Ferrimagnetic amorphous rare earth (RE)–transition metal (TM) Tb–Fe alloy thin films gained considerable attention in the past as a potential medium for thermomagnetic recording (Mimura et al., 1976a,b; Mansuripur, 1986; Hansen, 1987; Jamet et al., 1996; Suits et al., 1998) due to its low Curie temperature (Mimura et al., 1976a; Iijima et al., 1989) and tunable magnetic properties by varying composition (Mimura et al., 1976a, 1978; Satoh et al., 1985; Hassdenteufel et al., 2013). Today’s significance lies primarily in the field of exchange-biased heterostructures (Radu et al., 2012; Romer et al., 2012; Schubert et al., 2013; Tang et al., 2015), giving rise to giant exchange bias fields, and all-optical switching (AOS) (Stanciu et al., 2007; Hassdenteufel et al., 2013), where the orientation of the magnetization can be reversed by circularly polarized femtosecond laser pulses without any external magnetic field. This ability depends strongly on the material properties and underlying microstructure; thus its characterization and their dependence on growth conditions, film thickness, and composition is of great importance for the understanding of the underlying mechanism.

In this regard, a lot of effort has been made to investigate the intrinsic magnetic properties over a wide composition as well as temperature range, and how they are influenced by the growth conditions, like sputtering pressure (Jiang et al., 2010), substrate choice (Na et al., 2003), substrate bias voltage (Alperin et al., 1975), or external strain (Ohta et al., 2003). These research activities were encouraged by improved preparation techniques, which allowed preparing thin films in the thickness range of only some nanometers at reproducible high quality. However, more than 40 years ago, Rhyne et al. (1972) published already the first results on amorphous TbFe₂ bulk systems and shortly thereafter Mimura and Imamura (1976) reported on the properties of 900-nm-thick Tb–Fe films over a composition range between 10 and 50 at.% of Tb. At 21 at.% of Tb, the so-called room temperature compensation point is reached where the net magnetization vanishes as both antiparallelly aligned magnetic sublattices of Fe and Tb compensate each other. This is accompanied by a drastic increase in coercivity H_C. Below this compensation point, the Tb magnetization dominates while above this temperature the Fe magnetization is the leading one. The same behavior is also observed for other Tb–Fe samples of same composition but varying film thickness. However, there is a distinct dissimilarity; the compensation point varies with film thickness. This is at first glance a rather unexpected result. Nakada et al. (1987) gave a first explanation of this effect and proposed the formation of boundary layers at the film-buffer and film-capping interfaces. On the contrary, Malmhäll and Chen (1982) ascribed the thickness dependence to a microstructure-induced variation in the short range order during growth, which causes a change in the effective composition with increasing film thickness.

Another very important and rather surprising property of amorphous Tb–Fe thin films is the presence of strong perpendicular magnetic anisotropy (PMA), which was observed for a rather wide composition range between 15 and 28 at.% (Mimura and Imamura, 1976). This is mainly caused by a chemical anisotropy in the short range order of the atoms due to different atomic next neighbor distances and coordination numbers for Tb–Tb, Fe–Fe, and Tb–Fe pairs in out-of-plane and in-plane direction (pair-order anisotropy). In the out-of-plane direction (growth direction), a preference exists for the Tb–Fe near-neighbor pairing (Gambino and Cuomo, 1978; van Dover et al., 1985; Robinson et al., 1989; Tewes et al., 1991; Harris et al., 1992a,b; Hellman and Gyorgy, 1992; Hernando et al., 1996; Hufnagel et al., 1996), which can be induced by selective re-sputtering during the growth process (Gambino and Cuomo, 1978; Harris and Pokhil, 1999). This leads together with the interaction of the local crystal field with the 4f Tb orbital, which has a disk-like ellipsoidal shape (magnetic moment pointing out perpendicular to the plane of the ellipsoid), via spin-orbit coupling to an out-of-plane oriented sample magnetization (single ion anisotropy) (Prados et al., 1997; Skomski and Sellmyer, 2009). Hence, the magnetic order in Tb–Fe arises from the competition between the local magnetic anisotropies due to the local structural order and exchange interactions (Campbell, 1972; Rebouillat et al., 1977; Coey, 1978; Handrich and Kobe, 1980; Buschow, 1991; Duc, 1993; du Trémolet de Lacheisserie et al., 2005). This competition leads to a local distribution of the Tb and the Fe magnetic moments in the Tb and Fe sublattices (Coey, 1978), known as sperimagnetism (see Figure 1). For Fe moments, the angular distribution (fanning cone) in amorphous Tb–Fe alloys was directly measured by Mössbauer spectroscopy using ⁵⁷Fe ions (Eymery et al., 1988; Rusakov, 1992; Johnson, 1996; Ruckert et al., 1997; Danh et al., 2000; Fleury-Frenette et al., 2001). Ruckert et al. determined the typical fanning cone angle of Fe between 20° to 30° (Ruckert et al., 1997). They additionally could show that the Fe fanning does not vary strongly with film thickness or temperature.

Besides these structural peculiarities such as short range order, leading to PMA in amorphous RE-TM ferrimagnets, researchers at the Radboud University in Nijmegen observed in 2007 an ultra-fast magnetization reversal process induced by circularly or linearly polarized laser pulses in amorphous ferrimagnetic GdFeCo alloy films (Stanciu et al., 2007; Vahaplar et al., 2009, 2012; Radu et al., 2011). With this so-called AOS, the orientation of a magnetic domain can be reversed by a femtosecond laser pulse without any external magnetic field (Stanciu et al., 2007). Thus, AOS may lead to technological breakthroughs by using polarized light for ultrafast magnetization manipulation for a variety of applications. Since this pioneering experimental discovery, AOS has also been demonstrated for a variety of other amorphous ferrimagnetic RE–TM alloys, such as TbFe (Hassdenteufel et al., 2013, 2014, 2015; Schubert et al., 2014), TbCo (Alebrand et al., 2012), TbFeCo (Finazzi et al., 2013), DyCo (Mangin et al., 2014), HoFeCo (Mangin et al., 2014), and just very recently for antiferromagnetically coupled heterostructures (Mangin et al., 2014; Schubert et al., 2014) as well as for ferromagnetic materials (Lambert et al., 2014). Considerable recent effort has been made to investigate the physics of AOS and to reveal the underlying microscopic mechanisms. It was found that a rather small remanence magnetization M_R [<220 emu/cm³ (Hassdenteufel et al., 2015)] with strong temperature dependence (Atxitia et al., 2015) is an indispensable requirement for the AOS ability. In addition, different – sometimes very controversial – models have been proposed that particularly focused on the ferrimagnetic nature of the magnetic materials that show AOS and have been discussed along with recent experiments in Kirilyuk et al. (2013).

In this study, we first present a comprehensive investigation of the magnetic properties of Tb–Fe thin films with thicknesses between 5 and 85 nm over a wide composition range between 15 and 38 at.% of Tb. It will be shown that in particular the compensation point and remanent magnetization of the Tb–Fe samples depend not only on the composition but also on the thickness of the magnetic film. Thus, the ability of AOS was investigated and searched for correlations between AOS and the underlying magnetic properties of the samples.

Tb–Fe thin films were prepared under ultrahigh vacuum conditions by dc magnetron sputtering from element targets. The base pressure of the vacuum chamber was lower than 5 × 10⁻⁸ mbar. As sputtering gas argon (5N) with a partial pressure of p_Ar = 4.6 μbar was used. The sputtering rate for each element was measured before the deposition by a quartz balance to adjust the electric power of the magnetron sputter gun and the sputtering time with respect to the desired film thickness and composition. For the co-sputtering of Fe and Tb, the deposition rate of the Tb target was adjusted to values between 0.3 and 0.7 Å/s, depending on the desired composition while the Fe rate was kept constant at 0.6 Å/s. The deposition was carried out at room temperature on 375-μm-thick p-Si(100) substrates (p/boron, 10–20 Ω) with a 100-nm-thick thermally oxidized SiO₂ layer on top as well as on glass microscope slides. To ensure a homogeneous deposition, the substrate rotates during the sputtering process. Against oxidation, the magnetic film was sandwiched between 5-nm-thick Pt buffer and capping layers. The stoichiometry and thickness of the prepared samples were characterized by Rutherford backscattering spectrometry (RBS). The amorphous structure of the Tb–Fe films was confirmed by x-ray diffraction (XRD) and transmission electron microscopy (TEM). Compositional variations with film thickness were investigated by dynamic secondary ion mass spectroscopy (SIMS) studies. The SIMS depth profiles were measure by sputtering with a 3 keV Cs⁺ primary ion beam and detection of ⁵⁶Fe¹³³Cs⁺ and ¹⁵⁹Tb⁺ secondary ions. The integral magnetic properties of the samples were characterized by superconducting quantum interference device – vibrating sample magnetometry (SQUID-VSM). Two kinds of measurements were performed: remanent magnetization versus temperature (M_R–T) and magnetization versus field (M–H). For the M_R–T measurements, the following procedure was applied: first, the samples were saturated at room temperature in a perpendicular magnetic field of 70 kOe. Then the samples were cooled down to 4 K without applying an external field. Thereafter, the temperature was again ramped from 4 to 400 K, and the remanent magnetization M_R perpendicular to the sample plane was recorded. In addition, M–H loops were measured at room temperature for in-plane and out-of-plane magnetic field. To give an estimate of the uniaxial magnetic anisotropy the following equation was used, (K_u = 1/2 H_a M_R + 2π M_R²), which is corrected for the shape anisotropy contribution. Here, the anisotropy field H_a was extracted from the hard axis (in-plane) loop. The evolution of the fanning cone angle of the Tb moments can be obtained by analyzing the magnetization reversal at high magnetic fields. In particular, for Tb–Fe alloys, where the Tb moment dominate the net magnetization, an additional reversible increase in magnetization at higher external fields is observed, as shown in Figure 2 for a 14-nm-thick Tb₂₉Fe₇₁ film. This increase can be attributed to a more collinear alignment (compression) of the distributed magnetic moments of Tb along the external field direction. In contrast, for Fe rich Tb–Fe films where the Fe moment is dominating, no pronounced magnetic field dependent increase of the magnetization was observed due to the stronger TM–TM exchange coupling of Fe (Heiman, 1976). Please note that this approach does not allow determining the exact fanning cone angle of the Tb moments, as the Tb fanning cannot be fully compressed and the Fe cone will certainly expand at the same time, thus these results should be treated with care and serve only as a first indicator.

In order to investigate the AOS ability of Tb–Fe thin films, we used a Faraday imaging setup, revealing the orientation of sample magnetization as black (M−) and gray (M+) contrast. A regenerative laser amplifier system with pulse repetition rate of 250 kHz, center wavelength of 800 nm, and pulse duration at the sample position of 100 fs is used to provide the switching pulses. The polarization of these pulses are altered by an achromatic quarter wave plate and attenuated by a combination of a zero order half wave plate and polarizer. A detailed description of the setup can be found in Hassdenteufel et al. (2013). The switching experiment was performed as follows: first, the sample is homogeneously magnetized in one direction, e.g., M−. Subsequently, the sample is linearly moved below right-handed circularly polarized light (σ+) at the switching threshold fluence. As far as the domain structure (M+) is written, the helicity is changed to the opposite direction (e.g., σ−). At the same fluence, the domain is again irradiated and, in the case of AOS, erased. This process of “writing” and “erasing” demonstrates unambiguously the AOS ability.

In conclusion, we have prepared amorphous ferrimagnetic Tb–Fe film samples over a wide composition range from 15 up to 38 at.% of Tb and with magnetic film thicknesses between 5 and 85 nm. At a certain temperature, the compensation of the sample magnetization does not only depend on the composition but also on the specific thickness of the magnetic film. Growth-induced variations in the short range order resulting in a redistribution of the orientation of the Tb magnetic moments are responsible for the thickness dependence, while variations in composition with film thickness are insignificant. With increasing film thickness, the fanning cone angle of the Tb moments decreases, which causes an increasing contribution of the Tb sublattice magnetization to the total sample magnetization along the film normal. This behavior leads to a shift of the compensation temperature to higher temperatures with film thickness. Hence the magnetic properties of Tb–Fe can be controlled not only by composition or temperature but also by film thickness, which has to be taken into account. In a further study, the AOS ability was investigated and correlated to the sample’s magnetic properties. It was observed that AOS is connected to film samples, exhibiting low remanence (<220 emu/cm³), confirming the low remanence criterion. Furthermore, Tb–Fe films as thin as 9 nm and as thick as 85 nm could be switched all-optically, which might be relevant for prospective magneto-optic or spintronic applications.

BH, AH, HK, and PR prepared and characterized the thin film samples. BH, AH, and PR analyzed the magnetic data; BH, AH, and MA designed the research approach; BH, AH, and MA contributed to the development of the experiments and wrote the manuscript; all authors discussed the experiments and the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.