Non-coplanar spin structure in a metallic thin film of triangular lattice antiferromagnet CrSe

An antiferromagnetic metal with two-dimensional triangular network offers a unique playground of intriguing magneto-transport properties and functionalities stemming from interplay between conducting electrons and intricate magnetic phases. A NiAs-type CrSe is one of the candidates owing to alternate stackings of Cr and Se triangular atomic networks in its crystal structure. While fabrication of CrSe thin films is indispensable to develop functional devices, studies on its thin-film properties have been limited to date due to the lack of metallic samples. Here, we report on realization of metallic conductivities of CrSe thin films, which allows to investigate their intrinsic magneto-transport properties. The metallic sample exhibits co-occurrence of a weak ferromagnetism with perpendicular magnetic anisotropy and the antiferromagnetic behavior, indicating the presence of non-coplanar spin structures. In addition, control of polarity and tilting angle of the non-coplanar spin structure is accomplished by a sign of cooling magnetic fields. The observed non-coplanar spin structure, which can be a source of emergent magnetic field acting on the conducting electrons, highlights a high potential of the triangular lattice antiferromagnet and provide unique platform for functional thin-film devices composed of NiAs-type derivative Cr chalcogenides and pnictides.


I. Introduction
Triangular lattice antiferromagnets have long received attentions owing to various magnetic states [1,2] and related magneto-transport phenomena [3,4].A key feature of the triangular lattice antiferromagnets is suppression of conventional long-range orders by geometrical frustration [5,6], which makes system be sensitive to magnetic anisotropy, thermal and quantum fluctuations, external magnetic field, and the other competing exchange interactions.When the frustrated spin system is subjected to these external stimuli, a rich variety of magnetic phases emerge such as non-colinear [7] and noncoplanar [8] spin structures, magnetic skyrmion [9,10], a chiral spin liquid state [11,12], and disordered states known as spin glass state [13,14].Another intriguing feature, especially in non-coplanar magnets, is the emergent magnetic field associated with the scalar spin chirality [3], which corresponds to a solid angle subtended by neighboring spins so called the real-space Berry phase [15,16].In some non-coplanar magnetic conductors, the connection of conducting electrons to the real-space emergent magnetic field is revealed as topological Hall effect [10,17,18,19,20], non-reciprocal magnetoresistance [21], and electromagnetic induction [22].It has been suggested that properties of those exotic spin textures can be enriched in nanostructures [23,24,25] and heterointerfaces with conventional ferromagnets [26] or superconductors [27].In this aspect, exploration of magneto-transport properties in thin films composed of triangular lattice antiferromagnets is a central topic for further functionalization of their exotic magnetic properties and magnetoelectric effects.
The NiAs-type and its derivative compounds CrX (X = S, Se, Te, and Sb) exhibit diverse magnetism depending on the choice of chalcogen and pnictogen elements [28].
For instance, the CrTe shows a ferromagnetism in bulk and thin-film forms where ferromagnetic transition temperature and magnetic anisotropy can be tuned by the Cr and Te composition ratio [29,30,31].The CrSb has received recent attentions as a new class of antiferromagnet, namely an altermagnet, in which the spin-split electronic band structure originates from not relativistic spin-orbit interaction but its crystal symmetry [32,33].Thanks to the large spin-splitting band, the altermagnet can be a candidate material as an efficient spin polarizer [34].Among various types of magnetic materials, we focus on an antiferromagnetic CrSe, which has been long known as a triangular lattice antiferromagnet [35].Figure 1(a) illustrates crystal structure of the NiAs-type CrSe (P63/mmc) and suggested Cr spin configuration.The Cr and Se two-dimensional triangular networks are alternately stacked along the c axis while its spin structure has not been fully understood.The first neutron scattering experiment for CrSe reported that Cr spins in a basal plane are canted out toward the same direction [35], forming so called umbrella-like spin structure as shown in Fig. 1(a).Later experiment performed for the NiAs-type derivative Cr2Se3 reported more complex non-coplanar spin structure [36].In the Cr-Se binary phase diagram, there are some equilibrium intermetallic phases: Cr5Se8, Cr2Se3, Cr3Se4, and Cr7Se8, all of which are in the NiAs-type derivative crystal structure with ordered arrangement of Cr vacant sites [37], and a high-temperature NiAs-type (P63/mmc) and its derivative (P3 ̅ m1) CrSe phases [38].All binary phases at low and high temperature have the identical framework of crystal structure, where Cr atoms form edgesharing and face-sharing CrSe6 octahedra in the ab plane and along c axis, respectively.
The only differences among NiAs-type and its derivative Cr-Se compounds are fraction and position of Cr deficient sites.The Néel temperature increases from 43, 82, and 280 K for Cr2Se3, Cr3Se4, and CrSe, respectively, in the order of the filling fraction of Cr sites [39].As for the electrical transport properties, while a metallic conduction has been reported in bulk single crystals [39,40,41,42], being consistent with semimetallic band structure in first-principles calculations [43,44], some experimental studies have reported semiconducting behavior in bulk [45,46] and thin-film samples [47,48,49,50] with a small band gap (a few tens meV) [46,47].This is probably because the Fermi level and/or band gap are sensitive to a subtle off-stoichiometry or thickness in such a semimetal [43,44].
In particular, thin-film samples reported so far have exhibited only semiconducting behavior [47,48,49,50], hindering explicit determination of spin structure through the magneto-transport measurements.Nevertheless, some spin-related electrical transport experiments have been performed up to date through the interfacial effects showing exchange bias [48], topological Hall effect [49], and magnetic proximity effect [50] between an insulating CrSe layer and conducting ferromagnetic or topological materials.
Within the context of non-coplanar spin structure having a scalar spin chirality as mentioned above, preparation of the metallic CrSe thin films and exploration of magnetotransport properties should be tackled for in-depth understanding of its spin structures.
In this Article, we have found evolution toward metallic conduction in CrSe thin films by increasing growth temperature.Metallic conduction allows to investigate coupling of electric transport properties with spin structures via their magneto-transport measurements.From magnetic-field and temperature dependences of longitudinal and Hall resistivities, coexistence of a weak ferromagnetism with perpendicular magnetic anisotropy and antiferromagnetic spin-flop transition accompanied with memory effect was found in the metallic thin-film sample.We concluded that these features originate from a non-coplanar spin structure of CrSe.

II. Experimental methods
The CrSe thin films were grown on Al2O3(0001) substrates by pulsed-laser deposition

Magneto-transport properties of metallic CrSe thin film.
The impact of the spin structure on the electrical transport in CrSe was investigated by resistivity measurement of metallic sample under magnetic field.was observed in the very wide range of magnetic field up to 14 T at T = 4.2 K, which is extraordinarily larger than characteristic magnetic fields such as coercivity and saturation magnetic fields of the typical ferromagnetic compounds [30,31].The non-saturating negative MR can be ascribed to suppression of spin scattering due to reorientation of antiferromagnetically-coupled spins [45,52].Berry phase picture, the emergent magnetic field is developed by non-coplanar spin structures, which results in the non-monotonic hump structure, so called the topological Hall effect [17,20].Indeed, the observation of the non-monotonic  yx A () is consistent with the topological Hall effect, suggesting the presence of the non-coplanar spin structure in our CrSe thin film.
For interpretation of the intricate behaviors of  xx () and  yx A () , angular dependence of MR was measured.ferromagnetically coupled between the basal planes.In contrast, we consider the nearly isotropic high-field component of MR with its hysteresis closing at very high magnetic field to be the character of triangular antiferromagnets.When antiferromagnets are magnetized by a sufficiently strong magnetic field, antiferromagnetically coupled spins undergo flops accompanied with a sudden rotation of Néel vector, which renders distinct anomalies in magnetic and MR properties [53,54,55].Such spin-flop transition usually occurs only when the field is applied along the well-defined spin axis in colinear antiferromagnets.In the case of triangular antiferromagnets with competing interplane interaction, however, it is suggested that spin-flop transition may occur when the field is applied both parallel and perpendicular to the antiferromagnetic plane [56,57].The steplike and hysteretic behavior in negative MR implies a first-order nature of this magnetic transition.Another possibility is a spin-glass state, which emerges when the geometrical frustration is subjected to some amount of site disorders [58], leading to a broad and unsaturated MR [59].More detailed spin structure may be clarified by magnetization and magneto-transport measurement using high-field facilities.
In the presence of competing interplane weak ferromagnetism and intraplane geometrical frustration, the canting angle at the low temperature should depend on its history [60,61], in particular the magnetic field applied when the system was frozen.

4(c)
. The memory effect in MR polarities under the perpendicular magnetic field implies that the magnetic field in FC more effectively acts on the system than in ZFC to force the magnetic moment along the field.The observed non-saturating negative magnetoresistance accompanied with the memory effect implies antiferromagnetic features as reported in various non-coplanar and non-colinear antiferromagnetic conductors [45,59,60].
By considering co-occurrence of the weak ferromagnetism with uniaxial anisotropy perpendicular to the basal planes and the antiferromagnetic features, we conclude that our metallic CrSe thin film possesses the non-coplanar spin structure, as one of the ground states in antiferromagnetically coupled Cr triangular networks.It turns out that polarity and canting angle of the Cr spins, which is a source of the real-space emergent magnetic field, can be tuned by cooling under the magnetic field.

IV. Summary and outlook
In summary, we have obtained a semiconductor-to-metal transition in CrSe thin films by increasing growth temperature.The metallic CrSe thin film exhibits the hysteretic negative magnetoresistance, remanent anomalous Hall resistivity, and the small Cr magnetic moment when the perpendicular magnetic field is applied, revealing the presence of the weak ferromagnetic order with perpendicular magnetic anisotropy.In

( 5 T 1 .
PLD) at the substrate temperature Tsub = 250, 350, 450, 550, 650, 750, and 850 o C. The CrSe and Se targets used in PLD were synthesized by pelletizing commercially available stoichiometric CrSe and Se powders (Kojundo Chemical Laboratory Co., Ltd), respectively.For the electrical transport measurement, 50-nm-thick CrSe thin films were prepared followed by deposition of 10-nm-thick amorphous Se cap layer at room temperature.For preparing Se-rich sample as a reference, the Se target was ablated when the sample was cooled to room temperature after the CrSe thin film was grown at Tsub = 650 o C or 750 o C. The chemical composition ratio Se/Cr of the thin-film samples was determined by energy dispersive x-ray spectroscopy (EDX) and inductively coupled plasma optical emission spectroscopy (ICP-OES).For the ICP analysis, the 100-nm-thick samples without the cap layer were prepared at the identical growth condition.The crystallinity was evaluated by x-ray diffraction and atomic force micrography and thickness was determined by x-ray reflectivity.Temperature and magnetic field dependences of longitudinal and Hall resistivities were measured by standard five-terminal measurement in 4 He cryostat equipped with a superconducting magnet (Oxford Instruments, plc.).For subtracting the component of ordinary Hall effect from  yx (), linear fit was applied for high-field region in  0 H > for CrSe thin films grown at Tsub = 350, 450, 550, and 650 o C and  0 H > 11 T for Tsub = 750 o C. Magnetization measurement was performed by MPMS3 (Quantum Design, Inc.) with superconducting quantum interference device.Thin Film Growth and Structural Characterization.

Figure 1 (
Figure 1(b) shows 2theta-omega scan of x-ray diffraction (XRD) pattern of the

2 .
Variation of electrical transport properties of CrSe thin films on growthtemperature.

Figure 2
Figure 2 shows evolution of electrical transport properties of CrSe thin films upon

Figure 3 (
a) shows  xx () of the CrSe thin film for Tsub = 750 o C under the out-of-plane magnetic field of  0 H = 0 T [the same trace presented in Fig. 2(c)] and 14 T. Here, the magnetoresistance (MR) is defined as the difference of  xx () under  0  given by Δ xx () =  xx (,  0  = 14 T) −  xx (,  0  = 0 T), With decreasing T, the negative MR (Δ xx < 0) appears blow 180 K, which corresponds to the temperature where a kink was observed in  xx () at zero field (vertical dashed line).The coincidence of the kink feature, often assigned to the Néel temperature in metallic CrSe bulk crystals [39,42], and appearance of the negative MR at the same temperature suggests that the observed negative MR is spin-related phenomena.Figure 3(b) shows temperature dependence of magnetization [M(T) curve] measured at  0  = 1 T after 5 T field cooling.Despite the broad transition, the magnetization develops around T ~ 180 K, which further supports the relation of the kink and negative MR features in  xx () and magnetic transition.In addition, the slope of M(T) curve becomes steeper below T ~ 100 K, implying that the perpendicular magnetic anisotropy with ferromagnetism develops as will be discussed in Fig. 3(c) and 3(d).Nevertheless, the value of measured magnetic moment is as small as 0.051  B /Cr at the lowest temperature.In the situation that Cr spins are aligned antiferromagnetically in the ab-plane, such a very small magnetic moment should originate from a projection of the canted Cr magnetic moments along the c axis.Considering the low-spin state of 3d 4 electron configuration of Cr 2+ in CrSe, the residual moments of 0.051  B /Cr along the c axis out of the spin magnetic moment of 2  B /Cr yield a titling angle of Cr spins from the basal plane to be sin −1 (

Figure 3 (⁄
Figure 3(c) shows out-of-plane magnetic-field dependence of MR ratio at T = 4.2,

Figure 3 (
e) shows the MR ratios Δ xx  xx 0 ⁄ for the angle  = 0, 45, and 90 o .Here,  H is defined as the angle from the normal direction to the sample plane and H is fixed perpendicular to the electric current.Interestingly, for the in-plane sweep ( H = 90 o ), the Δ xx  xx 0 ⁄ for upward and downward sweeps collapse in the low-field regime ( 0 H < 3 T) and exhibits a positive MR while the hysteretic behavior remains in the high-field regime.The drastic change in the low-field MR with respect to  H is more visible in polar plots of ΔMR at  0 H = 1.5 T and 7.0 T, as shown in Fig. 3(f).Here, Δ MR is defined by difference between the values of Δ xx  xx 0 ⁄ for the upward and downward sweeps [green and blue arrows in Fig. 3(e)].The low-field ΔMR (at  0 H = 1.5 T) exhibits the strongly uniaxial anisotropy.For the high-field MR (at  0 H = 7.0 T), in contrast, the ΔMR shows less anisotropic dependence.The distinct difference in low-field and high-field MR in  H dependence recalls the presence of two magnetic interactions with different magnetic anisotropy.By considering the remanent anomalous Hall resistivity in Fig. 3(d), the low-field MR comes from the weak but spontaneous ferromagnetism from the canted Cr spins towards c-axis direction, which are

Figure 4
Figure4shows the out-of-plane MR at 4.2 K starting from the "unmagnetized" state