The following are several examples I find.
1. Though loan words from ancient Chinese are usually written in kanji. For loanwords from modern Chinese, katakana is used.
Japanese | Rōmaji | Meaning | Kanji | Romanization | Source language |
マージャン | mājan | 麻將 | májiàng | ||
ウーロン茶 | ūroncha | Oolong tea | 烏龍茶 | wūlóngchá | |
チャーハン | chāhan | 炒飯 | chǎofàn | ||
チャーシュー | chāshū | barbecued pork | 叉焼 | ||
シューマイ | shūmai | a form of dim sum | 焼売 | siu maai |
I think the reason why this is the case is that the modern Chinese words can not be well or correctly understood by Japanese people. The kanji Japanese people are using almost keeping their original meaning in ancient Chinese, while we Chinese add a lot of new meanings to Chinese characters. Even though some words are written in the same way, we have different understanding with Japanese. A simple example, "勉强" as kanji in Japanese it means study, however in Chinese it means “force somebody to do something he'/she does not want to do”; totally different meanings! Given there is no advantage of understanding for use kanji in these loanwords, I think katakana is more convenient for reading.^^
2. Katakana are also used for emphasis, especially on signs, advertisements, and hoardings. For example, it is common to see ココ ("here"), ゴミ ("trash"), or メガネ ("glasses").
Words the writer wishes to emphasize in a sentence are also sometimes written in katakana, mirroring the European usage of itlics.
3. ヒフ科("dermatology").
Some difficult-to-read kanji are written with katakana. For this example, the kanji is "皮膚科". The second kanji is rather complicated and difficult to read. Thus this word is commonly written as 皮フ科 or ヒフ科, mixing kanji and katakana.