MAGNETIC STRUCTURE AND DOMAIN CONVERSION OF THE QUASI-2D FRUSTRATED ANTIFERROMAGNET CuCr02
PROBED BY NMR
Yu. A. Sakhratova'b, L. E. Svistovc*, P. L. Kuhnsa, H. D. Zhoua>d, A. P. Reyes"
" National High Magnetic Field Laboratory, Tallahassee 32310, Florida, USA
bKazan State Power Engineering University 420066, Kazan, Russia
Kapitza Institute for Physical Problems Russian Academy Sciences 119334, Moscow, Russia
dDepartment of Physics and Astronomy, University of Tennessee, Knoxville 37996, Tennessee, USA
Received June 17, 2014
We measured a:i-a:'Cu NMR spectra in a magnetic field up to about 15.5 T on a single crystal of the multiferroic triangular-lattice antiferromagnet CuCrOa. The measurements were performed for perpendicular and parallel orientations of the magnetic field with respect to the e-axis of the crystal, and the detailed angle dependence of the spectra on the magnetic field direction in the ct&-plane was studied. The shape of the spectra can be well described in the model of spiral spin structure suggested by recent neutron diffraction experiments. When the field is rotated perpendicular to the crystal e-axis, we for the first time directly observed a remarkable reorientation of the spin plane simultaneous with rotation of the incommensurate wavevector, by quantitatively deducing the conversion of the energetically less favorable domain to a more favorable one. At high enough fields parallel to the e-axis, the data are consistent with either a field-induced commensurate spiral magnetic structure or an incommensurate spiral magnetic structure with a disorder in the e direction, suggesting that high fields may have influence on interplanar ordering.
DOI: 10.7868/S0044451014110121
1. INTRODUCTION
The problem of an antiferromagnet 011 a triangular planar lattice has been intensively studied theoretically fl 5]. The ground state in the Heisenberg and XY models is a "triangular" planar spin structure with three magnetic sublattices arranged 120° apart. The orientation of the spin plane is not fixed in the exchange approximation in the Heisenberg model. The applied static field does not remove the degeneracy of the classical spin configurations. Therefore, the usual small corrections such as quantum and thermal fluctuations and relativistic interactions in the geometrically frustrated magnets play an important role in the formation
* E-mail: svistov'fflkapitza.ras.ru
of the equilibrium state [2, 5, 6]. The magnetic phase diagrams of such two-dimensional magnets strongly depend 011 the spin value of magnetic ions.
CuCrO-2 is an example of the quasi-two-dimensional antiferromagnet (S = 3/2) with a triangular lattice structure. Below T>y « 24 Iv, CuCrO-2 exhibits spiral ordering to an incommensurate spiral magnetic structure with a small deviation from the regular 120° structure. The transition to the magnetically ordered state is accompanied by a small distortion of the triangular lattice. We present an NMR study of the low-temperature magnetic structure of CuCrO-2 in the fields up to 15.5 T. These fields are small in comparison with exchange interactions within the triangular plane (fioHgai. « 280 T). Hence, we can expect that in our experiments, the exchange structure within an individual plane is not distorted significantly and the field evo-
lution of NMR spectra in our experiments is to spin plane reorientation or a change in the interplane ordering. The microscopic properties of magnetic phases of this magnet are especially interesting because this material is multiferroic [7-9]. The possibility to modify electric and magnetic domains with electric and magnetic fields makes CuCr02 attractive for experimental study of the magnetoelectric coupling in this class of materials.
2. CRYSTAL AND MAGNETIC STRUCTURE
The CuCr02 structure consists of magnetic Cr3+ (3d3, S = 3/2), nonmagnetic Cu+, and triangular 02~ lattice planes (TLPs), which are stacked along the c-axis in the sequence Cr-O-Cu-O-Cr (space group i?3m, a = 2.98 A, and c = 17.11 A at room temperature [10]). The respective layer stacking sequences are «7/?, /?«7, and /3/3aaj~f for Cr, Cu, and O ions. The crystal structure of CuCr02 projected on the abplane is shown in top portion of Fig. 1. The distances between the nearest planes denoted by different letters for copper and chromium ions and the pairs of planes for oxygen ions are c/3, whereas the distance between the nearest oxygen planes denoted by the same letters is (1/3 - 0.22)c (Ref. [10]). No structural phase transition has been reported at temperatures higher than the Neel ordering temperature (T > T/v ~ 24 K). In the magnetically ordered state, the triangular lattice is distorted, such that one side of the triangle becomes slightly smaller than the other two sides: A a/a « 10~4 (Ref. [11]).
The magnetic structure of CuCrC^ has been intensively investigated by neutron diffraction experiments [10,12-15]. It was found that the magnetic ordering in CuCr02 occurs in two stages [15, 16]. At the higher transition temperature T/vi = 24.2 K, a two-dimensional (2D) ordered state within afr-planes sets in, whereas below T/v2 = 23.6 K, three-dimensional (3D) magnetic order with the incommensurate propagation vector = (0.329,0.329,0) along the distorted side of TLPs [11] is established. The magnetic moments of Cr3+ ions can be described by the expression
Mi = Afiei cos(qic • ri+<9)+M2e2 sin(qic • r¿+<9), (1)
where ei and e2 are two perpendicular unit vectors determining the spin plane orientation with the normal vector n = ei x e2, r^ is the vector to the ith magnetic ion, and 6 is an arbitrary phase. The spinplane orientation and the propagation vector of the
Fig. 1. Top: Crystal structure of CuCr02 projected on the ab-plane. The three layers, aft7, are the positions of Cr3+ ions. Bottom: Reference angles ip and <p as defined in the text; the grey bar corresponds to the projection of the spin plane. The incommensurate wavevector q¿c is collinear with the base of the triangle (thick line)
magnetic structure are schematically shown in the bottom of Fig. 1. For a zero magnetic field, ei is parallel to [001] with Mi = 2.8(2)/j,Bi while e2 is parallel to [110] with M2 = 2.2(2)fiB (Ref. [15]). The pitch angle between the neighboring Cr moments corresponding to the observed value of q¿c along the distorted side of the TLP is equal to 118.5° which is very close to 120° expected for the regular TLP structure. Realization of such magnetic structure has the natural explanation in the frame of Dzyaloshinskii-Landau theory of magnetic phase transitions (Ref. [17]).
Owing to the crystallographic symmetry in the ordered phase, we can expect six magnetic domains at T < T/v. The propagation vector of each domain can be directed along one side of the triangle and can be
(HCu
T = 40 K. v = 137 MHz
; H il [no] 0,Cu
JCu
"'Cu
1
'Cu
JL
'Cu
ÜJL
X
A
L
10
11
12
13
VoH, T
T = 20 K
lAil
10
il
12
13
VoH, T
Fig. 2. The Cu NMR spectra of a CuCrO- single
crystal (a) in the paramagnetic state and (b) in the
ordered state at the external magnetic field directed
perpendicular to c axis, H || [110]. The two sets of
lines correspond to the signals from quadrupolar split
(>3Cu and (>'Cu nuclei. The peaks marked with crosses
are spurious
probe
B:i'B~'Cu and 27AI NMR signals from the
positive or negative. As reported in Refs. [14,18], the distribution of the domains is strongly affected by the cooling history of the sample.
Inelastic neutron scattering data [19] have shown that CuCrO-2 can be regarded as a quasi-2D magnet.
The spiral magnetic structure is defined by the strong exchange interaction between the nearest Cr3+ ions within the TLPs with the exchange constant Ja¡, = = 2.3 meV. The inter-planar interaction is at least one order of magnitude weaker than the in-plane interaction.
Results of the magnetization, ESR, and electric polarization experiments [9,18] have been discussed in the framework of the planar spiral spin structure at fields studied experimentally: fioH < 14 T -C fioHgaL
(fioHgai. « 280 T). The orientation of the spin plane is defined by the biaxial crystal anisotropy. One hard axis for the normal vector n is parallel to the c direction and the second axis is perpendicular to the direction of the distorted side of the triangle. The anisotropy along the c direction dominates, with the anisotropy constant approximately hundred times larger than that within the
T = 40 K. v = 137 MHz ■H II [001]
03 Cu
14
ßüH, T
Fig. 3. Spectra similar to those in Fig. 2 but with the field applied parallel to c axis, H || [001]
«fr-plano resulting from distortions of the triangle structure. A magnetic phase transition was observed for the field applied perpendicular to one side of the triangle (H || [110]) at fioHc = 5.3 T, which was consistently described [9,14,18] by the reorientation of the spin plane from (110) (n ± H) to (110) (n || H). This spin reorientation occurs due to weak susceptibility anisotropy of the spin structure \ ii « 1 .()•"> \ . .
3. SAMPLE PREPARATION AND EXPERIMENTAL DETAILS
A single crystal of CuCrCb was grown by the flux method following Ref. [15]. The crystal structure was confirmed by single-crystal room-temperature X-ray spectroscopy. The magnetic susceptibility M(T)/H was measured at fi.0H = 0.5 T in the temperature range 2 300 Iv using a SQUID magnetometer. The obtained susceptibility curve was similar to the data in Refs. [8,20]. The Neel temperature T>y « 24 Iv and the Curie Weiss temperature 8cw = ^204 Iv obtained from the fitting of M(T) at temperatures 150 Iv < < T < 300 Iv are in agreement with the values given in Ref. [8].
NMR experiments were carried out using a home-built NMR spectrometer. Measurements were taken
Fig.4. The 63Cu NMR spectra (mi = -1/2 +1/2) measured at different angles between H applied within the ab-plane and the [110] direction of the sample (solid circles). ZFC to T = 20 K and v — 55.3 MHz. Solid lines are the
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.