Mn-induced Ferromagnetic Semiconducting Behavior with Linear Negative Magnetoresistance in Sr4(Ru1−xMnx)3O10 Single Crystals

Triple-layered Sr4Ru3O10 is a unique ferromagnet with the central RuO6 layer behaving differently from two outer layers both crystallographically and magnetically. We report that the partial substitution of Ru by smaller Mn gives rise to modification in crystal structure, electronic and magnetic properties of Sr4(Ru1−xMnx)3O10. Through the single crystal X-ray diffraction refinement, we find that (Ru/Mn)O6 octahedral rotation is no longer detectable at x ≥ 0.23, leading to the tetragonal structure. The magnetization measurements indicate the ferromagnetic transition temperature TC decreases from 105 K for x = 0 to 30 K for x = 0.41, with the reduced magnetic moment as well. Remarkably, Mn doping results in the change of magnetic anisotropy from the easy c axis in x = 0 to the easy ab plane seen in x = 0.34 and 0.41. Such change also removes the ab-plane metamagnetic transition observed in x = 0. Furthermore, the electrical resistivity increases with increasing x showing semiconducting behavior with Δ ~ 10 meV for x = 0.34 and 30 meV for x = 0.41. Under applied magnetic field, the magnetoresistance exhibits negative and linear field dependence in all current and field configurations. These results clearly indicate Sr4(Ru1−xMnx)3O10 is a novel ferromagnetic semiconductor with exotic magnetotransport properties.

The Ruddlesden-Popper (RP) ruthenates Sr n+1 Ru n O 3n+1 (n = 1, 2, 3 … ∞) have attracted great attention because of their exotic electronic and magnetic properties. While the only difference in their chemical composition is the number of RuO 6 octahedral layers n in the unit cell, their physical properties vary from a p-wave superconductor (n = 1) 1 , to a paramagnetic metal with magnetic field-induced quantum critical point (n = 2) 2 , to an unusual ferromagnetic metal with in-plane metamagnetism (n = 3) 3 , to a ferromagnetic polar metal (n = ∞) 4 . Both experimental 3,5-10 and theoretical studies [10][11][12] indicate that the fundamental building block RuO 6 octahedron plays an extremely important role in these unconventional properties. In the RP series, RuO 6 octahedra are connected by corner sharing O atoms within the n layers, which can be distorted in multiple ways such as elongation, compression, rotation, and tilt. For example, with increasing n, the rotation angle of RuO 6 octahedron changes from zero (n = 1) 13 , to 7° (n = 2) 14,15 , to 11.2° (n = 3) 16 to ~12° (n = ∞). According to theoretical calculations 11,17,18 , such distortion impacts the electronic distribution, thus changing the physical properties.
In the RP series, the members with odd n are particularly interesting. For Sr 2 RuO 4 with n = 1, the RuO 6 octahedron rotates about 9° at the surface 10 , even it is absent in bulk. Such rotation may stabilize ferromagnetism at the surface, which is ultimately connected to the Cooper pair formation with parallel spins in bulk. For Sr 4 Ru 3 O 10 with n = 3, the RuO 6 octahedron in the central layer apparently rotates double amount (~11.2°) than that in the two outer layers (~5.6°), corresponding to different magnetic moment as well 16 . According to density functional calculations 11,12 , the orthorhombic structure with the rotation of the RuO 6 octahedron is in favor of ferromagnetic coupling. In the previous study of Sr 3 (Ru 1−x Mn x ) 2 O 7 , partial replacement of Ru by smaller Mn leads to the decrease of (Ru/Mn)O 6 octahedral rotation, and long-range antiferromagnetic (AFM) ordering at T N 8 . Intriguingly, T N versus x is dome-like with both T N and the rotation vanishes at the same doping level. This suggests that the correlation between octahedral rotation and magnetic coupling is more complex than simple monotonic response. Given its magnetic ground state and the difference in local structure between outer and central layers 19,20 , Sr 4 Ru 3 O 10 could be much more susceptible to Mn doping than the case of n = 2. In this article, we report, for the first time, the experimental investigation of Mn doped Sr 4 Ru 3 O 10 single crystals, including the crystal structure, magnetization, and electrical transport properties. The partial replacement of Ru by Mn results in the modification of (1) crystal structure by removing octahedral rotation, (2) magnetic interaction by changing the easy axis from the c direction to the ab plane, and (3) electrical conduction from metallic to semiconducting with unusual magnetotransport behavior.

Results and Discussion
For both nominal x = 0.25 and 0.5 crystals, our single-crystal X-ray diffraction refinement results in structural and compositional information that are given in Tables 1 and 2, respectively. The refinement indicates that they form a tetragonal structure (S.G. I4/mmm) with actual x = 0.23 and 0.41, respectively. Note that the actual Mn concentration is the average value of Mn in the central layer (Mn1) and outer layers (Mn2). While Mn is randomly distributed within each layer, our structural refinement indicates that Mn1 concentration is slightly lower than Mn2 in both x = 0.23 and 0.41. As summarized in Tables 1 and 2 Fig. 1(a), both the number of Ru/Mn and O sites are reduced. The change from orthorhombic for x = 0 to tetragonal for x = 0.23, and 0.41 indicates the removal of octahedral rotation upon Mn doping. While a (b) (the values for parent compound are divided by 2 ) remains more or less a constant, lattice parameter c decreases with increasing x as plotted in Fig. 1(b). This means that the unit cell volume decreases with increasing x (see the inset of Fig. 1(b)). To understand the origin of unit cell shrinkage, we plot the x dependence of the bond lengths of Ru/Mn-O in four different octahedra (I, II, III and IV, referred from x = 0) in Fig. 1(c-f), respectively. With increasing x, while the in-plane bond length slightly decreases, the out-of-plane Ru/Mn-O bond length decreases more dramatically. By calculating the ratio of the average out-of-plane to in-plane Ru/ Mn-O distance, we obtain the x dependence of the Jahn-Teller (JT) distortion δ JT for I, II, III and IV, which are shown in Fig. 1(g). Note that δ JT for outer-layer octahedra (I and III) decrease from 1.05 to 1.00 while those for central-layer octahedra (II and IV) decrease from 1.01 to 0.99, as x increases from 0 to 0.41. These indicate Mn doping makes the outer-layer octahedra less elongated, and the central-layer ones slightly compressed. (2) K obtained through single crystal X-ray diffraction refinement. U eq is defined as one-third of the trace of the orthogonalized U ij tensor (Å 2 ).

Wyckoff.
Occupancy.  (2) χ ab > χ c for x = 0.34 and 0.41, indicating that the magnetic easy axis is along the ab plane. Compared to the case of x = 0, T C obviously is decreased and the magnetic easy axis is switched from the c direction to the ab plane upon Mn doping. In analyzing the high temperature susceptibility data using the Curie-Weiss law (χ 0 is a constant, N A is the Avogadro constant, and k B the Boltzmann constant), we obtain positive Curie-Weiss temperature θ CW and effective moment μ eff . For x = 0.34, χ 0 ~ −0.003 emu/mol, θ CW ~ 33 K and μ eff ~ 3.4μ B , and χ 0 ~ −0.01 emu/mol, θ CW ~ 37 K and μ eff ~ 3.2μ B for x = 0.41. The positive θ CW value indicates that magnetic interaction is ferromagnetic along both the ab plane and c axis, similar to the x = 0 case 3 . However, for x = 0.41, θ CW is higher than T C , which usually occurs in low-dimensional or frustrated magnetic systems. While there is little anisotropy in magnetic susceptibility above θ CW , the tetragonal structure disfavors magnetic frustration as well. One possibility is that the compressed central (Ru/Mn)O 6 layer [see Fig. 1(g)] may be in favor of antiferromagnetic interaction, while the elongated two outer (Ru/Mn)O 6 layers support ferromagnetic interaction according to theoretical calculations 11,12 . The mixed ferromagnetic and antiferromagnetic interactions result in higher θ CW but smaller μ eff in x = 0.41 compared to the case of x = 0.34. Although similar argument also should apply to the latter case, antiferromagnetic interaction is less dramatic own to smaller or close-to-zero compression of the central (Ru/Mn)O 6 octahedra [see Fig. 1(g)]. Nevertheless, the estimated μ eff for x = 0.34, and 0.41 corresponds to effective spin 1 < S eff ~1.19-1.28 < 3/2 for Ru/Mn, slightly higher than the undoped case with S = 1 21 . This suggests that Mn has the same valence as Ru 4+ , i.e., Mn 4+ , which gives S = 3/2.
To further identify the nature of the magnetic interaction in the doped systems, the magnetization hysteresis is measured at various temperatures, which is presented in Fig. 2  According to previous studies, small percentage of Mn doping in single-layered Sr 2 RuO 4 (n = 1) 22 and double-layered Sr 3 Ru 2 O 7 (n = 2) 8,23 results in antiferromagnetic insulating ground state. The same trend is observed in SrRuO 3 (n = ∞), in which more than 39% Mn doping turns the system into an AFM insulator as well 24,25 . The fact that Sr 4 (Ru 1−x Mn x ) 3 O 10 (x = 0.34 and 0.41) retains its ferromagnetic (FM) ordering is remarkable, suggesting that the magnetic interaction in the n = 3 system is different from those mentioned above. Figure 3(a-e) show temperature dependence of both in-plane (ρ ab ) and c-axis (ρ c ) resistivities for x = 0.34 (a-c) and 0.41 (d-e), respectively. Note that, for x = 0.34, ρ c shows a semiconducting behavior in the entire measured temperature range while the metal-insulator transition (MIT) temperature occurs at 215 K in the ab-plane (see Fig. 3(c)). For x = 0.41, we can speculate that this transition is beyond 300 K, as both ρ ab and ρ c are non-metallic below 300 K. While no anomaly is observed in ρ ab and ρ c at T C , the resistivity anisotropy ρ c /ρ ab , presented in Fig. 3(f), shows steep change below T C than that at higher temperatures. This is consistent with the magnetic anisotropy that stronger in-plane ferromagnetism (M ab > M c ) results in better electrical conduction along the ab plane. By replotting the temperature dependence of resistivities as lnρ versus T −1 in the inset of Fig. 3(a,b,d and  e), liner relationship is clearly revealed. This indicates that both ρ ab (T) and ρ c (T) can be described by the thermal activation model ρ = ρ 0 exp(Δ/k B T), where ρ 0 is a temperature-independent constant, and Δ is the thermal activation energy. By fitting experimental data to the formula, we obtain Δ ~10 meV and 30 meV for x = 0.34 and 0.41, respectively. The solid lines in the insets of Fig. 3(a,b,d and e) represent the fitting results, which describe the experimental data very well.  Fig. 4(e-h).
The negative MR for Sr 4 (Ru 1−x Mn x ) 3 O 4 (x = 0.34 and 0.41) is different from that seen in the parent compound, which is positive along both the ab plane and c direction prior to the metamagnetic transition field 26,27 . This confirms that the magnetic properties of Mn-doped system are different from the undoped case. Furthermore, the fact that MR ab // > ⊥ MR ab and ⊥ MR c > MR c // indicate that spin scattering is strong in the ab plane, and can be more effectively suppressed when H//ab. This is consistent with the observation that the magnetic easy axis in Sr 4 (Ru 1−x Mn x ) 3 O 4 (x = 0.34 and 0.41) is along the ab plane. The most remarkable feature is the linear-H dependence of negative MR in all configurations. While it is discussed in both classic and quantum scenarios, linear negative MR (LNMR) in all configurations is rare.
In normal circumstances, one would expect that MR exhibits the H 2 dependence in low fields and eventually saturates at high fields 28 . Linear MR can be found in materials with open Fermi surfaces 29 , disordered metals or semiconductors [30][31][32][33] , and in the extreme quantum limit with ω >  E c F (where ω c is the cyclotron frequency and E F is the Fermi energy) [34][35][36] . However, the MR is usually positive in these scenarios. LNMR has been discussed in non-magnetic disordered 2D gas systems with random corrugation and defects [37][38][39][40][41] , and polycrystalline graphite consisting of nano-sized particles 42 . In the latter case, the system exhibits semiconducting behavior with thermally activated electrical conduction. Due to its polycrystalline nature, it consists of weak localization (WL) 43 and diffuse scattering (DS) between grain boundaries 44 , giving rise to MR total = MR WL + MR DS = −K 1 H 1/2 − K 2 H 2 (K 1 and K 2 are constants) 42 . Experimentally, one would observe LNMR as the consequence of these two contributions. As T approaches 0 K, MR WL becomes dominant, leading to cusp-shaped H dependence of MR. While Sr 4 (Ru 1− x Mn x ) 3 O 10 exhibits thermally activated semiconducting conduction (see Fig. 3), the above scenario may not be feasible to explain LNMR in our case, because (1) our samples are single crystals with little or no grain boundaries and (2) there is no sign for cusp-shaped H dependence in MR up to 14 Tesla down to 2 K (see Fig. 4).
For Sr 4 (Ru 1−x Mn x ) 3 O 10 , the observed LNMR should be related to Mn doping as it is (1) absent in x = 0 26,27 , (2) larger in higher Mn doping level under the same condition (see Fig. 4), and (3) appearing below and above T C . The fact that LNMR occurs in all current and field configurations with small anisotropy for both x = 0.34 and 0.41 indicates that it is not related to dimensional confinement nor orbital nature in our system. Similar behavior was observed in Be-doped AlGaAs -GaAs quantum well structures, in which the LNMR is attributed to spin exchange interactions between localized states 40 . Under the application of magnetic field, spin disorder related to exchange interactions is suppressed and Zeeman energy activates carriers in the localized states to delocalized states, leading to LNMR 40,45 . This is consistent with our observation that the largest LNMR occurs when H is applied along the magnetic easy (ab-) plane and continuous increase of magnetization (see Fig. 2). However, this scenario cannot explain the increased LNMR with increasing x, as energy gap is enlarged and spin polarization becomes weaker. Theoretically, MR in doped ferromagnetic semiconductors is expected to be inversely proportional to the number of charge carriers per magnetic unit cell 30 . Our data is consistent with this picture, as Mn doping results in charge localization thus reducing charge carrier density in Sr 4 (Ru 1−x Mn x ) 3 O 10 .
In summary, we have successfully grown Mn-doped single crystalline Sr 4 (Ru 1−x Mn x ) 3 O 10 with x up to 0.41. Single crystal X-ray diffraction indicates that the partial substitution of Ru by Mn results in symmetry change from orthorhombic to tetragonal due to the removal of octahedral rotation. Both electrical and magnetic properties are changed as well. For x = 0.34 and 0.41, the system becomes ferromagnetic semiconducting with T C ~35 K and energy gap ~10 meV for x = 0.34 and T C ~30 K and 30 meV for x = 0.41, making Sr 4 (Ru 1−x Mn x ) 3 O 10 an excellent material system to study ferromagnetic semiconducting properties. One of remarkable features is its linear negative MR observed in a wide temperature and field range in all current and field configurations. Such behavior

Methods
High-quality Sr 4 (Ru 1−x Mn x ) 3 O 10 single crystals were grown via the floating-zone technique. For making both feed and seed rods, polycrystalline Sr 4 (Ru 1−x Mn x ) 3 O 10 was first prepared by heating the mixture with the molar ratio SrCO 3 : [(1 − x)Ru + xMnO 2 ] = 4: 3 up to 1400 °C for 24 h in oxygen atmosphere with quick cool off by quenching. It is then hydrostatically pressed into cylinder-shaped rods, and further sintered at 950 °C for another 12 h in oxygen atmosphere. Single crystals were grown through melting the feed rod and moving downward with the speed of 30 mm/h. To prevent oxygen deficiency, 0.9 MPa oxygen pressure was applied during the growth. In addition, both feed and seed rods were rotated in opposite directions at 20 rpm to improve homogeneity and reduce possible impurity.
For single-crystal X-ray diffraction (XRD), a single crystal was mounted on the tip of Kapton loop, and data were collected on a Bruker Apex II X-ray diffractometer with Mo radiation K α 1 (λ = 0.71073 Å). The SMART software was used for data acquisition over a full sphere of reciprocal space with 0.5° scans in ω with an exposure time of 10 s per frame. The 2θ range extended from 0° to 80°. Intensities were extracted and corrected for Lorentz and polarization effects with the SAINT program. Numerical absorption corrections were accomplished with XPREP which is based on face-indexed absorption. The crystal structure was determined based on full-matrix least-squares methods using the SHELXTL package 46 .
Physical property measurements were investigated in x = 0.34 and 0.41 single crystals. The magnetization was measured using the magnetic property measurement system (MPMS, Quantum Design), while the electrical resistivity was carried out in the physical property measurement system (PPMS, Quantum Design).