Dilution effects on the antiferromagnetic Kondo semiconductor CeOs2Al10

We have studied the effects of dilution of Ce sublattice on the unusual antiferromagnetic (AFM) order in the Kondo semiconductor CeOs2Al10 at 28.5 K by the magnetic, transport and specific-heat measurements of single crystals of Ce1-zLazOs2Al10. The effective magnetic moment and paramagnetic Curie temperature hardly change with z up to 0.5, indicating that the 4f state remains unchanged at high temperatures. The suppression of the Néel temperature TN is much weaker than that in 5d hole doped system, Ce(Os1-yRey)2Al10. Therefore, the AFM interaction is robust against the violation of the coherent Ce sublattice. The activation energy in the resistivity decreases in parallel with TN, confirming the argument that the presence of the c-f hybridization gap is a requisite for the unusual AFM order in this system.


Introduction
In the so-called Kondo semiconductors with renormalized gaps at the Fermi level, the ground states remain nonmagnetic due to the strong hybridization of the 4f states and conduction bands [1]. However, recently found Kondo semiconductors CeT2Al10 (T = Ru, Os) crystallizing in the orthorhombic YbFe2Al10-type structure order antiferromagnetically (AFM) at rather high temperature TN = 28 K [2][3][4]. In order to elucidate the mechanism for the unusual AFM order, we have studied the effects of electron-and hole-doping on the magnetic and transport properties [5,6], electron tunneling [7] and spingap formation [8] in Ce(Os1-yMy)2Al10 (M = Re, Ir). These studies have revealed that 5d hole doping with Re substitution for Os moves CeOs2Al10 to a valence fluctuation regime while 5d electron doping with Ir substitution moves to a localized Kondo regime. Furthermore, the 5d hole doping suppresses the TN more drastically than the 5d electron doping, whereby the suppressions of TN are well correlated with those of the activation energy in the electrical resistivity. Because the activation energy is a measure of the hybridization gap, this correlation suggested that the hybridization gap is necessary for the unusual AFM order in this system.
The effect of dilution of the Ce 4f sublattice on the physical properties of CeRu2Al10 was studied by substituting La for Ce [9][10][11]. It was expected that the La substitution expands the lattice and therefore the 4f state would be more localized. As z is increased from 0 to 1 in Ce1-zLazRu2Al10, the lattice parameters a and c increased by 0.25% and the b parameter increased by 0.15%. However, the magnetic susceptibility along the easy a axis for T > 100 K hardly changed with z up to z = 0.7 where the AFM order disappeared. Therefore, little change occurred in the effective magnetic moment per Ce atom and paramagnetic Curie temperature. The rather robust AFM order against dilution is in contrast with the strong suppression of the AFM order observed in Ce(Os1-xMx)2Al10 for M = Re and Ir [7]. In order to understand the contrasting responses to the substitution in the T sublattice and that in the Ce sublattice, we have studied the dilution effect on the AFM order in Ce1-zLazOs2Al10. Another issue in Ce1-zLazRu2Al10 is the reorientation of the ordered magnetic moment AF from //c to //b, which occurs at z  0.07 [11]. In this work, we have examined whether such reorientation occurs in the Os system Ce1-zLazOs2Al10.

Experimental
Single crystals of Ce1-zLazOs2Al10 were grown by the Al self-flux method as previously reported [4]. The chemical compositions were determined by the wave-length dispersive electron-probe microanalysis. The compositions of La (z) in the crystals were found to slightly deviate from the initial ones (Z). For example, starting with the compositions Z = 0.05, 0.10, 0.20, 0.30 and 0.5, the actual values of z were 0.043, 0.096, 0.15, 0.24 and 0.51, respectively. A small amount of impurity OsAl4 was detected. The xray diffraction analysis on the powdered samples indicated that a and c parameters increase linearly by 0.3% and the b parameter increases by 0.2% as z increases from 0 to 1.0.
Using the samples cut along the principal axes, we measured the electrical resistivity , magnetic susceptibility  and specific heat C in the temperature range from 2 to 300 K. The measurement of (T) was performed by the ac four-terminal method. Along the three principal axes, (T) was measured with bar shaped samples longer than 0.4 mm. A SQUID magnetometer (Quantum Design MPMS) was used for (T) measurements. The magnetization up to 14 T was measured by the extraction method using the Quantum Design PPMS. The measurement of C(T) was performed by the thermal relaxation method on the PPMS.

Results and Discussion
The magnetic susceptibility of Ce1-zLazOs2Al10 along the a axis is shown in figure 1 as 1/vs temperature T. The value is normalized per Ce mol. The Curie Weiss fit to the data above 200 K yielded the effective magnetic moment eff which stays at 2.62 -2.66 B/Ce for 0  z  0.51. The absolute values of the paramagnetic Curie temperature p stays at 22 -30 K, as is shown in the inset of figure 1. Both eff and p are insensitive to the La substitution, which are in common with those observed for Ce1-zLazRu2Al10 [9][10][11]. This result indicates that the 4f hole doping does not alter the c-f hybridization at high temperatures. It is in contrast with the strong effect of 5d hole doping by Re substitution for Os, which shifts the system to the valence fluctuation regime as is evidenced by the large increase in |p| (see the inset of figure 1) [5]. This opposite effect is not due to the volume effect because the unit cell volume increases by a similar ratio for both substitutions, La for Ce and Re for Os. In the latter, the a and c parameters enlarge by 0.2% and the b parameter enlarges by 0.3% as the Re content increases from 0 to 0.5 [5], whose elongations are comparable in the former as described in the previous section.
We note here that the b and c at T > 50 K are essentially unchanged with z but the drop in b and c at T < TN for z = 0 disappeared for z > 0.24. The presence of the hybridization gap in CeOs2Al10 manifests in the thermal activation type behaviour of resistivity,(T) = 0 exp(/2kBT) [4]. The results of (T) along the three principal axes for Ce1-zLazOs2Al10 are presented in figure 2 together with the Arrhenius plot of (I //a) in the inset. The vertical lines denote TN's determined by the specific heat measurement as will be described below. For z = 0, the thermal activation behaviour is observed in two regions, 5 < T < 16 K and 30 < T < 80 K. The increase in (T) at T < TN becomes stronger for z = 0.043 but is weakened as z is further increased to 0.096. However, the thermal activation behaviour above TN remains in (T) along the a axis as shown in the inset. For z = 0.24, (T)'s no longer follow the activation type form. We note here that the magnitudes of (T=2.5 K) for z = 0.043 and 0.096 are several times larger than those of the corresponding sample Ce1-zLazRu2Al10 [10]. The larger enhancement in the Os system than in the Ru system is consistent with the smaller value of the Sommerfeld coefficient in the former, as shown below. Figure 3 shows the temperature dependence of C/T for Ce1-zLazOs2Al10. The midpoint of the jump in C/T was taken as TN, which is 28.5 K for z = 0. With increasing z, the jump at the AFM order shifts to low temperatures and becomes broader. A weak anomaly is noticeable at 10 K for z = 0.24 but no jump is observed down to 2 K for z = 0.35. The Sommerfeld coefficient  was estimated by extrapolating  the C/T vs T 2 plot to T = 0. We discuss later the dependence of  on z in comparison with other doped systems. The dependences of TN and the thermal activation energy a in the resistivity along the a axis are plotted in the inset of figure 3. It is noteworthy that the decrease in TN follows that of a. This relation supports our argument that the hybridization gap is a requisite for the unusual AFM order, which has been derived from our systematic investigation of Ce(Os1-xMx)2Al10 for M = Re and Ir [5,6].
As mentioned in the introduction, the direction of AFM ordered moments AF in Ce1-zLazRu2Al10 changes from //c to //b as z is increased to 0.07 [10]. In order to examine whether such reorientation occurs in Ce1-zLazOs2Al10, we have measured the magnetization curves M(B) up to 14 T at 2 K. The results of M(B) for B//c are shown in figure 4. The metamagnetic anomaly at 6.5 T for z = 0 is the manifestation of the spin flop transition from AF//c to AFc [4,5]. When z increases to 0.24, the metamagnetic anomaly still exists at B//c = 2.5 T, indicating the direction of AF to be kept along the c axis. This result is consistent with the AFM structure for z = 0.1 with AF //c = 0.23B which was determined by neutron diffraction experiments [12]. We note that the M(B) curves for B//a and B//b did not show any anomaly up to 14 T (not shown). Figure 5 shows the variations of TN and the  value as a function of doping amount for the three systems: 4f hole doped systems Ce1-zLazOs2Al10 and Ce1-zLazRu2Al10 [9][10][11] and 5d hole doped system Ce(Os1-yRey)2Al10 [5]. Between the two La substituted systems, the degree of suppression of TN for the Os compound is stronger than that for the Ru compound. However, it is much milder when compared with that of Re substituted system. This is well correlated with the gradual increases in the  value as a function of z in Ce1-zLazOs2Al10 and Ce1-zLazRu2Al10 which are slower than that as a function of 2y in Ce(Os1-yRey)2Al10. Therefore, we conclude that the gapped electronic state in CeOs2Al10 below TN is much weakly affected by 4f hole doping compared with the 5d hole doping.

Summary
We have studied the effect of dilution of the 4f sublattice on the unusual AFM order in the Kondo semiconductor CeOs2Al10 by measuring the magnetic, thermal and transport properties of Ce1-zLazOs2Al10. The measurements indicate that the 4f hole doping hardly change both the Ce valence state and the c-f hybridization strength. The AFM order is mildly suppressed by the doping of 4f holes,  in contrast with the strong suppression caused by the 5d hole doping. The contrasting effects provide a strong constraint for the theory to explain the mechanism of the unusual AFM order in the presence of the hybridization gap in the Kondo semiconductor.