with a low iron content x are easy-plane ferromagnets with the four-fold anisotropy in the film plane [18,19]. Our conjecture is a possibility to switch the magnetic moment of a Pd1-xFex alloy film between the steady directions (90 degrees apart) as it had been done with the epitaxial iron films [20][21][22]. To realize this idea, it is necessary to find the particular angle of the applied magnetic field direction with respect to the in-plane four-fold easy axes. Once the conditions of magnetization rotation by 90-degrees are found, the addition of the second, magnetically more hard ferromagnetic layer with properly aligned in-plane easy axes makes it possible to achieve parallel, orthogonal, and antiparallel configurations of their magnetic 3 moments. Such a heterostructure can serve as a magnetic actuator for switching the MJJ from the singlet conduction mode to the triplet conduction mode and vice versa.
The experimental rotation of the magnetic moment by 90 degrees in epitaxial Pd1-xFex films has not been yet explored. In [18,19], based on magnetometry data, it was assumed that magnetization reversal occurs as a result of the coherent rotation of the magnetic moment by 180 degrees; and in the study of the Pd0.96Fe0.04/VN/Pd0.92Fe0.08 structure [23], stable parallel and antiparallel configurations of magnetic moments were obtained. However, the maximum amplitude of the triplet pairing component in the PdFe1/N/PdFe2 bilayer structure is achieved near the orthogonal magnetic configuration of the ferromagnetic layers PdFe1 and PdFe2 [6]. Therefore, it is instructive to investigate the switching properties of Pd1-xFex films and heterostructures based on this alloy targeting the controllable non-collinear magnetic configurations in the bilayer structure.

Experiment techniques
An epitaxial film of the Pd0.92Fe0.08 alloy with a thickness of 20 nm and an epitaxial thin-film heterostructure Pd0.92Fe0.08(20 nm)/Ag(20 nm)/Pd0.96Fe0.04(20 nm) were grown in an ultra-high vacuum (UHV) setup (SPECS, Germany) by the molecular beam deposition. Epi-polished MgO (100) single-crystal plates (Crystal GmbH, Germany) were used as substrates. The deposition routine and structural studies of similar films are described in Ref. [24], the magnetic properties measured by ferromagnetic resonance (FMR) and vibrating sample magnetometry (VSM) in magnetic fields along the easy and hard magnetic axes are presented in Refs. [18,19].
In this paper, the magnetization reversal in the Pd0.92Fe0.08 film at different in-plane orientations of the magnetic field was studied by measuring the anisotropic magnetoresistance (AMR) by the 4-probe method. For this purpose, the Pd0.92Fe0.08 film was cut with a diamond saw into rectangular 5.0 × 1.5 mm 2 and trapezoidal 3.0 × 1.5 mm 2 (shown in the Figures below) samples. In the first 4 sample, the current flowed along the <100> direction of the Pd0.92Fe0.08 film, in the secondat an angle of 25° with respect to the <100>. The current contacts were ultrasonically welded at several locations in a line across the width of the sample to ensure a uniform current distribution throughout the core part of the sample supplied with the potential terminals.
The magnetic hysteresis loops for the Pd0.92Fe0.08(20 nm)/Ag(20 nm)/Pd0.96Fe0.04 (20 nm) heterostructure were obtained by the vibrational sample magnetometry since the AMR measurement for this system is useless due to shunting with a silver layer. All the AMR and VSM experiments were carried out with the PPMS-9 system (Quantum Design).

Сurrent along the [100] direction
We start with the presentation of the results for a rectangular sample of the Pd0.92Fe0.08 film where the electrical current flowed along the [100] direction of the film (and the substrate). The reference frame orientation with respect to the sample is shown in the insets to Figure 1. When measuring the magnetoresistance, the magnetic field was applied at different angles in three main planes as shown in Figure 1. At any orientation, on approaching zero field, the resistivity returns to a common value of 15.8  cm, corresponding to the magnetic moment along the easy axes (see more details below). The resistivities hierarchy for the magnetic moment oriented along the X, Y, and Z axes, x > y > z, is typical for ferromagnetic films of comparable thickness [25]. The difference in resistances x and z (magnetic field perpendicular to the current) is usually associated with the geometrical size-effect [26]. A detailed study of the size effect for the Pd0.92Fe0.08 film is beyond the scope of this study. In addition to the anisotropic magnetoresistance associated with the mutual orientations of the magnetic moment and the direction of the current, there is a resistance drop with an increase of the magnetic field strengththe negative magnetoresistance. The latter effect is related to a decrease in electron-magnon scattering due to the suppression of spin waves in high magnetic fields [27].
At low temperatures, this effect is usually small, and a positive magnetoresistance caused by the action of the Lorentz force dominates [27,28]. However, in the Pd0.92Fe0.08 epitaxial film, the electron mean free path is small even at low temperatures and is determined by the mean distance between the iron atoms. Therefore, the Lorentzian contribution is small, and even at 5 K, the negative magnetoresistance is observed. As the temperature is increased, the number of magnons 6 grows, thereby leading to a larger negative slope /H (Figure 2a). A theoretical description of this process for elemental 3d-ferromagnets was proposed in [27]. The dependence of the resistance on magnetic field up to 100 T is described by the expression:  At a fixed magnetic field and temperature, the resistance value reflects the direction of the magnetic moment in space. In a spherical coordinate system, the resistance is described by the following expression [29]: where x, y, and z are the resistances for the cases of the magnetic moment oriented along the X, where i are directional cosines for the magnetic М with respect to crystallographic axes [100],

Current at an angle to [100] direction, field H in the XY plane
For the trapezoidal sample, with a current directed at an angle of ~ 25 degrees to the [100] axis, the double jumps are manifested much brighter (Figure 4a), since in this case, the easy axes are not equivalent in terms of the measured resistance. At the same time, the relative magnitude of the AMR effect (xy/xy)*100% turns out to be less pronounced than with the current along the heavy axis [100] -0.45% and 1.22%, respectively. This is in a qualitative agreement with the experiments on AMR of epitaxial iron films, where the AMR effect was also maximal when the current direction was along the heavy axis [30].  By measuring the residual resistance (after a field removal), it is possible to realize which easy axis was chosen by a system (Figure 4c). Near the direction of the heavy axis, there is a transition from the counter-clockwise rotation to the clockwise one. This transition spans over a notable range of angles. For example, within the angle range of 82 -90 degrees, in the course of the magnetization reversal, one fraction of the film rotates its moment clockwise, while the othercounter-clockwise (Figure 4c, inset).
As follows from Figure 4a, the coercive fields corresponding to the first step of the reversal (Hc1) and, especially, to the second one (Hc2) depend significantly on the direction of the applied field. Figure 5a illustrates this relationship. A detailed explanation of these behaviors was proposed in Reference [21]. It suggested the successive movements of two 90-degree domain walls. The values of the coercive fields are determined by the conditions when the energy gain due to a moment rotation overcomes the wall pinning energy: This is because at the second jump the domain wall in fact is not the 90°-type, the difference in the angles in the wall M is much smaller than 90º (see Figure 4b). Moreover, it depends on the angle of the applied field. Based on the experimental data for Hc2(H), this dependence can be calculated. Figure 5b shows the obtained dependences M(H). It can be seen that as the hard 13 axis is approached, the amplitude of the rotation angle of the moment in the domain wall decreases.
In this situation, it is no longer possible to assert that the pinning energy is constant since it decreases with decreasing the angle difference in the domain wall. For the field directions close to the hard axis (for example, at H = 87-90 degrees), it is generally difficult to describe the magnetization reversal, since the volume of the material is divided into two fractions that rotate their moments in opposite directions. In addition, at the fields of the second jump in magnetization, the height of the barrier for the coherent rotation also becomes insignificant. Therefore, in this range of angles, magnetization reversal is potentially possible by the macroscopic coherent rotation of the magnetic moment of the film.

14
The dependences of Hc1,c2(H) obtained in this work for the Pd0.92Fe0.08 film confirm the conjecture that three steady magnetic configurations, parallel (P), anti-parallel (AP), and orthogonal (OG) can be realized in the epitaxial PdFe1/N/PdFe2 heterostructure by choosing the appropriate magnetic field direction and varying the applied magnetic field pulse amplitude. An important condition for this is an absence of a substantial magnetic interaction between the PdFe1 and PdFe2 layers. It is achieved by introducing the non-magnetic spacer layer N of silver satisfying the epitaxial growth conditions. The different coercive fields were obtained choosing the Pd0.92Fe0.08 и Pd0.96Fe0.04 compositions for the ferromagnetic PdFe1 and PdFe2 layers [18].    film, in which significant demagnetization occurred on a time scale of ~ 100 sec [31].

Conclusions
Detailed measurements of the magnetoresistance have shown that the Pd0.92Fe0.08 epitaxial film, being an easy-plane ferromagnet with a pronounced in-plane anisotropy, undergoes magnetization switching between two (with collinear magnetization directions) or three (including orthogonal to the previously indicated two directions) single-domain states depending on the direction of the applied magnetic field. In the latter case, the magnetization reversal proceeds in 2 distinct stages, the first stage being the motion of the 90-degree domain wall, and the second one is the motion of the -degree domain wall, where the angle  depends on the angle of the applied field relative to crystallographic axes. The pinning energy of the 90-degree domain wall is ~ 6 kerg/cm 3 for the Pd0.92Fe0.08 film, and ~ 1.8 kerg/cm 3 for the Pd0.94Fe0.04 film. The use of two magnetic layers PdFe1 and PdFe2 with different coercive fields, separated by a nonmagnetic spacer N, makes it possible to realize parallel, orthogonal, and antiparallel configurations of magnetic moments. It has been experimentally demonstrated that the Pd0.92Fe0.08/Ag/Pd0.94Fe0.04 heterostructure can switch between P, OG, and AP steady magnetic configurations in the film plane by rotating the magnetic moment of the soft magnetic layer with respect to the magnetically harder layer.