  The electrocaloric effect (ECE) of BaZr$_{x}$Ti$_{1-x}$O$_3$ (BZT) is closely
related to the relaxor state transition of the materials. This work presents a
systematic study on the ECE and the state transition of the BZT, using a
combined canonical and microcanonical Monte Carlo simulations based a
lattice-based on a Ginzburg-Landau-type Hamiltonian. For comparison and
verification, experimental measurements have been carried on BTO and BZT
($x=0.12$ and $0.2$) samples, including the ECE at various temperatures, domain
patterns by Piezoresponse Force Microscopy at room temperature, and the P-E
loops at various temperatures. Results show that the dependency of BZT behavior
of the Zr-concentration can be classified into three different stages. In the
composition range of $ 0 \leq x \leq 0.2 $, ferroelectric domains are visible,
but ECE peak drops with increasing Zr-concentration harshly. In the range of $
0.3 \leq x \leq 0.7 $, relaxor features become prominent, and the decrease of
ECE with Zr-concentration is moderate. In the high concentration range of $ x
\geq 0.8 $, the material is almost nonpolar, and there is no ECE peak visible.
Results suggest that BZT with certain low range of Zr-concentration around
$x=0.12 \sim 0.3 $ can be a good candidate with relatively high ECE and
simutaneously wide temperature application range at rather low temperature.
