Magnetism of perovskite cobaltites with Kramers rare-earth ions
Z. Jirák, J. Hejtmánek, K. Knížek, P. Novák, E. Šantavá, and H. Fujishiro
Citation: Journal of Applied Physics 115, 17E118 (2014); doi: 10.1063/1.4862946
View online: http://dx.doi.org/10.1063/1.4862946
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JOURNAL OF APPLIED PHYSICS 115, 17E118 (2014)

Magnetism of perovskite cobaltites with Kramers rare-earth ions k,1,a) J. Hejtma
nek,1 K. Knızek,1 P. Nova
k,1 E. Santav
,1 and H. Fujishiro2Z. Jiraa
1Institute of Physics ASCR, Cukrovarnick
a 10, 162 00 Prague 6, Czech Republic
Faculty of Engineering, Iwate University, Morioka 020-8551, Japan2(Presented 6 November 2013; received 19 September 2013; accepted 28 October 2013; published
online 27 January 2014)
The band-gap insulators RECoO3 (RE ¼ Nd3þ, Sm3þ, and Dy3þ) with Co3þ ions stabilized in thenon-magnetic low-spin state have been investigated by specific heat measurements. The
experiments evidence an antiferromagnetic ordering of the rare earths with Neel temperature ofTN ¼ 1.25, 1.50, and 3.60 K for NdCoO3, SmCoO3, and DyCoO3, respectively. With increasing
external field, the lambda peak in specific heat, indicative of the transition, shifts to lower
temperatures and vanishes for field of about 3 T. Starting from this point, a broader Schottky peakis formed, centered in 1 K range, and its position is moved to higher temperatures proportionally toapplied field. The origin of the peak is in Zeeman splitting of the ground Kramers doublet, and thegradual shift with field defines effective g-factors for the rare-earth pseudospins in studiedcompounds. The results obtained are confronted with the calculations of crystal field splitting ofC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4862946]
the rare-earth multiplets. VThe rare-earth cobaltites RECoO3 possess a distorted
perovskite structure of the orthorhombic space group P bnm,
characterized by a tilt of CoO6 octahedra and location of
rare-earth ions in sites of low point symmetry Cs (the mirrorplane m). Since the octahedrally coordinated Co3þ ions arestabilized in a non-magnetic low-spin state, the magnetic
properties depend primarily on the existence of RE3þmoments and their (dipole-dipole or superexchange) interactions. It is essential that the free-ion multiplets of rare earths
are split by crystal field effects, resulting in Kramers doublets for ions with odd number of 4f electrons and singlets
for ions with the even number. In the case of a non-magnetic
singlet state, the low-temperature magnetic property is van
Vleck susceptibility arising due to mixing in external field of
the ground singlet with higher-lying levels. The well-known
example is Pr3þ (4f 2) showing linear paraprocess up to very
high fields, see e.g., Ref. 1. Exceptions of this rule are Tb3þ(4f 8) and Ho3þ (4f 10) with accidental degeneracy of twolowest singlets, forming a magnetic pseudodoublet.
The present work is focused to the cobaltite systems
with Nd3þ (4f 3), Sm3þ (4f 5), and Dy3þ (4f 9) ions thatexhibit Kramers degeneracy and display, therefore, finitemoments (the J 0 ¼ 1=2 pseudospins) in the ground state. The
study combines the low-temperature heat capacity experiments and extensive calculations of the rare-earth levels andtheir magnetic characteristics.
The determination of the Nd3þ, Sm3þ, and Dy3þ electronic levels was performed in two steps. Since the cobaltites(unlike the rare-earths aluminates) are non-transparent andno optical f–f transitions are available, the crystal fieldparameters had to be first calculated. For this task, a novel
method based on the first-principles electronic structure andWannier projection2,3 was applied. The parameters, derived
for the crystallographic data of real P bnm structures of thea)

Author to whom correspondence should be addressed. Electronic mail:jirak@fzu.cz.

0021-8979/2014/115(17)/17E118/3/$30.00

respective RECoO3,4–6 have been recently published in theAppendix of Ref. 7.
In the next step, the local Hamiltonian operating on the4f states in a determinantal basis of one-electron wavefunctions was constructed, including both the crystal field andZeeman interaction terms. The eigenvalue problem wassolved using “Lanthanide” program.8 The calculations weredone for different orientations and strengths of the appliedfield, so that not only the crystal field split levels but also
their magnetic characteristics were determined.
The crystal field splittings of free-ion multiplets of Nd3þ4( I9=2 ), Sm3þ(6 H5=2 ), and Dy3þ (6 H15=2 ) result in five, three,and eight Kramers doublets, respectively. Their calculated
energy schemes are available in Ref. 7. In addition, the anisotropic gJ 0 -factors and Van Vleck susceptibilities relative tothe doublets are tabulated for the orientation of applied fields
along the orthorhombic a, b, c axes and in the diagonal direction [110]. Following the Cs symmetry of rare-earth sites, theprincipal axes of respective tensors are z k c and x, y ? c,with x inclined to 6a from the a axis (here 6 refers to two
nonequivalent sites in P bnm structure). For the ground doublet of Nd3þ, the principal components of gJ0 -tensor aregx ¼ 2.818, gy ¼ 1.228, gz ¼ 3.015, and the angle of local
x-axis makes an angle ag ¼ 6 62.3o with the orthorhombic aaxis. The next doublet is situated at an excitation energy
D ¼ 13.2 meV, which means that it makes no contribution torare-earth moments in the investigated temperature range ofT < 30 K. The data obtained for the ground doublet of Sm3þare gx ¼ 0.703, gy ¼ 0.588, and gz ¼ 0.322, the orientation ofthe x-axis under the angle ag ¼ 633.2o and the first excitation energy D ¼ 29.6 meV. The situation for Dy3þ is specificby Ising character of the ground doublet, gx ¼ 19.44, gy  0,and gz  0, where the orientation of the Ising axis is underthe angle ag ¼ 664.0o with the orthorhombic a axis. The firstexcitation energy is calculated to D ¼ 29.8 meV.
In the experimental part, ceramic samples NdCoO3,SmCoO3, and DyCoO3 were prepared using a solid-state

115, 17E118-1

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 k et al.
JiraJ. Appl. Phys. 115, 17E118 (2014)

FIG. 1. The AFM arrangement of Cz
type in NdCoO3 below TN ¼ 1.25 K[Ref. 9] (left) and GxAy in DyCoO3below TN ¼ 3.60 K [Ref. 7] (right). Thescheme shows the octahedral tilts andrare-earth moments located at the mirror plane at c ¼ 1/4 level, while thoseat c ¼ 3/4 are oppositely oriented. Theblue lines mark the shortest RE-Obonds.

reaction. Raw powders of Nd2O3, Sm2O3, Dy2O3, and Co3O4
were weighted with proper molar ratios and ground using anagate mortar and pestle for 1 h. Mixed powders were calcinated at 1000  C for 24 h in air. They were pulverized andground. Then, they were pressed into pellets of 20 mm diameter and 4 mm thickness. Pellets were sintered at 1300  C for
24 h under air. The measured densities of each sample weregreater than 90% of the ideal density. Powder X-ray diffraction
patterns were taken for each sample using CuKa radiation; thesamples were confirmed to have a single phase orthoperovskite
P bnm structure. The lattice parameters and volume per f.u.
actually obtained are a ¼ 5.344 Å, b ¼ 5.335 Å, c ¼ 7.548 Å,
V/Z ¼ 53.79 Å3 for NdCoO3, a ¼ 5.283 Å, b ¼ 5.350 Å,c ¼ 7.496 Å, V/Z ¼ 52.97 Å3 for SmCoO3, and a ¼ 5.170 Å,b ¼ 5.410 Å, c ¼ 7.397 Å, V/Z ¼ 51.73 Å3 for DyCoO3. The
present values are in an agreement with the literature data forthe same compounds.
The specific heat was measured by Physical Properties
Measuring System (Quantum Design) using the two–s model.
The experiments at very low temperatures (down to 0.4 K)
were done using the 3He option. The data were taken on sample cooling at several runs, in zero field and selected fields upto 90 kOe (140 kOe for SmCoO3). The data for NdCoO3 inFig. 2 show a sharp k-peak at TN ¼ 1.25 K, which evidences
an antiferromagnetic ordering found for this compound byneutron diffraction, actually the Cz-type arrangement in
Bertaut’s notation,9 see Fig. 1. With increasing external field,
this k-peak shifts to lower temperatures and vanishes for fieldof about 30 kOe. Starting from this point, a broader Schottky
peak is formed, centered in 1 K range, and its position ismoved to higher temperatures proportionally to applied field.
Origin of this peak is in Zeeman splitting of the ground state
doublet, and the gradual shift with field defines an effective
g-factor for the Nd3þ pseudospins. A detailed analysis reveals
a broadening with respect to ideal Schottky form, which is incoherence with the pseudoaxial anisotropy of Nd3þ moments,
which can be expressed, using the calculated principal components gx ¼ 2.818, gy ¼ 1.228, and gz ¼ 3.015 for the grounddoublet, by a ratio 2gy/(gx þ gz) ¼ 0.42. Indeed, the bestexperimental fit in the lower panel of Fig. 2 is achieved forthe ratio gk/g?  0.35 and 0.54 for H ¼ 50 and 90 kOe,
respectively. The average value g ¼ 2.29 determined from thefield shift of Schottky peak for our polycrystalline sample(see the inset) is also in a reasonable agreement with thetheoretical value hgi ¼ 2:44.
Similar k-peak is observed for SmCoO3 at TN ¼ 1.50 K(Fig. 3). The detailed type of AFM arrangement is, however,uncertain since no neutron diffraction data are available forthis compound. This is due to extreme absorption of natural
samarium for neutrons which can be, nonetheless, overcome
by isotopic substitution. The AFM ordering is much morerobust in external fields than for NdCoO3, so that the k-peakthough decreasing and shifting to lower temperatures isobserved up to 90 kOe, where formation of Schottky peakjust starts. In still higher fields, only a slow upward shift ofSchottky maximum is observed. The reason is in a weak
Zeeman energy of Sm3þ. This follows from near canceling

FIG. 2. The specific heat of NdCoO3 in dependence on applied field. Thelower panel shows the least-squares fit of Schottky peak form, supposing theaxial symmetry of the g-factor. The average Zeeman splitting energy ispresented in the inset.

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JiraJ. Appl. Phys. 115, 17E118 (2014)

FIG. 3. The specific heat of SmCoO3 in dependence on applied field.

FIG. 4. The specific heat of DyCoO3 in dependence on applied field.

of the spin and orbital moments in 6 H5=2 multiplet (L ¼ 5,S ¼ 5/2, J ¼ L – S ¼ 5/2, gL ¼ 2/7), which is manifested
among others by low gJ0 -factor of the pseudospins in ground
Kramers doublet (gx ¼ 0.703, gy ¼ 0.588, and gz ¼ 0.322).
For DyCoO3, the AFM ordering is of a non-collinear
GxAy-type, see the right picture in Fig. 1. Such canted
arrangement is a consequence of Ising character of thegJ0 -tensor of Dy3þ ions and zigzag orientation of their easy
axes in the P bnm structure.7,10 The zero-field heat capacity
data in (Fig. 4) show TN ¼ 3.60 K, but the AFM ordering
quickly vanishes in external field, which should be related toa strong Zeeman energy associated with gk ¼ 19:44 of theDy3þpseudospins. Upon the collapse of the sharp k-peak, avery diffusive Schottky-like peak arises and broadens withincreasing field. Finally, it acquires the form of a notably
large linear term that adds to the common cubic term of lattice heat. This behavior of DyCoO3 is a natural consequenceof Ising moments in polycrystalline materials. Namely, when
external field is oriented under random angles h to local Ising
axes, the Zeeman splitting varies as cosh and, instead of two
sharp levels, the polycrystal as a whole exhibits a continuous
spectrum of excitations with constant density of states,
spreading from DE ¼ 0 to DEmax.11 The constant density ofstates then gives the strictly linear low-temperature term ofspecific heat.
This work was supported by Project No. P204/11/0713
of the Grant Agency of the Czech Republic.

1

R. M. Thomas, V. Skumryev, J. M. D. Coey, and S. Wirth, J. Appl. Phys.
85, 5384 (1999).
2P. Novak, K. Knızek, and J. Kunes, Phys. Rev. B 87, 205139 (2013).
3
P. Novak, K. Knızek, M. Marysko, Z. Jirak, and J. Kunes, J. Phys.:Condens. Matter 25, 4460001 (2013).
4K. Knızek, J. Hejtmanek, Z. Jirak, P. Tomes, P. Henry, and G. Andre,Phys. Rev. B 79, 134103 (2009).
5J. Perez-Cacho, J. Blasco, J. Garcıa, and R. Sanchez, J. Solid State Chem.
150, 145 (2000).
6J. A. Alonso, M. J. Martınez Lope, C. de la Calle, and V. Pomjakushin,
J. Mater. Chem. 16, 1555 (2006).
7K. Knızek, P. Novak, Z. Jirak, and C. R. dela Cruz, Solid State Sciences
28, 26 (2014).
8S. Edvardsson and D. Aberg, Comput. Phys. Commun. 133, 396 (2001).
9I. Plaza, E. Palacios, J. Bartolome, S. Rosenkranz, C. Ritter, and A. Furrer,Physica B 234–236, 632 (1997).
10A. Kappatsch, A. Quezel-Ambrunaz, and J. Sivardiere, J. Phys. France 31,369 (1970).
11J. M. D. Coey and S. von Molnar, J. Phys. Lett. 39, L327 (1978).

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