Effect of size on the magnetic properties and crystal structure of magnetically frustrated ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles

We synthesized magnetically frustrated ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles in pores of mesoporous silica, with particle sizes ranging from 7 to 20 nm, and investigated their magnetostructural correlation. We found that the lattice constants of the ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles deviated from those of the bulk crystal below $\sim 12$ nm and their crystallographic structures at the unit cell level were distorted. The size dependences of the blocking temperature and coercive field drastically change at $\sim 12$ nm. In addition, the Weiss temperature depends strongly on particle size, and its sign changes at $\sim 12$ nm. It is considered that such features can be realized owing to the distortion caused by the ligand atoms at the surface. The orbital structures of the magnetic sites are easily modified due to the distortion of the ligand ions at the surface, so that the correlation between the crystal structure and magnetic properties can be enhanced. Moreover, magnetization of the nanoparticle results in quasi-superparamagnetic behavior. Monte Carlo calculation of the nanoparticles indicates that such a feature is realized due to the quasi-free spins induced at the surface by magnetic frustration.

Figure 1

(a) Crystal structure of ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ showing distorted ${\mathrm{Mn}}^{4+}{\mathrm{O}}_6(S$=3/2) octahedra cross linked with distorted ${\mathrm{Mn}}^{3+}{\mathrm{O}}_5(S$ = 2) square pyramids. The five nearest-neighbor magnetic interactions between the spins of the Mn ions in the ab plane (b) and along $c$ axis (c) are also illustrated.

Figure 2

Powder XRD patterns for three ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles of particle sizes 7.2, 11.1, and 14.7 nm in SBA-15 and the simulated pattern for the bulk crystal. The wavelength of the incident x rays was 0.688 Å. The asterisks indicate the impurity phase ${\mathrm{Dy}}_2{\mathrm{O}}_3$.

Figure 3

TEM image of ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles synthesized in the pores of SBA-15 with a mean particle size of 8.5 nm. The inset shows a histogram of the particle-size distribution. The solid line represents the fitting curve based on a log-normal function.

Figure 4

Particle-size dependence of the lattice constants of ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles. The horizontal dashed lines show the lattice constants of the bulk crystal.

Figure 5

Temperature dependence of the dc magnetic susceptibilities of ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles of particle size 10.4 nm under an external magnetic field of 100 Oe in the field-cooled (red circle symbols) and zero-field-cooled (blue square symbols) conditions. The inset shows the particle-size dependence of the Weiss temperature estimated by Curie-Weiss fitting. The dashed line is the fitting result (please refer to the text).

Figure 6

(a) Magnetization curves for ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles of particle size 11.1 nm at 5 and 15 K. The inset shows a magnification of the low field region of the hysteresis loop. (b) Particle-size dependence of the coercive field at 15 K. (c) Temperature dependence of the coercive field for nanoparticles with $d=11.1$ nm.

Figure 7

(a) Temperature dependence of in-phase (upper panel) and out-of-phase (lower panel) susceptibilities for ${\mathrm{DyMn}}_2{\mathrm{O}}_5$ nanoparticles of particle size 11.3 nm in the frequency range 0.3–300 Hz in a zero dc field. (b) Particle-size dependence of the blocking temperature at 100 Hz.

Figure 8

Particle size dependence of the effective relaxation time. The inset shows the fitting results of ${\chi }^{\prime \prime }\left(\omega \right)$ for $d=9.3$ nm. The dashed line in inset is the fitting result.

Figure 9

Heisenberg model with $J_3,J_4,J_5$ interactions. The open (filled) circles represent ${\mathrm{Mn}}^{3+}\left({\mathrm{Mn}}^{4+}\right)$ cites. The point O is defined as the center of the nanoparticle. The lattice constants $a$ and $b$ are fixed as $a=7.294$ Å and $b=8.551$ Å [15]. ${\varphi }_i$ is fixed to be $\pi$/3 at the A-site and -$\pi$/3 at the B-site.

Figure 10

Magnetization of a nanoparticle with $d=10$ nm with increasing external magnetic ${\mathit{B}}^{ex}\left|\right|y$ at $T/J_5=0.1$. As a reference, the magnetization of the bulk system is also shown. The calculated results for the surface and core parts correspond to the magnetization owing to only the regions of the surface $(r\geqq 4$ nm) and core $(r\leqq 4$ nm) parts, respectively, where $r$ is the distance from the center of the nanoparticle.

Figure 11

Spin structure of a nanoparticle with $d=10$ nm when $\mathit{g}{\mu }_{\text{B}}{\mathit{B}}^{ex}/J_5$=0.$5\left({\mathit{B}}^{ex}\left|\right|y\right)$ and $T/J_5=0.1$. The center of the nanoparticle is located at O = (0, 0). The results for $x\geqq 0$ and $y\geqq 0$ are shown. The expectation values of the in-plane components of the spins $\left(\langle S_i^x\rangle ,\langle S_i^y\rangle \right)$ are shown by arrows and their color represents the $\langle S_i^y\rangle$ at each site. The nanoparticle (core) region is bounded by the yellow solid (white dashed) line.