Magnetodielectric detection of magnetic quadrupole order in Ba(TiO)Cu4(PO4)4 with Cu4O12 square cupolas

Abstract

In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has only been established experimentally for the toroidal moment. Here we propose a magnetic square cupola cluster, in which four corner-sharing square-coordinated metal-ligand fragments form a noncoplanar buckled structure, as a promising structural unit that carries an ME-active multipole moment. We substantiate this idea by observing clear magnetodielectric signals associated with an antiferroic ME-active magnetic quadrupole order in the real material Ba(TiO)Cu 4 (PO 4 ) 4 . The present result serves as a useful guide for exploring and designing new ME-active materials based on vortex-like spin arrangements.

Magnetoelectric Behavior from S=1/2 Asymmetric Square Cupolas

“…Furthermore, we successfully reproduce the dielectric anomaly and its scaling behavior observed in the prior experiments [7]. Our results indicate that the series of the compounds provides a unique playground where the electric polarization is controllable not only by a magnetic field or T but also by the asymmetry of square cupolas that modulates the orientation of DM vectors.…”

“…In the previous experiment, the dielectric constants ε [100] and ε [110] show an anomaly at the antiferromagnetic transition in B [100] and [110], respectively, but not in B [001]; furthermore, the fieldinduced components scale with B 2 [7]. We here compute the dielectric constant as ε [abc] = ( P · n E=∆En − P · n E=0 )/∆E, where n is the normalized vector directing (a,b,c), for the Hamiltonian H − E · P; E is the electric field, and P is the net polarization defined as P ≡ i,j q i n ij S i · S j , (we set ∆E=0.01).…”

“…Multifrequency electron spin resonance (ESR) measurements (600-1400 GHz) in pulsed magnetic fields were performed to obtain the g-values for the field directions along For understanding of the peculiar magnetization curves, we consider a localized spin model associated with S=1/2 spin degrees of freedom of each Cu cation. We take into account four dominant exchange interactions [7]: the intracupola exchange interactions J 1 and J 2 , together with the two intercupola couplings, intralayer J and interlayer J (see Fig. 1).…”

“…The sums for i, j , i, j , (i, j), and ((i, j)) run over J 1 , J 2 , J , and J bonds, respectively. For the intracupola exchange coupling constants, we adopt the estimates from the ab initio calculation: J 1 =3.0 meV and J 2 =0.5 meV [7]; we set J 1 as the unit of energy, namely, J 1 =1 and J 2 =1/6. On the other hand, for the intercupola J , we set a larger value J =1/2 than the ab initio estimate J =0.7 meV, because small J 0.4 leads to a nonmagnetic singlet state in the CMF approach (see below); we set J =1/100.…”

The spin-1/2 coupled tetramer system Ba(TiO) Cu4(PO4)4 probed by magnetization, specific heat, and 31P NMR

“…The magnetic susceptibility of BTCPO exhibits a broad maximum (∼ 17 K) possibly due to short range order in the layers or possibly within the cupola. Finally, three-dimensional (3D) long range order (LRO) sets in at 9.5 K due to interlayer interactions 1 .…”